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.