Higher order asymptotic crack-tip fields in simplified strain gradient elasticity

Abstract

Abstract Explicit representation for the higher order in-plane crack tip fields is derived by using Papkovich-Neuber stress functions within the simplified strain gradient elasticity (SGE). Presented solution has separable form and contains classical Williams' series as the particular case, when the gradient effects are negligible. The leading terms in the derived solution coincide with the previously known asymptotic solutions for the crack problems in SGE. The higher order terms have coupled amplitude factors and modified definitions for the angular distribution in comparison to the classical solution. Derived asymptotic fields are compared to the full-field numerical solution for the Mode I crack problem to quantify the amplitude factors and the zones of dominance for up to eight terms.