A Three-dimensional Numerical Study of Mixed Mode (I and II) Crack Tip Fields in Elastic–plastic Solids

The stress fields near a crack front in a ductile solid are essentially three-dimensional (3D) in nature. The objective of this paper is to investigate the structure of these fields and to establish the validity of two-dimensional (2D) plane stress and plane strain approximations near the crack front under mixed mode (combined modes I and II) loading. To this end, detailed 3D and 2D small strain, elastic–plastic finite element simulations are carried out using a boundary layer (small scale yielding) formulation. The plastic zones and radial, angular and thickness variations of the stresses are studied corresponding to different levels of remote elastic mode mixity and applied load, as measured by the plastic zone size with respect to the plate thickness. The 3D results are compared with those obtained from 2D simulations and asymptotic solutions. It is found that, in general, plane stress conditions prevail at a distance from the crack front exceeding half the plate thickness, although it could be slightly smaller for mode II predominant loading. The implications of the 3D stress distribution on micro-void growth near the crack front are briefly discussed.