STPZ at Cyclic Loading

Abstract

For structures that are subjected to cyclic loading above their elastic limits, the phenomena mentioned in Chap. 2 are important for their lifetime, in particular, the elastic-plastic strain ranges and the accumulated strains resulting from a possible ratcheting mechanism. With unlimited kinematic hardening, either elastic or plastic shakedown will be achieved under cyclic loading. With the Simplified Theory of Plastic Zones (STPZ), the nature of shakedown can be identified and all the quantities associated with the state of shakedown, such as maximum strain, mean strain, strain range, displacements, etc., can be approximately determined with relatively little effort. This chapter describes how the elastic-plastic strain ranges in the plastic shakedown condition and the accumulated strains in the elastic and plastic shakedown condition can be determined with the STPZ in the case of linear kinematic hardening and constant (i.e., temperature-independent) material parameters. Examples demonstrate the achievable quality of results. Chapter 5 then describes how a possible temperature dependence of the material parameters can be taken into account. In Chap. 7 an extension to multilinear kinematic hardening is performed.