Analytical model for three-dimensional non-uniform temperature field and welding stress of thick plates via friction stir weld

The non-uniform thermal field for thick plates jointed by friction stir welding (FSW) easily causes the complex stress state and affects the mechanical behaviour of welded components. The transient non-uniform temperature field for thick plates by FSW is analytically studied based on the heat conduction problem solved by three-dimensional Green’s function. The asymmetric volumetric heat source model is developed by considering the flux distributions in the thickness direction, which is used to obtain the semi-analytical temperature field for welded plates with nonhomogeneous boundary conditions. Then, the analytical model for welding stress is proposed for thick plates by FSW according to the non-uniform temperature field in the weld. The elastic-plastic boundary and the variations of welding stress in the thickness direction are discussed based on the temperature gradient in the welding process. The non-uniform stress distribution in the weld may be analytically predicted in the welding process. The residual stress in the weld is numerically calculated in the cooling process and compared with experiment data to verify the models for the non-uniform temperature field and stress distribution of thick plates. The results show that the three-dimensional temperature field may be used effectively to provide insights into the mechanical response by FSW.