This report presents a set of benchmark tests, designed to test the ability of finite element codes to follow the constitutive equations of creep. The objective of the report is to provide background and tests for fundamental creep behaviour in geometrically trivial problems, similar to the previously reported elastoplasticity benchmarks.

The tests are confined to standard power-law creep equations, of the type usually used for metals that are capable of modelling secondary and primary creep behaviour which should be available in most current finite elements codes. A test involving a combined primary-secondary creep law is also included. All the benchmarks presented in this report are geometrically trivial, and include plane stress, plane strain, three-dimensional and axisymmetric situations. Constant applied loads and displacements, as well as step changes in the applied loads are included to demonstrate time and strain hardening effects. Reference analytical and/or numerical solutions are shown for all the benchmarks.

The mathematical background to creep behaviour is outlined in the report. The reference analytical solutions for the benchmark tests are derived and presented in key equations. Simple time marching computer algorithms are also used to obtain reference solutions and presented in appendices. The description and solutions for each benchmark test are summarised in two-page summaries shown in appendices.

Contents

SUMMARY

CREEP BEHAVIOUR

• Creep Testing
  
• Mathematical Modelling of Uniaxial Creep
  
• Creep Rupture
  
• Variable Stress Creep Behaviour
  
• Stress Relaxation
  
• Multi-Axial Stresses
  

FINITE ELEMENT CREEP FORMULATIONS

REFERENCE BENCHMARK SOLUTIONS

• Constant Load Tests
  
• Constant Displacement Tests
  
• Stepped Load Tests
  
• Combined Primary-Secondary Tests
  

BACKGROUND TO THE BENCHMARKS

SECONDARY CREEP BENCHMARKS (GROUP A)

PRIMARY CREEP BENCHMARKS (GROUP B)

COMBINED PRIMARY-SECONDARY CREEP BENCHMARKS (GROUP C)
DISCUSSION

REFERENCES

APPENDICES

Appendix A: Computer Program for Fixed Load Plane Strain Tests

Appendix B: Computer Program for Fixed Displacement Tests

Appendix C: User Subroutine for Combined Primary-Secondary

Appendix D: Summary of the Benchmark Tests

Appendix E: Creep Benchmark Tests and Solutionss and Solutions