A study of crack tip fields and fracture in elastic-plastic materials.

Abstract

Asymptotic mode I crack-tip stress fields for elastic-perfectly plastic pressure-sensitive materials under plane strain and small-scale yielding conditions are presented in Chapters I and II. A Coulomb-type yield criterion described by a linear combination of the effective stress and the hydrostatic stress is adopted to incorporate pressure-sensitive yielding. In Chapter I, stationary crack-tip fields are obtained by both an asymptotic analysis and a finite element analysis. The computational results show that the magnitudes of the normalized radial stress and circumferential stress ahead of the crack tip decrease, the total angular span of the plastic sectors decreases, and the angular span of the elastic sectors bordering the crack surfaces increases as the pressure sensitivity increases. When nonsingular T stresses are considered along the boundary layer for the finite element computations, the hydrostatic stress ahead of the crack tip increases and the plastic zone shifts toward the crack surfaces as the T stress increases. When the discontinuities of $\sigma\sb{rr}$ and $\sigma\sb{33}$ along the border between the plastic sector and the elastic sector are allowed, the angular variations of the asymptotic crack-tip stress fields agree well with those of the finite element computations. In Chapter II, quasi-statically growing crack-tip fields are presented. By introducing two non-singular plastic sectors, fully continuous asymptotic crack-tip stress fields are constructed. The normalized hydrostatic stress and circumferential stress ahead of the crack tip decrease as the pressure sensitivity increases, but the magnitudes of the normalized stresses are higher than those of the corresponding stationary fully-yielded asymptotic crack-tip fields. In Chapter III, the effects of residual stresses on the near-tip fields for a crack in type 304 stainless steel weldment are presented. Thermal residual stresses induced by multi-pass butt welding processes are obtained by a classical thermoelastic-plastic finite element analysis. When a crack is introduced, the computed J-integral, as expected, does not show path independency. In order to characterize the crack-tip fields, the crack-tip opening angle (CTOA) is adopted. The CTOA is larger than that without the tensile residual stresses when the remote tensile stress is less than 80% of the tensile yield stress at room temperature.