AbaqusDirectCycling

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Direct Cyclic Procedure

L3.2

Direct Cyclic Procedure

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• 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

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• 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

Metal Inelasticity in Abaqus

L3.4

Direct Cyclic Procedure

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• 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.

Metal Inelasticity in Abaqus

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.

Metal Inelasticity in Abaqus

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

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*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

Metal Inelasticity in Abaqus

L3.7

Direct Cyclic Procedure

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

Metal Inelasticity in Abaqus

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.

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

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

Metal Inelasticity in Abaqus

L3.9

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

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*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

Metal Inelasticity in Abaqus

L3.10

Direct Cyclic Procedure

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• 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

Metal Inelasticity in Abaqus

L3.11

Direct Cyclic Procedure

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• 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.

Metal Inelasticity in Abaqus

L3.12

Direct Cyclic Procedure

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• 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.

Metal Inelasticity in Abaqus

L3.13

Direct Cyclic Procedure

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• 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.

Metal Inelasticity in Abaqus

L3.14

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

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• 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.

Metal Inelasticity in Abaqus