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 the essential features of the spall fracture. In this work, we present a computational micro-mechanics model to simulate spall fracture by using part of the multiscale micro-mechanics theory proposed the Wright and Ramesh (Wright and Ramesh [2008]) and a meshfree method. 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 features of void growth and overall kinematics of the RVE are made through the conservation of mass in a micro to macro process. Second, a coupled thermo-mechanical Johnson-Cook model is integrated into a meshfree formulation, i.e. the reproducing kernel particle method (RPKM). We then use the tangent modulus model to carry out the macroscale constitutive update, which is rate dependent, and it is required by the multiscale spall strength formula. Third, we develop a set of meshfree void growth algorithms that can specifically represent kinematics of void nucleation, growth and coalescence, these algorithms retain the conservation of mass, momentum, and energy during simulations of ductile spall fracture. Finally, based on the developed computational model, we have carried out numerical simulations of the spall fracture of a Ti-6Al plate under impact loads. The simulation results are compared with the experimental results. 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 essential features of the spall fracture, and it can be used to simulate the spall fracture in engineering applications.