Determination of the full elastic-plastic stress field of a tensile crack by minimization of the complementary energy

Abstract

In this paper, an energy method is proposed to study the full elastic-plastic field of a tensile crack. A statically admissible stress field is established by developing an expansion of the stress function in separable form. The unknown parameters are determined by minimizing the complementary energy of the structure. The results obtained by this method are compared with the fine finite element analysis in previous literature. This method shows some advantages for studying the elastic-plastic cracks, in the capacity to find out an algebraic expression of the stress field connecting the plastic near-tip field to the elastic far field, and in the highly accurate representation of the full elastic-plastic field surrounding the crack-tip and in the economical calculation, etc. It can also be used to evaluate some quantities in the analytical asymptotic expansion such as the amplitudes, the Q-stress etc.