Stress Intensity Factor KI and Crack–hard Inclusion Interaction Study of a Single Edge Cracked Plate by Adaptive Remeshing and Photoelasticity

Abstract

An adaptive remeshing and photoelasticity techniques are presented to determine the stress intensity factors KI and crack-hard inclusion interaction of a single edge cracked plate for two-dimensional fracture mechanics problems. The paper starts from describing two-dimensional linear fracture mechanics theory and an adaptive remeshing H method using the quadrilateral and triangular elements. The computational procedure and related finite element equations are explained. The photoelastic theory and its experimental procedure with the use of the stress optic laws are then described. The photoelasticity prototype is designed and built. Performance of adaptive remeshing method is evaluated by analyzing a single edge cracked plate made from polycarbonate. A crack plate with a hard inclusion is then studied for stress intensity factor and crack-hard inclusion interaction. The hard inclusion is made from aluminum. The KI stress intensity factor is found to be a function of the crack length per width. The results of adaptive remeshning method and the photoelasticity technique are compared with Brown’s study. This example demonstrates the efficiency of the adaptive remeshing method to provide accurate solutions as compared to those from the photoelastic technique. Then, crack-hard inclusion interaction is studied by varying stress intensity ratio and E ratio. The crack-hard inclusion interaction behavior is formulated in exponential equation, i.e. cracking tip shielding function. The cracking tip shielding function shows that maximum stress intensity ratio reduces rapidly if E ratio increases. The normalized stress intensity factor is as a convergence exponential function of E ratio.