Stress and Strain Distributions in a Thick-walled Cylinder of Strain-hardening Material, Elastic-plastically Strained by Internal Pressure

Chang Keng Liu

gen. del 1965 · NASA

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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.