Modeling damage in silicon carbide due to an impact stress below the HEL

The spall strength of silicone carbide processed by spark plasma sintering (SPS) has been previously studied. It was shown that SPS-silicone carbide, like other ceramics, exhibits a reduction in the spall stress when the impact stress exceeds roughly 7 GPa which is significantly lower than the stress at the Hugoniot Elastic Limit (HEL) which is over 15 GPa. A constitutive model is formulated that predicts a reduction in the spall stress below the HEL that is caused by rate-dependent damage evolution which is coupled to effective rates of inelastic distortion and porous dilation. It is shown that while damage and inelastic distortion may reduce the strength of the ceramic, porous dilation coupled to rate-dependent inelasticity may stiffen the stress loading wave so that the HEL of the material appears to be higher. The relationship between the spall stress and the impact stress obtained from the simulations is in good agreement with the test data. The results also indicate that the constitutive model captures behavior characteristic of a damage front propagating in brittle materials.