9.Failure.pdf

MSE 280: Introduction to Engineering Materials

Failure: Fracture, Fatigue, and Creep Reading: Callister Chapter 9 from waves. Adapted from Fig. 8.0, Callister 6e. (Fig. 8.0 is by Neil Boenzi, The New York Times Times.) .)

Adapted from Fig. 18.11W(b), 18.11W(b), Callister 6e. (Fig. 18.11W(b) is courtesy of National Semiconductor Corporation.)

Adapted from Fig. 17.19(b), Callister 6e.

Computer chip-cyclic thermal loading.

Hip implant-cyclic loading from walking.

© © 2007, 2007 University 2008 Moonsub Moonsub of Illinois Shim Board of Trustees. Trustees. All rights reserved.

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ISSUES TO ADDRESS... • • • • • • •

Ducti Ductile le vs. vs. Brittl Brittle e failu failure. re. Frac Fractu ture re tes testi ting ng.. aws, s ress concen ra on, an rac ure. Frac Fractu ture re toug toughn hnes ess. s. Frac Fractur ture e in polyme polymers: rs: crazin crazing. g. Fatigue Fatigue and crack crack propa propagati gation on rate. rate. Creep.

These issues are to u nderstand the mechanisms for failure, especially to prevent in-service failures via design. This can be accomplished via: - Materials Materials selection. - Processing (e.g. (e.g. strengthening). - Design Design Safety. Safety. 2

© 2007, 2008 Moonsub Moonsub Shim

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Ductile Fracture TS

Recall necking… g n i r s e e e r n t i s g n e

Typical response of a metal

strain

1. Neck formation (subsequent deformation is confined to the neck). . formation. 3. Further deformations leads to coalescence of voids into a crack. 4. Crack propagation. 5. Fracture. 3

© 2007, 2008 Moonsub Shim

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Moderately Ductile Failu re • Evolution to failure: necking

σ

• fracture surfaces

void nucleation

void growth and linkage

shearing at surface

fracture

50 50μμm m

(steel) 100 μm

particles serve as void nucleation sites.

From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 11.28, p. 294, John Wiley and Sons, Inc., 1987. (Orig. source: P. Thornton, J. Mater. Sci., Vol. 6, 1971, pp. 347-56.)

Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

Adapted from D. Johnson


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Stress-Strain Behavior versus Temperature • Ductility is reduced with temperature reduction.

So, Ambient and Operating temperatures can affect failure mode of materials. Such an effect shows Ductile to Brittle Transition. Adapted from D. Johnson

Choose materials with D-B transition T far away from its usage T © 2007, 2008 Moonsub Shim

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Ductile vs. Brittle Fracture Fracture: Separation of a material into two or more pieces in response to imposed stress. Ductile

Highly ductile

Moderately ductile

Brittle

Brittle 6


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Why brittle fracture in ceramics? Recall slip is the mechanism of plastic deformation in metals. What happens in ceramics (e.g. ionic crystals)?

Mg2+ O2-

O2-

O2-

O2-

Mg2+

Mg2+

O2-

O2-

Mg2+

Mg2+

Mg2+ O2-

Mg2+

O2Mg2+

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Brittle fracture No appreciable plastic deformation (catastrophic fracture without warning). Ra id crack ro a ation t

icall

er endicular to a

lied stress .

Transgranular: fracture cracks pass through grains. Intergranular: crack propagation along grain boundaries.

• Inter granular

• Transgranular

(between grains)

(across grains) 304 S. Steel (metal) Reprinted w/permission from "Metals Handbook", 9th ed, Fig. 633, p. 650. Copyright 1985, ASM International, Materials Park, OH. (Micrograph by J.R. Keiser and A.R. Olsen, Oak Ridge National Lab.)

316 S. Steel Reprinted w/ permission from "Metals Handbook", 9th ed, Fig. 650, p. 357. Copyright 1985, ASM International, Materials Park, OH. (Micrograph by D.R. Diercks, Argonne National Lab.)



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Brit tle Fracture Surface

Chevron marks From brittle fracture

Origin of crack an-s ape ridges coming from crack 9



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Charpy Impact Data: Energy vs Temperature Notched sample is hit and crack pro pagates. sample

(Charpy)

inal height

initial height

From Callister: Adapted from C. Barrett, W. Nix, and A.Tetelman,The Principles of Engineering Materials, Fig. 6-21, p. 220, Prentice-Hall, 1973.


y g e n E t c a p m I

Adapted from Fig. 8.11(a) and (b), Callister 6e. (Fig. 8.11(b) is adapted from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior , John Wiley and Sons, Inc. (1965) p. 13.)

i ) (e.g., C u, N FCC me ta ls BCC metals (e.g., iron at T < 914C) Brittle

More Ductile High strength materials (

σy >E/150)

Temperature Ductile-to-brittle transitio n temperature

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Ideal versus Real Behavior • Stress-strain behavior (Room T): E/10

σ perfect mat’l-no flaws

TSengineering << TSperfect

carefully produced glass fiber

E/100

typical ceramic 0.1

materials

materials

typical strengthened metal typical polymer

ε

... --the longer the wire, the smaller the load to fail it. • Reasons: --flaws cause premature failure. --Larger samples are more flawed! Adapted from D. Johnson

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Flaws and fracture Actual fracture strength in most materials are significantly lower than expected from bond strengths. Flaw/cracks can amplify or concentrate stress! Max stress at the crack tip:

For long microcracks:

Stress concentration factor: © 2007, 2008 Moonsub Shim

K t =

σ m σ o

=2

a ρ t

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Flaws and fracture Stress concentration factor: K t

=

σ m σ o

=2

a ρ t

• Large Kt promotes failure:

NOT SO BAD

K t =3

BAD!

K t >>3

σ w σmax

• Surface cracks are worse!


r, fillet radius

h

Minimize crack size (a) and maximize radius of curvature ( ρ t) if crack is unavoidable

Avoid sharp corners! 13

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Critical stress for crack propagation stress at which crack propagates E = elastic modulus s = γp = plastic deformation energy i.e. For a crack to propagate, enough stress must be applied to overcome energy needed to create surface and cause plastic deformation. Highly ductile

Brittle

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Fast Fracture Fast-Fracture Condition :

= c Units of MPa √m “stress intensity factor”

0

=

c

Hard to measure Internal flaws

= Measureable (fixed) materials properties

Gc = 2(γs+γp)

• fast fracture occurs when: 1) (in a material subjected to stress σo) a crack reaches some critical size “a” OR 2) when a material contains cracks of size “a” is subjected to some critical stress. • the critical combination of stress σo and crack length at which fast fracture occurs is a MATERIAL CONSTANT! 15


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Fracture toughness Measure of material’s resistance to brittle fracture. In the presence of a crack, it is related to critical stress for crack propagation and depends on: 1) material size & geometry 2) crack dimension & orientation 3) the manner in which the load is applied.

Fracture Toughness:

K c

Fast fracture occurs when: © 2007, 2008 Moonsub Shim

= Y σ c K ≥ K c

π a

Relates to how the load is applied, crack orientation etc.

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Plane strain fracture toughness For thin specimen: Kc will depend on B W

When B becomes large: Kc is independent of B -> Plane strain conditions

2a 2a

Plane strain fracture tou hness: B

K Ic

= Y σ

π a

K and KIc relation is analogous σ and σy. 17


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Example A) Determine if a ceramic material with characteristics given below will fail at an applied tensile stress of 750MPa. E = 250GPa Most severe crack (internal) a = 0.1 mm, ρt = 0.001 mm B) If it does not fail at 750MPa, at what stress level will it fail? C) If ρt = 10-9 m (i.e. a few atoms in size), at what stress level will it fail?

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Griffith’ s Criteria for Fracture and Failure Crack sizes, orientations and distr ibution s It should be almost intuitive that the relative lengths of cracks will control which crack will propagate under stress, such can be said of the orientation and distribution also.

A=A’=A” etc. ’

’

A B A”

*If cracks each act independently, then, if A < B, failure will not occur from A . *Failure will not oc cur from A' and B' because they are parallel to applied stress. *Thus, B-type crack is failure mode, as it has the highest stress concentration.

B”

Which will be the site of failure?


• Since fast fracture occurs when K ≥ K c , the largest, the most stressed cracks grow first!

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Designing Against Crack Growth • Crack growth condition:

K

≥ Kc

Yσ πa • Largest, most stressed cracks grow first! --Case 1: Max flaw size dictates design stress.

σdesign <

Kc Y

σ

πa max

fracture no fracture

--Case 2: Design stress dictates max. flaw size.

a max a

⎞ 2 ⎟ < ⎜⎜ π ⎝ Yσdesign ⎠⎟ 1⎛

Kc

fracture

a max

no fracture

σ 20



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Design Example: Aircraft Wing Material has Kc = 26 MPa-m0.5 • Two designs to consider... --use same material --largest flaw is 4 mm --What is failure stress?

--largest flaw is 9 mm --failure stress = 112 MPa

• Use:

σc =

Kc Y

πa max

• Key point: Y and Kc are the same in both designs. --

112 MPa

(σ

c

9 mm

a max

) = (σ A

4 mm

c

a max

)

B

Answer: • Reducing flaw size pays off! © 2007, 2008 Moonsub Shim

(σc )B = 168MPa 21 Adapted from D. Johnsonv

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Design Example: Gas tank Spherical gas/fluid tank under pressure p Circumferential wall stress: pr σ = 2t Two possible designs for safety: A) Plas ti c dis to rt io n b efo re leaki ng (i.e. the mechanical deformation before leak occurs). - Calculate relative maximum critical crack length where plastic deformation occurs before catastrophic crack propagation for 1040 Steel, Ti alloy and Stainless steel. B) Leak-before-break (e.g. to prevent pressure build-up leading to explosion). Achieved when ac = t (i.e. complete opening before crack propagation). - Calculate the relative maximum pressure for same 3 materials as A). 22


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Transformation toughening Density (g/cm3) Zirconi a (ZrO2)

Monoclinic Tetragonal

5.6 6.1

(metastable)

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What happens with further stress? © 2007, 2008 Moonsub Shim

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Fracture of polymers Thermosets: Brittle fracture via crack propagation (crosslinked and ne wor p o y mers – cova en on s ave o e ro en .

Thermoplastics: Both ductile and brittle fracture possible. Factors that favor brittle fracture: - low T. -

g s ra n ra e.

- flaws (scratches, cracks and sharp edges). - larger specimen thickness.

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Crazing Fracture mechanism in which polymers fracture via localized yielding with formation of small and interconnected microvoids (different from crack propaga on .

Crazing in poly(phenylene oxide) 25


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Fatigue • Fatigue = failure under cyclic stress. • Stress varies with time.. --key parameters are S and σm • Key points: Fatigue... --can cause part failure, even though σmax < σc. --causes ~ 90% of mechanical engineering failures. Fatigue failure: 1) Crack initiation (almost always on the surface; scratches, dents…) 2) Crack propagation (incrementally with each cycle) 3) Final failure (rapid after the crack reaches a critical size).

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Equal tensile and compressive stress

Asymmetric wrt zero stress

Random

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Fatigue l imit: Stress level below which fatigue failure will not occur. Fatigue str ength: Stress level at which failure will occur for some specified number of cycles (e.g. 107 cycles). Fatigue life: Number of cycles to cause failure at a specified stress level.

no fatigue limit

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Crack propagation rate What would happen if we were able to examine crack length (a) at each cycle of stress? What happens at higher stress?

Define crack propagation rate at a fixed crack size 29


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Crack propagation rate NOTE: n a y, sma propaga on rate but the rate increases with crack size. 2) For a fixed crack length, increasing stress leads to increased crack ro a ation rate.

Express rate as:

da dN

= A(ΔK )


m

A and m are material dependent constants. ΔK = Kmax – Kmin (K = stress intensity factor) 30 MSE280

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Crack propagation rate Take log of both sides of the rate equation:

⎛ da ⎞ = log( A(ΔK ) m ) ⎟

log⎜

⎛ da ⎞ = m log ΔK + log A ⎟ ⎝ dN ⎠

log⎜

constant

Region II da = A(ΔK ) m Using:

N f

=

ΔK = Y Δσ ac

1 Aπ

m/2

(Δσ )

m

π a

da

∫ Y a m

m/ 2

ao


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Predict cycles to failure!

MSE280

Fatigue life prediction example Large steel sheet under cyclic stress: tensile 150 MPa compressive 50MPa Prior to stress: largest crack a = 2 mm

Estimate fatigue life given the foll owing inf ormation. KIc = 25 MPa m1/2 m = 3.0 = Y = 1 (assume independent of crack length)

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Improving Fatigue Life S = stress amplitude Adapted from Fig. 8.22, Callister 6e.

1. Impose a compressive surface stress (to suppress

near zero or compressive m la rg er te ns ile σm

cracks from rowin

σm

N = Cycles to failure

--Method 1: shot peening

--Method 2: carburizing

shot

C-rich gas

put surface into compression

2. Remove stress concentrators.

better

bad

Adapted from Fig. 8.23, Callister 6e.

bad

better

3. Polish surface (remove surface cracks) and optimize processing conditi ons to minimi ze internal defects 33 © 2007, 2008 Moonsub Shim

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Creep • Time-dependent permanent deformation due to static mechanical stress (usually at elevated temperatures;T > 0.4 Tm for most metals). • Undesirable and limits lifetime of materials. • Creep test: apply constant stress at constant T and measure deformation (strain) over time.

Accelerated creep due to, e.g., grain boundary separation, crack nucleation etc.. Decreasing slope: strain hardening

Steady-state creep: competition between strain hardening and recovery


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Stress and temperature effects Steady-state creep rate: •

Increasing T or σ

ε s

= K 1 σ n

Material dependent constants

Including T dependence: •

ε s

Q ⎞ = K 1σ n exp⎛ ⎜− c ⎟ ⎝ RT ⎠ Arrhenius behavior at fixed stress 35


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To minimize creep… First, we need to know what the possible mechanisms are. Several mechanism su ested for cree . • Stress-induced vacancy diffusion. • GB diffusion and sliding. • Dislocation motion. Each gives different slope for stress vs. creep rate. Possible solutions: • • • •

se s ng e crys a s usua y a cos y so u on . Increase grain size. Solid solutions. Precipitation hardening.

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Concepts to remember • Engineering materials don't reach theoretical strength. • premature failure. • Sharp corners produce large stress concentrations and premature failure. • Failure type depends on T and stress: -for noncyclic σ and T < 0.4Tm, failure stress decreases with: increased maximum flaw size or rate of loading, or decreased T, -for cyclic σ: cycles to fail decreases as Δσ increases.

-for higher T (T > 0.4Tm): time to fail decreases as σ or T increases. 37


Adapted from D. Johnsonv

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9.Failure.pdf

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