Higher-order coefficients of the Williams series expansion for near crack-tip fields and their extraction from FEM experiments and digital photoelasticity method

Abstract

Multi-parameter stress field near the Mode I crack tip in an isotropic linear elastic material is presented. The coefficients of the Williams series expansion of the stress field in the vicinity of the Mode I crack in the isotropic linear elastic material are obtained by the digital photoelasticity technique and by finite element analysis. The main objective of this study is to determine first fifteen coefficients with good accuracy and to compare the numerical results with the analytical solution for the infinite plate with the central crack. It is shown that the coefficients of the higher-order terms of the Williams series expansion are extracted with good accuracy. Comparison of the coefficients of the Williams series known from the theoretical solution for an infinite plate with the central crack and the coefficients extracted from the photoelasticity method and from finite element analysis is given. The FEM analysis is performed for a series of cracked specimens with a small crack and for a series of cracked specimens considered in the phototelasticity experiments. It is shown significant importance of higher-order terms in the Williams series expansion.