An asymptotic analysis of a tensile crack in creeping solids coupled with cumulative damage—Part I. 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 treated in two distinct limiting cases. In Part I of the context, a parameter perturbation method is used to study the tip stress field with small damage. Taking a dimensionless coefficient as a perturbation parameter, which characterizes the concerned damage scale, a series of asymptotic solutions can be obtained with the zeroth order approximation being the HRR type of solution. By the results derived one is able to arrive at the distribution of stress and strain, with the coupling effect of damage being taken into account. In this way one is expected to gain a detailed understanding to how the damage influences the HRR tip field. Discussion to another limiting case, which is concerned with the large damage zone very near the crack tip, will be carried out in Part II (Lu, M., Lee, S. B., Kim, J. Y. and May, H. C. (1996). An asymptotic analysis of a tensile crack in creeping solids coupled with cumulative damage--part II. Large damage region very near the crack tip. Int. J. Solids Structures (accepted)). © 1997 Elsevier Science Ltd.