Total Lagrangian SPH modelling of necking and fracture in electromagnetically driven rings

This paper describes research on the prediction of necking and failure in metals at very high strain rates. The model developed in this paper uses a total Lagrangian SPH formulation with a normalised kernel. The detailed data from electromagnetically driven ring experiments by Zhang and Ravi-Chandar (Int J Fract 142:183-217, 2006) is used to evaluate the accuracy of the model predictions. In order to correctly model fracture in the total Lagrangian SPH formulation a visibility criterion based on a truncated cone has been implemented to remove particles obscured by a failed particle. A Johnson-Cook plasticity model is used in combination with a Lemaitredamage model to describe the plastic deformation and fracture of the rings. The effect of Joule heating due to the current induced in the ring is taken into account in the constitutive model. The acceleration due to the ring currents was implemented in the SPH code as a body force. The results demonstrate that this type of model is capable of predicting the number of fragments as well as the time of fracture. In agreement with experimental data, the model also predicts arrested necks and bending in the fragments.