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# How to Undertake Creep Analysis with Finite Elements

**This book is aimed at analysts who have a minimum of one year’s experience of static elastic stress analysis and who wish to undertake a creep analysis. Whilst elastic/plastic stress analysis commonly involves designing a structure to sustain a load, creep analysis is used to design a structure for a life . Time is the important new variable – just as, in fatigue analysis, a number of cycles is the important new variable.**

*Creep* is the permanent time-dependent deformation occurring in structures. Lead creeps at room temperature and figure 1.1 illustrates creep in lead pipes that have carried waste from a Cambridge College kitchen for many years.

All materials can creep but attention will be focused here on the creep of metals. A parallel NAFEMS How to book on the creep of *visco-elastic* materials by Oyadiji deals with the rubber and glass regimes of rubbers, elastomers, polymers, epoxies and plastics.

Chapter 2 assesses the impact of creep calculations on engineering decisions and chapter 3 gives a history of the study of creep and its calculation. Chapter 4 provides a summary of the metal physics of creep and its relation to metal lattice weaknesses. Creep becomes important when design and operation are affected and chapter 5 lists some of the major creep Finite Element calculations that have been made over the last ten years or so.Creep Finite Element calculations require creep data to be turned into rules. For new materials, you may well find the analysis of the creep data the most difficult part of your work.

Chapter 6 will help you to build up a description of single and multiple creep tensile tests and to understand the impact of scatter.

Chapter 7 addresses two quandaries that must be faced when extending tensile data to real problems – the extension of tensile data to three dimensions and the effect of changing stress.

Chapter 8 gives a non-rigorous account of how the creep equations are integrated numerically and the difficulties that arise from proceeding in discrete steps. The chapter covers the meaning of the key new words of the subject (e.g. stability limit, error measure and error tolerance).

When you have taken all this information aboard, it is time to do some elementary creep FE calculations. There are two basic types of creep calculation – the tensile test (up to large strain) and the corresponding relaxation test on a tensile specimen. Two of the original NAFEMS Benchmarks devised by Becker [1993] are used and key points of the solution are discussed in chapter 9.

When you have finished your calculations you will be asked what checks you have done to establish that the answers are correct. This very difficult question is addressed in chapter 10 covering the verification and validation of solutions.

Research into creep at all levels from the atomic level to the large structure is very active and two topics (faster computing and failure) have been chosen for chapter 11 to give the reader some idea of this effort.

Chapter 12 provides some ways in which you may get help.

Some concluding remarks (chapter 13) and acknowledgements (chapter 14) are added together with sufficient references (chapter 15) to form a reasonable bibliography.

A Glossary is appended. The first occurrence of the words and phrases is shown in the text in *italics.*

## Contents

### 1. Introduction

### 2. What are the executive implications of creep?

**2.1 Creep is life limiting****2.2 Creep is usable for a purpose****2.3 Creep occurs with uncertain effects**

### 3. A brief history of creep analysis

### 4. When does creep occur?

**4.1 The basic problem 7****4.2 Atomic and molecular bonding****4.3 Lattices****4.4 Lattice imperfections****4.4.1 Thermal excitation****4.4.2 Irradiation damage****4.5 Polymers and other non-lattice structures**

### 5. When is creep important?

**5.1 Introduction****5.2 Aircraft Engines 13****5.3 Power generation 14****5.4 Ground transport systems****5.5 Chemical, oil and pharmaceutical industry****5.6 Electronics industry****5.7 Product manufacture****5.8 Civil engineering structures****5.9 Generic ranking of metals and ceramics**

### 6. What does typical creep data look like?

**6.1 Elastic strain****6.2 Primary creep (0< m <1)****6.3 Secondary creep (m = 1)**- 6.3.1 The creep stress index - n
- 6.3.2 The creep activation energy - Q

**6.4 Summary of primary and secondary creep****6.5 Tertiary creep****6.6 Multiple creep tests and creep scatter.****6.7 Putting creep rules into FE codes**

### 7. How are tensile data extended to structures?

**7.1 How does tensile data extend to 3-dimensions?****7.2 How do I deal with changing stresses?**

### 8. How do codes solve the FE creep equations?

**8.1 The forward difference method****8.2 The backward difference method**

### 9. How do I solve basic creep problems?

**9.1 The creep tensile test (NAFEMS Benchmark Test 1(a))**- 9.1.1 Description of Problem 1
- 9.1.2 Material preliminaries.
- 9.1.3 Setting up the problem.
- 9.1.4 Running the problem
- 9.1.5 Assessment of the results
- 9.1.6 Ductile failure
- 9.1.7 Conclusions.

**9.2 The creep relaxation test (NAFEMS Benchmark Test 8(b))**- 9.2.1 Description of Problem 2.
- 9.2.2 Material preliminaries.
- 9.2.3 Setting up the problem
- 9.2.4 Running the problem
- 9.2.5 Assessment of the results
- 9.2.6 Conclusions.

### 10. How do I check my answers?

**10.1 Verification****10.2 Validation**

### 11. What are the main creep research areas?

**11.1 Faster computing**- 11.1.1 Faster computers
- 11.1.2 Faster solution methods
- 11.1.3 Summary

**11.2 Failure**- 11.2.1 Continuum damage
- 11.2.2 Crack development
- 11.2.3 Combined crack and continuum damage
- 11.2.4 Thermal cycling and creep fatigue
- 11.2.5 Design Codes

### 12. Where can I get help?

- 1
**2.1 Code developers** **12.2 BENCHMARK****12.3 University Departments****12.4 The Internet****12.5 Your bookshelf**

### 13. Concluding remarks

### 14. Acknowledgements

### 15. References

### Glossary

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# About

R. Anderson

First Published - March 2002

Softback, 71 Pages