Oxford University Press, 1998. — IX, 355 p. — ISBN: 0198503679.Written by one of the leaders in the field and first published in 1950, this book remains a classic treatment of the mathematical theory of plastic materials.Contents. Introduction. Definition of the subject. Historica loutline. Physical background. The stress-strain curve. Foundations of the Theory. The ideal plastic body. The criterion of yielding. Strain-hardening. The complete stress-strain relations. The Levy-Mise s and Reuse equations. The Henck y stress-strain equations. Other theories. General Theorems. The plastic potential. Uniqueness of a stress distribution under given boundary conditions. Extremum and variational principles. The Solution of Plastic-Elastic Problems. Introduction. Theory of Hohenemser's experiment. Combined torsion an d tension of a thin-walled tube. Combined torsion and tension of a cylindrica l bar. Compression under conditions of plane strain. Bending under conditions of plane strain. Bending of a prismatic beam. Torsion of a prismatic bar. Torsion of a bar of non-uniform section. The Solution of Plastic-Elastic Problems. The expansion of a spherical shell. The expansion of a cylindrica l tube. Theory of the autofrettage process. Expansion of a cylindrica l cavity in an infinite medium. Plane Plastic Strain and the Theory of the Slip Line Field. Assumption of a plastic-rigid material. The plane strain equations referred to Cartesian coordinates. The plane strain, equations referred to the slip-lines. Geometry of the slip-line field. The numerical calculation of slip-line fields. The numerical calculation of the velocity distribution. Analyti c integration of the plane strain equations. Discontinuities in the stress. Two-DimensionaL Problems of Steady Motion. Formulation of the problem. Sheet-drawing. Ironing of a thin-walled cup. Sheet-extrusion. Piercing. Strip-rolling. Machining. Flow through a converging channel. Non-Steady Motion Problems in Two Dimensions. Geometric similarity and the unit diagram. Wedge-indentation. Compression of a wedge by a flat die Expansion of a semi-cylindrical cavity i n a surface. Compression of a block between rough plates. Non-Steady Motion Problems in Two Dimensions. Introduction. Formulation of the problem. Yielding of notched bars under tension. Plastic yielding round a cavit y indentation and the theory of hardness tests. Axial Symmetry. Fundamental equations. Extrusion from a contracting cylindrical container. Compression of a cylinder under certain distributed loads. Cylindrical tube under axial tension and internal pressure. Tube-sinking. Stress distribution i n the neck of a tension specimen. Compression of a cylinder between rough plates. Relations along slip-lines and flow-lines. Miscellaneous Topics. Deep-drawing. General theory of sheet-bending. Plane strain of a general plastic material. The theory of plane plastic stress, with applications. Completely plastic states of stress in a prismatic bar. Plastic Anisotropy. The yield criterion. Relations between stress and strain-increment. Plastic anisotropy of rolled sheet. Length changes in a twisted tube. The earing of deep-drawn cups. Variation of the anisotropic parameters during cold-work. Theory of plane strain for anisotropic metals. Appendixes. Author Index. Subject Index.
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