Combined Analysis

Chapter 7

Residual Strain-Stress Analysis

Diffracting planes are used as strain gages for elastic deformations. Stresses are then calculated via continuum mechanics equations. The formalism of these methods is extensively described in the works by Cullity [CUL 78], Maeder [MAE 86], Noyan and Cohen [NOY 87], Noyan et al. [NOY 95], and Hauk [HAU 97].

7.1. Strain definitions

The total elastic strain for a grain at the position X in the sample can be expressed in the sample reference frame K_A by:

[7.1] 

where ε^I is the macroscopic strain (first order) averaged over all grains within the macroscopic irradiated volume V_d. This macroscopic strain is induced by macroscopic stresses σ^I (Figure 7.1). ε^III is the intergranular strain (second order), which characterizes the strain deviation from the macroscopic value ε^I for a particular grain. Intergranular strains can be present in the material for several reasons, elastic anisotropy giving rise to ε^IIe, thermal anisotropy ε^IIti, plastic anisotropy ε^IIpi. ε^III is defined as the position-dependent deviation from the average macroscopic strain of the crystal. The latter are often referred to as microstrains, with an average value over one crystallite being zero. Microstrains are accessible by a profile analysis of the diffraction peaks.

Figure 7.1. Phenomenological classification of internal stresses. σ^I, σ^II and σ^III are respectively macro-, ...