Intersonic shear crack propagation using peridynamic theory

Abstract

Dynamic crack propagation of mode-II cracks is simulated using bond-based Peridynamic Theory (PD) implemented in finite element analysis software ABAQUS. The specimen is a bonded homogeneous Homalite plate with a pre-notch that is subjected to impact shear loading simulating the experiments of Rosakis et al. (1999). The PD bonds at the bonding interface are utilized with a scalar critical stretch value that corresponds to mode-II fracture toughness of the interface. The crack initiation and propagation are naturally captured in the bond-based PD simulations by modifying the original prototype microelastic brittle law formulation introduced by Silling and Askari (2005). Impact loading is introduced at the specimen as a pulse speed field boundary condition. Using bond-based PD, sub-Rayleigh and intersonic regimes of crack growth are obtained as a function of fracture toughness ( $$G_{II}$$ ) and impact speed ( $$V_i$$ ) values. The intersonic crack growth is discerned from the sub-Rayleigh crack growth by the existence of shear Mach waves in the particle velocity magnitude contours. For critical values of $$G_{II}$$ and $$V_i$$ , a crack growing at a speed just below the Rayleigh wave speed is observed to transition to an intersonic speed with a Burridge-Andrews mechanism. The sustained intersonic crack tip speed is found to be between $$1.57c_S$$ ( $$c_S$$ is the shear wave speed) and $$c_D$$ ( $$c_D$$ is the dilatational wave speed). For a reduced impact pulse duration, an intersonic crack is found to approach the theoretical value of $$\sqrt{2}c_S$$ , which, however is not maintained. The results are in qualitative agreement with the experiments of Rosakis et al. (1999) and previous simulations in the literature.