This article is dedicated to the analysis of visco-plastic and damageable structures submitted to thermomechanical loadings embedding some uncertain parameters. In particular, complex time evolutions of the loadings are considered, at two different time scales. An homogenized-in-time model is used to provide kind of a surrogate model for damage evolution analysis. Then a stochastic analysis using polynomial chaos expansion with collocation can be performed. Indeed, though this is a non-intrusive approach, it belongs to the category of many-query problems, so the surrogate model allows to reduce the computational cost in order to be affordable. Focus is herein on the complex time evolutions, the considered test case is mono-dimensional, but up to 300 000 cycles are used.