Mesoscale Model for Spall in Additively Manufactured Metals*

A new approach for modeling spall in additively manufactured (AM) metals is described. The method uses a nonlocal continuum theory, known as peridynamics, with a meshless numerical discretization. The peridynamic theory uses integro-differential equations, rather than partial differential equations. This feature makes peridynamics more compatible with the physical nature of fractures as discontinuities than standard continuum mechanics.

To model spall, the microstructure of a sample is incorporated into the model from electron backscatter diffraction (EBSD) images. These provide not only the shapes of the grains, but also the crystal orientations. These orientations are used in a crystal plasticity model (Maudlin and Schiferl, 1996) that captures the anisotropic nature of each grain’s elastic and plastic mechanical response. The formulation includes an energy balance through a nonlocal form of the first law of thermodynamics. The Mie-Gruneisen equation of state is used.

The simulations initiate spall using a new damage formulation, called the Spall Kinetics model. This model evolves damage at a finite rate at each material point where sufficiently large tensile hydrostatic stress occurs. Some of the material parameters are obtained from published data, while others are calibrated using test data from plate impact experiments.

The model is demonstrated through comparison with experiments on AM 304L stainless steel. Acceptable agreement with free surface velocity measurements is generally obtained. The predicted morphology of the spall surfaces shows features similar to what is seen in post-test images from experiments. The effect of the shapes and sizes of the grains, as well as grain boundary strength, can be investigated with the simulations. The effect of these features in AM material can be seen through comparison with results on conventional wrought material. The orientation of the impact plane relative to the AM build direction can also be investigated with this modeling approach.