Polynomial Estimation of J-integral for Through-thickness Crack in Elastic Perfectly-Plastic Conditions

Norwahida Yusoff, Feizal Yusof


Through the means of finite element analysis, -integral for a straight through-thickness crack has been consistently reported to decrease along the crack front with the maximum and minimum values are at the midplane and the free-surface, respectively. The present study aims to examine the through-thickness profile of -integral and represent it mathematically that it could be used to replace the demanding works of finite element analysis. The -integral profile was numerically examined using finite element analysis of three-dimensional boundary layer formulation that is subjected to a uniform load on the outermost boundary of the model. The results verify that in three-dimensional cracked bodies, although the applied load is uniform, the intensity of deformation in terms of -integral varies along the crack front and the profile has been expressed in a polynomial equation. The analytical solution allows experimentalists to estimate the crack-tip deformation in terms of local  for a known value of  that is applied on a related test specimen.


Finite element; J-integral; Polynomial; Three-dimensional; Through-thickness crack.

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