Mechanical-Nonlin 13.0 Ch06 Rate Dependent Creep

Customer Training Material

L t 6Lecture 6

Rate Dependent Creepp p

ANSYS MechanicalANSYS Mechanical Structural Nonlinearities

L6-1ANSYS, Inc. Proprietary© 2010 ANSYS, Inc. All rights reserved.

Release 13.0December 2010

ANSYS Mechanical – Rate Dependent Creep

Customer Training MaterialChapter Overview

• This chapter will address the wide range of implicit creep laws available in ANSYS Mechanical.

• We will cover the following topics:A. Background on CreepB Definition of TermsB. Definition of TermsC. General Creep EquationD. Available Creep ModelsE. Material InputF. Solution ProcedureG. Review Creep ResultsG. Review Creep ResultsH. Workshop




Customer Training MaterialA. 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– 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 temperaturesoccur 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.mechanism which also contributes to creep deformation.




Customer Training Material... Background on CreepAlthough 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.

( ) ( ) ( ) ( )Tftfffcr 4321 εσε =&

The functions f1-4 are dependent on the creep law selected.

– Associated creep constants are usually obtained through various tensile tests at different 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).



q ( p p y)


Customer Training Material... Background on Creep• ANSYS Mechanical uses the additive strain decomposition when

calculating elastic, plastic, and creep strain:

crplel εεεε &&&& ++=Additive decomposition

• Plastic strains (flow rule) are calculated in a similar fashion as described in the previous chapter. Creep strains are evaluated based

th t i t ti ifi f f hi h ill bon the creep strain rate equations, specific forms of which will be discussed later.

• The elastic, creep, and plastic strains are all evaluated on the , p, p(current) stress state, but they are calculated independently (not based on each other).




Customer Training Material... Background on Creep• 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.




Customer Training Material... Background on Creep• As noted earlier, creep and viscoplasticity are the same from a

material standpoint.

In engineering usage creep is generally used to describe a thermally-– 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 are used to describe high-strain-rate applications (e.g., impact loading). Inelastic strains are treated in a strongly coupled manner.




Customer Training MaterialB. 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 increasesrate associated with it. In the tertiary stage, the strain rate increases rapidly until failure (rupture).

ε

SecondaryPrimary

Rupture

y

Tertiary

y



t


Customer Training Material... 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 Mechanical.

– 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

h t i d th dshorter period than secondary creep.




Customer Training Material... Definition of Terms

• Creep– Under constant applied stress,

strain increases.ε

• Stress Relaxation– Under constant applied strain,

t

stress decreases. σ

t



t


Customer Training Material... Definition of Terms• Time-hardening

– Assumes that the creep strain rate depends only upon the time from

εcσ1depends only upon the time from

the beginning of the creep process. In other words, the curve shifts up/down As stress changes from

σ2A

nt∝ε&up/down. As stress changes from σ1 to σ2, the different creep rates are calculated at points A to B.

t

B cr t∝ε

• Strain-hardening

– Assumes that the creep rate depends only on the existing strain of the

εcσ1

σ2only on the existing strain of the material. In other words, the curveshifts left/right. As stress changesfrom σ1 to σ2 the different creep strain t

AB

ncr εε ∝&



from σ1 to σ2, the different creep strainrates are calculated at points A to B.

t


Customer Training Material... Definition of Terms• Implicit creep

– Implicit creep refers to the use of backward Euler integration for creep strains This method is numerically unconditionally stable This meansstrains. 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

( )L& ,,, ttttttcr Tf Δ+Δ+Δ+= εσε

– 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-stepbut it is still dependent on the time-step size. A small enough time-step must be used to capture the path-dependent behavior accurately.




Customer Training MaterialC. 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

( ) ( ) ( ) ( )Tftfffcr 4321 εσε =&

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 creep sections.creep sections.

– The implicit creep equations are also covered in the Elements Manual, Ch. 2.5.




Customer Training Material... General Creep Equation• Primary creep usually exhibits either time- or strain-hardening.

– Time-hardening is the inclusion of a time-dependent term:

St i h d i i th i l i f t i d d t t

mcr t∝ε&

– Strain-hardening is the inclusion of a strain-dependent term:

ncrcr εε ∝&

– Determination of which to use (strain- or time-hardening) is based upon material data available. Strain-hardening tends to approximate primary creep of metals more accurately although time-hardening tends to be more popular.

– Secondary creep does not exhibit time- or strain-hardening Creep strain



Secondary creep does not exhibit time or strain hardening. Creep strain rate is usually constant for secondary stage.


Customer Training Material... General Creep Equation

• Temperature-dependency

– Creep effects are thermally activated, and its temperature dependence is usually expressed through the Arrhenius law:usually expressed through the Arrhenius law:

RTQ

e−

∝ε&

– where Q is the activation energy, R is the universal gas constant, and T is

RTcr e∝ε

absolute temperature.





• Stress dependency

– Creep strain is also usually stress-dependent, especially with dislocation creep. The steady-state creep behavior (secondary creep) is expressedcreep. The steady state creep behavior (secondary creep) is expressed in various ways.

– Norton’s law (a.k.a. power law):

ncr σε ∝&

– A common modification to the above is the exponential law:

σε Ccr e∝&

– The hyperbolic sine law is yet another common function used to describe secondary (constant) creep rate:



( )σε Acr sinh∝&



• Below is a summary of implicit creep laws available in WB-Mechanical which will be reviewed in the following section:

Creep Equation Description TypeStrain Hardening PrimaryTime Hardening PrimaryGeneralized Exponential PrimaryGeneralized Exponential PrimaryGeneralized Graham PrimaryGeneralized Blackburn PrimaryModified Time Hardening PrimaryModified Strain Hardening PrimaryModified Strain Hardening PrimaryGeneralized Garofalo (Hyperbolic sine) SecondaryExponential Form SecondaryNorton SecondaryTime Hardening BothgRational Polynomial BothGeneralized Time Hardening PrimaryUser Creep




Customer Training MaterialD. Available Creep Models

1) Strain HardeningPrimary creep

/TCCCcr eεσCε 432

1−=&

2) Modified Strain HardeningPrimary creep ( )[ ]{ }( ) /TCCCC

cr eεCσCε 4332 11

31 1 −++=&

These two creep laws contain Norton’s law as well as a strain-h d i t Si th t t C i ll ti th lhardening term. Since the constant C3 is usually negative, these laws are able to model primary creep where the creep strain rate decreases as ε increases. They can also capture some secondary

ffcreep effects since, as ε increases, the creep strain rate can become nearly constant. Note that these laws also contain the Arrhenius equation.




Customer Training Material... Available Creep Models

3) Time HardeningPrimary creep

/TCCCcr etσCε 432

1−=&

6

ft TC

r −&

4) Generalized Time HardeningPrimary Creep

σσσσ 3

32

21

CCrCCCf

eftε Trcr

+++=

=

5) Modified Time Hardening

σ54 CCr +=

( )1

1432

=−+ etσCε

/TCCC

crPrimary creep

The above three creep laws include the Arrhenius equation and Norton’s law, as well as a time-hardening term. The exponential term

( )13 +Ccr

Norton s law, as well as a time hardening term. The exponential term for t is usually between -0.5 and -1.0 to model the decreasing creep strain rate for primary creep. Hence, this model may also approximate a significant part of secondary creep where creep strain



approximate a significant part of secondary creep where creep strain rate is constant.



6) Generalized BlackburnPrimary creep

( )5

72

3

61 1C

σCrtσCcr

CCr

teCeeCε

⎟⎠⎞⎜

⎝⎛=

+−= −

σ

&

7) Generalized GrahamPrimary creep

4C ⎠⎝

( ) /TCCCCCcr etCtCtσCε 87532

641−++=&

8) Generalized ExponentialP i

rtCcr reσCε 2

1−=&

Primary creep

These are some variants of time hardening creep laws (see previous

/TCC eσCr 435

−=

These are some variants of time-hardening creep laws (see previous slide for discussion on time-hardening creep). Note that Generalized Blackburn uses exponential law instead of Norton’s law and, like G li d E ti l it i l d ti l f f th ti



Generalized Exponential, it includes an exponential form for the time-hardening term.



9) Time HardeningPrimary + Secondary ( )

/TCC/TCCC

cr teσCC

etσCε 76432

53

11

1−

−+

++

=

10) Rational Polynomial1

ccr t

εCε&∂∂

=10) Rational Polynomial

Primary + Secondary

121198

43

107

2

10 1

CCm

CCm

CσCmmc

σεCpσεCc

σCεtεpt

cptε

&&

&&

==

=++

=

Both of these time-hardening laws can be used to model primary and secondary creep effects directly If one takes the time derivative of

107 mm p

secondary creep effects directly. If one takes the time derivative of Time Hardening (TBOPT=11), one may notice that it is both time-hardening (TBOPT=2) and Norton’s law (TBOPT=10). The Rational P l i l f i l d f t l i th l i d t



Polynomial form is commonly used for steels in the nuclear industry.



11) Generalized GarofaloSecondary creep ( )[ ] /TC C

cr eσCCε 4321 sinh −=&

12) Exponential FormSecondary creep

/TCσ/Ccr eeCε 32

1−=&

13) NortonS d

/TCCcr eσCε 32

1−=&

Secondary creep

These last three creep laws were previously discussed BecauseThese last three creep laws were previously discussed. Because they do not include any time or strain dependence on creep strain rate, these are suitable to model secondary creep range (i.e., constant creep strain rate)



constant creep strain rate).


Customer Training Material

C fE. Material Data Input• From the Engineering Data Toolbox, open the Creep folder:

– Highlight the creep model of interests (in the example below, modified time hardeningRMB th t i l d l d li k “I l d P t ”– RMB on the material model and click on “Include Property”

– The creep model will then appear in the Properties Dialogue box.

– The yellow blank boxes are now available for user



to define the necessary coefficients.– As with all material properties, be sure to use consistent units


Customer Training Material... Material Data Input• Creep models also support temperature dependent properties via

Tabular input.Notes: ( )1

11

432

=−+

CetσCε

/TCCC

crThe fourth constant (C4) in the modified time hardening model above is also related to temperature via Arrhenius equation .

( )13 +Ccr

User has the option to define creep temperature dependency by way of Arrhenius equation with nonzero value for C4 or by multiple sets of temperature dependentor by multiple sets of temperature dependent data (as in this example) or both.

The Arrhenius function relies on an absolute temperature scale. Temperature units are automatically offset to absolute temperature by solver (See TOFFST command documentation).




Customer Training MaterialD. Analysis Settings for Creep• The Analysis Settings will be similar for

most nonlinear problems

– Although “time” has importance in a creepAlthough time has importance in a creep problem, the solution can be static or transient. This would exclude or include inertial effectsinertial effects.

– Ensure that the time step size is small enough to capture the path dependent response adequately.

– Large Deflection = ON is recommend

F l d l ith l ti d– For large models with long run times and potential convergence trouble, consider setting up a Restart Control strategy in the

t th t dj t t t ti t



event that adjustment to time step range or convergence criteria is necessary


Customer Training Material… Analysis Settings for Creep• The creep strain calculation can be turned on or off during an

analysis.

– This is useful to establish initial conditions In this situation a very smallThis is useful to establish initial conditions. In this situation, a very small ending TIME value (e.g., 1e-8) should be set, and creep effects turned off. Solve initial stress state as 1st load step. Then, to turn creep effects ON and specify the real end time for load step 2and specify the real end time for load step 2.

Load Step 1 Load Step 2




Customer Training Material… Analysis Settings for Creep• Because creep is a path-dependent phenomenon,

it is important to ensure that the response is adequately captured.

– One measure of this which the solver uses is the Creep Strain Ratio defined as:

et

cr

sCεεΔ

=

– where Δεcr is the equivalent creep strain increment and εet is the modified equivalent elastic strain (see Ch. 4.2/4.3 of the Theory Manual for details).

– Creep Limit Ratio is the maximum allowable limit to the Creep Strain Ratio



p


Customer Training Material… Analysis Settings for Creep• If, during a timestep, the solver calculates a Creep Strain Ratio

larger than the Creep Limit Ratio (default =1.0), then the solution is automatically bisected until the creep limit is satisfied or the minimum time step is reached.




Customer Training Material… Analysis Settings for Creep• Implicit creep is unconditionally stable. However, this does not mean

that implicit creep is “unconditionally accurate.”

– Although WB-Mechanical sets this limit to 1.0 by default, a creep limitAlthough WB Mechanical sets this limit to 1.0 by default, a creep limit ratio of 0.1 to 10 (10-1000%) is generally recommended, depending on the magnitude of the equivalent elastic strain developed and the level of accuracy requiredaccuracy required.

– Also, one should be sure to specify a small enough initial, min, and max time step as well.




Customer Training MaterialG. Reviewing Creep Results• In addition to reviewing elastic, thermal, and plastic strains, one can

also review creep strains.




Customer Training MaterialH. Workshop ExercisePlease refer to your Workshop Supplement:• Workshop 6A: Stress Relaxation



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Mechanical-Nonlin 13.0 Ch06 Rate Dependent Creep