Elastoplastic BIE analysis of cracked plates and related problems. Part 2: Numerical results

Abstract

AbstractPart 1 of this paper reports on the formulation of an advanced boundary—integral equation model for fracture mechanics analysis of cracked plates, subject to elastoplastic behaviour or other, related body force problems. The basis of this formulation contrasts with other BIE elastoplastic formulations in the use of the Green's function for an infinite plane containing a stress free crack. This Green's function formulation assures that the total elastic strain field for the crack problem is accurately imbedded in the numerical model. The second part of this paper reports on the numerical implementation of this algorithm, as currently developed. The anelastic strain field (residual strains, thermal strains, plastic strains, etc.) is approximated as piecewise constant, while the boundary data is modelled with linear interpolations. An iteration solution scheme is adopted which eliminates the need for recalculation of the BIE matrices. The stability and accuracy of the algorithm are demonstrated for an uncracked, notch geometry, and comparison to finite element results is made for the centre‐cracked panel. The data shows that even the crude plastic strain model applied is capable of excellent resolution of crack tip plastic behaviour.