Two new penetration models for ballistic clay incorporating strain-hardening, strain-rate and temperature effects

Ballistic clay, such as Roma Plastilina No. 1 (RP # 1) clay, has been used as a standard backing material in back-face signature (BFS) tests of body armor. Hence, it is important to thoroughly understand penetration mechanics of ballistic clay. In the current paper, two analytical solutions for dynamic spherical cavity expansion in an infinite elastic-plastic solid are first derived by including the strain-hardening effect, strain-rate dependence and temperature influence. The elastic region in the solid is treated as either compressible or incompressible and described using Hooke's law, while the plastic region is regarded as incompressible and characterized using two different constitutive models, one of which is the well-known Johnson-Cook model and the other is a modified Johnson-Cook model simplified from a recently proposed model for ballistic clay. Based on these two dynamic spherical cavity expansion solutions, two models for penetration into a ballistic clay by a rigid projectile with a spherical or an ogival nose are then developed, which incorporate the coupled strain-hardening, strain-rate and temperature effects for the first time. The depth of penetration and impact time relations are obtained for non-penetration impacts, and the ballistic limit and residual velocity are determined for penetration impacts by each type of projectile. To quantitatively illustrate the two newly developed penetration models, they are directly applied to simulate drop tests and impact tests of RP # 1 clay. It is found that the predictions by the current new models agree fairly well with existing experimental data and simulation results.