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The Split Hopkinson Pressure Bar (SHPB) is a materials testing apparatus primarily designed for the analysis of viscoplastic material behavior at very high strain rates.
Because of its complexity it is common practice to simplify the underlying exact mechanical theory by making strong assumptions. On the one hand this has to be done to achieve any results at all on the other hand one commits systematic errors. Therefore we utilize different numerical and Simulation methods to analyze and minimize these errors.
A phase field model of brittle fracture has been developed to simulate the Hertzian crack induced by penetration of a rigid sphere to an isotropic linear-elastic half-space. The fracture formation is regarded as a diffusive field variable, which is zero for the intact material and unity if there is a crack. Crack growth is assumed to be driven by a strain invariant. The numerical implementation is performed with the finite element method and an implicit time integration scheme. The mechanical equilibrium and the phase field equations are solved in a staggered manner, sequentially updating the displacement field and the phase field variable. Numerical examples demonstrate the capability of the model to reproduce the nucleation and growth of the Hertzian cone crack.