Keywords: creep, continuum damage, finite element analysis, ABAQUS.

Creep continuum damage facilities are currently not included in commercial general-purpose finite element (FE) codes, but have been usually incorporated in in-house FE codes or as user-defined codes (user-subroutines) within standard commercial FE packages. Benchmarks on the numerical modelling of continuum damage mechanics using the results obtained from an in-house FE damage code [1] and a user-subroutine UMAT within ABAQUS [2] have been published [3]. Both of the codes are written for a Kachanov type single damage variable material constitutive equation [4,5].

The writing of a UMAT damage code is complicated and leads to lengthy numerical calculations, because the solution procedure is fully coupled, requiring the evaluation and update of the material Jacobian. In addition, the implementation of the UMAT code for damage analyses requires extensive experience in order to ensure stability and convergence, and the damage calculations usually are very time consuming. Therefore, there is a need to use simplified procedures, which can be used for creep damage analyses with reasonable accuracy. For this reason, a user defined, partially-coupled procedure is used in conjunction with a standard user-subroutine, CREEP, within ABAQUS [6], for the purpose of providing an alternative to the ABAQUS UMAT approach previously used for continuum damage analyses.

Creep damage FE calculations are performed using constitutive equations of the form:

and

where is the creep strain, is the equivalent (von Mises) stress and is the deviatoric stress. , , , and are material constants and is the damage parameter . is a rupture stress, which is assumed to be a linear combination of the maximum principal stress, , and the equivalent stress, , as follows:

where is a material constant which ranges from (maximum principal stress dominant) to (equivalent stress dominant).

FE creep and damage calculations were performed for a number of simple geometry models, using a user-subroutine CREEP within ABAQUS. The results obtained are compared to the corresponding solutions obtained using the fully-coupled user-subroutine UMAT with the same type of constitutive equations. The FE creep damage results obtained for four different test cases representing uniaxial, biaxial, triaxial and multi-material creep and damage situations, obtained using the CREEP and UMAT user-subroutines within ABAQUS, are shown to be in good agreement. The test cases can be used as benchmarks to check the validity and accuracy of an easily programmed, simplified user defined code, CREEP, by comparing the results with those obtained from a more accurate but complicated user-defined code, UMAT, within ABAQUS.

The results of these test cases demonstrate the validity of using the CREEP user-subroutine in the FE creep damage calculations in general creep applications, provided that creep strains within the components considered are not extremely large. Since the writing of a UMAT subroutine requires considerable effort and experience on the part of the user, the use of the CREEP user subroutine provides a useful alternative for practical application of continuum damage analyses.

1

Becker, A.A., Hyde, T.H. and Sun, W., "FE-DAMAGE Users Manual", University of Nottingham, 1994.

2

Moberg, F., "Implementation of constitutive equations for creep damage mechanics into the ABAQUS finite element code", SAQ/FoU-Report 95/05, 1995.

3

Becker, A.A., Hyde, T.H., Sun, W. and Andersson, P., "Benchmarks for finite element analysis of creep continuum damage mechanics", J. Computational Materials Science, 25, 34-41, 2002. doi:10.1016/S0927-0256(02)00247-1

4

Kachanov, L.M., Izv, Akad. Nauk., SSSR, 8, 26, 1958.

5

Hayhurst, D.R., "Creep rupture under multi-axial states of stress", J. Mech. Phys. Solids, 20, 381-390, 1972. doi:10.1016/0022-5096(72)90015-4

6

ABAQUS Users Manuals, Version 5.8, Hibbitt, Karlsson and Sorenson, Inc, 1998.

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