Mathematical study of the effects of applied stress, T-stress and back stress in photoelastic fringe patterns

Abstract

This work is an attempt at developing a novel mathematical model to describe the stresses near the crack tip, taking into consideration the effects of plasticity. The focus is on describing how the applied stress normal to the crack, herein referred to as the K-stress, Tstress and ‘back stress’ induced by plasticity along the crack flank and in the crack tip plastic zone influence the crack tip elastic stress fields. The important features emerging from this study are that the sign and magnitude of each term can substantially alter the crack tip stress fields, and hence influence the photoelastic fringe patterns. To validate the mathematical model, polycarbonate compact tension specimens have been used and observed in a transmission polariscope in order to study the single effect of a pure ‘back stress’ (acting as an interfacial shear stress at the elastic-plastic boundary) and combination effects of K-stress, Tstress and ‘back stress’. It is observed that the fringe patterns obtained through experiment show good agreement with those derived by mathematical modelling.