Crack growth with a part-through process zone in thin plates

Abstract

A cohesive zone model has been proposed to model crack growth with a part-through process zone in a thin solid. With the solid being modeled in Kirchhoff’s plate theory, the crack with a relatively long, inclined front is modeled as a line discontinuity with a finite cohesive zone within the plate. A cohesive force law is adopted to capture the effect of residual strength and residual rigidity of a plate cross-section gradually cracking through the thickness. It is derived by a plane-strain elasticity analysis of a cross section normal to the part-through crack. It is then applied in the plate formulation of a line crack to simulate its propagation within the plate plane. This model essentially resolves the originally three-dimensional crack problem in two hierarchical steps, i.e., in the thickness and in the in-plane directions. In the present study, the bending case is considered. A boundary element method is applied to numerically derive the cohesive force law and simulate the crack growth in a thin titanium-alloy plate. The computational efficiency of the model is demonstrated. The plate is shown to fracture in a nominally brittle or ductile manner depending on its thickness.