Three-dimensional analytical model for residual stress in the weld of thick plates by friction stir welding

The residual stress is non-uniform in the thickness direction for thick plates jointed by friction stir welding (FSW). An analytical method by using the material flow in the welding process is proposed to solve the non-uniform residual stress of thick plates. The streamline model for the material flow is established in terms of the relationship between stream function and velocity fields in the weld. The cumulative plastic strain is computed by integrating the strain rate along each streamline. The residual stress field is obtained based on characteristic strain theories. Experiments of FSW are conducted for thick plates of aluminum alloy 2024-T3. The residual stresses in the welded region are measured by both X-ray diffraction and the contour method. The relative error of the predicted residual stress in the top surface of the weld is 4.8%. The accuracy of the analytical model can be verified. The analytical and experimental results show that the distribution of residual stress is asymmetric with a conventional "M" shape, and the distance of the two peak stresses is 40.63 mm in the top surface of the weldment. The flow mechanism of material and residual stress in different regions of thick plates by FSW are revealed. The proposed model may be used for the prediction and analysis of the non-uniform distribution of residual stress in thick plates jointed by FSW.