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An Elastic-Plastic Cylinder with Free Ends and Internal Heat Generation

William A. Beyer

Nuclear Science and Engineering / Volume 17 / Number 2 / Pages 179-184

October 1963


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The elastic-plastic deformation of a long cylinder subjected to uniform heat generation Q is considered using Tresca's yield function and an associated flow rule for perfectly plastic material. The ends of the cylinder are assumed to be free and all elastic and thermal parameters temperature-independent. We suppose that the outer surface is insulated and that heat is removed from the inner surface. If Q is allowed to increase at a sufficiently slow rate so that time effects can be neglected, then yielding commences on the inner surface. For the Poisson ratio v = 0.3, immediately after initiation of yield two inner plastic regions and an elastic region form. One of the plastic regions corresponds to a singular regime of the Tresca yield function. The interfaces of the regions propagate outward as Q is increased. For outer to inner cylinder radius ratio equal to 5 it was found that, for Q about 4 times the value giving the initial plastic yielding, a third plastic region formed in the interior of the elastic region. The work was stopped at this point. The equations involved were solved numerically.

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