The Stresses in an Elastoplastic Bar Subjected to a Sudden Change of Surface Temperature

Abstract

An analysis is given for the stress history in an elastoplastic bar subjected to a sudden change of surface temperature. The type of behavior is found to depend on the ratio of thermal strain (αV) to yield strain (σy/E). For EαV/σy < 1, the stresses are entirely elastic. For 1 < EαV/σy < 2.04 there are two transient zones of compressive yielding. For 2.04 < EαV/σy < 4.4 there are two transient zones of compressive yielding and two enduring zones of tensile yielding. For EαV/σy > 4.4 there are two transient zones of compressive yielding, one transient zone of tensile yielding, and two enduring zones of tensile yielding. The investigation is restricted to the range 0 ⩽ EαV/σy ⩽ 5 and the particular case EαV/σy → ∞. Detailed solutions are given for EαV/σy = 1, 2, 3, 4, 5, and ∞.