Lower bound for LCF lifetime and its application to safe design of elastic viscoplastic structures

The theory of shakedown is applied to obtain an upper estimation of LCF lifetime of structures. A model of elastic viscoplastic material similar to the Perzyna one with isotropic strain hardening and isotropic damage is adopted. Assumptions: viscoplastic strain rate is proportional to the access of the yield function over zero; the rate of damage evolution is equal to a function of hardening and damage parameters with the coefficient of fluidity, as a factor of proportionality; damage process is coupled with the viscoplastic deformation process; the hardening parameter is equal to accumulated viscoplastic deformation. The yield surfaces form a family of self-similar surfaces with the diameter as the parameter. The shakedown condition of the Melan type is formulated relatively to the initial yield surface. Features of the stress path lead to an equation with min–max problem of the mathematical programming in the left side, which determines a safe value of the virtual residual stress. The equation provides an opportunity to compute the maximal value of the strain hardening parameter possible under the prescribed loading program. This value allows to obtain an upper estimate to safe work time of the structure, which results in a sufficient condition of the structure integrity during the prescribed time period. An example of the developed theory application to resolve various problems arising from designing of structures is considered.