Analytically Modeling Hypervelocity Penetration of Thick Ceramic Targets

Abstract

Hypervelocity impact of thick ceramic targets was examined through an analytic model for penetration. Three ceramic materials (SiC, B 4 C and All were modeled and compared to available test data for impacts from 1.5 to 4.5km/s. The analytic model is based on a centerline momentum balance - a method that has proven to be an effective way to produce analytic models of penetration. A number of assumptions are required to develop the analytic penetration model, including assumptions about material motion and constitutive response of the target material. The constitutive model for the failed brittle material used in the penetration model development was a Drucker-Prager yield surface with cutoff. Such a constitutive model allows pressure dependent strength for failed material, which is the type of response seen in extensively fractured ceramic. A cutoff is used since the total strength of the failed brittle material has an upper limit. The use of this constitutive model for the failed brittle material leads to an interior boundary problem within the damaged region, demarcating the region of material flow where the strength is the cutoff and the region that is controlled by the pressure dependent strength. It is shown that excellent agreement between the model and the data across the full range of penetration velocities (1.5 to 4.5 km/s) is obtained when large slopes (on the order of 2) and large cutoff values (on the order of 3 GPa) are used. (The actual values differ for each ceramic.) Excellent agreement between the analytic model and large-scale numerical simulations with exactly the same constitutive model verify that the model correctly includes the intended physics.