Effect of inhomogeneities on dynamic crack growth in an elastic solid

Abstract

The role of toughness inhomogeneities on crack branching and on limiting crack growth speeds in isotropic elastic solids is analysed using a framework where the continuum is characterized by two constitutive relations; one relates stress and strain in the bulk material, the other relates the traction and separation across a specified set of cohesive surfaces. The cohesive parameters include a strength and the work of separation per unit area so that, from dimensional considerations, a characteristic length enters the formulation. Crack initiation and crack growth emerge naturally as outcomes of the imposed loading, without any ad hoc assumptions concerning crack growth or crack path selection criteria. Full transient analyses are carried out for a plane strain block with an initial central crack subject to tensile loading. The inhomogeneities have the form of spatially nonuniform distributions of cohesive strength. The amplitude, size and density of the inhomogeneities are varied. Inhomogeneities are found to promote deviations from a straight crack growth path to a wavy or zig-zag path and to lead to the onset of crack speed oscillations at a lower crack speed, but they tend to increase the amount of crack growth preceding the onset of crack branching. However, many of the main qualitative features of the crack growth behaviour, such as crack speed oscillations, crack branching and the limiting crack speed, are the same as for homogeneous solids.