hr. 1. Engng Sci. Vol. 29, No. 11, pp. 1391-1408,1991 0020-7225/91 $3.00+ 0.00 Printed in Great Britain. All rights reserved Copyright @ 1991 Pergamon Press plc EFFECT OF VISCOPLASTIC FLOW RULES ON STEADY STATE PENETRATION OF THERMOVISCOPLASTIC TARGETS R. C. BATRA and ASLAM ADAM Department of Mechanical and Aerospace Engineering and Engineering Mechanics, University of Missouri-Rolla, Rolla, MO 65401-0249, U.S.A. Ah&act-Steady state thermomechanical deformations of a thick viscoplastic target being penetrated by a fast moving long rigid cylindrical penetrator are analysed by the finite element method. Two different constitutive relations, the Bodner-Partom flow rule, and the Litonski-Batra flow rule, are used to model the viscoplastic response of the material. The two flow rules are calibrated to give essentially similar shear stress-shear strain curves during the overall adiabatic simple shearing deformations of a block deformed at an average strain-rate of 3300 s-l. For the Bodner-Partom flow rule, the effect on target deformations of the penetrator nose shape, penetrator speed, and the variation in the values of material parameters of the target is also studied. 1. INTRODUCTION Given the penetrator and target geometries, materials, target support conditions, penetrator speed, and the angle of attack, one would like to find out whether or not the target will be perforated, and if yes, the speed of the penetrator when it comes out of the target. If not, the shape and size of the hole made in the target is of interest. A complete analysis of this problem within reasonable resources is still not possible. There have been numerous attempts made to analyze simplified versions of the problem. Backman and Goldsmith [l] have reviewed the open literature on ballistic penetration till 1977. It describes various physical mechanisms involved in the penetration and perforation processes, and also discusses many engineering models. Other review articles and books include those by Wright and Frank [2], Anderson and Bodner [3], Zukas et al. [4], Blazynski [5], and Macauley [6]. Ravid and Bodner [7], Ravid et al. [8], and Forrestal et al. [9] have proposed engineering models of varying complexity. When a fast moving long rod strikes a very thick target, the deformations of the two appear to be steady to an observer situated at the stagnation point and moving with it after the rod has penetrated into the target a few rod diameters. This steady state lasts until the stagnation point reaches close to the other end of the target. For very high striking speeds, the steady deformations of the target and the penetrator can be assumed to be governed by purely hydrodynamic incompressible flow processes. Tate [lo, 111 and Alekseevskii [12] modified this model by incorporating the effects of material strengths of the target and the projectile. These were assumed to equal some multiple of the uniaxial yield stress of the respective materials, but the multiplying factor was unspecified. Tate [13, 141, Pidsley [15], Batra and Gobinath [16], and Batra and Chen [17] have estimated these multiplying factors. Whereas Tate used a solenoidal fluid flow model to simulate the steady state penetration process, the other investigations relied on a numerical solution of the problem. One of the unresolved issues in penetration mechanics is the choice of the most appropriate constitutive relation for the penetrator and target materials. In order to assess the effect of the constitutive models used for the target material, we presume herein that the penetrator is rigid and use two different constitutive relations for the target material. The two constitutive relations give virtually the same shear stress-shear strain curves during the numerical simulation of overall adiabatic simple shearing of a viscoplastic block deformed at an average strain-rate of 3300 s-l. For the Bodner-Partom flow rule [18], the effect of varying the penetrator nose shape, the penetration speed, and the values of material parameters on the deformations of the target has also been explored. A similar study for the Litonski-Batra flow rule has already been conducted by Batra [19]. 1391