The generation of plastic slip and residual stress by thermal processes is particularly difficult to understand and simulate. Modelling such problems is computationally expensive when approached numerically and extremely complex to approach analytically. ‘Semi-analytical’ models, in which analytical thermoelastic solutions are combined with approximate models of plasticity, offer a way to bridge this gap and have the potential to allow the rapid testing of parameter sensitivities before one launches a time-consuming full numerical model. However the construction of such models within such a thermal framework poses its own problems. An initial requirement for any such semi-analytical model is a complete solution to the elastic only response of the material to the given loading process. In this paper we focus on the formulation of such a solution for the simplest case relevant to welding or similar thermal processing. We verify the solution developed against finite element predictions and then further investigate it. In doing so we explain how the nature of this solution, especially its predicted yielding behaviour, has ramifications for the successful creation of a full semi-analytical solution.

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