EXPLICIT FORMULA FOR DEPTH OF PENETRATION OF CONE-NOSED IMPACTOR INTO ANISOTROPIC SHIELDS
The field of application of Functionally Graded Materialsis steadily expanding, which stimulates research in the relevant areas. In relation to penetration mechanics, these are primarily experimental studies of multilayer barriers consisting of plates "in contact" with various mechanical properties. Despite intensive research, explicit formulas for integral penetration characteristics (penetration depth and ballistic limit) cannot be obtained, except for the case when sequential penetration of layers (barriers with large gaps between layers). In this article, explicit formulas for the depth of penetration into an semi-infinite shield and for the ballistic limit velocity applying penetration into a shield of a finite thickness are derived assuming that the hardness of the barrier material varies continuously depending on barrier depth. The theoretical analysis is based on a model that represents the normal stress at points on the surface of the penetrating body that are in contact with the barrier as a quadratic function of the normal component of local impactor velocity with a zero linear term (the Vitman-Stepanov model). Difference of the dynamic hardness in different points of impactor-barrier contact is taken into account. It is also assumed that the nose of the striker has the form of a straight circular cone and the initial stage of penetration when the striker is not completely immersed in the barrier is ignored.