Internal Stresses in Deformed Crystalline Aggregates

Abstract

This Chapter is an introduction to the various length scales of internal stresses, the causes of internal stresses and in particular their measurement by neutron diffraction. Some of the approaches used to model and interpret internal stresses are also introduced, and the use of these approaches to interpret deformation mechanisms illustrated through a number of examples. In nearly every case when an engineering material is employed it will experience some stresses, if only those due to its own weight. Real materials are not the uniform continuum they are sometimes considered to be, and local differences in structure or properties mean that the local ‘internal’ stress is not necessarily equal to any external applied stress. These internal stresses are fundamental in controlling the deformation and failure of materials; they can have a considerable effect on material properties, including fatigue resistance, fracture toughness and strength. These stresses can vary greatly as a function of position within a body, due to the processes experienced during its production. Consequently, their measurement and interpretation is of considerable interest (e.g., Hutchings 1990), and great efforts have been employed over the years in developing accurate and precise measurement techniques. Such stresses can develop in a deformed material at many length scales and from many mechanisms. Fundamentally, internal stresses arise due to the elastic response of the material when an inhomogeneous distribution of non-elastic strains is imposed. These non-elastic strains could be due to plastic strain, precipitation, phase transformations, thermal expansion, etc. (Noyan and Cohen 1987). The origins in all cases thus come down simply to two aspects: heterogeneity and constraint. That is, when the various constituent parts of a component or material would, if unconstrained, exhibit different responses to the applied load (be that stress, temperature, electric field, etc.) the constraints imposed by the bulk of the …