A SPH-based numerical study of the crack arrest behaviour of rubber toughened PMMA under impact loading

The objective of the present work is to propose an engineering-oriented numerical methodology capable of reproducing crack initiation and arrest in semi-brittle structures under high loading rate. With this aim in view, the SPH-based method implemented in LS-DYNA is employed to reproduce the three-dimensional crack initiation, propagation and arrest in a rate- and temperature-dependent grade of RT-PMMA under Kalthoff and Winkler-type impact loading. The ability of critical maximum principal stress- and critical plastic strain-controlled failure criteria, first individually and then combined to reproduce the crack arrest was evaluated by comparison with experimental results. In spite of the overall brittle nature of the PMMA matrix, it was shown that the most pertinent criterion for the material of interest is the one expressed in terms of critical plastic strain, as a consequence of the gain in ductility brought by the embedded rubber nanoparticles. In pratice, the real crack pattern can be reproduced only if the two criteria are used together. Following a design of experiment, an optimised set of values for the critical maximum principal stress and plastic failure strain were found. A good agreement in terms of crack advance (as a function of the impact velocity) and propagation angle is seen between the experimental and numerical results.