According to Eshelby's theory, inelastically inhomogeneous inclusions in a metallic matrix give rise to a distribution of internal stresses. In the case of particle strengthened materials, such as nickel base superalloys, the presence and evolution of this back-stress leads to various observable effects, such as primary creep, back-flow upon loading, and memory of prior deformation. This article presents the background of the concept of back-stress and how it applies to the scenario of creep. A derivation of an evolution equation for back-stress in the context of primary creep is also presented. The results from neutron diffraction with in-situ creep experiments on directionally solidified nickel superalloys are presented in order to demonstrate the validity of the proposed equation and the corollaries derived therefrom.Crystals 2020, 10, 306 2 of 13 accumulation around non-deforming particles. They proposed that relaxation by tangle formation would cease when the local stress generated by work-hardening equaled the internal stress. In the approaches of both Brown and Stobbs and Ashby, the conclusion is that the stress in the dislocation structure around the non-deforming particles is equal in magnitude to the back-stress. Subsequent researchers used their conclusion to explain work-hardening in other composites [7].
Back-Stress in CreepResearchers in creep borrowed the idea of back-stress and proposed that the back-stress causes creep to decelerate. For instance, Dyson and co-workers [8,9] proposed that the evolution of the back-stress leads to primary creep and this was a significant advancement in the theory of creep in superalloys and other technologically important materials. They called this process 'stress redistribution' or 'stress transfer'. In the case of pure metals, stress redistribution occurs when a dislocation cell structure is developed. Thus, primary creep in pure metals occurs over a large strain and time range. Dyson et al. proposed that stress redistribution occurs between the creeping matrix and the non-deformable reinforcing particles in the case of particle-strengthened composites. Thus, primary creep in superalloys typically occurs over a small strain and time interval and the onset of secondary creep signals the end of this stress redistribution. Dyson [10] proposed the following equation to describe the stress transfer process .