Elastic Plastic Torsion Problem For Strain Hardening Materials

This publication is based upon lectures given during a well-received course on physical metallurgy and originally intended for students specializing in fields related to metallic materials. But, as the author points out, metallic materials are the most widely investigated group of materials and their study therefore gives a good basis for understanding how other materials can be made to reveal interrelationships between their structures and properties; especially with regard to those properties associated with strain. Similar types of rule can then be applied to other materials, in spite of their apparent differences.

An attempt is made to extend Allen and Sopwith's solution for an elastic-plastic thick-walled cylinder of ideally plastic material to strain-hardening material. Tresca's criterion of yielding is modified so that the effective stress (usually considered a function of the effective strain) is proportional to a simple power function of the radius in the plastic zone. An analysis of Allen and Sopwith's solution for ideally plastic material seems to support and justify the proposed modification of the yielding criterionZ The exponent of the power function is taken as -3/2, -5/4, 1, and -1/2, in each case yielding an analytic solution corresponding to a particular strain-hardening material. Examples worked are for the case of plane strain and for a ratio of outer to inner radii of 2. 0. When the exponent is taken to be zero, the solution becomes identical to that of Allen and Sopwith. For exponents other than the five mentioned above, numerical or graphical methods of integration may be used.

This volume comprises two classic essays on the mathematical theories of elasticity and plasticity by authorities in this area of engineering science. Undergraduate and graduate students in engineering as well as professional engineers will find these works excellent texts and references. The Mathematical Theory of Elasticity covers plane stress and plane strain in the isotropic medium, holes and fillets of assignable shapes, approximate conformal mapping, reinforcement of holes, mixed boundary value problems, the third fundamental problem in two dimensions, eigensolutions for plane and axisymmetric states, anisotropic elasticity, thermal stress, elastic waves induced by thermal shock, three-dimensional contact problems, wave propagation, traveling loads and sources of disturbance, diffraction, and pulse propagation. The Mathematical Theory of Plasticity explores the theory of perfectly plastic solids, the theory of strain-hardening plastic solids, piecewise linear plasticity, minimum principles of plasticity, bending of a circular plate, and other problems.