Residual Stress Reconstruction by Variational Eigenstrain Procedures

Residual stress can be found in engineering components as a result of non-uniform plastic strain introduced through a variety of manufacturing processes such as rolling, casting, hot forging, cold working, shot-peening, laser shock peening, welding, etc. The numerical simulation of the resulting residual stress field requires the use of sophisticated coupled microstructural and thermomechanical models that rely on profound understanding of the constitutive laws and detailed knowledge of material parameters. In practice this level of understanding is not generally available, leading to the use of simplified models that are unable to reproduce or predict reliably the real residual stress distributions. This leads to the necessity of using increased safety factors and utilising overly conservative designs. A rational approach to the description of residual stress states is proposed that relies on the use of eigenstrain distributions as sources of residual stress. The problem of residual stress evaluation can then be replaced by the problem of determining the underlying eigenstrain distribution. An approach to this problem is proposed based on a simple variational formulation. Some examples of its application are shown, and the difficulties and challenges that may arise are discussed.