AbaqusDirectCycling

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Direct Cyclic Procedure

L3.2



• Overview • Direct cyclic analysis is a cost-effective technique for predicting the low-cycle fatigue life of an elastic-plastic structure subjected to cyclic thermo-mechanical loading. • It can be used to predict the likelihood of plastic shakedown as well as plastic ratcheting in the structure. • It can be also used to model low-cycle fatigue in ductile metals (discussed in Lecture 5). • Example: A hot component in the automotive industry such as a cylinder head subjected to cyclic temperature fluctuations and clamping loads.

Metal Inelasticity in Abaqus

L3.3

Direct Cyclic Procedure • Motivation


• The classical approach to obtaining a stabilized state is to apply multiple loading cycles to the structure until the cycle stabilizes. • This can be very expensive as it may take many loading cycles before the response stabilizes. • Difficult to determine when all material points have stabilized since they may not all stabilize simultaneously.

50-60 cycles


L3.4



• The direct cyclic analysis procedure avoids considerable numerical expense associated with a transient analysis. • It uses a modified Newton method in conjunction with Fourier representations of the displacement solution variables and righthand-side vectors to obtain the stabilized cyclic response directly.


L3.5

Direct Cyclic Procedure • User interface • Direct cyclic procedure with fixed time incrementation: *DIRECT CYCLIC | www.3ds.com | © Dassault Systèmes |

• Direct cyclic procedure with automatic time incrementation: *DIRECT CYCLIC, CETOL=tolerance, DELTMX=Dq

• Direct cyclic procedure with time points directly specified by the user: *DIRECT CYCLIC *TIME POINTS

• The last two options can be combined to use automatic time incrementation between fixed time points.


L3.6

Direct Cyclic Procedure • Defining the direct cyclic procedure

T: time of a single loading cycle Dtmin: minimum time increment allowed Dtmax: maximum time increment allowed

controls the incrementation

Dt0: initial time increment

controls the Fourier series representations


*DIRECT CYCLIC, [CETOL=tolerance, DELTMX=Dqmax] Dt0, T, Dtmin, Dtmax, n0, nmax, Dn, imax

n0: initial number of terms in the Fourier series nmax: maximum number of terms in the Fourier series Dn: increment in number of terms in the Fourier series imax: maximum number of iterations allowed in a step

controls the iteration


L3.7



• The number of Fourier terms can be adapted automatically from iteration to iteration


L3.8

Direct Cyclic Procedure • Multiple direct cyclic steps can be included in a single analysis. A direct cyclic procedure can follow a general step or another direct cyclic step.


*STEP *DIRECT CYCLIC *END STEP *STEP *DIRECT CYCLIC *END STEP

or *STEP *STATIC *END STEP *STEP *DIRECT CYCLIC *END STEP


L3.9

Direct Cyclic Procedure • You can restart a direct cyclic step from a general step or another direct cyclic step.


*RESTART, READ, STEP=, ITERATION=, ENDSTEP, WRITE, FREQ= *DIRECT CYCLIC, CONTINUE=YES (NO)

• The maximum number of Fourier terms can be increased upon restart. • Contact conditions in a direct cyclic step are fixed. • Abaqus/Viewer supports visualization of field and history output generated from the direct cyclic procedure. • The element output includes stress; strain; energies; and the values of state, field, and user-defined variables. • The nodal output variable includes displacements, reaction forces, and current coordinates


L3.10



• Post-analysis output of a direct cyclic step can be obtained to recover additional results for iterations rather than the final stabilized iteration. • The following example creates a new output database ( .odb) file, which contains stress and strain of the elements in the element set ELIST from each increment in iterations 5 and 10 of Step1. *POST OUTPUT, STEP=1, ITERATION=5 *OUTPUT, HISTORY *ELEMENT OUTPUT=ELSET=ELIST S,E *POST OUTPUT, STEP=1, ITERATION=10 *OUTPUT, HISTORY *ELEMENT OUTPUT=ELSET=ELIST S,E


L3.11



• Use *CONTROLS, TYPE=DIRECT CYCLIC to set non-default parameters that will be used to control the stabilized state and plastic ratcheting detections, and to specify when to impose the periodicity condition.


L3.12



• Prescribed boundary conditions must have an amplitude definition that is cyclic over the step: the start value must be equal to the end value. • Prescribed loads *CLOAD or *DLOAD must have an amplitude definition that is cyclic over the step where the start value must be equal to the end value. • Prescribed predefined fields/temperatures must be cyclic over the step: the start value must be equal to the end value (use *AMPLITUDE). • If the temperatures are read from the results file, use the BTRAMP parameter on the *TEMPERATURE option to ramp the temperatures back to their initial condition values. It may take a long time for the structure to cool down; simulating the cool down may not add much value to the analysis; thus, increase the cool down rate artificially.


L3.13



• Results and performance: CPU time (seconds) for the cylinder head with 80,000 Dofs

Decomposition

Direct Cyclic (31 terms; 200 x 120 Increments)

Classical Approach (60 x 120 Increments)

51 (performed once; subsequent passes

38

through solver only involve backsubstitution)

Backsubstitution

15

Total (excl. output)

4.3E5

direct cyclic

classical

6.3E5

The area enclosed is more important than the curves themselves; there is some arbitrariness in where the stabilized cycle is.


L3.14

Direct Cyclic Procedure • Summary • The direct-cyclic procedure:


• is a quasi-static analysis; • can be the only step, can follow a general or linear perturbation step, or can be followed by a general or linear perturbation step; • is ideally suited for very large problems in which many load cycles must be applied to obtain the stabilized response if transient analysis is performed; • avoids the considerable numerical expense associated with a transient analysis; • assumes geometrically linear behavior and fixed contact conditions; • uses the elastic stiffness at the beginning of the analysis as the Jacobian, so that the equation system is inverted only once.


AbaqusDirectCycling

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