Metal comforming

Universidad Nacional del Sur Departamento de Ingeniería Ingeniería Mecánica

Conformado de metales Carpeta para final 2018

Alumno

Ehulech Gonzalez, Germán

1

2

3

Fundamentals of metalworking

1

1.1

Subjects of interest

1

1.2

Objectives

1

1.3

Classification of metal forming processes

1

1.4

Mechanics of metal working

3

1.5

Flow curves

7

1.6

Working processes

8

1.7

Hot working

9

1.8

Cold working

15

1.9

Effects of metallurgical structure on working processes

15

1.10

Effects of speed of deformation

18

1.11

Effects of friction and lubrication

18

Forging

23

2.1


23

2.2

Objectives

23

2.3

Introduction

23

2.4

Classification of forging processes

25

2.5

Hammer and press forging processes

26

2.6

Mechanical press forging

28

2.7

Open-die forging

29

2.8

Closed-die design

32

2.9

Calculation of forging loads

36

2.10

Effect of forging on microstructure

43

2.11

Residual stresses in forging

44

2.12

Typical forging defects

44

Rolling of metals

47

3.1


47

3.2

Objectives

47

3.3

Introduction-Definition of rolling process

47

3.4

Rolls

49

3.5

Different types of rolling processes

52

3.6

Hot-rolling

57

3.7

Cold-rolling

59

3.8

Forces and geometrical relationships in rolling

61

3.9

Simplified analysis of rolling load

67

3.10

Problems and defects in rolled products

72

3.11

Rolling mill control

76

3.12

Theory of cold rolling

78

3.13

Theory of hot-rolling

80

3.14

Torque and power

81

4

5

6

Extrusion

83

4.1


83

4.2

Objective

83

4.3

What is extrusion?

83

4.4

Classification of extrusion processes

84

4.5

Extrusion equipment (Presses, dies and tools)

88

4.6

Hot extrusion

91

4.7

Deformation in extrusion, lubrication and defects

94

4.8

Analysis of the extrusion process

97

4.9

Cold extrusion and cold forming

101

4.10

Hydrostatic extrusion

102

4.11

Extrusion of tubing

103

4.12

Production of seamless pipe and tubing

104

Drawing of rods, wires and tubes

106

5.1


106

5.2

Objectives

106

5.3

Introduction

107

5.4

Rod and wiredrawing

107

5.5

Analysis of wiredrawing

112

5.6

Tube drawing processes

118

5.7

Analysis of tube-drawing

120

5.8

Residual stresses in rod, wire and tubes

122

Sheet-metal forming

123

6.1

Objectives

123

6.2

Introduction

123

6.3

Deformation geometry

126

6.4

Forming equipment

127

6.5

Shearing and blanking

134

6.6

Bending

137

6.7

Stretch forming

139

6.8

Deep drawing

140

6.9

Forming limit criteria

145

6.10

Defects in formed parts

146

German Ehulech Gonzalez

1

Fundamentals of metalworking

1.1




Introduction/objectives



Classification of metal processes



Mechanics of metalworking



Flow curves



Effects of temperature on metalworking 

Hot working



Cold working



Effects of metallurgical structure on forming processes



Effects of speed of deformation on forming processes



Effects of friction and lubricant

1.2 

Objectives

This chapter provides classification of metal forming processes based on types of forces applied onto metals.



Mechanics of metal forming will be outlined to understand stress criterion for plastic deformation.



Differences between hot and cold working will be highlighted and advantagesdisadvantages of hot and cold working will be given.



Effects of deformation speed and friction on metal working process will be included

1.3

Classification of metal forming processes

(based on the type of force applied on to the workpiece as it is formed into shape). 

Direct-compression-type processes



Indirect-compression processes



Tension type processes



Bending processes



Shearing processes

1.3.1

Direct-compression type processes:

the applied force is normal to the direction of the metal flow in compression, i.e., forging and rolling processes.

1


1.3.2 Indirect-compression type processes: the primary forces are frequently tensile, with indirect compressive forces developed by the reaction of the workpiece. The metal flow is therefore under the combined stress state, i.e., extrusion, wiredrawing, tube drawing.

1.3.3 Tension type processes: the applied force is tensile, i.e., stretching forming.

1.3.4 Bending processes: the applied force involves the application of bending moments to the sheet.

1.3.5 Shearing processes: the applied force involves the application of shearing forces of sufficient magnitude to rupture the metal in the plane of shear.

2


1.3.6 Classification of metal forming by subgroups

1.4

Mechanics of metal working

Metal working occurs due to plastic deformation which is associated with analysis of complex stress distribution. require simplification. 

Only (large) plastic strain is considered while elastic strain is very small and can be neglected.



Strain hardening is often neglected.



Metal is considered to be isotropic and homogeneous.

Normally plastic deformation is not uniform and also have frictions, but we need to simplify the stress analysis in order to determine the force required to produce a given amount of deformation to obtain a product in a required geometry. 

Required theory of plasticity, and for plastic deformation

 a

constant-volume

relationship is required.

In metalworking, compressive stress and strain are predominated. If a block of initial height h0 is compressed to h1, the axial compressive strain will be: For true strain

For conventional strain

3


Note: the calculated strain is negative  compressive strains. 

However, the convention is reversed in metalworking problems so that compressive stresses and strains are defined as positive.



Note: ec is used as strain in deformation process.

And the fractional reduction (reduction of area) in metal working deformation is given by

From the constant-volume relation

Example: Determine the engineering strain, true strain, and reduction for (a) a bar which is doubled in length and (b) a bar which is halved in length. (a) For a bar which is double in length, L2=2L1

(b) For a bar which is halved in length, L2=L1/2

1.4.1 Yield criteria and stress-strain relations Yielding in unidirectional tension test takes place when the stress σ=F/A reaches the critical value.

4


Yielding in multiaxial stress states is not dependent on a single stress but on a combination of all stresses.



Von Mises yield criterion (Distortion energy criterion)



Tresca yield criterion (maximum shear stress)

1.4.2 Von Mises yield criterion Yielding occurs when the second invariant of the stress deviator J 2>critical value k2.

In uniaxial tension, to evaluate the constant k, note σ1=σ0, σ2-σ3=0, where σ0 is the yield stress; therefore

Substituting k

In pure shear, to evaluate the constant k, note σ1=σ3=τy, σ2=0, where σ0 is the yield stress; when yields: τ y2+τy2+4τy2=6k2 then k=τy By comparing with Eq. 9 we then have

1.4.3 Tresca yield criterion Yielding occurs when the maximum shear stress τ max reaches the value of the shear stress in the uniaxial-tension test, τ0.

5


Where σ1 is the algebraically largest and σ3 is the algebraically smallest principal stress. For uniaxial tension, σ1=σ0, σ2=σ3=0, and the shearing yield stress τ 0=σ0 /2.

Therefore, the maximum-shear stress criterion is given by

In pure shear, σ1=-σ3=k, σ2=0, τmax=τy

Therefore, from von Mises and Tresca yield criteria we have Tresca yield criterion

Von Mises yield criterion

The differences in the maximum shear stress prediction from both criteria lie between 015%. However, experiments confirmed that the von Mises criterion is more accurate to describe the actual situations. Once the metal has reached its yield point, the metal starts to flow under the influence of stress state. This is in the plastic regime where stress is not directly proportional to strain. The manner of flow or deformation is dependent on the stress state. 1.4.4 FEM analysis Finite element method (FEM) is used in metalworking plasticity where stresses are complex. FEM is a very powerful technique for determining stress-strain distributions in plane strain or plane stress conditions.

6


Distortion of FEM grid in forging of a compressor disk.

1.5

Flow curves

Flow curve indicates whether metal is readily deformed at given conditions, i.e., strain rate, temperature. Flow curve is strongly dependent on strain rate and temperature.

Flow curves of some metals at room temperature

1.5.1

Determination of flow curve

Stress-strain curve

7


True stress-strain curve of a ductile metal under uniaxial tensile loading. Hook’s law is followed up to the yield point, σ0. Beyond σ0, metal deforms plastically (strain hardening). Unloading from A immediately decreases the strain from ε1 to ε2=σ/E the strain decrease ε1-ε2 is the recoverable elastic strain.

Where: σ is true stress; ε is true strain; K is constant; n is work hardening exponent (this is valid from the beginning of plastic flow to the maximum load at which the specimen begins to neck down.)

Temperature ↑ Flow stress ↓

Strain hardening occurred when an iron wire had been drawn to a specific true strain.

True stress-strain curve for iron wire deformed by wiredrawing at room temperature.

1.6

Working processes

The methods used to mechanically shape metals into other product forms are called Working Processes.

8


Hot working (0.6-0.8Tm) Definition: deformation under conditions of temperature and strain rate such that recrystallization process take place simultaneously with the deformation. Examples: rolling, forging, extrusion Cold working (< 0.3Tm) Definition: deformation carried out under conditions where recovery processes are not effective. Examples: rolling, forging, extrusion, wire/tube drawing, swaging, coining The products resulting from the working of metals are called Wrought Products. such as sheet, plate, bar, forging. Primary mechanical working process Plastic working processes can also be divided into: Designed to reduce an ingot or billet to a standard mill product of simple shape, i.e., sheet, plate, bar. Secondary mechanical working process Steel plates Primary sheets, plates or bars are formed into final finished shapes, i.e., wire & tube drawing, sheet metal forming operation.

1.7

Hot working

Hot working involves deformation at temperatures where recrystallization can occur (0.60.8 Tm). Examples of hot working temperatures for each metal

Effects of temperature on metal forming

9


Annealing mechanisms in cold worked metals

1.7.1

Recrystallization during hot working

The minimum temperature at which reformation of the crystals occurs is called Recrystallization Temperature.

Above the recrystallization temperature the kinetic energy of atoms increases and therefore they are able to attach themselves to the newly formed nuclei which in turn begin to grow into crystals. This process continues until all the distorted crystals have been transformed. Hot working results in grain refining. 1.7.2 Recrystallization Recrystallization takes place at higher temperatures than recovery which leads to a new formation of grains. The process includes 1) primary recrystallization and 2) secondary recrystallization and grain growth.

Recrystallized grain with annealing twins surrounded by deformed matrix with high density of dislocations. Primary recrystallization 

Primary recrystallization occurs at the beginning of the new grain formation process.



Recrystallization temperature does not depend on the metal alone, but on a whole number of variables temperature, strain and minimum dislocation density available (amount of deformation)



Small impurities in pure metals can considerably increase the recrystallization temperature.

10


1.7.3 Recrystallized grain size and prior plastic strain The greater the driving force (greater prior plastic deformation), the greater the number of nuclei that will form and the finer will be the final grain size.

1.7.4 Effects of grain size and strain on recrystallization temperature

Schematic of recrystallization diagram

1.7.5 Effects of grain size on properties

Small grains make dislocations more difficult to move More slip plane, therefore, greater ductility

11


1.7.6 Effects of strain rate and temperature

Flow stress of aluminium as a function of strain at different temperature Temp ↑ Flow Stress ↓

Flow curves of Cu Zn28 Strain Rate ↑ Flow stress ↑

1.7.7 Secondary recrystallization and grain growth At higher temperature and longer annealing time, further grain growth processes take place in the primary recrystallization structure. The driving force energy from the energy gained by lowering the ratio of the grain boundary area to the enclosed volume. Mechanical property deterioration Secondary recrystallization: Only individual grains grow preferentially, resulting in very large grains present near the primarily recrystallized grains. Grain growth: Result in an increase in average grain diameter. Ductility ↓ Formability ↓ 1.7.8 Recovery Recovery is a thermally activated process, which results in lower density of dislocations or rearrangement of dislocation structure (as a consequence of strain hardening during deformation process). Recovery process includes annihilation of dislocation, polygonization of dislocation, dislocation climb. Certain amount of stored energy is released during annealing without an obvious change in optical microstructure.

12


Recovery of 38% cold-rolled aluminium showing different sizes of subgrains.

Polygonization

1.7.9 Effect of recovery annealing on stress-strain diagram Recovery process depends strongly on temperature. Increasing temperature (T ≥ 0.5Tm) during step tensile tests fig. (b) reduces the yield stress, due to the rearrangement and reactions of dislocations during recovery.

Effect of recovery annealing on stress-strain diagram

1.7.10 Static and dynamic changes of structure during hot forming During plastic deformation, new dislocations and vacancies are produced continuously, which leads to a new state of equilibrium through d ynamic recrystallization and dynamic recovery. These two processes take place in the forming zone during plastic deformation at corresponding stresses and strain rates.

13


Note: During forming, structure changes through dynamic recrystallization and dynamic recovery. During cooling or heating, structure changes through static recrystallization and static recovery. 1.7.11 Static and dynamic changes of structure during hot forming Dynamic and static recovery are strongly encouraged in metals with high stacking fault energy (easy for climb and cross slip) such as aluminium, α –Fe, ferritic alloys. Hot flow curve with a constant or slightly drop of yield stress are typical for dynamic recovery. On the contrary, the flow curves with dynamic recrystallization (after initial hardening) show a sudden drop in yield stress.

Schematic form of hot flow curves by (a) dynamic recovery alone (b) both dynamic recovery and recrystallization. 1.7.12 Advantages and disadvantages of hot working Advantages 

Higher ductility – more deformation without cracking.



Lower flow stress – less mechanical energy required for deformation.



Pores seal up.



Smaller grain size.



Microsegregation is much reduced or removed due to atomic diffusion, which is higher at high temperatures.



Stronger, tougher and more ductile than as-cast metals due to breaking down and refinement of coarse columnar grains in the cast ingot.

Disadvantages 

Surface reactions between the metal and the furnace atmosphere, i.e., oxidation (oxide scales), decaburisation in steels.



Hot shortness, when the working temperature exceeds the melting temperature of constituent at grain boundaries such as FeS.

14




Dimension tolerance is poor due to thermal expansion at high temperatures.



Handling is more difficult (from furnace to machine).

1.8

Cold working

Normally performed at room temperature but in general < 0.3T m, where recovery is limited and recrystallization does not occur. Work hardening occurs (strength and hardness increase but ductility decreases). The extent of deformation is rather limited if cracks are to be avoid, therefore intermediate anneals that enable recrystallization are frequently used afterwards. The materials suitable for cold working should have a relatively low yield stress and a relatively high work hardening rate (determined primarily by its tensile properties). 1.8.1

Advantages and disadvantages of cold working

Advantages 

Provide work hardening, materials are stronger.



Provide fine grain size and good surface finish.



Dimension tolerance is better than in hot working.



Easier handling (low operating temperatures).

Disadvantages 

Use high amount of deformation due to low operating temperatures, therefore, require soft materials.



Equipment (rolls, dies, presses) is big and expensive.



Reduced ductility, therefore, require subsequent annealing treatments.

1.8.2 Properties of steels (C10) after hot-cold working

1.9

Effects of metallurgical structure on working processes

The presence of preferred orientation causes anisotropy of mechanical properties, especially in rolled sheets.

15


The development of texture is the formation of deformation bands or shear bands, which are regions of distortion where a portion of grains have rotated towards another orientation to accommodate the applied strain.

Fibrous texture in rolled plate.

1.9.1

Example: Plastic working in two-phase alloys

The plastic working characteristics of two-phase alloys depends on the microscopic distribution of the two phases. A high Vf of hard uniformly dispersed particles increases the flow stress and makes working difficult. Hard and massive particles tend to fracture on deformation with softer matrix. Second phase particles or inclusions will be distorted in the principal working direction (fibrous structure)-affect mechanical properties. Precipitation hardening during hot working results in high flow stress and lowered ductility.

16


1.9.2 Effect of principal stresses in metal working When there is no shear stresses acting on the planes giving the maximum normal stress acting on the planes. These planes are called the principal planes, and stresses normal to these planes are the principal stresses σ1, σ2 and σ3 which in general do not coincide with the Cartesian coordinate axes x, y, z. Directions of principal stresses are 1, 2 and 3.

Biaxial-plane stress condition Two principal stresses, σ1 and σ2.

Triaxial-plane strain condition Three principal stresses, σ1, σ2 and σ3, where σ1 > σ2 > σ3.

17


1.10 Effects of speed of deformation High deformation speed (high strain rate): 

High flow stress.



Increased the temperature of the workpiece.



Improved lubrication at the tool-metal interface.

Flow stress dependence on strain rate and temperature

Note: 

If the speed of deformation is too high, metal cracking is possible.



Can cause plastic instability in cold working



Can cause hot shortness in hot working

1.11 Effects of friction and lubrication Friction at tool-workpiece interface depends on geometry of the tooling and the geometry of the deformation, temperature, nature of metal, speed of deformation.

18


Die-workpiece interface (a) on the macroscale, (b) on the microscale.

When two surfaces are brought into contact, the high spot (asperities) will come into contact. As we increase the load, the metal at the asperities deform plastically and produce subshear zone. The coefficient of friction is given by

Where 

μ=frictional coefficient



τ=the shearing stress at the interface



P=the load normal to the interface



F=the shearing force



Ar=summation of asperity areas in contact



p=the stress normal to the interface

(a) Contact at asperities (b) overlap of deformation zones to produce subsurface shear zone.

19


1.11.1 Example: homogeneous compression of a flat circular disk Assumption: no barreling and small thickness, then the frictional conditions on the top and bottom faces of the disk are described by a constant coefficient of Coulomb friction;

Where 

μ=frictional coefficient



τ=the shearing stress at the interface



p=the stress normal to the interface



Deformation pressure in compression as a function of u and a/h.

Deformation pressure in compression as a function of u and a/h.

1.11.2 Example: friction in forging Functions of a metal working lubricant:

20



Reduces deformation load



Increases limit of deformation before fracture



Controls surface finish



Minimizes metal pickup on tools



Minimizes tool wear



-Thermally insulates the workpiece and the tools



Cools the workpiece and/or tools


1.11.3 Effect of residual stresses Residual stresses is generated by non-uniform plastic deformation when external stresses are removed.

(a) Inhomogeneous deformation in rolling of sheet, (b) resulting distribution of longitudinal residual stress over thickness of sheet.

Ex: in rolling process, the surface grains in the sheet are deformed and tend to elongate, while the grain in the center are unaffected. Due to continuity of the sheet, the central fibers tend to restrain the surface fibers from elongating while the surface fibers tend to stretch the central fibers. Residual stress pattern consisting of high compressive stress at the surface and tensile stress in the center. Residual stresses are only elastic stresses. The maximum value which a residual stress can reach is the yield stress of the material. Residual stresses can be considered the same as ordinary applied stresses. Compressive residual stress can effectively subtract from the applied tensile stresses. Metals containing residual stresses can be stress relieved by heating to a temperature where the yield strength of the material is the same or lower than the value of the residual stress such that the material can deform and release stress. However slow cooling is required otherwise residual stress can again develop during cooling. 1.11.4 Workability Workability is concerned with the extent to which a material can be deformed in a specific metal working process without the formation of cracks.

21


Cracks which occur in metal working processes can be grouped into three broad categories: 

Cracks at a free surface



Cracks that develop in a surface where interface friction is high



Internal cracks.

Dependence of forming limit of mean normal stress σ m.

Examples of cracks in metalworking (a) free surface crack (b) surface cra ck from heavy die friction in extrusion, (c) center burst or chevron cracks in a drawn rod.

22


2

Forging

2.1







Classification of forging processes 

Hammer or drop forging



Press forging



Open-die forging



Closed-die forging






Effect of forging on microstructure



Residual stresses in forgings



Typical forging defects

2.2 

Objectives

This chapter provides fundamental of metal working process for forging in order to understand mathematical approaches used in the calculation of applied forging loads required to cause plastic deformation to give the final product.



Classification of metal forging methods is also provided with descriptions of defects observed from the forging processes.



The solutions to tackle such defects will also be addressed.

2.3

Introduction



Forging is the working of metal into a useful shape by hammering or pressing.



The oldest of the metalworking arts (primitive blacksmith).



Replacement of machinery occurred during early the Industrial revolution.



Forging machines are now capable of making parts ranging in size of a bolt to a turbine rotor.



Most forging operations are carried out hot, although certain metals may be coldforged.

23


2.3.1 Forging operations Edging is used to shape the ends of the bars and to gather metal. The metal flow is confined in the horizontal direction but it is free to flow laterally to fill the die.

Drawing is used to reduce the cross-sectional area of the workpiece with concurrent increase in length.

Piercing and punching are used to produce holes in metals.

Fullering is used to reduce the cross-sectional area of a portion of the stock. The metal flow is outward and away from the center of the fuller.

i.e., forging of connecting rod for an internal combustion engine. 

Fullers come in different shapes



Fullers move fast and moves metal perpendicular to the face

Swaging is used to produce a bar with a smaller diameter (using concave dies).

24




Swaging provides a reduced round cross section suitable for tapping, threading, upsetting or other subsequent forming and machining operations.



Swaging is a special type of forging in which metal is formed by a succession of rapid hammer blows

Swaging at the ends, ready for next forming process.

2.4 Classification of forging processes 



By equipment 

Forging hammer or drop hammer



Press forging

By process 

Open-die forging



Closed-die forging

2.4.1 Forming machines There are four basic types of forging machines

25


2.5

Hammer and press forging processes

Forging hammers There are two basic types of forging hammers used; 

Board hammer



Power hammer

Forging presses There are two basic types of forging presses available; 

Mechanical presses



Hydraulic presses

2.5.1 Board hammer –forging hammer The upper die and ram are raised by friction rolls gripping the board. After releasing the board, the ram falls under gravity to produce the blow energy.

The hammer can strike between 60-150 blows per minute depending on size and capacity. The board hammer is an energy restricted machine. The blow energy supplied equal the potential energy due to the weight and the height of the fall. Potential energy=mgh

This energy will be delivered to the metal workpiece to produce plastic deformation. Provide rapid impact blows to the surface of the metal. Dies are in two halves: 

Lower: fixed to anvil



Upper: moves up and down with the TUP.

Energy (from a gravity drop) is adsorbed onto the metal, in which the maximum impact is on the metal surface. Dies are expensive being accurately machined from special alloys (susceptible to thermal shock). Drop forging is good for mass production of complex shapes.

26


2.5.2 Example: Forging hammer or drop hammer The energy supplied by the blow is equal to the potential energy due to the weight of the ram and the height of the fall. Potential energy=mgh 2.5.3 Power hammer Power hammer provides greater capacity, in which the ram is accelerated on the down stroke by steam or air pressure in addition to gravity. Steam or air pressure is also used to raise the ram on the upstroke.

The total energy supplied to the blow in a power drop hammer is given by

Where 

m =mass



v



g =acceleration of gravity



p =air or steam pressure acting on ram cylinder on down stroke



A =area of ram cylinder



H =height of the ram drop

=velocity of ram at start of deformation

2.5.4 Hydraulic press forging Using a hydraulic press or a mechanical press to forge the metal, therefore, gives continuous forming at a slower rate. Provide deeper penetration. Better properties (more homogeneous). Equipment is expensive.

27


2.5.5 Example: Hydraulic Press forging Hydraulic presses are load restricted machines in which hydraulic pressure moves a piston in a cylinder. The full press load is available at any point during the full stroke of the ram. Therefore, hydraulic presses are ideally suited for extrusion-type forging operation. Due to slow speed, contact time is longer at the die-metal interface, which causes problems such as heat lost from workpiece and die deterioration. Also provide close-tolerance forging. Hydraulic presses are more expensive than mechanical presses and hammers.

2.6

Mechanical press forging

Crank press translates rotary motion into reciprocating linear motion of the press slide. The ram stroke is shorter than in a hammer or hydraulic press.

Presses are rated on the basis of the force developed at the end of the stroke. The blow press is more like squeeze than like the impact of the hammer, therefore, dies can be less massive and die life is longer than with a hammer. The total energy supplied during the stroke of a press is given by

Where

28




“I” is moment of inertia of the flywheel



ω is angular velocity,



ω0-original,



ωf -after deformation,

2.6.1 Typical values of velocity for different

2.6.2 Closed and open die forging processes

2.7

Open-die forging

Open-die forging is carried out between flat dies or dies of very simple shape. The process is used for mostly large objects or when the number of parts produced is small. Open-die forging is often used to pre-form the workpiece for closed-die forging.

29


2.7.1 Closed-die forging (or impression-die forging) The workpiece is deformed between two die halves which carry the impressions of the desired final shape. The workpiece is deformed under high pressure in a closed cavity. Normally used for smaller components. The process provides precision forging with close dimensional tolerance. Closed dies are expensive.

Closed-die forging operation

Billet

Preshaped

Roughforge

Finishing Die

Trimming Die

Typical curve of forging load vs. stroke for closed-die forging.

30

Final product


Flash is the excess metal, which squirts out of the cavity as a thick ribbon of metal. Functions of flash The flash serves two purposes: 

Acts as a ‘safety value’ for excess metal.



Builds up high pressure to ensure that the metal fills all recesses of the die cavity.

Remark : It is necessary to achieve complete filling of the forging cavity without generating excessive pressures against the die that may cause it to fracture. 2.7.2 Example: Die set and forging steps for the manufacturing of an automobile engine connecting rod 

Preforming of a round piece in an open die arrangement.



Rough shape is formed using a block die.



The finishing die is used to bring the part to final tolerances and surface finish.



Removal of flash (excess metal).

31


Steering

Rail

Flange

knuckle

2.8

Closed-die design

Usually the deformation in closed-die forging is very complex and the design of the intermediate steps to make a final precision part requires considerable experience and skill. The design of a part for production by closed-die forging involves the prediction of 

workpiece volume and weight



number of preforming steps and their configuration



flash dimensions in preforming and finishing dies the load and energy requirement for each forging operation, for example; the flow stress of the materials, the fictional condition, the flow of the material in order to develop the optimum geometry for the dies.

2.8.1 Shape classification The degree of difficulty increases as the geometry moves down and toward the right.

Simple parts are symmetry shape, or parts with circular, square and similar contours.

32


More complicated parts have pronounced longitudinal axis and are curved in several planes. Preform design is the most difficult and critical step in forging design. Proper preform design assures defect-free flow, complete die fill, and minimum flash loss.

Metal flow consists only of two basic types 

extrusion (flow parallel to the direction of the die motion)



upsetting (flow perpendicular to the direction of the die motion).

However, both types of metal flow occur simultaneously. We need to identify the neutral surface since metal flows away from the neutral surface in a direction perpendicular to the die motion. 2.8.2 Metal flow in forging Finite element analysis was originally developed to model the elastic deformation of complex structures but recently has been extended to cover large plastic deformation under real stress system.

Finite element analysis of upsetting an aluminium cylinder

It is a numerical modelling technique that involves splitting the whole of a body into a series of simple geometrical elements that are joined together at points (nodes) where both equilibrium (lower bound) and compatibility (upper bound) requirement are established.

33


2.8.3 General considerations for preform design 

Area of each cross section=area in the finished cross section + flash.



Concave radii of the preform > radii on the final forging part.



Cross section of the preform should be higher and narrower than the final cross section, so as to accentuate upsetting flow and minimize extrusion flow.

Shape with thin and long sections or projections (ribs and webs) are more difficult to process because they have higher surface area per unit volume  increasing friction and temperature effects.

Some typical nomenclature

2.8.4 General rules of closed-die design 

The die set should be designed for smooth metal flow – symmetry dies (spherical or blocklike) are the easier than thin and long section.



Shape changes in section are to be avoided.



Dies should be designed for the minimum flash to do the job.



Generous fillet dimensions should be allowed, therefore, forging dies must be tapered or drafted to facilitate removal of the finished piece.



Draft allowance is approximately 3-5° outside and 7-10° inside.



Dies with inclined angles should have counterlock to prevent the dies from sliding apart from each other due to side thrust.

2.8.5 Die materials Required properties:

34



Thermal shock resistance



Thermal fatigue resistance




High temperature strength



High wear resistance



High toughness and ductility



High hardenability



High dimensional stability during hardening



High machinability

Die materials: alloyed steels (with Cr, Mo, W, V), tool steels, cast steels or cast iron. (Heat treatments such are nitriding or chromium plating are required to improve die life)

Forging die

Note: 

Carbon steels with 0.7-0.85% C are appropriate for small tools and flat impressions.



Medium-alloyed tool steels for hammer dies.



Highly alloyed steels for high temperature resistant dies used in presses and horizontal forging machines.

Common steels used for forging dies:

Die life can be increased by 

Improving die materials such as using composite die or



Using surface coating or self-lubricating coatings

35


Ultra hard surface coatings Ultra hard surface coating on die surface is used to 

Improve die life.



Reduce energy input.



Reduce die-related uptime and downtime.



Reduce particulate emission from lubricants.

2.8.6 Die failures

Different types of die failure

Different parts of dies are liable to permanent deformation and wear resulting from mechanical and thermal fatigue. Important factors: shape of the forging, die materials, how the workpiece is heated, coating of die surface, the operating temperature (should not exceed the annealing temperature).

2.9


The calculation for forging load can be divided into three cases according to friction:

36



In the absence of friction



Low friction condition (lower bound analysis or sliding condition)




High friction condition (sticky friction condition)

The total energy required for deformation process; U total=U ideal + U friction + U redundant

Note: redundant work=work that does not contribute to shape change of the workpiece Efficiency of a given deformation process η is Note: η=0.3-0.6 for extrusion =0.75-0.95 for rolling =0.10-0.20 for closed die forging 2.9.1 In the absence of friction By assuming that there is no friction at die-workpiece interface, the forging load is therefore the compressive force (P) acting on a round metal bar. Then

Where P

is the compressive force

σ0

is the yield stress of the metal

A

is the cross sectional area of the metal.

And the compressive stress (p) produced by this force P can be obtained from

Note: from volume constant

Where h

is the instantaneous height of the metal bar during forging

h0

is the original height of the metal bar

D0

is the original diameter of the metal bar.

We have engineering strain in compression,

And true strain in compression,

The relationship between e and ε is

37


2.9.2 Low friction condition (Lower bound analysis) By considering the equilibrium of forces acting on the workpiece at any instant of deformation.

For example, if we consider the effect of friction on an upset forging operation in plane strain condition (rigid-plastic behavior, see Fig). To calculate the total forming load, we have to determine the local stresses needed to deform each element of a workpiece of height h and width 2a. In plane strain condition, as the workpiece is reduced in height, it expands laterally and all deformation is confined in the x-y plane. This lateral expansion causes frictional forces to act in opposition to the movement. Assuming that there is no redundant work and the material exhibits rigid-plastic behavior, and all stress on the body are compressive. Consider the force acting on a vertical element of unit length and width dx. The element is at some distance x from the central ‘no-slip’ point, in this case to the right. The vertical force acting on the element is

If the coefficient of friction for the die-workpiece interface is μ, the magnitude of the friction force will be μσydx. The frictional force acts at both ends of the element so the total horizontal force from the right is 2μσydx. Acting on the left will be the force σxh and from the right the force (σx+dσx) h. The horizontal compressive stress σx varies from a maximum at the center of the workpiece to zero at the edge and changes by dσx across the element width dx. Balancing the horizontal forces acting on the element:

Rearranging, we have

and therefore

38


As the frictional force μσy is usually much smaller than both σx and σy, which are principal stresses. Thus we can use them in the yield criterion when the slab will yield

Where σ0‘ is the yield stress in plane strain. Differentiation of the yield condition gives dσy=dσx, and substituting for dσx in Eq. 12 gives

Integrating both sides of this differential equation gives

or

where C0 is a constant of integration. We can evaluate C by looking at the boundary conditions. At the edge of the workpiece where x=a, σx=0 and from the yield criterion σ y-σx= σ0‘, so σy= σ0‘ and therefore:

So

Using this in, we find

Friction hill

39


The total forging load, P, is given

Where p w

is the average forming pressure across the workpiece is the width of the workpiece (in the plane of the paper).

This equals σ y and can be estimated by integrating:

The integration can be simplified if we make the following approximation. The general series expansion for exp x is

Since μ is usually small (<1) we can approximate exp x as (1+x) for small x. Thus we can approximate the equation as

and Equation becomes

Integrating this gives:

So that the average axial tooling pressure, p, is

We can see that as the ratio a/h increases, the forming pressure p and hence the forming load rises rapidly. Example:

40


The flash has high deformation resistance than in the die (due to much higher a/h ratio), therefore the material completely fills the cavity rather than being extruded sideward out of the die.

2.9.3 High friction condition (sticky friction) In the situation where the friction force is high, the stress acting on the metal is

And the mean forging pressure is

Under these conditions, the forming load is dependent on the flow stress of the material and the geometry of the workpiece. For example: if the a/h ratio is high, say a/h=8, then p=5 σ0‘. The local stress on the

tooling can therefore be very high indeed and 5 σ0‘ is probably high enough to deform the tooling in coldest forming operation. Solutions: 

reducing μ to ensure that sticking friction conditions do not apply.



changing the workpiece geometry.



reducing σ0‘ by increasing the temperature.

In the case of sticky friction, if we replace the force μσy with k (the average shear stress of the material) in

then we have

41


Integrating

Since σy= σ0‘ at x=a, then

Replacing C, we then have

Example: A block of lead 25x25x150 mm3 is pressed between flat dies to a size 6.25x100x150 mm3. If the uniaxial flow stress σ0=6.9 MPa and μ=0.25, determine the pressure distribution over the 100 mm dimension (at x=0, 25 and 50 mm) and the total forging load in the sticky friction condition. Since 150 mm dimension does not change, the deformation is plane strain.

Where

At the centerline of the slab (x=0)

Likewise, at 25 and 50 mm, the stress distribution will be 58.9 and 8.0 MPa respectively. The mean forging load (in the sticky friction condition) is

We calculate the forging load on the assumption that the stress distribution is based on 100 percent sticky friction. Then The forging load is P =stress x area

42


=(39.8x106). (100x10-3). (150x10-3) =597 kN =61 tonnes.

2.10 Effect of forging on microstructure

grain structure resulting from (a) forging, (b) machining and (c) casting.

The formation of a grain structure in forged parts is elongated in the direction of the deformation. The metal flow during forging provides fibrous microstructure (revealed by etching). This structure gives better mechanical properties in the plane of maximum strain but (perhaps) lower across the thickness. The workpiece often undergo recrystallization, therefore, provide finer grains compared to the cast dendritic structure resulting in improved mechanical properties. 2.10.1 Forming textures Redistribution of metal structures occurring during forming process involves two principle components; 

redistribution of inclusions and



crystallographic orientation of the grains

2.10.2 The redistribution of inclusions

Redistribution during forming of

43




soft inclusions



hard inclusions

2.10.3 Crystallographic Crystallographic orientation of the grains

Cast iron structure

Fiber structure in forged steels

Mainly epitaxial, dendritic or equiaxed

Redistribution of grains in the working

grains

directions

2.11 Residual stresses in forging The residual stress produced in forgings as a results of inhomogeneous deformation are generally small because the deformation is normally carried out well into the hot-working region. However, appreciable residual stresses and warping can occur on the quenching of steel forgings in heat treatment. Large forgings are subjected to the formation of small cracks, or flakes at the center of the cross section. This is associated with the high hydrogen content usually present in steel ingots of large size, coupled with the presence of residual stresses. Large forgings therefore have to be slowly cooled from the working temperature. Examples: burying the forging in ashes for a period of time or using a controlled cooling furnace. Finite element analysis is used to predict residual stresses in forgings.

2.12 Typical forging defects

44



Incomplete die filling.



Die misalignment.



Forging laps.



Incomplete forging penetration-should forge on the press.



Microstructural differences resulting in pronounced property variation.



Hot shortness, due to high Sulphur concentration in steel and nickel.


Fluorescence penetrant reveals Forging laps

Pitted surface, surface, due to oxide scales occurring at high temperature stick on the dies. Buckling, Buckling, in upsetting forging. Subject to high compressive stress. Surface cracking, cracking, due to temperature differential between surface and center, or excessive working of the surface at too low temperature. Microcracking, Microcracking, due to residual stress.

Buckling

Flash line crack , after trimming-occurs more often in thin workpieces. Therefore, should increase the thickness of the flash. fl ash. Cold shut or fold, fold, due to flash or fin from prior forging steps is forced into the workpiece. Internal cracking, cracking, due to secondary tensile stress.

45


2.12.1 Summary Mainly hot forging – Blacksmith, now using water power, steam, electricity, hydraulic machines. Heavy forging 

Hydraulic press=slow, high force squeeze.



Pieces up to 200 tons with forces up to 25,000 tons.



Simple tools squeeze metal into shape (open-die forging).



Sufficient deformation must be given to break up the ‘as cast’ structure. cast’ structure.



Reheating is often needed to maintain sufficient temperature for hot working.



Forging is costly but eliminates some as-cast defects



Continuous ‘grain flow’ in the direction of metal flow is revealed is revealed by etching.



Impurities (inclusions and segregation) have become elongated and (unlike casting) gives superior properties in the direction of elongation.

46


3

Rolling of metals

3.1







Rolling mills



Classification of rolling processes



Hot rolling



Cold rolling



Forces and geometry relationships in rolling



Simplified analysis of rolling load: Rolling variables



Problems and defects in rolled products



Rolling-mill control



Theories of cold rolling



Theories of hot rolling



Torque and power

3.2

Objectives

This chapter provides information on different types of metal rolling processes which can also be divided in to hot and cold rolling process. Mathematical approaches are introduced for the understanding of load calculation in rolling processes. Finally, identification of defects occurring during and its solutions are included.

3.3

Introduction-Definition of rolling process

Definition of Rolling: The process of plastically deforming metal by passing it between rolls. Rolling is the most widely used forming process, which provides high production and close control of final product. The metal is subjected to high compressive stresses as a result of the friction between the rolls and the Rolling process metal surface.

Note: rolling processes can be mainly divided into 

hot rolling

47




cold rolling.

3.3.1 Introduction-Hot and cold rolling processes Hot rolling The initial breakdown of ingots into blooms and billets is generally done by hot-rolling. This is followed by further hot rolling into plate, sheet, rod, bar, pipe, rail.

Cold rolling The cold-rolling of metals has played a major role in industry by providing sheet, strip, foil with good surface finishes and increased mechanical strength with close control of product dimensions.

3.3.2 Sheet rolling machines

Rolled strips

48


Rollforming machine

3.3.3 Terminology Semi-finished products Bloom is the product of first breakdown of ingot (cross sectional area >230 cm 2). Billet is the product obtained from a further reduction by hot rolling (cross sectional area >40x40mm2). Slab is the hot rolled ingot (cross sectional area >100 cm 2 and with a width ≥2x thickness).

Further rolling steps: Mill products Plate is the product with a thickness > 6 mm. Sheet is the product with a thickness < 6 mm and width > 600 mm. Strip is the product with a thickness < 6 mm and width < 600 mm.

3.4 Rolls 3.4.1 Mill rolls

3.4.2 Ring rolls 

Ring rolls are used for tube rolling, ring rolling.

49




Ring rolls are made of spheroidized graphite bainitic and pearlitic matrix or alloy cast steel base.

Cantilever mill roll

Tube mill roll

Universal roll

3.4.3 Typical arrangement of rollers for rolling mills

Two-high mill, pullover

Two-high mill, reversing

Three-high mill

The stock is returned to the

The work can be passed

Consist of upper and lower

entrance

for

further back and forth through the driven rolls and a middle

reduction.

Four-high mill

rolls by reversing their

roll,

which

direction of rotation.

friction.

rotates

by

Cluster mill or Sendzimir mill

Small-diameter rolls (less strength & Each of the work rolls is supported by two rigidity) are supported by larger-diameter backing rolls. backup rolls 3.4.4 Continuous rolling Use a series of rolling mill and each set is called a stand. The strip will be moving at different velocities at each stage in the mill.

50


A four stand continuous mill or tandem mil.

The speed of each set of rolls is synchronized so that the input speed of each stand is equal to the output speed of preceding stand. The uncoiler and windup reel not only feed the stock into the rolls and coiling up the final product but also provide back tension and front tension to the strip. 3.4.5 Typical arrangement of rollers for rolling mills

Planetary mill

Consist of a pair of heavy backing rolls surrounded by a large number of planetary rolls. Each planetary roll gives an almost constant reduction to the slab as it sweeps out a circular path between the backing rolls and the slab. As each pair of planetary rolls ceases to have contact with the workpiece, another pair of rolls makes contact and repeat that reduction. The overall reduction is the summation of a series of small reductions by each pair of rolls. Therefore, the planetary mill can hot reduce a slab directly to strip in one pass through the mill. The operation requires feed rolls to introduce the slab into the mill, and a pair of planishing rolls on the exit to improve the surface finish. 3.4.6 Rolling mills Rolling mill is a machine or a factory for shaping metal by passing it through rollers

51


A rolling mill basically consists of 

rolls



bearings



a housing for containing these parts



a drive (motor) for applying power to the rolls and controlling the speed

Modern rolling mill 

Requires very rigid construction, large motors to supply enough power (MN).



Successive stands of a large continuous mill

Plus: 

skills



engineering design



construction

needs huge capital investment

3.5

Different types of rolling processes

There are different types of rolling processes as listed below; 

Continuous rolling



Transverse rolling



Shaped rolling or section rolling



Ring rolling



Powder rolling



Continuous casting and hot rolling



Thread rolling

3.5.1 Conventional hot or cold-rolling The objective is to decrease the thickness of the metal with an increase in length and with little increase in width.

52


The material in the center of the sheet is constrained in the z direction (across the width of the sheet) and the constraints of undeformed shoulders of material on each side of the rolls prevent extension of the sheet in the width direction. This condition is known as plane strain. The material therefore gets longer and not wider. Otherwise we would need the width of a football pitch to roll down a steel ingot to make tin plate!

3.5.2 Transverse rolling Using circular wedge rolls. Heated bar is cropped to length and fed in transversely between rolls. Rolls are revolved in one direction.

3.5.3 Shaped rolling or section rolling A special type of cold rolling in which flat slap is progressively bent into complex shapes by passing it through a series of driven rolls. No appreciable change in the thickness of the metal during this process. Suitable for producing molded sections such as irregular shaped channels and trim.

53


A variety of sections can be produced by roll forming process using a series of forming rollers in a continuous method to roll the metal sheet to a specific shape Applications:

54



construction materials,



partition beam



ceiling panel



roofing panels.



steel pipe



automotive parts



household appliances



metal furniture,



door and window frames



other metal products.


3.5.4 Seamless rings The donut shape preform is placed between a free turning inside roll and a driven outside roll. The ring mills make the section thinner while increasing the ring diameter.

Ring rolling

Simulation of ring rolling

3.5.5 Seamless ring rolling

3.5.6 Powder rolling Metal powder is introduced between the rolls and compacted into a ‘green strip’, which is subsequently sintered and subjected to further hot-working and/or cold working and annealing cycles. Advantage: 

-Cut down the initial hot-ingot breakdown step (reduced capital investment).



-Economical-metal powder is cheaply produced during the extraction process.



-Minimize contamination in hot-rolling.



-Provide fine grain size with a minimum of preferred orientation.

55


3.5.7 Continuous casting and hot rolling Metal is melted, cast and hot rolled continuously through a series of rolling mills within the same process. Usually for steel sheet production.

3.5.8 Thread rolling Dies are pressed against the surface of cylindrical blank. As the blank rolls against the infeeding die faces, the material is displaced to form the roots of the thread, and the displaced material flows radially outward to form the thread's crest.

56


A blank is fed between two grooved die plates to form the threads. The thread is formed by the axial flow of material in the workpiece. The grain structure of the material is not cut, but is distorted to follow the thread form. Rolled threads are produced in a single pass at speeds far in excess of those used to cut threads. The resultant thread is very much stronger than a cut thread. It has a greater resistance to mechanical stress and an increase in fatigue strength. Also the surface is burnished and work hardened.

Cut thread and rolled thread

3.6

Hot-rolling

The first hot-working operation for most steel products is done on the primary roughing mill (blooming, slabbing or cogging mills). These mills are normally two-high reversing mills with 0.6-1.4 m diameter rolls (designated by size).

57


Plate rolling

The objective is to breakdown the cast ingot into blooms or slabs for subsequent finishing into bars, plate or sheet. In hot-rolling steel, the slabs are heated initially at 1100 -1300 oC. The temperature in the last finishing stand varies from 700-900 oC, but should be above the upper critical temperature to produce uniform equiaxed ferrite grains. 3.6.1 Example for hot strip mill process

Flat plate of large thickness (10-50 mm) is passed through different set of working rolls, while each set consecutively reduces thickness. Hot strip is coiled to reduce its increasing length due to a reduction of thickness. Reducing the complication of controlling strips of different speeds due to different thicknesses. (thinner section moves faster)

58


Plate rolling Hot rolled coil produced on strip mill

3.7

Cold-rolling

Cold rolling is carried out under recrystallization temperature and introduces work hardening. The starting material for cold-rolled steel sheet is pickled hot-rolled breakdown coil from the continuous hot-strip mill. The total reduction achieved by cold-rolling generally will vary from about 50 to 90%. The reduction in each stand should be distributed uniformly without falling much below the maximum reduction for each pass. Generally, the lowest percentage reduction is taken place in the last pass to permit better control of flatness, gage, and surface finish.

Cold rolling mill

59


3.7.1 Example for cold strip mill process

3.7.2 Cold-rolling Cold rolling provides products with superior surface finish (due to low temperature no oxide scales) Better dimensional tolerances compared with hot-rolled products due to less thermal expansion. Cold-rolled nonferrous sheet may be produced from hot-rolled strip, or in the case of certain copper alloys it is cold-rolled directly from the cast state. Cold rolled metals are rated as ‘temper’: Skin rolled: Metal undergoes the least rolling ~ 0.5-1% harden, still more workable. Quarter hard: Higher amount of deformation. Can be bent normal to rolling direction without fracturing Half hard: Can be bent up to 90°. Full hard: Metal is compressed by 50% with no cracking. Can be bent up to 45°. 3.7.3 Fundamental concept of metal rolling Assumptions: 

The arc of contact between the rolls and the metal is a part of a circle.



The coef ficient of friction, μ, is constant in theory, but in reality μ varies along the arc of contact.



60

The metal is considered to deform plastically during rolling.




The volume of metal is constant before and after rolling. In practical the volume might decrease a little bit due to close-up of pores.



The velocity of the rolls is assumed to be constant.



The metal only extends in the rolling direction and no extension in the width of the material.



The cross sectional area normal to the rolling direction is not distorted.

3.8

Forces and geometrical relationships in rolling

A metal sheet with a thickness h 0 enters the rolls at the entrance plane xx with a velocity v0. It passes through the roll gap and leaves the exit plane yy with a reduced thickness h f and at a velocity v f . Given that there is no increase in width, the vertical compression of the metal is translated into an elongation in the rolling direction. Since there is no change in metal volume at a given point per unit time throughout the process, therefore

Where b v

is the width of the sheet is the velocity at any thickness h intermediate between h0 and hf .

Given that b0=bf

61


Then we have

When ho > hf , we then have vo < vf

The velocity of the sheet must steadily increase from entrance to exit such that a vertical element in the sheet remain undistorted.

At only one point along the surface of contact between the roll and the sheet, two forces act on the metal: 1) a radial force P r and 2) a tangential frictional force F. If the surface velocity of the roll vr equal to the velocity of the sheet, this point is called neutral point or no-slip point. For example, point N. Between the entrance plane (xx) and the neutral point the sheet is moving slower than the roll surface, and the tangential frictional force, F, act in the direction (see Fig) to draw the metal into the roll.

62


On the exit side (yy) of the neutral point, the sheet moves faster than the roll surface. The direction of the frictional fore is then reversed and oppose the delivery of the sheet from the rolls. Pr is the radial force, with a vertical component P (rolling load-the load with which the rolls press against the metal).

The specific roll pressure, p, is the rolling load divided by the contact area.

Where b Lp

is the width of the sheet. is the projected length of the arc of contact.

The distribution of roll pressure along the arc of contact shows that the pressure rises to a maximum at the neutral point and then falls off. The pressure distribution does not come to a sharp peak at the neutral point, which indicates that the neutral point is not really a line on the roll surface but an area.

63


The area under the curve is proportional to the rolling load. The area in shade represents the force required to overcome frictional forces between the roll and the sheet.

The area under the dashed line AB represents the force required to deform the metal in plane homogeneous compression. 3.8.1 Roll bite condition For the workpiece to enter the throat of the roll, the component of the friction force must be equal to or greater than the horizontal component of the normal force.

But we know

64


Therefore

F

is a tangential friction force

Pr

is radial force

If

tan α > μ

the workpiece cannot be drawn.

If

μ=0

rolling cannot occur.

Therefore, Free engagement will occur when μ > tan α 

Increase the effective values of μ, for example grooving the rolls parallel to the roll axis.



Using big rolls to reduce tan α or if the roll diameter is fixed, reduce the h 0

3.8.2 The maximum reduction

From triangle ABC, we have

65


As a is much smaller than R, we can then ignore a 2.

Where Δh=h0-hf =2a

3.8.3 Problem with roll flattening When high forces generated in rolling are transmitted to the workpiece through the rolls, there are two major types of elastic distortions: 

The rolls tend to bend along their length because the workpiece tends to separate them while they are restrained at their ends.  Thickness variation.



The rolls flatten in the region where they contact the workpiece. The radius of the curvature is increased R



R’. (roll flattening)

According to analysis by Hitchcock,

Where C=16(1-ν2)/πE=2.16 x 10-11 Pa-1 for steel rolls. P’=rolling load based on the deformed roll radius. 3.8.4 Example: Determine the maximum possible reduction for cold rolling a 300 mm-thick slab when μ=0.08 and the roll diameter is 600 mm. What is the maximum reduction on the same mill for hot rolling when μ=0.5? From

For cold-rolling

For hot-rolling

Alternatively, we can use the relationship below

66


3.9

Simplified analysis of rolling load

The main variables in rolling are: 

The roll diameter.



The deformation resistance of the metal as influenced by metallurgy, temperature and strain rate.



The friction between the rolls and the workpiece.



The presence of the front tension and/or back tension in the plane of the sheet.

We consider in three conditions: 

No friction condition



Normal friction condition



Sticky friction condition

3.9.1 No friction situation In the case of no friction situation, the rolling load (P) is given by the roll pressure (p) times the area of contact between the metal and the rolls (bL p).

Where the roll pressure (p) is the yield stress in plane strain when there is no change in the width (b) of the sheet 3.9.2 Normal friction situation In the normal case of friction situation in plane strain, the average pressure p can be calculated as.

Where Q = μLp /h h = the mean thickness between entry and exit from the rolls. From

We have

67


Roll diameter ↑ Rolling load ↑

Therefore, the rolling load P increases with the roll radius R1/2, depending on the contribution from the friction hill. The rolling load also increases as the sheet entering the rolls becomes thinner (due to the term eQ ). At one point, no further reduction in thickness can be achieved if the deformation resistance of the sheet is greater than the roll pressure. The rolls in contact with the sheet are both severely elastically deformed. Small-diameter rolls which are properly stiffened against deflection by backup rolls can produce a greater reduction before roll flattening become significant and no further reduction of the sheet is possible.

Backup rolls

Example: the rolling of aluminium cooking foil. Roll diameter < 10 mm with as many as 18 backing rolls. Frictional force is needed to pull the metal into the rolls and responsible for a large portion of the rolling load.

High friction results in high rolling load, a steep friction hill and great tendency for edge cracking. The friction varies from point to point along the contact arc of the roll. However, it is very difficult to measure this variation in μ, all theories of rolling are forced to assume a constant coefficient of friction.

68



For cold-rolling with lubricants, μ ~ 0.05 – 0.10.



For hot-rolling, μ ~ 0.2 up to sticky condition.


Example: Calculate the rolling load if steel sheet is hot rolled 30% from a 40 mm-thick slab using a 900 mm-diameter roll. The slab is 760 mm wide. Assume μ=0.30. The plane-strain flow stress is 140 MPa at entrance and200 MPa at the exit from the roll gap due to the increasing velocity.

3.9.3 Sticky friction situation What would be the rolling load if sticky friction occurs? Continuing the analogy with compression in plane strain

From example;

69


Example: The previous example neglected the influence of roll flattening under very high rolling loads. If the deformed radius R’ of a roll under load is given, using C=2.16x10-11 Pa-1, P’=13.4 MPa from previous example.

Where C=16(1-ν2)/πE, P’=Rolling load based on the deformed roll radius.

We now use R’ to calculate a new value of P’ and in turn another value of R’

The difference between the two estimations of R’ is not large, so we stop the calculation at this point. 3.9.4 Relationship of μ, rolling load and torque We have known that the location of the neutral point N is where the direction of the friction force changes. If back tension is applied gradually to the sheet, the neutral point N shifts toward the exit plane. The total rolling load P and torque MT (per unit of width b) is given by

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Friction acts in opposite directions

Where μ is obtained by measuring by measuring the torque and the rolling load at constant roll speed and reduction with the proper back tension. 3.9.5 Back and front tensions in sheet The presence of back and front tensions in the plane of the sheet reduces the rolling load.

Back tension may be produced by controlling the speed of the uncoiler relative to the roll speed. Front tension may be created by controlling the coiler. Back tension is ~ twice as effective in reducing the rolling load P as front tension. The effect of sheet tension on reducing rolling pressure p can be shown simply by

71


Where σh=horizontal sheet tension. If a high enough back tension is applied, the neutral point moves toward the roll exit



rolls are moving faster than the metal. If the front tension is used, the neutral point will move toward the roll entrance.

3.10 Problems and defects in rolled products 3.10.1 Defects from cast ingot before rolling Defects other than cracks can result from defects introduced during the ingot stage of production. Porosity, cavity, blow hole occurred in the cast ingot will be closed up during the rolling process. Longitudinal stringers of non-metallic inclusions or pearlite banding are related to melting and solidification practices. In severe cases, these defects can lead to laminations which drastically reduce the strength in the thickness direction. 3.10.2 Defects during rolling There are two aspects to the problem of the shape of a sheet. 

Uniform thickness over the width and thickness – can be precisely controlled with modern gage control system.



Flatness – difficult to measure accurately.

3.10.3 Uniform thickness Under high rolling forces, the rolls flatten and bend, and the entire mill is elastically distorted. Mill spring causes the thickness of the sheet exiting from the rolling mill to be greater than the roll gap set under no-load conditions. Precise thickness rolling requires the elastic constant of the mill. Calibration curves are needed, see Fig.

72


(1– (1–3 GNm-1 for screw-loaded rolling mills, 4 GNm-1 for hydraulically loaded mills). Roll flattening increases the roll pressure and eventually causes the rolls to deform more easily than the metal. The limiting thickness is nearly proportional to μ, R, σ0‘but inversely ‘but inversely proportional to E. For example, in steel rolls the limiting thickness is given by

In general, problems with limiting gauge can be expected when the sheet thickness is below 1/400 to 1/600 of the roll diameter. 3.10.4 Flatness The roll gap must be perfectly parallel to produce sheets/plates with equal thickness at both ends. The rolling speed is very sensitive to flatness. A difference in elongation of one part in 10,000 between different locations in the sheet can cause waviness.

3.10.5 Solutions to flatness problems Camber and crown can be used to correct the roll deflection (at only one value of the th e roll force). Or use rolling mill equipped with hydraulic h ydraulic jacks to permit the elastic distortion of the rolls to correct deflection.

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(a) The use of cambered rolls to compensate for roll bending. (b) Uncambered rolls give variation of thickness.

The roll cross angle of rolls incorporated in a stand of each rolling mill is set at a predetermined value beforehand. If there is a roll cross angle that will enable a target sheet crown to be applied to each sheet and the roll bender load of each stand is adjusted on-line, thereby effecting sheet crown control. Hot mill can be provided with facilities for crown control to improve the control of the profile of hot strip mill. For example, work roll bending with continuous variable crown and pair cross mills. 3.10.6 Possible effects when rolling with insufficient camber Thicker center means the edges would be plastically elongated more than the center, normally called long edges. This induces the residual stress pattern of compression at the edges and tension along the centerline.

This can cause centerline cracking (c), warping (d) or edge wrinkling or crepe-paper effect or wavy edge (e). Thicker edges than the center means the center would be plastically elongated more than the edges, resulting in lateral spread. The residual stress pattern is now under compression in th e centerline and tension at the edges (b). This may cause edge cracking (c), center splitting (d), centerline wrinkling (e). Shape problems are greatest when rolling in thin strip (<0.01 in) because fractional errors in the roll gap profile increase with decrease in thickness, producing larger internal stress. Thin sheet is also less resistant to buckling.

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Mild shape problems may be corrected by stretch levelling the sheet in tension or by bend flexing the sheet in a roller-leveler. see Fig.

Roller-leveler

Edging can also be caused by inhomogeneous deformation in the thickness direction. If only the surface of the workpiece is deformed (as in a light reduction on a thick slab), the edges are concaved (a). The overhanging material is not compressed in the subsequent step of rolling, causing this area under tensile stress and leading to edge cracking. This has been observed in initial breakdown of hot-rolling when h/Lp > 2.

With heavy reduction, the center tends to expand more laterally than the surface to produced barreled edges (b). This causes secondary tensile stresses by barreling, which are susceptible to edge cracking. Alligatoring (c) will occur when lateral spread is greater in the center than the surface (surface in tension, center in compression) and with the presence of metallurgical weakness along the centerline. Surface defects are more easily in rolling due to high surface to volume ratio. Grinding, chipping or descaling of defects on the surface of cast ingots or billets are recommended before being rolled. Laps due to misplace of rolls can cause undesired shapes.

Flakes or cooling cracks along edges result in decreased ductility in hot rolling such as blooming of extra coarse grained ingot. Scratches due to tooling and handling. Variation in thickness due to deflection of rolls or rolling speed.

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3.11 Rolling mill control Modern continuous hot-strip and cold rolling mills operated under automatic control provides high throughput and production rate. Of all the metal working processes, rolling is the best suited for the adoption of automatic control because it is an essentially steady-state process in which the tooling geometry (roll gap) may be changed readily during the process. Automatic control in rolling such as the development of online sensors to continuously measure sheet thickness. The most widely used instruments are 

flying micrometer



x-ray or isotope, gauges which measure thickness by monitoring the amount of radiation transmitted through the sheet.

More recently control procedures have been aimed at controlling strip shape as well as thickness. 3.11.1 Problem of gauge control For a normal situation For a given set of rolling conditions, the rolling load varies with the final sheet thickness, according to the plastic curve

The elastic curve for mill spring indicates that a sheet of initial thickness h o will have a final thickness hf and the load on the mill would be P in normal situation.

Characteristic elastic and plastic curves for a rolling mill

Situation where μ or flow stress increase In order to maintain a constant thickness hf1, under these new condition, the roll gap would have to be decreased. This moves the elastic curve to the left and further increases the rolling load to P3.

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Use of characteristic curves to show changes in rolling condition.

μ ↑ due to lubricant breakdown σ ↑ due to Temp ↓ The plastic curve will be raised. Therefore,

rolling load

P1  P2

final thickness

hf1  hf2

Example: If the sheet thickness increases, the plastic curve will move to the right relative to the elastic curve. If the there is an increase in strip tension, the plastic curve will move to the left. 3.11.2 Thickness measurement in continuous hot mill In a continuous hot mill, the strip thickness is measured indirectly by measuring the rolling load and using the characteristic curve of the mill to establish the thickness. The error signal is feedback to the rolling mill screws to reposition them so as to minimize the error. An x-ray gauge is used after the last stand to provide an absolute measurement of sheet gauge. Thickness is measured by x-ray gauges while the error in the thickness following the first stand is usually feedback to adjust the gap sitting on the first stand. Gauge control in subsequent stands usually is achieved by controlling the strip tension through controlling the relative roll speed in successive stands or the coiler speed. Gauge control through control of strip tension has faster response time than control through change in roll setting.

sensors

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Thickness gauging is achieved by using two opposing sensors with laser spots aimed at opposite sides of a target. The sensor readings are subtracted from the sensor separation distance to yield a real-time thickness measurement.

3.12 Theory of cold rolling A theory of rolling is aimed at expressing the external forces, such as the rolling load and the rolling torque, in terms of the geometry of the deformation and the strength properties of the material being rolled. Assumptions 

The arc of the contact is circular – no elastic deformation of the roll.



The coefficient of friction is constant at all points on the arc of contact.



There is no lateral spread, so that rolling can be considered a problem in plain strain.



Plane vertical section remain plane: i.e., the deformation is homogeneous.



The peripheral velocity of the rolls is constant



The elastic deformation of the sheet is negligible in comparison with the plastic deformation.



The distortion-energy criterion of yielding, for plane strain, holds.

Yield stress in plane strain condition

3.12.1 The stresses acting on an element of strip in the roll gap At any point of contact between the strip and the roll surface, designated by the angle θ, the stresses are the radial pressure Pr and the tangential shearing stress τ=μ Pr. These stresses are resolved into their horizontal and vertical components (b).

The stress σx is assumed to be uniformly distributed over the vertical faces of the element.

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Taking summation of the horizontal forces on the element results in

Which simplifies to

The forces acting in the vertical direction are balanced by the specific roll pressure p. Taking the equilibrium of forces in the vertical direction results in a relationship between the normal pressure and the radial pressure.

The relationship between the normal pressure and the horizontal compressive stress σx is given by the distortion energy criterion of yielding for plane strain.

Where p is the greater of the two compressive principal stresses. The solution of problems in cold rolling are complicated. Some simplification to this problem has been provided by Bland and Ford. By restricting the analysis to cold rolling under conditions of low friction and for angles of contact < 6°, then we can put sin θ ~ θ and cos θ ~ 1. Thus Equation can be written

It is also assumed that p r ~ p, so that can be written σx=pr- σ0‘. By substituting this and integrating, relatively simple equations of the radial pressure result.

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Roll entrance to neutral point:

Neutral point to roll exit:

Where

and

σxb =

back tension

σxf =

front tension

The rolling load or total force P is the integral of the specific roll pressure over the arc of contact.

Where b= α=

width of sheet contact angle

The solution is replaced by the modern digital computer.

3.13 Theory of hot-rolling In hot working processes, the flow stress for hot-rolling is a function of both temperature and strain rate (speed of rolls) 3.13.1 Calculation of rolling load by Sims

Where Qp is a complex function of the reduction in thickness and the ratio R/h f . Values of Qp may be obtained from

80


3.14 Torque and power Torque is the measure of the force applied to a member to produce rotational motion. Power is applied to a rolling mill by applying a torque to the rolls and by means of strip tension. The power is spent principally in four ways 

The energy needed to deform the metal.



The energy needed to overcome the frictional force.



The power lost in the pinions and power-transmission system.



Electrical losses in the various motors and generators.

Remarks: Losses in the windup reel and uncoiler must also be considered. The total rolling load is distributed over the arc of contact in the typical friction-hill pressure distribution. However, the total rolling load can be assumed to be concentrated at a point along the act of contact at a distance a form the line of centers of the rolls.

Schematic diagram illustrating roll torque

The ratio of the arm moment a to the projected length of the act of contact L p can be given as

Where λ is 0.5 for hot-rolling and 0.45 for cold-rolling. The torque MT is equal to the total rolling load P multiplied by the effective moment arm a. Since there are two work rolls, the torque is given by

During one revolution of the top roll the resultant rolling load P moves along the circumference of a circle equal to 2πa. Since there are two work rolls, the work done W is equal to

81


Since power is defined as the rate of doing work, i.e., 1 W=1 J s -1, the power (in watts) needed to operate a pair of rolls revolving at N Hz (s -1) in deforming metal as it flows through the roll gap is given by

Where P is in newton’s and a is in meters. Example: A 300 mm-wide aluminium alloy strip is hot-rolled in thickness from 20 to 15 mm. The rolls are 1 m in diameter and operate at 100 rpm. The uniaxial flow stress for aluminium alloy can be expressed as σ=140ε0.2 (MPa). Determine the rolling load and the power required for this hot reduction. From

b=0.3 m, R=0.5 m, ho=0.02 m and hf=0.015 m, we need to know σ 0‘ and Q p.

Qp can be found from graph (~1.5) w hen reduction r and R/hf are known.

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4

Extrusion

4.1







Classification of extrusion processes



Extrusion equipment (Presses, dies and tools)



Hot extrusion



Deformation, lubrication, and defects in extrusion



Analysis of the extrusion process



Cold extrusion and cold-forming






Extrusion of tubing




4.2 Objective This chapter aims to provide useful information on different extrusions processes, which can be mainly divided into direct and indirect extrusion processes. This also includes basic background on hydrostatic extrusion, extrusions of tubing and production of seamless pipe and tubing. Principal background and concept of extrusion will be addressed along with the utilization of mathematical approaches to understand the calculation of extrusion load. The role of lubricants on the deformation process which results in the improvement in extrusion products will be provided. Finally, defects and its solutions occurring in the extrusion process will be emphasized.

4.3 What is extrusion? Extrusion is the process by which a block/billet of metal is reduced in cross section by forcing it to flow through a die orifice under high pressure. In general, extrusion is used to produce cylindrical bars or hollow tubes or for the starting stock for drawn rod, cold extrusion or forged products.

Most metals are hot extruded due to large amount of forces required in extrusion. Complex shape can be extruded from the more readily extrudable metals such as aluminium.

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

The products obtained are also called extrusion.

The reaction of the extrusion billet with the container and die results in high compressive stresses which are effective in reducing cracking of materials du ring primary breakdown from the ingot.

This helps to increase the utilization of extrusion in the working of metals that are difficult to form like stainless steels, nickel-based alloys, and other high-temperature materials. Similar to forging, lower ram force and a fine grained recrystallized structure are possible in hot extrusion. However, better surface finish and higher strengths (strain hardened metals) are provided by cold extrusion. 4.3.1 Extrusion products Typical parts produced by extrusion are trim parts used in automotive and construction applications, window frame members, railings, aircraft structural parts. Example: Aluminium extrusions are used in commercial and domestic buildings for window and door frame systems, prefabricated houses/building structures, roofing and exterior cladding, curtain walling, shop fronts, etc. Furthermore, extrusions are also used in transport for airframes, road and rail vehicles and in marine applications.

Aluminium extrusions

4.4 Classification of extrusion processes There are several ways to classify metal extrusion processes; 



By direction 

Direct / Indirect extrusion



Forward / backward extrusion

By operating temperature 



By equipment 

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Hot / cold extrusion Horizontal and vertical extrusion


4.4.1 Direct and indirect extrusions 4.4.2 Direct extrusion

The metal billet is placed in a container and driven through the die by the ram. The dummy block or pressure plate, is placed at the end of the ram in contact with the billet. Friction is at the die and container wall requires higher pressure than indirect extrusion. 4.4.3 Indirect extrusion

The hollow ram containing the die is kept stationary and the container with the billet is caused to move. Friction at the die only (no relative movement at the container wall) requires roughly constant pressure. Hollow ram limits the applied load. 4.4.4 Extrusion can also be divided to: Forward and backward extrusion 4.4.5 Forward extrusion Metal is forced to flow in the same direction as the punch. The punch closely fits the die cavity to prevent backward flow of the material.

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4.4.6 Backward extrusion Metal is forced to flow in the direction opposite to the punch movement. Metal can also be forced to flow into recesses in the punch, see Fig.

4.4.7 Cold extrusion Cold extrusion is the process done at room temperature or slightly elevated temperatures. This process can be used for most materials-subject to designing robust enough tooling that can withstand the stresses created by extrusion.

Cold extrusion

Examples Examples of the metals that can be extruded are lead, tin, aluminium alloys, copper, titanium, molybdenum, vanadium, steel. Examples of parts that are cold extruded are collapsible tubes, aluminium cans, cylinders, gear blanks. Advantages 

No oxidation takes place.



Good mechanical properties due to severe cold working as long as the temperatures created are below the recrystallization temperature.



Good surface finish with the use of proper lubricants.

Collapsible tubes and Aluminium cans

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4.4.8 Hot extrusion Hot extrusion is done at fairly high temperatures, approximately 50 to 75 % of the melting point of the metal. The pressures can range from 35-700 MPa (5076-101,525 psi). The most commonly used extrusion process is the hot direct process. The cross-sectional shape of the extrusion is defined by the shape of the die. Due to the high temperatures and pressures and its detrimental effect on the die life as well as other components, good lubrication lubr ication is necessary. Oil and graphite work at lower temperatures, whereas at higher temperatures glass powder is used.

4.4.9 Tube extrusion Tubes can be produced by extrusion by attaching a mandrel to the end of the ram. The clearance between the mandrel and the die wall determines the wall thickness of the tube. Tubes are produced either by starting with a hollow billet or by a twostep extrusion in which a solid billet is first pierced and then extruded.

4.4.10 Impact extrusion Produce short lengths of hollow shapes, such as collapsible toothpaste tubes or spray cans. Requires soft materials such as aluminium, lead, copper or tin are normally used in the impact extrusion.

A small shot of solid material is placed in the t he die and is impacted by a ram, which causes cold flow in the material. It may be either direct or indirect extrusion and it is usually performed on a high speed mechanical press.

87


Although the process is generally performed cold, considerable heating results from the high speed deformation. 

Small objects, soft metal, large numbers, good tolerances

Extrusion was originally applied to the making of lead pipe and later to the lead sheathing on electrical cable.

Extrusion of lead sheath on electrical cable.

4.5 Extrusion equipment (Presses, dies and tools) Extrusion equipment mainly includes presses, dies and tooling. 



Presses 

Most extrusions are made with hydraulic presses.



These can be classified based on the direction of travel of the ram. Horizontal presses



Vertical presses

Extrusion dies 





Die design, Die materials

Tools 

Typical arrangement of extrusion tools.

4.5.1 Horizontal extrusion presses (15-50 MN capacity or up to 140 MN) Used for most commercial extrusion of bars and shapes. Disadvantages: deformation is non-uniform due to different temperatures between top and bottom parts of the billet.

88


4.5.2 Vertical extrusion presses (3-20 MN capacity) Chiefly used in the production of thin-wall tubing. Advantages: 

Easier alignment between the press ram and tools.



Higher rate of production.



Require less floor space than horizontal presses.



Uniform deformation, due to uniform cooling of the billet in the container.

Requirements: 

Need considerable headroom to make extrusions of appreciable length.



A floor pit is necessary.

Vertical extrusion machine

4.5.3 Ram speed Require high ram speeds in high-temperature extrusion due to heat transfer problem from billet to tools. Ram speeds of 0.4-0.6 m s-1 for refractory metals  requires a hydraulic accumulator with the press. Ram speeds of a few mm s -1 for aluminium and copper due to hot shortness  requires direct-drive pumping systems to maintain a uniform finishing temperature. 4.5.4 Die design Die design is at the heart of efficient extrusion production. Dies must withstand considerable amount of stresses, thermal shock, and oxidation. Die design

CAD/CAM

Milling

Wire

sparkling

erosion

Finishing

Inspection

Die design consideration 

Wall thickness: different wall thicknesses in one section should be avoided.



Simple shapes: the simpler shape the more cost effective.



Symmetrical: more accurate.



Sharp or rounded corners: sharp corners should be avoided.

89




Size to weight ratio:



Tolerances: tolerances are added to allow some distortions (industrial standards).

4.5.5 Die materials Dies are made from highly alloy tools steels or ceramics (zirconia, Si 3N4). (for cold extrusion offering longer tool life and reduced lubricant used, good wear resistance). Wall thickness as small as 0.5 mm (on flat dies) or 0.7 mm (on hollow dies) can be made for aluminium extrusion. Heat treatments such as nitriding are required (several times) to increase hardness (10001100 Hv or 65-70 HRC). This improves die life  avoiding unscheduled press shutdown.

There are two general types of extrusion dies: 

Flat-faced dies



Dies with conical entrance angle.

4.5.6 Flat-faced dies Metal entering the die will form a dead zone and shears internally to form its own die angle. A parallel land on the exit side of the die helps strengthen the die and allow for reworking of the flat face on the entrance side of the die without increasing the exit diameter.

4.5.7 Dies with conical entrance angle requires good lubricants. decreasing die angle



increasing homogeneity, lower

extrusion pressure (but beyond a point the friction in the die surfaces becomes too great. for most operation, 45° < α < 60°

90


Remarks; transfer equipment (for hot billets) is required. Prior heating of the container. 4.5.8 Typical arrangement of extrusion tooling The die stack consists of the die, which is supported by a die holder and a bolster, all of which are held in a die head. The entire assembly is sealed against the container on a conical seating surface by pressure applied by a wedge. A liner is shrunk in a more massive container to withstand high pressures.

The follower pad is placed between the hot billet and the ram for protection purpose. Follower pads are therefore replaced periodically since they are subject to many cycles of thermal shock.

4.6 Hot extrusion The principal variables influencing the force required to cause extrusion; 

Type of extrusion (direct / indirect)



Extrusion ratio



Working temperature



Deformation



Frictional conditions at the die and the container wall.



Extrusion pressure=extrusion force /cross sectional area

The rapid rise in pressure during initial ram travel is due to the initial compression of the billet to fill the extrusion container. For direct extrusion, the metal begins to flow through the die at the maximum pressure, the breakthrough pressure. As the billet extrudes through the die the pressure required to maintain flow progressively decreases with decreasing length of the billet in the container.

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At the end of the stroke, the pressure rises up rapidly and it is usual to stop the ram travel so as to leave a small discard in the container.

Extrusion pressure vs. ram travel

For indirect extrusion, extrusion pressure is ~ constant with increasing ram travel and represent the stress required to deform the metal through the die. Since hollow ram is used in indirect extrusion, size of the extrusions and extrusion pressure are limited. 4.6.1 Extrusion ratio Extrusion ratio, R, is the ratio of the initial cross-sectional area, Ao, of the billet to the final cross-sectional area, Af , after extrusion.



R ~ 40:1 for hot extrusion of steels.



R ~ 400:1 for aluminium.

Fractional reduction in area, r

and

Note: R is more descriptive at large deformations! Ex:

R=20:1 and 50:1  r=0.95 and 0.98 respectively.

Extrusion ratio, R, of steel could be 40:1 whereas R for aluminium can reach 400:1. The velocity of the extruded product is given by   ℎ   =    

Extrusion force may be expressed as

92


where k=extrusion constant, an overall factor which accounts for the flow stress, friction, and inhomogeneous deformation. 4.6.2 Effects of temperature on hot extrusion 

Decreased flow stress or deformation resistance due to increasing extrusion temperature.



Use minimum temperature to provide metal with suitable plasticity.



The top working temperature should be safely below the melting point or hotshortness range.



Oxidation of billet and extrusion tools.



Softening of dies and tools.



Difficult to provide adequate lubrication.

The temperature of the workpiece in metal working depends on; 

The initial temperature of the tools and the materials



Heat generated due to plastic deformation



Heat generated by friction at the die/material interface (highest)



Heat transfer between the deforming material and the dies and surrounding environment.

Note: Working temperature in extrusion is normally higher than used in forging and rolling due to relatively large compressive stresses in minimizing cracking. Usually the temperature is highest at the material/tool interface due to friction. If we neglect the temperature gradients and the deforming material is considered as a thin plate, the average instantaneous temperature of the deforming material at the interface is given by

Where To

=temperature at the workpiece

T1

=temperature at the die

h

=heat transfer coefficient between the material and the dies

δ

=material thickness between the dies.

If the temperature increase due to deformation and friction is included, the final average material temperature Tm at a time t is

Td

=Temp for frictionless deformation process

Tf

=Temp increase due to friction

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4.6.3 Ram speed, extrusion ratio and temperature A tenfold increase in the ram speed results in about a 50% increase in the extrusion pressure. Low extrusion speeds lead to greater cooling of the billet. The higher the temperature of the billet, the greater the effect of low extrusion speed on the cooling of the billet. Therefore, high extrusion speeds are required with high-strength alloys that need high extrusion temperature. The selection of the proper extrusion speed and temperature is best determined by trial and error for each alloy and billet size. 4.6.4 Relationships between extrusion ratio, temperature and pressure For a given extrusion pressure, extrusion ratio R increases with increasing Extrusion temperature. For a given extrusion temperature, a larger extrusion ratio R can be obtained with a higher extrusion pressure. Extrusion temperature

↑

Extrusion pressure

↑

Extrusion ratio (R)

↑

4.6.5 Relationships between extrusion speed and heat dissipation extrusion speeds ↑

heat dissipation ↓

extrusion speeds ↓

heat dissipation ↑

allowable extrusion ratio ↑

4.7 Deformation in extrusion, lubrication and defects

(a) Low container friction and a well-lubricated billet – nearly homogeneous deformation. (b) Increased container wall friction, producing a dead zone of stagnant metal at corners which undergoes little deformation. Essentially pure elongation in the center and extensive shear along the sides of the billet. The latter leads to redundant work (c) For high friction at the container-billet interface, metal flow is concentrated toward the center and an internal shear plane develops – due to cold container.

94


In the sticky friction, the metal will separate internally along the shear zone. A thin skin will be left in a container and a new metal surface is obtained. (d) Low container friction and a well lubricated billet in indirect extrusion. 4.7.1 Hot extrusion lubricants Low shear strength. Stable enough to prevent breakdown at high temperature. Molten glass is the most common lubricant for steel and nickel based alloys (high temp extrusion).  Ugine-Sejournet process Graphite-based lubricants are also being used at high extrusion temperature.

4.7.2 Ugine-Sejournet process The billet is heated in an inert atmosphere and coated with glass powder before being pressed. The glass pad placed between the die and the billet provide the main source of lubricant. This glass coating is softening during extrusion to provide a lubricant film (~25 μm thick), which serves not only as a lubricant but also a thermal insulator to reduce heat loss to the tools. The coating thickness depends on a complex interaction between the optimum lubricant, the temperature and the ram speed. Lubricant film must be complete and continuous to be successful,otherwise defects such as surface crack will result. too low ram speed

 thick

lubricant coatings with low initial extrusion pressure

 limit

the length of extrusions. too high ram speed  dangerously thin coatings. 4.7.3 Example: Extrusion of aluminium Aluminium billet is heated to around 450-500oC and pressed through flat die to produce solid sections such as bars, rods, hollow shapes, tubes. Aluminium heat treatments may be required for higher strength in some applications.

95


Hot aluminum billet (450-500°C)

Press through dies (dies are preheated)

length cutting

streching both ends

heat treatment (reorientati on of grains imporves mechanical properties)

finishing and inspection

4.7.4 Extrusion defects 4.7.5 Inhomogeneous deformation Inhomogeneous deformation in direct extrusion provide the dead zone along the outer surface of the billet due to the movement of the metal in the center being higher than the periphery. After 2/3 of the billet is extruded, the outer surface of the billet (normally with oxidized skin) moves toward the center and extrudes to the through the die, resulting in internal oxide stringers. -transverse section can be seen as an annular ring of oxide. Container wall friction ↑

extrusion defects ↑

Container wall temp

extrusion defects ↑

↓

If lubricant film is carried into the interior of the extrusion along the shearbands, this will show as longitudinal laminations in a similar way as oxide. Solutions: Discard the remainder of the billet (~30%) where the surface oxide begins to enter the die not economical. Use a follower block with a smaller diameter of the die to scalps the billet and the oxidized layer remains in the container (in brass extrusion). 4.7.6 Surface cracking Surface cracking, ranging from a badly roughened surface to repetitive transverse cracking called fir-tree cracking, see Fig. This is due to longitudinal tensile stresses generated as the extrusion passes through the die.

Surface cracks from heavy die friction in extrusion

In hot extrusion, this form of cracking usually is intergranular and is associated with hot shortness. The most common case is too high ram speed for the extrusion temperature. At lower temperature, sticking in the die land and the sudden building up of pressure and then breakaway will cause transverse cracking.

96


4.7.7 Centre burst or chevron cracking Centre burst or chevron cracking, see Fig, can occur at low extrusion ratio due to low frictional conditions on the zone of deformation at the extrusion die.

Centre burst or chevron cracks

High friction (at the tool-billet interface)  a sound product. Low friction  center burst. 4.7.8 Variations in structure and properties Variations in structure and properties within the extrusions due to non-uniform deformation for example at the front and the back of the extrusion in both longitudinal and transverse directions. Regions of exaggerated grain growth, see Fig, due to high hot working temperature.

Grain growth - Extrusion direction (  )

4.7.9 Hot shortness (in aluminium extrusion). High temperatures generated cause incipient melting, which causes cracking.

Hot shortness

4.8 Analysis of the extrusion process Using the uniform deformation energy approach, the plastic work of deformation per unit volume can be expressed for direct extrusion as

97


The work involved is

Where σ is the effective flow stress in compression so that

* Neither friction nor redundant deformation.

The actual extrusion pressure pe is given by

Where the efficiency of the process η is the ratio of the ideal to actual energy per unit volume. DePierre showed that the total extrusion force P e is the summation of the forces below;

Where Pd

is the die force

Pfb

is the frictional force between the container and the upset billet.

Pff

is the frictional force between the container liner and the follower ~0.

Assuming the billet frictional stress is equal to τi ~ k, the ram pressure required by container friction is

and

Where τi

=uniform interface shear stress between billet and container liner

L

=length of billet in the container liner

D

=inside diameter of the container liner.

Using a slab analysis to account for friction on extruding through a conical die, Sash has performed the analysis for Coulomb sliding friction

This analysis includes die friction but excludes redundant deformation

Where B

98

=μ cot α

α

=semi die angle

R

=extrusion ratio

=Ao /A


Using slip-line field theory for plane-strain condition without considering friction, the solution is as follows;

Where typically a=0.8 and b=1.5 for axisymmetric extrusion. Using upper-bound analysis, Kudo found the following expression for extrusion through rough square dies (2α=180°)

Using upper-bound analysis based on a velocity field, Depierre use the following equation to describe die pressure in hydrostatic extrusion;

Where m=τ /k and a and b are evaluated as follows: i

4.8.1 Variation of local strain rate Using the technique of visioplasticity to map out the distribution of strain and strain rate and to calculate the variation of temperature and flow stress within the extrusion.

Strain rate distribution in a partially extruded steel billet. R=16.5, ram speed=210 mm.s-1 , Temp=1440 K.

There are local maxima near the exit from the die on the surface, and along the center line of the extrusion. The average strain rate for extrusion is usually defined by the time for material to transverse through a truncated conical volume of deformation zone, which is defined b y the billet diameter Db and the extrusion diameter De. For a 45°semicone angle,

99


For a ram velocity ν, the volume extruded per unit time is

And the time to fill the volume of the deformation zone is

Then

The time average mean strain rate is given by For a 45° semi cone angle,

For the general semi die angle α,

Example: An aluminium alloy is hot extruded at 400oC at 50 mm.s -1 from 150 mm diameter to 50 mm diameter. The flow stress at this temperature is given by σ=200(ε)0.15 (MPa). If the billet is 380 mm long and the extrusion is done through square dies without lubrication, determine the force required for the operation. The extrusion load is P=peA

100


We need to know, p e, pd, τi, ̇ ,̅ and R

Since we use square dies without lubrication, see Fig, a dead metal zone will form in the corners of the container against the die.

We can assume that this is equivalent to a semi die angle α =60°. Therefore, the extrusion pressure due to flow through the die is

μ is assumed ~ 0.1

The maximum pressure due to container wall friction will occur at break-through when L=380 mm. Aluminium will tend to stick to the container and shear internally.

4.9 Cold extrusion and cold forming Cold extrusion is concerned with the cold forming from rod and bar stock of small machine parts, such as spark plug bodies, shafts, pins and hollow cylinders or cans. Cold forming also includes other processes such as upsetting, expanding and coining. Precision cold-forming can result in high production of parts with good dimensional control and good surface finish.

101


Because of extensive strain hardening, it is often possible to use cheaper materials with lower alloy content.

Cold extrusion products

The materials should have high resistance to ductile fracture and th e design of the tooling to minimize tensile-stress concentrations.

4.10 Hydrostatic extrusion The billet in the container is surrounded with fluid media, is also called hydrostatics medium. The billet is forced through the die by a high hydrostatic fluid pressure. The rate, with which the billet moves when pressing in the direction of the die, is thus not equal to the ram speed, but is proportional to the displaced hydrostatics medium volume. The billet should may have large length-to-diameter ratio and may have an irregular cross section.


4.10.1 Advantages and disadvantages in hydrostatic extrusion Advantages: 

Eliminating the large friction force between the billet and the container wall. extrusion pressure vs ram travel curve is nearly flat.

102



Possible to use dies with a very low semi cone angle (α ~ 20°)



Achieving of hydrodynamic lubrication in the die.


Limitations: 

Not suitable for hot-working due to pressurized liquid.



A practical limit on fluid pressure of around 1.7 GPa currently exists because of the strength of the container.



The liquid should not solidify at high pressure this limits the obtainable

Extrusion ratios

Mild steel

R should be less than 20:1

Aluminium

R can achieve up to 200:1.

4.10.2 Augmented hydrostatic extrusion Due to the large amount of stored energy in a pressurised liquid, the control of the extrusion on the exit form die maybe a problem. This is however solved by augmented hydrostatic extrusion in which the axial force is applied either to the billet or to the extrusion.

The fluid pressure is kept at less than the value required to cause extrusion and the balance is provided by the augmenting force much better control over the movement of the extrusion.

4.11 Extrusion of tubing To produce tubing by extrusion from a solid billet, the ram may also be fitted with a piercing mandrel. As the ram moves forward, the metal is forced over the mandrel and through the hole in the die, causing a long hollow tube. Just like toothpaste, only hollow.

Extrusion of tubing from a solid billet

If the billets are hollow, a rod that matches the diameter of the cast hole in the billet (but slightly smaller than the hole in the die at the opposite end of the chamber) are used.

103


Note: the bore of the hole will become oxidized resulting in a tube with an oxidized inside surface.

Extrusion of tubing from a hollow billet

4.11.1 Extrusion tubing with a porthole die The metal is forced to flow into separate streams and around the central bridge, which supports a short mandrel.

A sketch of a porthole extrusion die

The separate streams of metal which flow through the ports are brought together in a welding chamber surrounding the mandrel, and the metal exits from the die as a tube.

Porthole extrusion

Since the separate metal streams are jointed within the die, where there is no atmosphere contamination, a perfectly sound weld is obtained. Porthole extrusion is used to produce hollow unsymmetrical shapes in aluminium alloys.

Example: pyramid porthole dies

4.12 Production of seamless pipe and tubing Extrusion is suited for producing seamless pipe and tubing, especially for metals which are difficult to work.

104


The red-hot billet is rotated and drawn by rolls over a piercing rod, or mandrel. The action of the rolls causes the metal to flow over and about the mandrel to create a hollow pipe shell.

Stainless steel seamless pipes

After reheating, the shell is moved forward over a support bar and is hot rolled in several reducing/sizing stands to the desired wall thickness and diameter.


(a)The Mannesmann mill is used for the rotary piercing of steel and copper billets using two barrel-shape driven rolls, which are set at an angle to each other. The axial thrust is developed as well as rotation to the billet. (b)The plug rolling mills drive the tube over a long mandrel containing a plug. (c) The three-roll piercing machine produces more concentric tubes with smoother inside and outside surface. (d)The reeling mill burnishes the outside and inside surfaces and removes the slight oval shape, which is usually one of the last steps in the production of pipe or tubing.

105


5

Drawing of rods, wires and tubes

5.1







Rod and wiredrawing









Analysis of tube drawing



Residual stress in rod, wire and tubes

5.2

Objectives

This chapter provides fundamental background on processes of drawing of rods, wires and tubes. Mathematical approaches for the calculation of drawing load will be introduced. Finally drawing defects occurring during the process will be highlighted and its solutions will be included. 5.2.1 Introduction wire drawing Wire drawing involves reducing the diameter of a rod or wire by passing through a series of drawing dies or plates. The subsequent drawing die must have smaller bore diameter than the p revious drawing die.

5.2.2 Introduction: Tube drawing Tube drawing involves reducing the cross section and wall thickness through a draw die.

Brass tubes for heat exchanger – cheap, strong, good corrosion resistant

106


The cross section can be circular, square hexagonal or in any shapes.

5.3

Introduction

Drawing operations involve pulling metal through a die by means of a tensile force applied to the exit side of the die. The plastic flow is caused by compression force, arising from the reaction of the metal with the die. Starting materials: hot rolled stock (ferrous) and extruded (nonferrous). Material should have high ductility and good tensile strength. Bar wire and tube drawing are usually carried out at room temperature, except for large deformation, which leads to considerable rise in temperature during drawing. The metal usually has a circular symmetry (but not always, depending on requirements).

5.4 Rod and wiredrawing Reducing the diameter through plastic deformation while the vol ume remains the same. Same principals for drawing bars, rods, and wire but equipment is different in sizes depending on products.

Metal rods – metal wires

Rods

 relatively

Wires

 small

larger diameter products.

diameter products < 5 mm diameter.

5.4.1 Rod drawing Rods which cannot be coiled, are produced on draw benches.

Rod is swages

Insert through the die

Clamped to the jaws of the drawhead

The drawhead is moved by a hydraulic mechanism

107


Machine capacity: 1 MN drawbench, 30 m of runout, 150-1500 mm.s -1 draw speed

5.4.2 Wire drawing die Conical drawing die Shape of the bell causes hydrostatic pressure to increase and promotes the flow of lubricant into the die. The approach angle – where the actual reduction in diameter occurs, giving the half die angle α. The bearing region produces a frictional drag on the wire and also remove surface damage due to die wear, without changing dimensions.

The die nib made from cemented carbide or diamond is encased for protection in a thick steel casing. The back relief allows the metal to expand slightly as the wire leaves the die and also minimizes abrasion if the drawing stops or the die is out of alignment. 5.4.3 Example of wiredrawing dies

108


A drawing of wire drawing die

Wire drawing die made from cemented tungsten carbide with polycrystalline diamond core.

5.4.4 Drawing die materials Most drawing dies are cemented carbide or industrial diamond (for fine wires). Cemented carbides are the most widely used for drawing dies due to their superior strength, toughness, and wear resistance.

Polycrystalline Diamond (PCD) used for wire drawing dies – for fine wires. Longer die life, high resistance to wear, cracking or bearing. Cemented carbide is composed of carbides of Ti, W, Ni, Mo, Ta, Hf. 5.4.5 Wire drawing equipment The wire is first passed through the overhead loop and pulley, brought down and then inserted through the die of the second drum and drawn through this die for further reduction.

Bull block drawing machines

Multiple bull block machines-common

Thus, the wire is drawn through all the wire drawing drums of the set in a continuous manner to get the required finished diameter of the wire. Speed of each draw block has to be synchronized to avoid slippage between the wire and the block. The drawing speed

~ up to 10 m.s-1 for ferrous drawing ~ up to 30 m.s-1 for nonferrous drawing.

109


5.4.6 Wire drawing process

Hot rolled rod

Pickling Descaling

Lubricating

Drawing

Pickling, descaling: Remove scale -causing surface defects. Lubricating: Cu and Sn are used as lubricants for high strength materials. Or conversion coating such as sulphates or oxalates. 

Oils and greases for wire drawing



Mulsifiable oils for wet wire drawing



Soap drawing for dry drawing.

Bull block drawing allows the generation of long lengths.

Area reduction per drawing pass is rarely greater than 30-35%.

5.4.7 Example: Drawing of stainless wire

Stainless steels: 304, 304L, 316, 316L – Stainless steel rope

Applications: redrawing, mesh weaving, soft pipe, steel rope, filter elements, making of spring. Larger diameter stainless wire is first surface examined, tensile and hardness tested, diameter size measured.

110


Surface preparation by pickling in acid (ferritic and martensitic steels) and basic solutions (austenitic steels). The prepared skin is then coated with lubricant. Cold drawing is carried out through diamond dies or tungsten carbide dies till the d esired diameter is obtained. Cleaning off oil/lubricant is then carried out and the wire is heat-treated (annealing at about 1100°C or plus skin pass). 5.4.8 Stepped-cone multiple-pass wiredrawing

More economical design. Use a single electrical motor to drive a series of stepped cones. The diameter of each cone is designed to produce a peripheral speed equivalent to a certain size reduction. 5.4.9 Heat treatments Nonferrous wire / low carbon steel wire

 Tempering

(ranging from dead soft to full

hard). This also depends on the metal and the reduction involved. Steels (C content > 0.25%) normally 0.3-0.5% require Patenting heat treatment before being drawn. Patented wire has improved reduction of area up to 90% due to the formation of very fine pearlite. Heating above the upper critical temp T~970°C  Provide austenitic structure with rather large grain size. Cooling in a lead bath at T~315°C

 Rapid

cooling plus small cross section of wire

change microstructure to very fine pearlite preferably with no separation of primary ferrite. As result, we obtain a good combination of strength and ductility. 5.4.10 Defects in rod and wiredrawing Defects in the starting rod (seams, slivers and pipe). Defects from the deformation process, i.e., center burst or chevron cracking (cupping). Centre burst or chevron cracks

111


This defect will occur for low die angles at low reductions. For a given reduction and die angle, the critical reduction to prevent fracture increases with the friction.

5.5


From the uniform-deformation energy method, a draw stress is given by

(This however ignore friction, transverse stress and redundant deformation.) Consider the problem of strip drawing of a wide sheet, (Dieter p. 509) A wide strip is being drawn through a frictionless die with a total included angle of 2α. Plane strain condition is applied (no strain in the width direction.)

The equilibrium of forces in the x direction is made up of two components 1) Due to the change in longitudinal stress with x increasing positively to the left.

2) Due to the die pressure at the two interfaces.

Taking the equilibrium of force in the x direction and neglect dσxdh

We shall now consider the problem of strip drawing where a Coulomb friction coefficient μ exists between the strip and the die.

The equilibrium now includes 2μpdx.

112


Taking equilibrium of forces in the x direction the last equation then becomes

Since h=2x tan α, and dh=2 dx tan α, then 2dx=dh/tan α We now have

Since the yield condition for plane strain is σx + p=σ0‘and B=μ cot α, the differential equation for strip drawing is

If B and σ0‘are both constant, the last equation can be integrated directly to give the draw stress σxa.

For wiredrawing conducted with conical dies,

5.5.1 Analysis for wiredrawing with friction by Johnson and Rowe The surface area of contact between the wire and the die is given by

p

is the mean normal pressure on this area.

Pd

is the draw force.

Balancing the horizontal components of the frictional force and the normal pressure.

In the absence of friction, B=0 and

113


The draw stress with friction is given by

Example: Determine the draw stress to produce a 20% reduction in a 10-mm stainless steel wire. The flow stress is given by σ0=1300ε0.30 (MPa). The die angle is 12° and μ=0.09.

~ 20% difference

If the wire is moving through the die at 3 m.s-1, determine the power required to produce the deformation.

Drawing force

Power

If redundant work is included, the expression becomes

Where φ is a factor for the influence of redundant work, which can be defined as

114


Where φ ε*

=the redundant work factor. =the “enhanced strain” corresponding to the yield stress of the metal, which has been homogeneously deformed to a strain ε.

5.5.2 Procedure for determining redundant deformation of drawn wire

The flow curve of a drawn wire is superimposed on t he flow curve for the annealed metal. The origin of the curve for the drawn metal is displaced along the strain axis=drawing reduction, ε = ln (A b /Aa ) = ln [1/(1-r)].

Due to redundant work, the yield stress of the drawn metal is above the basic flow curve To determine φ, the flow curve for the drawn metal is moved to the right to ε* where the curves coincide. 5.5.3 Based on deformation-zone geometry For drawing of round wire

Where α r

=the approach semi-angle, in radians =the drawing reduction

Commercially, α is in the range 6 to 10° and r of about 20%. and the redundant work φ is related to Δ by

Where Δ

=h/L=mean thickness / the length of the deformation zone

For strip, Δs is based on a plane-strain reduction rs=1-(h1 /h0) For wire or rod, Δw is based on an axisymmetric reduction rw=1-(d1 /d0) where 5.5.4 The effect of die angle on the total energy required to cause deformation Ideal work of plastic deformation UP independent of die angle α. α↑

Work to overcome friction

Uf ↓

α↑

Redundant work

Ur ↑

115


The summation of Up, Uf and Ur gives the total energy U T. This has a minimum at some optimum die angle α*. The reduction and the friction ↑ α∗ ↑

Components of total energy of deformation

5.5.5 Development of limit on drawability For steady-state wiredrawing σxa can be expressed most simply by

Where the efficiency of the deformation process, η=Up/UT At a given strain ε=ln (Ab /Aa)  draw stress σxa and the flow stress σε.

116


As the material is being deformed through the die, strain hardening occurs and if the material is severely strain-hardened

 necking  fracture.

The drawing limit is reached when σ d=σε If the material follows a power-law hardening relationship relationship σε=Kεn, then

Substituting the criterion for the maximum drawing strain in a single pass, that is, σd= σd=σε,

Since ε=ln (Ab /Aa)

And by the definition of the reduction r=1-(Aa /A /Ab)

For repeated reductions through a series of dies, n

 0,

r↓

Example: Example: From previous example, a 10 mm stainless steel wire is drawn using a die angle=12°, angle=12°, μ=0.09, and flow stress is given by σ0 =1300σ0.30. Determine the largest possible reduction. To a first approximation the limit on drawing reduction occurs when σxa=σ.

A better estimate is to let σxa=σ0 at ε=0.71, ε=0.71, i.e. σxa=1173 MPa

117


Note: Note: in the case of no friction/ redundant work, η=1, η=1, no strain hardening (n=0), we have

5.6 


Following the hot forming process, tubes are cold drawn using dies, plugs or mandrels to the required shape, size, tolerances and mechanical strength.



provides good surface finishes.



Increase mechanical properties by strain hardening.



Can produce tubes with thinner walls or smaller diameters than can be obtained from Other hot forming methods.



Can produce more irregular shapes.

5.6.1 Classification of tube drawing processes There are three basic types of tube-drawing processes



Sinking



Plug drawing





Fixed plug



Floating plug

Mandrel drawing.

5.6.2 Tube sinking The tube, while passing through the die, shrinks in outer radius from the original radius Ro to a final radius R of . No internal tooling (internal wall is not supported), the wall then thickens slightly.

118


Uneven internal surface. The final thickness of the tube depends on original diameter of the tube, t ube, the die diameter and friction between tube and die. Lower limiting deformation.

5.6.3 Fixed plug drawing Use cylindrical / conical plug to control size/shape of inside diameter. Use higher drawing loads than floating plug drawing. Greater dimensional accuracy than tube sinking. Increased friction from the plug limit the reduction in area (seldom > 30%). Can draw and coil long lengths of tubing.

5.6.4 Floating plug drawing A tapered plug is placed inside the tube. As the tube is drawn the plug and the die act together to reduce both the outside/inside diameters of the tube. Improved reduction in area than tube sinking (~ 45%). Lower drawing load than fixed plug drawing. Long lengths of tubing are possible. Tool design and lubrication can be very critical.

119


5.6.5 Moving mandrel drawing Draw force is transmitted to the metal by the pull on the exit section and by the friction forces acting along the tube -mandrel interface. Minimized friction. Vmandrel=Vtube The mandrel also imparts a smooth inside finish surface of the tube. Mandrel removal disturbs dimensional tolerance.

example: Schematic alternate pass reduction schedule for tube making

5.7

Analysis of tube-drawing

The greatest part of deformation occurs as a reduction in wall thickness. The inside diameter is reduced by a small amount equal to dimensions of the plug or mandrel inserted before drawing.

120


There is no hoop strain and the analysis can be based on planestrain conditions. For tube drawing with a plug, the draw stress can be expressed by

Where μ1

=friction coefficient between tube and die wall.

μ2

=friction coefficient between tube and plug.

α

=semi die angle of the die.

β

=semi cone angle of the plug.

In tube drawing with a moving mandrel, the friction forces at the mandrel-tube interface are directed toward the exit of the die. For a moving mandrel, B’ can be expressed as

If μ1=μ2, which is often be the case, then B’=0. The differential equation of equilibrium for this simple case is

Integration of this equation and by using Boundary condition σxb=0 and h=hb, the draw stress becomes

Ideal homogeneous deformation

It is possible that μ2 > μ1, B is negative, the draw stress is there for less than required by frictionless ideal deformation. The stresses in tube sinking have been analyzed by Sachs and Baldwin. Assumption: the wall thickness of the tube remains constant. The draw stress at the die exit is similar to wiredrawing. The cross sectional area of the tube is related to the mid-radius r and the wall thickness h by A ~ 2πrh.

Where σ0‘~ 1.1σ0 to account for the complex stresses in tube sinking.

121


5.8

Residual stresses in rod, wire and tubes

Two distinct types of residual-stress patterns in cold-drawn rod and wire:

5.8.1 Effects of semi die angle and reduction per pass on longitudinal residual stress in cold-drawn brass wire (by Linicus and Sachs) At a given reduction, α ↑ longitudinal stress ↑ Maximum values of longitudinal residual stress ~ 15-35% reduction in area.

5.8.2 Defects in cold drawn products Longitudinal scratches (scored die, poor lubrication, or abrasive particles) Slivers (swarf drawn into the surface). Long fissures (originating in ingot). Internal cracks (pre-existing defects in starting material or ruptures in the center due to overdrawing). Corrosion induced cracking due to internal residual stresses.

122


6

Sheet-metal forming

Subjects of interest 







Forming equipment






Bending



Stretch forming



Deep drawing






Defects in formed parts

6.1

Objectives

Methods of sheet metal processes such as stretching, shearing, blanking, bending, deep drawing, redrawing are introduced. Variables in sheet forming process will be discussed together with formability and test methods. Defects occurring during the forming process will be emphasized. The solutions to such defect problems will also be given.

6.2

Introduction

Sheet metal forming is a process that materials undergo permanent deformation by cold forming to produce a variety of complex three dimensional shapes. The process is carried out in the plane of sheet by tensile forces with high ratio of surface area to thickness. Friction conditions at the tool-metal interface is very important and controlled by press conditions, lubrication, tool material and surface condition, and strip surface condition. High rate of production and formability is determined by its mechanical properties.

6.2.1 Classification of sheet metal parts (based on contour) a) Singly curved parts b) Contoured flanged parts, i.e., parts with stretch flanges and shrink flanges. c) Curved sections. d) Deep-recessed parts, i.e., cups and boxes with either vertical or sloping walls. e) Shallow-recessed parts, i.e., dishshaped, beaded, embossed and corrugated parts.

123


f)

Beaded section

6.2.2 Classification of sheet metal forming (based on operations)

6.2.3 Stress state in deformation processes The geometry of the workpiece can be essentially three dimensional (i.e., rod or bar stock) or two dimensional (i.e., thin sheets). The state of stress is described by three principal stresses, which act along axes perpendicular to principal planes. The principal stresses are by convention called σ1, σ2 and σ3 where σ1> σ2 > σ3

124


Shear stresses provide driving force for plastic deformation. Hydrostatic stresses cannot contribute to shape change b ut involve in failure processes Tensile  crack growth or void formation Compressive  hinder crack, close void.

In bulk deformation processes (i.e. forging, rolling and extrusion), the workpiece is subjected to triaxial stresses, which are normally compressive. In sheet deformation processes (i.e., sheet metal forming, vacuum forming, blow moulding), the workpiece is subjected to two dimensional biaxial stresses. (also depending on geometry)

125


Stress system in (a) sheet processes and (b) bulk processes.

6.3


Plane stress

Plane stress condition

Principal stresses σ1 and σ2 are set up together with their associated strain in the x-y plane. The sheet is free to contact (not constrained) in the σ3 (z) direction. There is strain in this direction but no stress, thus σ3=0., resulting in biaxial stress system. Since the stress are effectively confined to one plane, this stress system is known as plane stress. Plane strain

Plane strain condition

126


Deformation (strain) often occurs in only two dimensions (parallel to σ1 and σ2). σ3 is finite, preventing deformation (strain) in the z direction (constrained), which is known as plane strain. Example: the extrusion of a thin sheet where material in the center is constrained in the z direction.

6.4 Forming equipment Forming equipment include 

Forming presses



Dies



Tools

Equipment in sheet metal forming process

6.4.1 Forming machines Using mechanical or hydraulic presses. 

Mechanical presses 

energy stored in a flywheel is transferred to the movable slide on th e down stroke of the press.

 

quick-acting, short stroke.

Hydraulic presses 

slower-acting, longer stroke.

Hydraulic deep drawing press -Shearing machine (mechanical)

127


6.4.2 Actions of presses (according to number of slides, which can be operated independently of each other.) 



Single-action press 

one slide



vertical direction

Double-action press 

two slides



the second action is used to operate the hold-down, which prevents wrinkling in deep drawing.



Triple-action press 

two actions above the die, one action below the die.

Example: Press brake – single action A single action press with a very long narrow bed. Used to form long, straight bends in pieces such as channels and corrugated sheets.

6.4.3 Tooling Basic tools used with a metalworking press are the punch and the die. Punch

 A

convex tool for making holes by shearing, or making surface or displacing

metal with a hammer. Die

 A

concave die, which is the female part as opposed to punch which is the male

part.

Punches and dies - Punch and die in stamping

Die materials: High alloy steels heat treated for the punches and dies.

128


6.4.4 Compound dies Several operations can be performed on the same piece in one stroke of the press. Combined processes and create a complex product in one shot. Used in metal stamping processes of thin sheets.

Compound die

6.4.5 Transfer dies Transfer dies are also called compounding type dies. The part is moved from station to station within the press for each operation.

Transfer die

A die set is composed of: 

Punch holder which holds punch plate connected with blankin g and piecing punches for cutting the metal sheet.



Die block consists of die holder and die plate which was designed to give the desired shape of the product.



Pilot is used to align metal sheet at the correct position before b lanking at each step.



Striper plate used for a) alignment of punch and die blocks b) navigate the punch into the die using harden striper inserts and c) remove the cut piece from the punch.

pilot

129


Schematic diagram of a die set

6.4.6 Forming method There are a great variety of sheet metal forming methods, mainly using shear and tensile forces in the operation. 

Progressive forming



Rubber hydroforming



Bending and contouring



Spinning processes



Explosive forming






Stretch forming



Deep drawing

6.4.7 Progressive forming Punches and dies are designed so that successive stages in the forming of the part are carried out in the same die on each stroke of the press. Progressive dies are also known as multi-stage dies. Example: progressive blanking and piercing of flat washer.

The strip is fed from left to right. The first punch is to make the hole of the washer.

130


The washer is then blanked from the strip. The punch A is piercing the hole for the next washer.

washers

6.4.8 Progressive die Optimize the material usage. Determining factors are 

volume of production



the complexity of the shape

Progressive die with Metal sheet used in blanking process

6.4.9 Rubber hydroforming Using a pad of rubber or polyurethane as a die. A metal blank is placed over the form block, which is fastened to the bed of a singleaction hydraulic press.

Guerin process

During forming the rubber (placed in the retainer box on the upper platen of the press) transmits a nearly uniform hydrostatic pressure against the sheet.

131


Pressure ~ 10 MPa, and where higher local pressure can be obtained by using auxiliary tooling. 6.4.10 Hydroforming Used for sheet forming of aluminium alloys and reinforced thermoplastics.

Stamp hydroforming machine setup with a fluid supplied from one side of the draw blank

A drawing of hydroforming setup with fluid supplied from to both sides of the materials.

6.4.11 Bending and contouring (a) Three-roll bender: sometimes does not provide uniform deformation in thin-gauge sheet due to the midpoint of the span

 localization

of the strain. Often need the forth

roll. (b) Wiper-type bender: The contour is formed by successive hammer blows on the sheet, which is clamped at one end against the form block. Wiper rolls must be pressed against the block with a uniform pressure supplied by a hydraulic cylinder. (c) Wrap forming: The sheet is compressed against a form block, and at the same time a longitudinal stress is applied to prevent buckling and wrinkling. Ex: coiling of a spring around a mandrel.

Bendmachine

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6.4.12 Bending and contouring machines

6.4.13 Spinning processes Deep parts of circular symmetry, such as tank heads, television cones. Materials: aluminium and alloys, high strength-low alloy steels, copper, brass and alloys, stainless steel.

The metal blank is clamped against a form block, which is rotated at high speed. The blank is progressively formed against the block, by a manual tool or by means of small-diameter work rolls. Note: (a) no change in thickness but diameter, (b) diameter equals to blank diameter but thickness stays the same.

6.4.14 Explosive forming Produce large parts with a relatively low production lot size.

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The sheet metal blank is placed over a die cavity and an explosive charge is detonated in medium (water) at an appropriate standoff distance from t he blank at a very high velocity. The shockwave propagating from the explosion serves as a ‘friction-less punch’

6.5


The separation of metal by the movement of two blades operated based on shearing forces. A narrow strip of metal is severely plastically deformed to the point where it fractures at the surfaces in contact with the blades. The fracture then propagates inward to provide complete separation. Clearance (normally 2-10% thickness) Proper

 clean

fracture surface.

Insufficient

 ragged

fracture surface.

Excessive

 greater

distortion, greater energy required to separate metal.

Thickness ↑ clearance ↑

6.5.1 Maximum punch force No friction condition. The force required to shear a metal sheet ~ length cut, sheet thickness, shearing strength. The maximum punch force to produce shearing is given by

where σu=the ultimate tensile strength h=sheet thickness L=total length of the sheared edge

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The shearing ↓ force by making the edges of the cutting tool at an inclined angle Blanking: The shearing of close contours, when the metal inside the contour is the desired part.

Punching or piercing: The shearing of the material when the metal inside the contour is discarded.

Notching: The punch removes material from the edge or corner of a strip or blank or part.

Parting: The simultaneous cutting along at least two lines which balance each other from the standpoint of side thrust on the parting tool.

Trimming: Operation of cutting scrap off a partially or fully shaped part to an established trim line.

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Slitting: Cutting or shearing along single lines to cut strips from a sheet or to cut along lines of a given length or contour in a sheet or workpiece.

Shaving: A secondary shearing or cutting operation in which the surface of a previously cut edge is finished or smoothed by removing a minimal amount of stock.

Fine blanking: Very smooth and square edges are produced in small parts such as g ears, cams, and levers.

Ironing: A continuous thinning process and often accompanies deep drawing, i.e., thinning of the wall of a cylindrical cup by passing it though an ironing die.

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6.6

Bending

A process by which a straight length is transformed into a curved length. Produce channels, drums, tanks.

The bend radius R=the radius of curvature on the concave, or inside surface of the bend. Fibers on the outer surface are strained more than fibers on the inner surface are contracted. Fibers at the mid thickness is stretched. Decrease in thickness (radius direction) at the bend to preserve the constancy of volume.

R ↓ thickness on bending ↓ Condition: 

No change in thickness



The neutral axis will remain at the center fiber.



Circumferential stretch on the top surface ea=shrink on the bottom surface, eb

R ↓ strain ↑

The minimum bend radius 

For a given bending operation, the smallest bend radius can be made without cracking on the outer tensile surface.



Normally expressed in multiples of sheet thickness.

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Example: a 3T bend radius means the metal can be bend without cracking though a radius equal to three times the sheet thickness T. 6.6.1 Effect of b/h ratio on ductility 

Stress state is biaxial (σ2 / σ1 ratio)



Width / thickness b/h ratio

b/h ↑ biaxiality ↑  Strain, ductility ↓  Cracks occur near the center of the sheet

Effect of b/h on biaxiality and bend ductility

6.6.2 Springback Dimensional change of the formed part after releasing the pressure of the forming tool due to the changes in strain produced by elastic recovery. Yield stress ↑ Elastic modulus ↓

Plastic strain ↑ Spring back ↑

Springback is encountered in all forming operations, but most easily occurs in bending. For aluminium alloys and austenitic stainless steels in a number of cold-rolled tempers, approximate springback in bending can be expressed by

Where Ro=the radius of curvature before release of load Rf =the radius of curvature after release of lead and

Ro < Rf

Solutions: compensating the springback by bending to a smaller radius of curvature than is desired (overbending). By trial-and- error. The force Pb required to bend a length L about a radius R may be estimated from

6.6.3 Tube bending Bending of tube and structural material for industry, architecture, medical, refinery.

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Heat induction and hot slap bending require the heating of pipe, tube or structural shapes. Heat Induction bending is typically a higher cost bending process and is primarily used in large diameter material.

6.7

Stretch forming

Forming by using tensile forces to stretch the material over a tool or form block. Used most extensively in the aircraft industry to produce parts of large radius of curvature. (Normally for uniform cross section). Required materials with appreciable ductility. Springback is largely eliminated because the stress gradient is relatively uniform.

Stretch forming feasible for aluminium, stainless steel, titanium.

6.7.1 Stretch forming equipment Using a hydraulic driven ram (normally vertical). Sheet is gripped by two jaws at its edges. Form block is slowly raised by the ram to deform sheet above its yield point. The sheet is strained plastically to the required final shape.

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Examples: large thin panel, most complex automotive stamping involve a stretching component. 6.7.2 Diffuse necking (a limit to forming) In biaxial tension, the necking which occurs in uniaxial tension is inhibited if σ2 / σ1>1/2, and the materials then develops diffuse necking. (not visible) The limit of uniform deformation in strip loading occurs at a strain equals to the strainhardening exponent n.

6.7.3 Localized necking Plastic instability of a thin sheet will occur in the form of a narrow localized neck



followed by fracture of the sheet. Normal strain along X’2 must be zero.

Localized necking in a strip in tension φ ~ 55° for an isotropic material in pure tension

6.8

Deep drawing

The metalworking process used for shaping flat sheets into cup-shaped articles. Examples: bathtubs, shell cases, automobile panels. Pressing the metal blank of appropriate size into a shaped die with a punch.

It is best done with double-action press. Using a blank holder or a hold down ring Complex interaction between metal and die depending on geometry. No precise mathematical description can be used to represent the processes in simple terms.

140


As the metal being drawn, 

Change in radius



Increase in cup wall

Metal in the punch region is thinned down

 biaxial

tensile stress.

Metal in the cup wall is subjected to a circumference strain, or hoop and a radial tensile strain. Metal at the flange is bent and straightened as well as subjected to a tensile stress at the same time.

6.8.1 Redrawing Use successive drawing operations by reducing a cup or drawn part to a smaller diameter and increased height – known as redrawing. Examples: slender cups such as cartridge case and closedend tubes. 

Direct or regular redrawing: smaller diameter is produced by means of a holddown ring. The metal must be bent at the punch and unbent at the die radii see Fig (a). Tapered die allows lower punch load, Fig (b).

141




Reverse or indirect redrawing: the cup is turned inside out the outside surface becomes the inside surface, Fig (c). Better control of wrinkling and no geometrical limitations to the use of a hold down ring.

6.8.2 Punch force vs. punch stroke ℎ  =  +  + ()

Fdeformation

-varies with length of travel

Ffrictional

-mainly from hold down pressure

Fironing

-after the cup has reached the maximum thickness.

6.8.3 Drawability (deep drawing) Drawability is a ratio of the initial blank diameter (D o) to the diameter of the cup drawn from the blank ~ punch diameter (DP) Limiting draw ratio (LDR)

Where η

is an efficiency term accounting for frictional losses.

Normally the average maximum reduction in deep drawing is ~ 50%. 6.8.4 Practical considerations affecting drawability Die radius – should be about 10 x sheet thickness. Punch radius – a sharp radius leads to local thinning and tearing. Clearance between punch and die should be about 20- 40% > sheet thickness. Hold-down pressure – about 2% of average σ0 and σu. Lubrication of die side-to reduce friction in drawing. Material properties-low yield stress, high work hardening rates, high values of strain ratio of width to thickness R. Since the forming load is carried by the side wall of the cup, failure therefore, occurs at the thinnest part. In practice the materials always fail either at (a) the shoulder of the die and (b) the shoulder of the punch.

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6.8.5 Practical considerations for round and rectangular shells Different pressures (tension, compression, friction, bending) force the material into shape, perhaps with multiple successive operations.

Round shell - Rectangular shell

Different flow patterns at sides and corners. Corners require similar flow as round shells while sides need simple bending. The corner radii control the maximum draw depth. Centre to center distance of corners ≥ 6 x corner radius Bottom radius ≥ corner radius 6.8.6 To improve drawability To avoid failures in the thin parts (at the punch or flange), metal in that part need to be strengthened, or weaken the metal in other parts (to correct the weakest link). If sufficient friction is generated between punch and workpiece, more of the forming load is carried by the thicker parts. Concerning about crystallographic texture (slip system), degree of anisotropy or strain ratio R.

143


The dependence of limiting draw ratio on R and work hardening rate, n

The plastic strain ratio R measures the normal anisotropy, which denotes high resistance to thinning in the thickness direction.

Where wo and w are the initial and final width ho and h are the initial and final thickness. But it is difficult to measure thickness on thin sheets, therefore we have

Example: A tension test on a special deep-drawing steel showed a 30% elongation in length and a 16% decrease in width. What limiting draw ratio would be expected for the steel?

From Fig. 20-16 Dieter page 673, the limiting draw ratio ~ 2.7

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6.9


Tensile test only provides ductility, work hardening, but it is in a uniaxial tension with frictionless, which cannot truly represent material behaviors obtained from unequal biaxial stretching occurring in sheet metal forming. Sheet metal formability tests are designed to measure the ductility of a materials under condition similar to those found in sheet metal forming. 6.9.1 Erichsen cupping test 

Simple and easy.



Symmetrical and equal biaxial stretching.



Allow effects of tool-workpiece interaction and lubrication on formability to be studied.



The sheet metal specimen is hydraulically punched with a 20 mm diameter steel ball at a constant load of 1000 kg.



The distance d is measured in millimeters and known as Erichsen number.

Results of cupping test on steel sheets.

6.9.2 The forming limit diagram The sheet is marked with a close packed array of circles using chemical etching or photo printing techniques.

Grid analysis (a) before (b) after deformation of sheet.

The blank is then stretched over a punch, resulting in stretching of circles into ellipses.

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The major and minor axes of an ellipse represent the two principal strain directions in the stamping. The percentage changes in these strains are compared in the diagram. Comparison is done in a given thickness of the sheet.

Forming limit diagram

Example: A grid of 2.5 mm circles is electroetched on a blank of sheet steel. After forming into a complex shape the circle in the region of critical strain is distorted into and ellipse with major diameter 4.5 mm and minor diameter 2.0 mm. How close is the part to failing in this critical region? Major strain

Minor strain

The coordinates indicate that the part is in imminent danger of failure.

6.10 Defects in formed parts Edge conditions for blanking. Local necking or thinning or buckling and wrinkling in regions of compressive stress. Springback tolerance problems. Cracks near the punch region in deep drawing

 minimized

by increasing punch radius,

lowering punch load.

Springback problem - Crack near punch region

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Metal comforming

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