Chapter Four Creep.

Chapter Four Creep

Implicit and Explicit Creep Chapter Overview
Whereas the previous chapter dealt with rate-independent plasticity, analyzing creep behavior in ANSYS will be discussed in this chapter. Although what is referred to as creep and viscoplasticity are the same from a material standpoint, the usage of the constitutive models vary. Hence, the topic of rate-dependent plasticity will be divided into two sections, this one pertaining to creep. This chapter will address the wide range of implicit and explicit creep laws available in ANSYS. We will focus on creep in metals. However, various points of the discussion are also applicable to creep in other materials such as plastics or concrete. ANSYS has both an implicit and explicit creep procedure. General information on creep will be discussed first, then details on performing implicit or explicit creep will be covered. Creep is usually not considered the same as viscoplasticity since the plasticity term is uncoupled (weakly coupled) and is rate-independent. September 30, 2001 Inventory #001491 4-2

Implicit and Explicit Creep … Chapter Overview
In this chapter, we will cover the following topics: A. Phenomenological Aspects of Creep B. Definition of Terms C. General Creep Equation D. Implicit Creep Procedure E. Explicit Creep Procedure F. ANSYS Solution Procedure for Creep Models G. Comparison of Implicit vs. Explicit Creep September 30, 2001 Inventory #001491 4-3

Implicit and Explicit Creep A. Background on Creep
In crystalline materials, such as metals, creep mechanism is linked to diffusional flow of vacancies and dislocation movement. Vacancies are point defects, and they tend to favor grain boundaries that are normal, rather than parallel, to the applied stress. Vacancies tend to move from regions of high to low concentrations. Diffusional flow can occur at low stresses but usually require high temperatures. Dislocations in grains are line defects. The movement of dislocations (climb, glide, deviation) tend to be activated by high stresses, although it may also occur at intermediate temperatures. Grain boundary sliding is sometimes considered as a separate mechanism which also contributes to creep deformation. Diffusional flow through crystal lattice (Nabarro-Herring Creep) Diffusional flow along grain boundaries (Coble creep) Grain boundary sliding Dislocation creep (Power law creep) September 30, 2001 Inventory #001491 4-4

Implicit and Explicit Creep ... Background on Creep
Although a detailed discussion of material science is beyond the scope of this seminar, it may suffice to say that the aforementioned physical mechanics contribute to creep. The dependency of creep deformation on stress, strain, time, and temperature are generally modeled with a form similar to the following: The functions f1-4 are dependent on the creep law selected. Associated creep constants are usually obtained through various tensile tests at different strain rates and temperatures. Assuming isotropic behavior, the von Mises equation is used to compute the effective stress, and the equivalent strain is used in the creep strain rate equation (similar to rate-independent plasticity). September 30, 2001 Inventory #001491 4-5

ANSYS uses the additive strain decomposition when calculating elastic, plastic, and creep strain: Plastic strains (flow rule) are calculated in a similar fashion as described in the previous chapter. Creep strains are evaluated based on the creep strain rate equations, specific forms of which will be discussed later. The elastic, creep, and plastic strains are all evaluated on the (current) stress state, but they are calculated independently (not based on each other). Note that there is a difference between calculations performed using implicit creep vs. explicit creep. Additive decomposition Stress-strain September 30, 2001 Inventory #001491 4-6

Creep, like plasticity, is an irreversible (inelastic) strain which is based on deviatoric behavior. The material is assumed to be incompressible under creep flow. On the other hand, creep, unlike rate-independent plasticity, has no yield surface at which inelastic strains occur. Hence, creep does not require a higher stress value for more creep strain to occur. Creep strains are assumed to develop at all non-zero stress values. As noted earlier, creep and viscoplasticity are the same from a material standpoint. In engineering usage, creep is generally used to describe a thermally-activated process with a low strain rate. Rate-independent plastic and implicit creep strains are treated in a weakly coupled manner. Conversely, viscoplasticity constitutive models in ANSYS are used to describe high-strain-rate applications (e.g., impact loading). Inelastic strains are treated in a strongly coupled manner. Note to instructors: For explanation of strong/weak coupling terminology, please see later sections on creep+plasticity as well as RATE+plasticity (next chapter). September 30, 2001 Inventory #001491 4-7

Implicit and Explicit Creep ... Example Creep Analysis
An example of a solder ball creep analysis (thermal cycling). Element 185 (B-Bar), with hyperbolic sine implicit creep model ANSYS model courtesy of Bret Zahn, ChipPAC ( September 30, 2001 Inventory #001491 4-8

Implicit and Explicit Creep B. Definition of Terms
Three stages of creep: Under constant load, the uniaxial strain vs. time behavior of creep is shown below. In the primary stage, the strain rate decreases with time. This tends to occur over a short period. The secondary stage has a constant strain rate associated with it. In the tertiary stage, the strain rate increases rapidly until failure (rupture). t  Secondary Tertiary Primary Rupture September 30, 2001 Inventory #001491 4-9

Implicit and Explicit Creep ... Definition of Terms
Three stages of creep (cont’d): The creep strain rate may be a function of stress, strain, temperature, and/or time. For engineering analysis, the primary and secondary stages of creep are usually of greatest interest. Tertiary creep is usually associated with the onset of failure (necking, damage) and is short-lived. Hence, tertiary creep is not modeled in ANSYS. The strain rate associated with primary creep is usually much greater than those associated with secondary creep. However, the strain rate is decreasing in the primary stage whereas it is usually nearly constant in the secondary stage (for the aforementioned uniaxial test case at constant stress and temperature). Also, primary creep tends to be of a shorter period than secondary creep. September 30, 2001 Inventory #001491 4-10

Under constant applied stress, creep strain increases. Stress Relaxation Under constant applied strain, stress decreases. t e t s September 30, 2001 Inventory #001491 4-11

Time-hardening Assumes that the creep strain rate depends only upon the time from the beginning of the creep process. In other words, the curve shifts up/down. As stress changes from s1 to s2, the different creep rates are calculated at points A to B. Strain-hardening Assumes that the creep rate depends only on the existing strain of the material. In other words, the curve shifts left/right. As stress changes from s1 to s2, the different creep strain rates are calculated at points A to B. t e s1 s2 A B t e s1 s2 A B September 30, 2001 Inventory #001491 4-12

Explicit creep means that the forward Euler method is used for the calculation of creep strain evolution. The creep strain rate used at each time step corresponds to the rate at the beginning of the time step and is assumed to be constant throughout that time step Dt. Because of this, very small time steps are required to minimize error. For explicit creep with plasticity, plasticity correction is performed first followed by creep correction. These two corrections occur at different stress values; therefore, it may be less accurate. September 30, 2001 Inventory #001491 4-13

Implicit creep Implicit creep refers to the use of backward Euler integration for creep strains. This method is numerically unconditionally stable. This means that it does not require as small a time-step as the explicit creep method, so it is much faster overall. For implicit creep plus rate-independent plasticity, the plasticity correction and creep correction done at the same time, not independently. Consequently, implicit creep is generally more accurate than explicit creep, but it is still dependent on the time-step size. A small enough time-step must be used to capture the path-dependent behavior accurately. Implicit creep is the recommended method in ANSYS for the reasons stated above (efficiency, accuracy). Details on both creep procedures will be discussed later. September 30, 2001 Inventory #001491 4-14

Implicit and Explicit Creep C. General Creep Equation
As noted earlier, the creep equations are usually of a rate form similar to the one below: However, the type of material being analyzed determines the choice of a specific creep equation. Some general characteristics will be discussed presently. Specific models will be covered in the implicit and explicit creep sections. The implicit and explicit creep equations are also covered in the Elements Manual, Ch. 2.5. September 30, 2001 Inventory #001491 4-15

Implicit and Explicit Creep ... General Creep Equation
Temperature-dependency Creep effects are thermally activated, and its temperature dependence is usually expressed through the Arrhenius law: where Q is the activation energy, R is the universal gas constant, and T is absolute temperature. Stress dependency Creep strain is also usually stress-dependent, especially with dislocation creep. Norton’s law is: A common modification to the above power law is as follows: September 30, 2001 Inventory #001491 4-16

Primary creep usually exhibits either time- or strain-hardening. Time-hardening is the inclusion of a time-dependent term: Strain-hardening is the inclusion of a strain-dependent term: Determination of which to use (strain- or time-hardening) is based upon material data available. Secondary creep does not exhibit time- or strain-hardening. Creep strain rate is usually constant for secondary stage. September 30, 2001 Inventory #001491 4-17

Below is a summary of creep laws available in ANSYS: As noted earlier, implicit creep is the recommended method to use, whenever possible. Note to instructors: Explicit creep (e.g., C6  9) tends to be used only for specific cases such as those outlined in “Nuclear Systems Material Handbook”. See Elements Manual, Explicit Creep for details. September 30, 2001 Inventory #001491 4-18

Section D Implicit Creep

Implicit and Explicit Creep D. Implicit Creep Procedure
In this subsection, the procedure for performing implicit creep analyses will be covered. As noted earlier, implicit creep is the preferred method to use since it is generally more robust, accurate, and efficient (faster) than the explicit method. This is due to the implicit integration (backward Euler method) used for this formulation. There may be situations where the creep law or the element types implemented necessitate use of explicit creep instead. September 30, 2001 Inventory #001491 4-20

Implicit and Explicit Creep ... Element Types Supported
Element types supported for implicit creep material: “Core” elements: PLANE42, SOLID45, PLANE82, SOLID92, and SOLID95 “18x” family of elements: LINK180, SHELL181, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, BEAM188, and BEAM189. The 18x family of elements are the recommended choice for implicit creep analyses. Because of the wide range of element technology available in the 18x series (refer to Chapter 2 of this seminar), these elements offer greater flexibility and power. These formulations include B-Bar, URI, Enhanced Strain, and Mixed U-P. The 18x series also support more constitutive models than the core elements, including hyperelasticity. September 30, 2001 Inventory #001491 4-21

Implicit and Explicit Creep ... Plasticity Models Supported
Recall that creep is decoupled with rate-independent plasticity. Implicit creep allows combinations with the following rate-independent plasticity models (see Chapter 3): BISO, MISO, and NLISO with CREEP (creep with isotropic hardening) BKIN with CREEP (creep with kinematic hardening) HILL and CREEP (anisotropic creep) BISO, MISO, and NLISO with HILL and CREEP (anisotropic creep with isotropic hardening) BKIN with HILL and CREEP (anisotropic creep with kinematic hardening) September 30, 2001 Inventory #001491 4-22

Implicit and Explicit Creep ... Defining Implicit Creep Model
To define an implicit creep model, you can use commands or through the GUI (discussed on next slide). For implicit creep, temperature-dependency can be defined in two ways: Temperature-dependent constants may be defined through TBDATA (or Materials GUI) Many creep equations include the aforementioned Arrhenius equation The choice of either or both methods to include temperature-dependency is determined by the user. September 30, 2001 Inventory #001491 4-23

When defining implicit creep through commands, use TB,CREEP with the specific creep model defined as TBOPT. TB, CREEP, mat, ntemp, npts, TBOPT TBTEMP defines temperature-dependent constants TBDATA defines the actual constants. For the example below, TBOPT = 2 specifies that the time-hardening creep equation will be used. Temperature dependent constants are specified using the TBTEMP command, and the four constants associated with this equation are specified as arguments with the TBDATA command TB,CREEP,1,1,4,2 TBTEMP,100 TBDATA,1,C1,C2,C3,C4 September 30, 2001 Inventory #001491 4-24

All implicit creep models can be selected in the Materials GUI under: Structural > Nonlinear > Inelastic > Rate Dependent > Creep Make sure to define the necessary linear elastic material properties first (EX and PRXY). September 30, 2001 Inventory #001491 4-25

After selecting the appropriate implicit creep model, a separate dialog box will appear with the required input. In the example below, a primary creep equation has been defined, and the user is prompted to input four creep constants. Temperature-dependent constants may also be input. NEED TO UPDATE SLIDE (TBOPT=13 NOT PRESENT) September 30, 2001 Inventory #001491 4-26

Implicit and Explicit Creep ... Available Implicit Creep Models
The table below shows the available implicit creep laws. The equations will be covered in the next slides. NEED TO UPDATE SLIDE (TBOPT=13 NOT PRESENT) September 30, 2001 Inventory #001491 4-27

1) Strain Hardening TBOPT=1 Primary creep 2) Time Hardening TBOPT=2 Primary creep 3) Generalized Exponential TBOPT=3 Primary creep 4) Generalized Graham TBOPT=4 Primary creep September 30, 2001 Inventory #001491 4-28

5) Generalized Blackburn TBOPT=5 Primary creep 6) Modified Time Hardening TBOPT=6 Primary creep 7) Modified Strain Hardening TBOPT=7 Primary creep September 30, 2001 Inventory #001491 4-29

8) Generalized Garofalo TBOPT=8 Secondary creep 9) Exponential Form TBOPT=9 Secondary creep 10) Norton TBOPT=10 Secondary creep September 30, 2001 Inventory #001491 4-30

11) Time Hardening TBOPT=11 Primary + Secondary 12) Rational Polynomial TBOPT=12 Primary + Secondary 13) Generalized Time Hardening TBOPT=13 Primary Creep September 30, 2001 Inventory #001491 4-31

Implicit and Explicit Creep ... Workshop Exercise
Please refer to your Workshop Supplement: Workshop 6: Stress Relaxation September 30, 2001 Inventory #001491 4-32

Section E Explicit Creep

Implicit and Explicit Creep E. Explicit Creep Procedure
In this subsection, the procedure for performing explicit creep analyses will be covered. Recall that implicit creep is the preferred method over explicit creep, due to efficiency and accuracy concerns. Explicit creep uses forward Euler method which requires a very small timestep and, hence, many iterations. Unlike implicit creep, the plasticity calculations are not done simultaneously. The plastic analysis is done first, then the creep calculation (superposition). Plastic strains, etc. are not readjusted for that time step. Whenever possible, implicit creep should be used. However, there may be situations where the creep law or the element types implemented necessitate use of explicit creep instead. September 30, 2001 Inventory #001491 4-34

Implicit and Explicit Creep ... Explicit Creep Procedure
Element types supported for explicit creep material: “Core” elements: PLANE42, SOLID45, PLANE82, SOLID92, and SOLID95 Other elements: LINK1, PLANE2, LINK8, PIPE20, BEAM23, BEAM24, SHELL43, SHELL51, PIPE60, SOLID62, and SOLID65 Note that 18x series of elements do not support explicit creep. Plasticity constitutive models supported with explicit creep: Any plasticity model supported by the element type in use can be combined with explicit creep (e.g., BISO, MISO, BKIN, KINH/MKIN, DP). Recall that this is non-simultaneous modeling of plasticity and creep (plasticity calculations done first, then creep calculations). Note to instructors: There are no ‘recommended’ element types for use with explicit creep analysis. The element type will be dictated by the problem. For example, the general purpose ‘core’ elements will probably be used most of the time, but if the user has concrete, shells, etc., then only specific elements can be chosen for that application. September 30, 2001 Inventory #001491 4-35

To define an explicit creep model, you can use commands or through the GUI (discussed on subsequent slides). Explicit creep cannot have temperature-dependent constants. Temperature-dependency is accounted for by creep equations. The explicit creep constants are defined and input as C1, C2, etc., where C1 is 1st constant, C6 is sixth constant, etc. Not all constants need to be defined. The number of constants which are used depends on the creep equation selected. September 30, 2001 Inventory #001491 4-36

When defining explicit creep through commands, use TB,CREEP with TBOPT=0 (or leave blank). TB, CREEP, mat, ntemp, npts TBDATA defines the actual constants. Primary creep is usually specified with C6 constant (choice of C6=0 to 15). If C1  0 or if T + Toffset  0, no primary creep is computed. Secondary creep is chosen with C12 constant (C12=0 or 1). Primary creep equations C6=9-11, already include secondary creep effects, so secondary creep C12 is bypassed. If C7  0 or if T + Toffset  0, no secondary creep is computed. Irradiation-induced creep can be specified with the C66 constant. This equation can be used with C6=0 to 11. If C55  0 and C61  0 or if T + Toffset  0, no secondary creep is computed. September 30, 2001 Inventory #001491 4-37

Implicit and Explicit Creep ... Defining Explicit Creep Model
All explicit creep models can be selected in the Materials GUI under: Structural > Nonlinear > Inelastic > Rate Dependent > Creep Make sure to define the necessary linear elastic material properties first (EX and PRXY). September 30, 2001 Inventory #001491 4-38

Implicit and Explicit Creep ... Defining Explicit Creep Model
After selecting the appropriate explicit creep model, a separate dialog box will appear with the required input. In the example below, a creep equation has been defined, and the user is prompted to input the various creep constants. September 30, 2001 Inventory #001491 4-39

Implicit and Explicit Creep ... Available Explicit Creep Models
The table below shows the available implicit creep laws. The equations will be covered in the next slides. Note that many of the creep laws for specific materials have built-in units (For example, C6=11). Please review Ch. 2.5 of the Elements Manual to ensure that the right system of units have been used. September 30, 2001 Inventory #001491 4-40

1) Strain Hardening C6=0 Primary creep 2) Time Hardening C6=1 Primary creep 3) Generalized Exponential C6=2 Primary creep 4) Creep laws for steel C6=9, 10, 11, 14, or 15 Primary & secondary creep Refer to Elements Manual Ch. 2.5 on options for defining ec. September 30, 2001 Inventory #001491 4-41

5) Power Function Creep Law C6=12 Primary creep 6) Sterling Power Function C6=13 Primary & secondary creep 7) Exponential Form C12=0 Secondary creep 8) Norton C12=1 Secondary creep September 30, 2001 Inventory #001491 4-42

Creep Solution Procedure
Section F Creep Solution Procedure

Implicit and Explicit Creep F. Solving Creep Problems
Earlier, some of the differences regarding implicit and explicit creep in ANSYS were discussed. Available creep laws are dependent on creep method Input of creep constants vary Supported element types differ Implicit creep is the preferred method In this section, areas concerning the solution of models with creep materials will be reviewed: Solution options Postprocessing Differences between implicit and explicit creep solution procedure will be noted when applicable. September 30, 2001 Inventory #001491 4-44

Implicit and Explicit Creep ... Solution Options for Creep
The solution of models containing creep materials is similar to other nonlinear problems, but there are some special considerations when solving problems with creep. Creep can be large or small strain, depending on the problem. If unsure, it is a good idea to turn on large deformation effects Unlike other static nonlinear analyses with rate-independent materials, “time” has significance in creep analyses. Make sure that the ending time is appropriate for the model and time domain of interest Note that the analysis does not have to be a transient analysis. Inertial effects (TIMINT) may be on or off, depending on the problem. Generally speaking, however, creep analyses do not consider inertial effects (ANTYPE,STATIC or TIMINT,OFF) because the time domain is long. September 30, 2001 Inventory #001491 4-45

Specify solution type for creep analyses Main Menu > Solution > -Analysis Type- Sol’n Control… Solution Controls > -Basic Tab- Analysis Options Specify large displacement solution (NLGEOM,ON), as needed. The default Solution Control (SOLCONTROL) settings are recommended. By default, Solution Control is on. If explicit creep is the only source of nonlinearity present (e.g., no contact or plasticity), the solution may benefit from using the modified Newton-Raphson (MNR) method in conjunction with the frontal solver. September 30, 2001 Inventory #001491 4-46

Use an appropriate time at end of loadstep (TIME). Solution Controls > -Basic Tab- Time Control Unlike other static analyses, TIME has meaning in a creep analysis since creep is rate-dependent. The analysis can be static or transient (exclude or include inertial effects), but TIME should be in real units. Specify an adequate initial time step (DELTIM) to capture nonlinear effects. Ensure that min and max time steps are also reasonable. In the example on the right, in the Solution Controls dialog box, an ending time of 1300 has been specified. Initial timestep is 1.0 with minimum of 0.5 and maximum of 10. (Demonstration purposes only) September 30, 2001 Inventory #001491 4-47

Implicit and Explicit Creep ... Toggling Implicit Creep Effects
For implicit creep only, the RATE (“Include strain rate effect”) command can be used to turn creep effects on or off during an analysis. Solution Controls > -Nonlinear Tab- Creep Option This is useful to establish initial conditions. In this situation, a very small ending TIME value (e.g., 1e-8) should be set, and rate effects turned off (RATE,OFF). Solve as usual. Then, to turn creep effects on, use RATE,ON and specify the real end time. The RATE command is only applicable for the following cases: Implicit creep with 18x elements (von Mises potential) Anisotropic implicit creep with 18x or core elements (Hill potential) September 30, 2001 Inventory #001491 4-48

Implicit and Explicit Creep ... Creep Strain Ratio
Because creep is a path-dependent phenomenon, it is important to ensure that the response is adequately captured. One measure of this which ANSYS uses is the creep ratio Cs, defined as: where Decr is the equivalent creep strain increment and eet is the modified equivalent elastic strain (see Ch. 4.2/4.3 of the Theory Manual for details). September 30, 2001 Inventory #001491 4-49

Use Cutback Control (CUTCONTROL) to specify a maximum equivalent creep strain ratio, if desired. Solution Controls > -Nonlinear Tab- Cutback Control CUTCONTROL,CRPLIMIT,crvalue,1 will impose a maximum creep ratio of crvalue for implicit creep. By default, no implicit creep limit control is specified. CUTCONTROL,CRPLIMIT,crvalue,0 will impose a maximum creep ratio of crvalue for explicit creep. By default, the explicit creep limit is 10%. If, during a timestep, ANSYS calculates a creep strain ratio larger than crvalue, then the solution is automatically bisected until the creep limit is satisfied or the minimum time step is reached. September 30, 2001 Inventory #001491 4-50

As noted earlier, explicit creep has a stability limit. This corresponds to a creep limit of 0.25 (25%), so a limit cannot be specified more than this value. The default value of (10%) is a good value to use. On the other hand, implicit creep is unconditionally stable, so there is no stability limit. Consequently, by default, no limit is imposed. However, this does not mean that implicit creep is “unconditionally accurate.” A creep ratio limit of 1 to 10 ( %) is generally recommended, and be sure to specify a small enough initial, min, and max time step as well. The creep ratio is printed in the output file/window as shown below: *** LOAD STEP SUBSTEP COMPLETED. CUM ITER = *** TIME = TIME INC = *** CREEP RATIO = E-03 September 30, 2001 Inventory #001491 4-51

Implicit and Explicit Creep ... Specifying Temperature Offset
Specify an absolute temperature offset with TOFFST. Main Menu > Preprocessor > Material Props > Temperature Units Oftentimes, thermal loads may be in ºC or ºF. TOFFST can be used to have ANSYS internally convert to absolute units. Creep equations rely on absolute temperature specification, such as in the Arrhenius function September 30, 2001 Inventory #001491 4-52

Implicit and Explicit Creep ... Reviewing Creep Results
In addition to reviewing elastic, thermal, and plastic strains, one can review creep strains. Main Menu > General Postproc > Plot Results > Nodal Solu … Main Menu > General Postproc > Plot Results > Element Solu … In the dialog box shown on the right, the creep strain category is selected on the left. Components, principal, and effective creep strains can be selected on the right-hand choices. Note that, at v6.0, Eff Nu is not required. Actual equivalent strains are calculated and stored. September 30, 2001 Inventory #001491 4-53

Implicit and Explicit Creep ... Reviewing Creep Results
Creep strain energy density can also be retrieved and plotted or listed. Main Menu > General Postproc > Plot Results > Nodal Solu … Main Menu > General Postproc > Plot Results > Element Solu … September 30, 2001 Inventory #001491 4-54

Implicit and Explicit Creep G. Comparison of Implicit vs. Explicit
MN MX X Y Z ANSYS 5.6 JAN 00:00:00 PLOT NO. 2 NODAL SOLUTION STEP=2 SUB =51 TIME=100000 EPCREQV (AVG) EffNu=0 DMX =1.978 SMN =.112E-03 SMX =1.097 .112E-03 .73167 1.097 MN MX X Y Z ANSYS 5.5 JAN 00:00:00 PLOT NO. 2 NODAL SOLUTION STEP=2 SUB =5358 TIME=100000 EPCREQV (AVG) EffNu=0 DMX =2.053 SMN =.117E-03 SMX =1.147 .117E-03 .12752 1.019 1.147 September 30, 2001 Inventory #001491 4-55

Implicit and Explicit Creep ... Comparison of Implicit vs. Explicit
ANSYS 5.6 SOLID185, UI 147 elements, 352 nodes Creep model, 1 End time, 1E5 CPU sec. E. time sec. S. steps 51, tot. iter. 82 Uy = mm ANSYS 5.5 SOLID45, UI 147 elements, 352 nodes Creep model, 1 End time, 1E5 CPU sec. E. time sec. S. steps , tot. iter Uy = mm (Explicit algorithm) (Implicit algorithm) Taken from Guoyu Lin & John Thompson’s presentation. At end of calculation average tensile/creep strain is about 10% September 30, 2001 Inventory #001491 4-56

Implicit and Explicit Creep ... Comparison of Implicit vs. Explicit
The table below summarizes the differences between implicit and explicit creep: 1For explicit creep, the creep calculations are bypassed if T+TOFFSET < 0.0, time step < 1e-6, or C1 < 0.0 (for primary creep) September 30, 2001 Inventory #001491 4-57

Implicit and Explicit Creep ... Workshop Exercise
Please refer to your Workshop Supplement: Workshop 7: Power Law Creep September 30, 2001 Inventory #001491 4-58

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