Creep crack growth simulation under transient stress fields
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INTRODUCTION
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A full understanding
of creep crack growth requires a synthesis of the macromechanics of cracks in creeping solids, and the micromechanisms of creep damage. The first yields information on the time dependent nature of the stress-strain fields ahead of a crack, while the latter yields information on the nucleation, growth, and coalescence of cavities in an arbitrary (local) stress field. In this paper we survey our current understanding of these two processes and develop an approach to combining them in a computational model of creep crack growth. When a crack is initially loaded, the stress field surrounding the crack tip is predominantly elastic. If the material is very brittle, then the elastic stress field continues to dominate throughout the crack growth process and a correlation between crack growth and stress intensity factor K can be expected. However, for materials with reasonable ductility, stresses relax considerably ahead of the crack. Eventually a steady-state field is achieved which, for a power-law creeping material, is expected to exhibit the HRR type singularity. The amplitude of this field is C*, the high temperature analogue of the J-integral. For many situations of practical interest the time required to establish a steady state may be comparable to the life of a component or laboratory test. During this transition period the creep strains are higher than the elastic strains over an extensive region ahead of the crack tip. Therefore, the crack tip fields can no longer be characterized by the stress-intensity factor using the small scale yielding approximation. However, the C-integral is path dependent. Therefore neither C * nor K are valid parameters. We have studied this transition previously for a stationary crack using FEM analysis, under conditions of a planestrain crack under mode-1 loading.2 Figure 1 shows a typical result for the C-integral, calculated along various paths ahead of the crack, as a function of time. It is clear that eventually C ( t ) becomes path independent and converges to the tabulated value 3 for C*. These studies have shown that during the transition period, the stress field near the crack tip has the HRR singularity (see Figure 2), but that its amplitude is given by: D. S. WILKINSON is Associate Professor and Chairman, Department of Materials Science and Engineering, McMaster University, 1280 Main Street, West, Hamilton, ON, Canada, Lgs 4L7. S. B. BINER is Assistant Professor, Department of Manufacturing, Bradley University, Peoria, IL 61625. This paper is based on a presentation made in the symposium "Crack Propagation under Creep and Creep-Fatigue" presented at the TMS/AIME fall meeting in Orlando, FL, in October 1986, under the auspices of the ASM Flow and Fracture Committee. METALLURGICALTRANSACTIONS A
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