Introduction

Abstract

Engineering interest in the plastic deformation and flow of metals originated during prehistoric times when our ancestors first began to hammer and forge metals into shape. The art developed leisurely over the ages. During the nineteenth century, however, industrial activities in forming metals and in the application of metals to elevated temperature service stimulated not only the art of metal forming but also the science of plasticity of metals. During this time the fundamental facts concerning the conditions under which plastic deformation begins were studied by St. Venant, Tresca, Föppl, Guest, and others. In the early quarter of the twentieth century this interest increased at an exponential rate, and appreciable progress was made by such engineers as Ludwik, von Kârmân, Lode, Ros, Eichinger, Taylor, and Quinney in uncovering the gross relationships between stress and plastic strain. In spite of this fact the knowledge on plastic deformation and flow of metals was found to be inadequate for the needs of production and use of materials for the recent World War. Extensive investigations into these fields were sponsored by the various industries, Governmental agencies, and the armed forces from 1941 to 1945. Methods of analysis and procedures of application of theory to engineering practice were developed and new technological advances in the art were made. At the close of the War many engineers entertained the thought that a decrease in the research and development activities on plastic deformation and flow might be expected in consequence of reduced sponsorship of investigations in this field resulting from the decreased urgency and needs; but the lessons learned in the War concerning the benefits to be derived from research and development and the ever-increasing demands for knowledge on plastic deformation, flow, and creep of metals stimulated ever greater activity in this field. Although progress has been made in uncovering some of the basic factors involved in plastic deformation, much yet remains to be done before we can approach the subject with the same confidence we now have regarding elastic deformations. One source of difficulty arises from the fact that the shear-distortion energy hypothesis for yielding of isotropic materials is known to be only a first approximation. It has been suggested that yielding is a function of both the quadratic and cubic invariants of the deviator stresses, but this hypothesis has not yet been subjected to critical experimental test. Another difficulty arises from the fact that most existing theories on plastic deformation are predicated on the assumption that the material is isotropic, whereas the actual facts reveal that most wrought metals are anisotropic. In their paper on “The Experimental Exploration of Plastic Flow in Sheet Metals,” Jackson and Lankford have proposed a simple theory for plastic flow of anisotropic sheet metals based on the assumptions that the coefficients of anisotropy are invariant with strain and that the strain-hardening is based on the shear-distortion energy principle. Experimental investigations have shown that this theory is useful under conditions wherein the assumptions are valid. One of the major objectives of investigations on plastic deformation of metals is the analytical determination of forces involved in forming parts and the evaluation from simple test data such as the tension test the limit to which metal parts can be formed without introducing plastic buckling, local plastic flow or necking, and fracturing. In many problems difficulties of achieving a complete solution to such problems become almost insurmountable. In consequence, the analyses of these problems are frequently obtained by compounding good engineering judgment with the purely analytical approach. The success of such analyses is clearly revealed in Schroeder's paper on “Forming Parameters and Criteria for Design and Production.”