An eigenstrain based model for residual stress arising from transient local surface heating

We present a model for approximating residual stresses arising from thermally induced plasticity and apply it to a simple two-dimensional (plane strain) test problem of transient heating. The model uses stress fields derived from simple eigenstrains to perturb an initially elastic-only solution in a way that mimics plastic flow. The plane strain condition of the test problem gives rise to plastic strains in the out-of-plane direction, owing to constraints on thermal expansion. However, the model is able to cope with the challenges this poses and also encapsulates the time-dependent nature of the problem. We show that the model agrees well with finite-element simulations under moderate strength heat sources provided that appropriate plastic flow rules are used. There exists sufficient generality in the model to allow its extension to more realistic scenarios.