参考教程说明meti-l06creep

1、Lesson content:Basic AssumptionsElasticityStress PotentialsDeviatoric Creep ModelsVolumetric SwellingInelastic Flow in Creep/Swelling ModelsTemperature and Field Variable DependenceAnalysis ProceduresCreep Integration and Time IncrementationWorkshop 3: Sagging of a Pipe (IA)Workshop 3: Sagging of a

2、Pipe (KW)Lesson 6: Creep and Swelling1 hourBoth interactive (IA) and keywords (KW) versions of the workshop are provided. Complete only one.Basic AssumptionsThe creep and swelling models assume that some inelastic deformation will occur whenever the stress in the material is nonzero*.This assumption

3、 is usually valid when the material is at a high temperature: q qm , where qm is the materials melting temperature on an absolute scale.The inelastic creep deformation is purely deviatoric.The elastic deformation of the material using a creep model is linear.Volumetric swelling models also assume th

4、at the elastic deformation is linear.Creep and volumetric swelling models are available only in Abaqus/Standard.*Nonzero deviatoric stress required for creep; nonzero hydrostatic stress required for swelling.ElasticityDefine the elastic constants of the material with the linear elastic material mode

5、l.Elastic properties can be specified as isotropic or anisotropic.Elastic properties may depend on temperature (q ) and/or predefined field variables ( fi ).As noted earlier, linear elasticity should not be used if the elastic strains in the material are large.*MATERIAL, NAME=Material-1*ELASTIC 2.e1

6、1, 0.3Stress Potentials (1/3)Creep models use an equivalent uniaxial deviatoric stress potential, , to define the inelastic deformation that occurs in the material. Abaqus can use either the Mises stress potential or Hills anisotropic stress potential.Stress Potentials (2/3)Mises Stress PotentialThe

7、 Mises stress potential is defined aswhere S is the deviatoric stress tensor (S = s + pI).Creep behavior defined with this stress potential is isotropic.The Mises stress potential is the default for all creep models.Stress Potentials (3/3)Hills anisotropic stress potentialHills anisotropic stress po

8、tential is defined as Abaqus calculates the values of the constants F, G, H, L, M, and N from creep stress ratios:The creep stress ratios can be dependent on q and/or fi .Deviatoric Creep Models (1/12)Two simple creep laws are built into Abaqus/Standard: the power law and the hyperbolic-sine law.The

9、se two creep models are simple and are intended for modeling secondary or steady-state creep.They model deviatoric creep behavior only See Lecture2 for details about observed creep behavior.*MATERIAL,NAME=Material-1*ELASTIC 20E6, 0.3 *CREEP, LAW=TIME 1.E-24, 5., 0. Deviatoric Creep Models (2/12)More

10、 complicated creep behavior is usually defined using user subroutine CREEP.An additional choice for modeling creep in stainless steels is the Oak Ridge National Laboratory (ORNL) model, which is an empirical model for creep in stainless steels under cyclic loads. This model is not discussed in this

11、seminar.Deviatoric Creep Models (3/12)Power law: Time hardeningThis simple creep law is valid only at lower magnitudes of stress.The time hardening power law is most suitable when the state of stress in the material remains essentially constant.The time hardening power law has the following form:whe

12、re is the uniaxial equivalent creep strain rate; is the equivalent deviatoric stress; t is the time; and A, n, m are user-defined parameters. Time can be specified as:Creep time (default): Abaqus uses the time accumulated in all visco procedures for the creep calculationsTotal time: Abaqus uses the

13、time accumulated in all general procedures for the creep calculationsThis may produce unexpected results in multi-step analyses that include a combination of static and visco proceduresDeviatoric Creep Models (4/12)Defining a time-hardening power law creep model: *MATERIAL,NAME=Material-1*ELASTIC 20

14、E6, 0.3 *CREEP, LAW=TIME, Time=Total|Creep 1.E-24, 5., 0. A n mAnmDeviatoric Creep Models (5/12)Power law: Strain hardeningThis simple creep law is valid only at lower magnitudes of stress.The strain hardening power law is most suitable when the state of stress in the material varies during the simu

15、lation.The strain hardening power law has the following form:where the only variable not identical to those in the time hardening law is the equivalent creep strain,Deviatoric Creep Models (6/12)Defining a strain-hardening power law creep model: *MATERIAL,NAME=Material-1*ELASTIC 20E6, 0.3 *CREEP, LA

16、W=STRAIN 1.E-24, 5., 0. A n mAnmDeviatoric Creep Models (7/12)Either form of the hardening law predicts only reasonable behavior if A and n are positive and -1 m 0.The parameters A, n, m can be functions of q and/or fi.The parameter A may be very small, depending on the choice of units. Avoid possib

17、le numerical difficulties by keeping A greater than 10 -27.Deviatoric Creep Models (8/12)Hyperbolic-sine lawThe hyperbolic-sine law provides reasonable results at higher stress magnitudes ( where s 0 is yield stress). The hyperbolic-sine law has the following format:where A, B, n are user-defined pa

18、rameters; q is the temperature; q z is the value of absolute zero on the temperature scale being used; DH is the activation energy; and R is the universal gas constant.Deviatoric Creep Models (9/12)Defining a hyperbolic-sine creep model:*MATERIAL,NAME=Material-1*ELASTIC 20E6, 0.3 *CREEP, LAW=HYPERB2

19、.5E-27, 4.4E-4, 5, 0.0, 8.314AB n DH RABnDH RDeviatoric Creep Models (10/12)Defining the value of absolute zero: If the creep behavior is not temperature dependent, set DH = 0.The parameters A, B, n can be functions of fi .The parameter A may be very small, depending on the choice of units. Avoid po

20、ssible numerical difficulties by keeping A greater than 10 -27.*PHYSICAL CONSTANTS, ABSOLUTE ZERO=0.0double-clickDeviatoric Creep Models (11/12)User-defined creep lawsComplex creep laws, which may account for primary creep behavior, are usually specified with user subroutine CREEP.The increment of e

21、quivalent creep strain, must be defined in user subroutine CREEP. A general function of the formcan be used to calculate Here, p is the equivalent pressure stress, is the volumetric swelling strain, is the equivalent creep strain, and SVi are the user-defined state variables.Deviatoric Creep Models

22、(12/12)Defining the creep behavior in user subroutine CREEP:SVi can be updated in user subroutine CREEP if they evolve with the simulation.If the explicit time integration algorithm is used, is the only quantity that needs to be defined.If the implicit time integration algorithm is used to integrate

23、 the creep equations, the variations of with respect to must be calculated in the subroutine as well.*MATERIAL,NAME=Material-1*ELASTIC 20E6, 0.3 *CREEP, LAW=USER, Time=Total|CreepVolumetric Swelling (1/4)The *SWELLING option can be used as a suboption of *CREEP to define volumetric swelling. By defa

24、ult (LAW=INPUT on the *SWELLING option), the swelling rate is defined by the following expression:where the fi are user-defined field variables and q is temperature.By default, the volumetric swelling behavior is isotropic.Volumetric Swelling (2/4)In most practical cases the swelling rate is defined

25、 with user subroutine CREEP.Set the parameter LAW=USER to invoke user subroutine CREEP.The increment of volumetric swelling strain, must be defined in user subroutine CREEP. A general function of the form,can be used to calculate Here, p is the equivalent pressure stress, is the volumetric swelling

26、strain, is the equivalent creep strain, and SVi are the user-defined state variables. Volumetric Swelling (3/4)SVi can be updated in user subroutine CREEP if they evolve with the simulation.If the explicit time integration algorithm is used, is the only quantity that needs to be defined.If the impli

27、cit time integration algorithm is used to integrate the creep equations, the variations of with respect to must be calculated in the subroutine.Volumetric Swelling (4/4)Anisotropic swellingUse the *RATIOS option in conjunction with the *SWELLING option to define anisotropic swelling ratios, rii. The

28、 rii are given as data on the *RATIOS option.The rii may be a function of temperature and predefined field variables.The direct components of swelling strain are calculated using the ratiosInelastic Flow in Creep/Swelling ModelsThe inelastic flow of material when creep and swelling models are active

29、 are defined by the following flow rule:where is the increment of swelling strain; R is the matrix of anisotropic swelling ratios orif isotropic swelling is usedthe identity matrix, I; is the increment of equivalent creep strain; and n is the gradient of deviatoric stress potential:where is the Mise

30、s or Hills stress potential. The tensor s will include the stress ratios if anisotropic creep has been used.Temperature and Field Variable DependenceMost material parameters can be made functions of temperature (q ) and user-defined field variables ( fi ). Examples include:The parameters (F, G, H, L

31、, M, and N ) of Hills stress potential.The anisotropic swelling ratios, rii.Specify the number of field variables that influence a materials behavior by using the DEPENDENCIES parameter on the Abaqus input option. Usage: *RATIOS, DEPENDENCIES=3Analysis Procedures (1/2)The creep and the swelling mode

32、ls are activated only by the following procedures:*COUPLED TEMPERATURE-DISPLACEMENT*SOILS, CONSOLIDATION*VISCOThey are inactive in all other procedures.Analysis Procedures (2/2)If creep is inactive during a *SOILS, CONSOLIDATION or a *COUPLED TEMPERATURE-DISPLACEMENT step, you can suppress the creep

33、 calculation by setting CREEP= NONE on the analysis procedure option.If the creep or swelling model uses the total analysis time to define the creep behavior, as the *CREEP, LAW=TIME creep law does, use very small values of step time for steps where creep is not intended to be active.Toggling this o

34、ff is equivalent to CREEP=NONECreep Integration and Time Incrementation (1/6)Abaqus/Standard can use either explicit integration, which is conditionally stable, or implicit integration, which is unconditionally stable, in a creep analysis.Explicit or implicit integrationIf a creep model is used in a

35、 geometrically linear analysis, Abaqus/Standard will attempt to use explicit integration of the creep constitutive model.This usage works well for many design problems, since the total creep strain accumulated over the life of the system must be limited to avoid failure. By default, Abaqus/Standard

36、will switch to the implicit integration procedure automatically when the time increment, Dt, consistently exceeds the current stability limit, Dts .Creep Integration and Time Incrementation (2/6)The CREEP parameter can be set to EXPLICIT to force explicit integration of the creep constitutive behavi

37、or. *VISCO or the *COUPLED TEMPERATURE-DISPLACEMENT procedure options onlyIt can be efficient to use this parameter in analyses where the only active nonlinearity is the result of creep. The time increment will be bounded by the stability limit if this option is used.In a geometrically nonlinear ana

38、lysis that has creep behavior, Abaqus/Standard will use the implicit scheme unless CREEP=EXPLICIT is used to force the use of the explicit scheme.Creep Integration and Time Incrementation (3/6)Coupled creep and plasticityAbaqus/Standard can correctly calculate coupled creep and plastic deformation w

39、ith the implicit integration algorithm if both inelastic behaviors (creep and plasticity) are isotropic. Thus, coupled creep and plasticity should be used only with the isotropic hardening model; however, Abaqus/Standard does not perform any checks to prevent the user from doing otherwise.When a mat

40、erial has both plastic and creep behavior defined, Abaqus/Standard will use implicit integration of the creep equations automatically if the material begins to yield. Abaqus will ignore the CREEP parameter in this situation.If the plastic deformation occurs during a rapid preloading phase of the ana

41、lysis and the creep deformation occurs during a much longer holding phase, where the load does not increase and no further plastic deformation occurs, the coupling of the creep and plasticity equations can be ignored.Substantial errors may occur if there is anisotropic inelastic behavior and if impl

42、icit integration is used with larger time increments.Abaqus/Standard integrates the creep equations without considering the plastic deformation that has occurred during the increment.Minimize the errors by limiting the maximum allowable time increment size.Creep Integration and Time Incrementation (

43、4/6)Stability limit of explicit integrationAbaqus/Standard monitors the stability limit of the creep equations when explicit integration is used. The stability limit is calculated using the following expression:where q is the Mises stress potential and is an effective elastic modulusfor isotropic el

44、asticity it is approximately equal to the Youngs modulus of the material.When using explicit integration, Abaqus/Standard compares Dts to the maximum allowable time increment predicted by the creep strain toleranceDtcand uses the smaller of the two values.If Dts is consistently smaller than Dtc, Abaqus/Standard will switch to implicit integration if possible.Cre