Meshfree simulations of spall fracture

Shock wave induced spall fracture is a complex multiscale phenomenon, and it is a challenge to build a constitutive and computational model that can capture essential features of the spall fracture. In this work, we present a computational micro-mechanics model to simulate spall fracture by utilizing the multiscale micro-mechanics theory proposed by Wright and Ramesh [36] and a RKPM meshfree method. The focus of this work is to develop and demonstrate a simulation tool that is capable of simulations of spall fracture in engineering application. First, based on a well-known empirical formula, we relate the macroscale spall strength to the kinematics of micro void growth in a Representative Volume Element (RVE). The connection between micro void growth and overall kinematics of the RVE is made through the conservation of mass in the micro to macro transition process. Second, we develop a set of meshfree void growth algorithms that is tailored to represent kinematics of void nucleation, growth and coalescence, and these algorithms retain the conservation of mass, momentum, and energy during simulations of ductile spall fracture. Third, based on the Johnson–Cook model, we developed a meshfree computational formulation, and we have carried out simulations of the spall fracture of a Ti–6Al plate under impact loads to validate the model. From the simulation, we find that the interaction between the first two inelastic wave pulses plays an important role in the mechanism of spall fracture. The numerical results show that the proposed method can capture some features of the spall fracture, and it may be used to simulate the spall fracture in engineering applications.