A numerical study of dynamic crack growth in elastic-viscoplastic solids

Abstract

Dynamic crack growth is analyzed numerically for a plane strain block with an initial central crack subject to impact tensile loading. The material is characterized as an isotropically hardening elastic-viscoplastic solid. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the crack plane. In this formulation crack initiation, crack growth and crack arrest emerge naturally as outcomes of the imposed loading, without any ad hoc assumptions concerning crack growth criteria. Full transient analyses are carried out using two characterizations of strain rate hardening; power law strain rate hardening and a combined power law-exponential relation that gives rise to enhanced strain rate hardening at high strain rates. The effects of the strain rate hardening characterization on crack initiation, crack growth and crack arrest are investigated. Enhanced strain rate hardening is found to lead to higher crack speeds, to lower toughness values and to crack tip fields that are more like those of an elastic solid than for the power law rate hardening solid. Additionally, some parameter studies varying the cohesive surface strength and the material flow strength are carried out. The effective stress intensity factor is found to increase dramatically at a certain value of the crack speed that depends on the cohesive surface strength, the material flow strength, the characterization of strain rate hardening and the impact velocity, but there is a range where the crack speed at which the increase in effective stress intensity factor occurs is not very sensitive to impact velocity.