AN ASYMPTOTIC ANALYSIS OF A TENSILE CRACK IN CREEPING SOLIDS COUPLED WITH CUMULATIVE DAMAGE .1. SMALL DAMAGE REGION AROUND THE CRACK-TIP

In a material that undergoes creeping deformation coupled with damage, the stress field around the tip of a stationary Mode I crack is treat ed in two distinct limiting cases. In Part I of the context, a paramet er perturbation method is used to study the tip stress field with smal l damage. Taking a dimensionless coefficient as a perturbation paramet er, which characterizes the concerned damage scale, a series of asympt otic solutions can be obtained with the zeroth order approximation bei ng the HRR type of solution. By the results derived one is able to arr ive at the distribution of stress and strain, with the coupling effect of damage being taken into account. In this way one is expected to ga in a detailed understanding to how the damage influences the HRR tip f ield. Discussion to another limiting case, which is concerned with the large damage zone very near the crack tip, will be carried out in Par t II (Lu, hi., Lee, S. B., Kim, J. Y. and May, H. C. (1996). An asympt otic analysis of a tensile crack in creeping solids coupled with cumul ative damage-part II. Large damage region very near the crack tip. Int . J. Solids Structures (accepted)). (C) 1997 Elsevier Science Ltd.