An Inverse Method for Reconstruction of the Residual Stress Field in Welded Plates

Welding process is widely used in manufacturing of many important engineering components. For such structures, the most important problem is the development of residual stresses and distortion due to welding. Welding tensile residual stresses have a detrimental effect and play an important role in an industrial environment. Crack initiation and propagation in static or fatigue loading, or in stress corrosion can be greatly accelerated by welding tensile stresses. Practically, however, it is often very difficult to characterize the residual stress state completely, while the knowledge of the complete residual stress distribution in structures is essential for assessing their safety and durability. In this research, based on the concept of the Airy stress function, an inverse approach would be presented to reconstruct the residual stress field from limited incomplete measurements of the residual stresses existing in a welded plate. In contrast to the published methods, a general solution based on the approximated stress function would be proposed together with satisfying all of the requirements of continuum mechanics; also, there exist a flexibility to impose the type of the physical behavior of residual stresses to attain the meaningful stress field. The efficiency of the method has been demonstrated by achieving an excellent agreement between the model prediction and experimental measured stresses in the sense of least-square approximation; also, the solution of the inverse problem has been stabilized using the Tikhonov–Morozov stabilization theory.