Problems of residual stress analysis can be formulated in terms of so-called eigenstrain or inelastic strain. Although the concept is almost 100 year old, the use of it by the residual stress community is quite limited, due to complexities of the associated mathematics. When mathematical difficulties are resolved and eigenstrain is reconstructed, the use of it can be beneficial in several ways. Firstly, the eigenstrain is essentially a generator function for residual elastic stress and elastic strain and it can be used, for generation of any stress field in FE models. Furthermore, eigenstrain distributions are frequently localized, even though the elastic stress or strain distributions are not. Both these properties can be used for effective data reduction. Another advantage of the use of the eigenstrain concept is that experimental data may be interpreted in a more meaningful way by using a narrower context, in terms of plastic deformation, thermal expansion/misfit and deformation caused by phase transformation, rather than just residual stress/strain field. The sample geometry and symmetry play an important role in resolving eigenstrain distributions from residual stress and elastic strain fields. Generally the equations are difficult to solve, however for a sample geometry of high symmetry, eigenstrain can be resolved and expressed as a solution of a relatively simple integral equation; which is the Fredholm of the second type with the kernel of the integral operator defined by the sample geometry/symmetry. Several such symmetries are investigated, yielding analytical solutions that are applied and contrasted to experimental data. An important issue for residual stress analysis is the uniqueness of the solution is also discussed.
Elastic Stress Analysis of a Three-Dimensional Crack Using the Layer Potential : (Indirect Boundary Integral Method)