Smoothed particle hydrodynamics modelling for failure in metals

Abstract

It is generally regarded to be a difficult task to model multiple fractures leading to fragmentation in metals subjected to high strain rates using numerical methods. Meshless methods such as Smoothed Particle Hydrodynamics (SPH) are well suited to the application of fracture mechanics, since they are not prone to the problems associated with mesh tangling. This research demonstrates and validates a numerical inter-particle fracture model for the initiation, growth and subsequent failure in metals at high strain rate, applicable within a Total Lagrangian SPH scheme. Total Lagrangian SPH performs calculations in the reference state of a material and therefore the neighbourhoods remain fixed throughout the computation; this allows the inter-particle bonds to be stored and tracked as material history parameters. Swegle (2000) showed that the SPH momentum equation can be rearranged in terms of a particle-particle interaction area. By reducing this area to zero via an inter-particle damage parameter, the principles of continuum damage mechanics can be observed without the need for an effective stress term, held at the individual particles. This research makes use of the Cochran-Banner damage growth model which has been updated for 3D damage and makes the appropriate modifications for inter-particle damage growth. The fracture model was tested on simulations of a 1D flyer plate impact test and the results were compared to experimental data. The test showed that the model can recreate the phenomena associated with uniaxial spall to a high degree of accuracy. Some limited modelling was also conducted in 2 and 3 dimensions and promising results were observed. Research was also performed into the mesh sensitivity of the explosively driven Mock- Holt experiment. 3D simulations using the Eulerian SPH formulation were conducted and the best results were observed with a radial packing arrangement. An in-depth assessment of the Monaghan repulsive force correction was also conducted in attempt to eliminate the presence of the SPH tensile instability and stabilise the available Eulerian SPH code. Successful results were observed in 1D, although the results could not be replicated consistently in 2D. A further study was also conducted into an approach that makes use of a partition of unity weighting to two different SPH approximations of the same flow-field; one local and one non-local (or extended). Unfortunately this approach could not be made to stabilise the code.