Compurers & Stmcrwes Vol. 42, No. 4. pp. 48-95, 1992 cw5-7949j92 ss.00 + 0.00 Rimed in Great Britain. 01992mm*plc STEADY-STATE PENETRATION OF TRANSVERSELY ISOTROPIC RIGID/PERFECTLY PLASTIC TARGETS R. C. BATRA~ and A. ADAM Department of Mechanical and Aerospace Engineering and Engineering Mechanics, University of Missouri-Rolla, Rolla, MO 65401-0249, U.S.A. (Received 11 December 1990) Ahstraet-Axisymmetric deformations of a transversely isotropic, rigid/perfectly plastic target being penetrated by a long rigid cylindrical rod with an ellipsoidal nose have been analyzed. The deformations of the target appear steady to an observer situated at the penetrator nose tip. The contact between the target and the penetrator is assumed to be smooth. Computed results show that the deformation geld adjacent to the penetrator nose surface is significantly inlIuencecl by the nose shape, and the ratio of the yield stress in the axial direction to that in the transverse direction. The axial resisting force expetienced by the penetrator is found to depend strongly upon the nose shape and the ratio of the yield stress in the axial to that in the transverse direction, but weakly upon the square of the penetration speed. 1. INTRODUCI’ION For very thick targets, the steady-state portion of the penetration process constitutes a significant part of the entire penetration event. Accordingly, a consider- able amount of work has been done in studying this process. For example, Tate [ 1,2] and Alekseevskii [3] have modified models in which the steady defor- mations of the target and the penetrator are assumed to be governed by purely hydrodynamic incompress- ible flow processes by incorporating the effects of the material strengths of the target and the penetrator. These strengths were assumed to be some multiple of the yield stress of the respective materials, the multi- plying factor has recently been given by Tate [4,5] by using a solenoidal fluid flow model. Pidsley [6], Batra and Gobinath [7l, and Batra and Chen [8] have esti- mated these multiplying factors from their numerical solutions of the problem. We refer the reader to the review articles of Back- mann and Goldsmith [9], Wright and Frank [lo], Anderson and Bodner [l 11, and books by Zukas et al. [12], Blaxynski [13], and Macauley [ 141 for a dis- cussion of various aspects of the penetration prob- lem, and for a list of references on the subject. Ravid and Bodner [ 151, Ravid et al. [ 161,Forrestal et al. [ 171, and Batra and Chen [8] have proposed engineering models of different complexity. The works referred to above have assumed the target material to be isotropic. However, manufactur- ing processes such as rolling induce anisotropy in the material properties. For example, in heavily-rolled brass, the tensile yield stress transverse to the direc- tion of rolling may be as much as ten percent greater than that parallel to the direction of rolling [18]. Greater variations may be obtained by an appropri- ate combination of mechanical and heat treatments, tAlso Senior Research Investigator, Intelligent Systems Center. which produces a tinal recrystallization texture close to that of a single crystal [19]. Here we assume the target material to be transversely isotropic, and study the effect of varying the yield stress in the axial direction upon the deformation fields during steady- state penetration of the target by a rigid cylindrical penetrator. It is assumed that the degree of an- isotropy, defined as the ratio of the yield stress in the axial direction to that in the transverse direction, stays constant during the deformation process. The effect of the speed of penetration as well as the nose shape on the deformations of the target is also investigated. 2. FORMULATION OF THE PROBLEM We use a cylindrical coordinate system with origin at the center of the penetrator nose and z-axis pointing into the target. We presume that the defor- mations of the target are axisymmetric and appear steady to an observer situated at the penetrator nose tip and moving with it at a uniform velocity u,e, e being a unit vector in the direction of motion of the rigid penetrator, which we take to be the z-axis. Equations governing the target deformations are div v = 0, (2.1) p (v . grad)v = div u. (2.2) Here v is the velocity of a target particle relative to the observer situated at the penetrator nose tip, p is the mass density for the target material, and u is the Cauchy stress tensor. We neglect elastic deformations of the target and have assumed in (2.1) that its deformations are isochoric. Equations (2.1) and (2.2) express, respectively, the balance of mass and the balance of linear momentum. We assume that the target material obeys Hill’s yield criterion [20], which for transversely isotropic 489