Comparative Study on High Strain Rate Fracture Modelling Using the Application of Explosively Driven Cylinder Rings

Abstract

The effect of different constitutive modelling choices is crucial under a high strain rate as encountered in ballistic applications. Natural fragmentation of explosively driven cylinder rings is chosen as a simplified example to describe the ability of numerical simulations to describe fractures. The main research interests are the importance of (i) material imperfections, (ii) the accuracy of fracture models vs. damage models, (iii) the plasticity algorithm (stress update), (iv) the introduction of a triaxiality cutoff criterion to the damage models, and (v) different constitutive models (plasticity and damage). Due to the complexity of the propagation and coalescense of multiple cracks in classical methods, smoothed-particle hydrodynamics (SPH) is used as a tailor-made method to discretise the model. An elasto-plasticity model, a damage model and an equation of state describe the material behaviour. The required material parameters are determined based on stress–strain curves from quasi-static and dynamic tests. The Johnson–Cook model, with and without a modification of the strain rate term, and the Rusinek–Klepaczko model are used to describe plasticity. These plasticity models are combined either with the Johnson–Cook, the Lemaitre, or the Dolinski–Rittel damage model and the Mie–Grüneisen equation of state. The numerical results show that (i) a random distribution of initial damage increases irregularity of cracks, and gives more realistic fragment shapes, (ii) a coupling of plasticity model and fracture criterion has only a small effect on the fracture behaviour, (iii) using an iterative plasticity solver has a positive effect on the fracture behaviour, although this effect is marginal, (iv) adding a triaxiality cutoff criterion to the damage models improves the predicted fragment masses in the numerical simulations significantly, and (v) good accordance between experiments and numerical simulations are found for the Dolinski–Rittel and Lemaitre damage model with both plasticity models.

Keywords

• constitutive modelling
• damage modelling
• smoothed-particle hydrodynamics
• highly dynamic expansion
• fragmentation