Analytical modelling of residual stress in additive manufacturing

A physics-based analytical model to assess residual stresses in additive manufacturing made of metallic materials is presented and validated experimentally. The model takes into consideration the typical multi-pass aspect of additive manufacturing. First, the thermal signature of the process is assessed by predicting the temperature for the problem of a moving heat source, then, the thermally induced stresses in a homogenous semi-infinite medium are determined. Taking the thermal stresses as input, the residual stresses are calculated analytically to obtain the distribution across the depth. Good agreement is obtained between the analytical prediction and X-ray measurements made on Selective Laser Melted 316L Stainless Steel. In addition, the analytical approach enables in-depth interpretations of results with basis in the true mechanisms of the process. Thus, the present model appears as a promising tool for optimization of process parameters in additive manufacturing, which in turn will improve the understanding of process parameters and their effect on properties of the final product.