Abstract
The singular stress field at the tip of an elastic sharp notch was reported by Atkinson et al. [12]. Kuang and Xu [72] presented the leading-order terms of the stress and strain fields under the J2 deformation plasticity theory for mode I plane strain cases. Based on asymptotic analysis, it has been confirmed that the near-tip fields have a variable-separable form in r and ϑ. The stress intensity of the near-tip fields can be characterized by a single parameter. It is most interesting to know about dominance of such an asymptotic solution around the tip. According to analysis for cracks [125], the near-tip fields can be described by the asymptotic solutions, only if the region dominated by the leading-order terms is sufficiently larger than the region in which the material failure micro-processes take place. If the dominance zone is not large enough or even smaller than the fracture process zone, two or more parameters may enter the material failure criterion [16, 95]. Thus, the asymptotic solution including leading-order terms alone cannot characterize the near-tip field accurately [145, 151].
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