Penetration resistance of armor ceramics: Dimensional analysis and property correlations

• Dimensional analysis is used to derive a new penetration depth equation for projectile impact.
• Targets consist of one of six different ceramics backed by a thick metallic plate.
• Two material parameters enter the equation: a length scale and an energy per unit mass.
• Data suggest the length scale correlates with the ratio of surface energy to elastic modulus.
• Data suggest the energy correlates with dynamic shear strength divided by mass density.

A new dimensionless relationship for analysis of ballistic penetration data is derived and applied to polycrystalline ceramic materials. Targets consist of ceramic tiles backed by thick metallic plates within which residual penetration depths have been reported in experimental studies. Particular ceramics analyzed here are low- and high-purity alumina, aluminum nitride, boron carbide, silicon carbide, and titanium diboride. Data for penetration depth versus ceramic tile thickness tend to fall on lines of constant slope regardless of impact velocity, suggesting effects of penetrator velocity and tile thickness may be represented by a separable function of rank two for normalized depth of penetration. The particular relationship developed here contains two material parameters: a length scale and an energy per unit mass. Simultaneous consideration of results of the dimensional analysis and material properties suggest that the length scale, which is related to decreasing penetration depth with increasing tile thickness, correlates with the ratio of surface energy to elastic modulus. The energy per unit mass, which is linked to the relationship between penetration depth and penetrator velocity, correlates with dynamic shear strength of failed ceramic reported from plate impact experiments, divided by mass density. The dimensional analysis provides a structured framework under which future multiscale simulations and validation experiments can be organized and compared.