Eigenstrain analysis of residual strains and stresses

Experimental stress evaluation procedures often rely on the measurement of some component(s) of elastic strain followed by point-wise calculation of stress based on continuum elasticity assumptions. Such point-wise assessments are, however, incomplete and not entirely satisfactory, as calculations conducted for different points can easily give rise to values that may not satisfy requirements of global force balance. The real purpose of experimental data interpretation is in fact to obtain a reasonably internally consistent description of the state of stress everywhere in the object to the greatest possible level of detail. What is usually being sought is a residual-stress-admissible (RS-admissible) field, i.e. such that would satisfy boundary conditions imposed both in terms of tractions and displacements, and would correspond to a divergence-free stress field (i.e. such that satisfies stress equilibrium conditions everywhere). Note, however, that elastic strains are no longer required to be compatible. The lack of compatibility of elastic strains arises from the presence of incompatible plastic strains, acting as the origin of residual stresses throughout the object. The present study considers the practical challenge of finding the most probable RS-admissible stress-strain field that corresponds to a set of experimental measurements of residual elastic strains at a number of experimental points. A simple optimization formulation is introduced, and the procedure for finding the unknown underlying distribution of eigenstrains is described. It is then illustrated using examples of one- and two-dimensional residual stress profiles. The implications of this approach are discussed for the analysis of residual stress effects on the durability of engineering structures and assemblies.