The Incremental Strain Growth of an Elastic-Plastic Body Loaded in Excess of the Shakedown Limit

This paper considers the problem of a body composed of an elastic/perfectly plastic solid that is subjected to constant applied load P and a time-varying cyclic temperature distribution, characterized by a maximum thermoelastic stress σ_t. For sufficiently large P and σ_t, in excess of the shakedown limit, the body will begin to suffer incremental growth. A linearized theory is used to obtain a relationship between the increase in displacement Δu per cycle and the increase in ΔP and Δσ_t, above the shakedown limit. From the result, a simple lower bound is derived for Bree-type problems, which for kinematically determinate structures shows that for moderate thermal loading the displacement increment per cycle is four times the elastic displacement of the body if it were subjected only to the increase ΔP. From a practical point of view the analysis indicates that ratchet rates are always high, in the sense that only a small increase of load above shakedown will produce substantial ratcheting within relatively few cycles.