Statistics of energy dissipation in the hypervelocity impact shock failure transition

Abstract

In the hypervelocity impact event, shock waves subject material to failure transitions with the attendant dissipation of the imparted energy. Under shock compression, failure and dissipation entail intense inelastic shear and compaction. Through shock interactions, states of dynamic tension are achieved and further failure dissipation involves fracture and fragmentation. The nature of failure of solids in the shock environment has encouraged considerable experimental effort through the past several decades. Such efforts have yielded results that suggest a level of universality in the shock failure transition over significant spans of shock intensity and solid material types. Examples include the fourth-power relation between pressure and strain rate in solid-material compressive shock waves, and power-law relations capturing spall fracture strength and fragmentation size scale in dynamic tensile failure. Comparable power-law relations also describe the shock compaction of distended solids. The present paper explores a statistical perspective of the underlying micro failure dynamics for the purpose of achieving better understanding of the macro failure trends noted above. A statistical correlation function description of the random micro velocity field is introduced. Through the attendant kinetic dissipation, the statistical fluctuation-dissipation principle is applied to the shock failure transition. From this statistical approach, power-law relations for compressive and tensile shock failure emerge that replicate the reported experimental behaviors. Results are compared with selected experimental data.