Introduction to the mechanics of plastic forming of metals

The plastic forming of metals is a branch of technology, in which great progress has been achieved mainly by collecting practical data resulting from long-time experience. The contribution of theoretical analysis to this progress is not significant. The common argument was, that such an analysis is too difficult and often even impossible. However, the constantly increasing significance of coldwork processing in industrial practice and the progress in the automatic control of these processes, demanding a broad knowledge of the influence of various parameters, and also the need to improve the mechanical behaviour of coldworked elements have proved beyond doubt that better understanding of the theory of plastic forming processes is necessary. This general trend has become evident in several recent publications in recent years, even though these represent only the engineering, approximate approach to theoretical analysis. Recent significant progress in the mathematical theory of plasticity allows to build an analysis of plastic forming processes on a more sound basis. In particular there have been developed graphical methods by means of which slip-line and hodograph meshes are constructed for plane strain and axially symmetric problems. These graphical methods yield not only the required forces but also the. mode of plastic deformation, even for very complex problems. Numerical procedures also give good results if the digital computer technique is employed.

1. Mechanical Properties of Metals.- 1.1 The plastic behaviour of metals.- 1.2 Effect of strain rate on resistance of metals to deformation.- 1.3 Idealized stress-strain curves.- 2. Stresses, Strains and Flow Velocities.- 2.1 The state of strass.- 2.2 The state of strain.- 2.3 Strain rates.- 2.4 Equations of motion and equations of equilibrium.- 3. Yield Conditions and Flow Laws.- 3.1 General remarks.- 3.2 Huber-Mises yield condition.- 3.3 Tresca yield condition.- 3.4 Experimental verification of the yield condition.- 3.5 Effect of plastic deformation on yield condition.- 3.6 Strain-hardening hypotheses.- 3.7 Stress-strain rate relations.- 3.8 Drucker’s postulate; convexity of the yield surface.- 3.9 Extremum principles of plasticity.- 3.10 Brief summary; equations of the three-dimensional plastic flow.- 4. The Theory of Plane Plastic Flow.- 4.1 Basic relations.- 4.2 Determination of the stress field.- 4.3 Properties of slip-lines.- 4.4 Elementary nets of slip-lines.- 4.5 Basic boundary value problems.- 4.6 Graphical construction of slip-line nets.- 4.7 Determination of the velocity field.- 4.8 Stress and velocity discontinuities.- 4.9 The velocity hodograph.- 4.10 The condition of non-negative rate of internal energy dissipation.- 5. Indentation and Compression Operations.- 5.1 Introduction.- 5.2 Indentation of a flat punch into a half-space.- 5.3 Indentation of a plastic block by two opposite narrow punches.- 5.4 Compression of a plastic block between two flat rough plates.- 5.5 Compression of a block between partially rough plates.- 5.6 Wedge indentation.- 5.7 Cutting of a strip with a knife-edged tool.- 5.8 Compression of a plastic wedge by a flat plate.- 6. Two-Dimensional Steady-State Operations.- 6.1 General remarks.- 6.2 Sheet drawing through a smoothwedge-shaped die.- 6.3 Drawing through a rough die.- 6.4 Sheet drawing with small reduction in thickness.- 6.5 Dynamic effects in sheet drawing.- 6.6 Drawing through a curvilinear die.- 6.7 Extrusion operations.- 6.8 Piercing.- 7. Some Two-Dimensional Non-Steady State Operations.- 7.1 Introduction.- 7.2 Press forging in dies.- 7.3 Combined extrusion and piercing.- 8. Axially Symmetric Plastic Flow.- 8.1 Introduction.- 8.2 Basic relations.- 8.3 Determination of stresses.- 8.4 Determination of velocities.- 8.5 Indentation of a plastic half-space by a flat circular punch.- 8.6 Indentation of a rigid cone. Rockwell hardness test.- 8.7 Compression and press forging of axially symmetric elements.- 8.8 Special problems in axially symmetric flow.- 9. Plane Stress.- 9.1 General relations.- 9.2 Solution of plane stress equations for the Huber-Mises yield condition.- 9.3 Velocity field associated with the Huber-Mises yield condition.- 9.4 Velocity discontinuities.- 9.5 Solution of plane stress equations under the Tresca yield condition.- 9.6 Plane stress problems under axial symmetry.- 9.7 Plastic deformation of flat rings.- 9.8 Strain-hardening solutions of axially symmetric plane stress problems.- 9.9 Drawing of cups from circular blanks.- 10. Axially Symmetric Problems of Plastic Forming of Shells under Conditions of Plane Stress.- 10.1 Introduction.- 10.2 The steady-state forming operations.- 10.3 Dynamic solution to the tube drawing.- 10.4 Non-stationary forming operations.- 10.5 Non-stationary process as the final stage of a stationary process.- 10.6 The passage from non-stationary to stationary stage of the process.- 11. Drawing and Stretchforming of Thin-Walled Shells of Arbitrary Double Curvature.- 11.1 Introduction.- 11.2 Basic relations.- 11.3 Characteristics of the stress field for the Huber-Mises yield criterion.- 11.4 Characteristics of the velocity field associated with the Huber-Mises yield criterion.- 11.5 Characteristics of the stress field for the Tresca yield criterion.- 11.6 Characteristics of the velocity field associated with the Tresca yield condition.- 11.7 Stretchforming of thin-walled shells.- 11.8 Drawing through a die, Huber-Mises yield condition.- 11.9 Drawing through a die, Tresca yield condition.- 11.10 Drawing through a die, influence of the friction on the die-sheet interface.- Appendix 1.- Appendix 2.- References.- Supplementary references.- Author index.