Intergranular strain/stress

The SODF is itself a macroscopic quantity, as is the following difference, called intergranular strain/stress ... 

The following sections develop three subjects the classical approximations for the strain/stress in isotropic polycrystals, isotropic polycrystals under hydrostatic pressure and the spherical harmonic analysis to determine the average strain/stress tensors and the intergranular strain/stress in textured samples of any crystal and sample symmetry. Most of the expressions that are obtained for the peak shift have the potential to be implemented in the Rietveld routine, but only a few have been implemented already. 

Finally, we note that the hydrostatic state can be also described in the frame of the classical models, but this is not a full description as one or another intergranular strain/stress is ignored. If in Equation (107) we set... 

Macroscopic and Intergranular StrainjStress. Similar to the case of texture we can call 8, g) = Oq, (P2) the strain/stress orientation distribution functions (SODF) (a,- is still a placeholder). In contrast to the texture case, the average of the SODF over all variables is not unity but is the macroscopic strain/stress ... 

The present hypothesis fully describes the hydrostatic strain/stress state in isotropic samples. Indeed, from the refined parameters e, the macroscopic strain and stress e, x can be calculated and also the intergranular strains and stresses Ae,(g), Ax,(g), both different from zero. Note that nothing was presumed concerning the nature of the crystallite interaction, which can be elastic or plastic. From Equations (112) it is not possible to obtain relations of the type (84) but only of the type (86). For this reason a linear homogenous equation of the Hooke type between the macroscopic stress and strain cannot be established. 

Arguments for recent developments of the spherical harmonics approach for the analysis of the macroscopic strain and stress by diffraction were presented in Section 12.2.3. Resuming, the classical models describing the intergranular strains and stresses are too rough and in many cases cannot explain the strongly nonlinear dependence of the diffraction peak shift on sin even if the texture is accounted for. A possible solution to this problem is to renounce to any physical model to describe the crystallite interactions and to find the strain/ stress orientation distribution functions SODF by inverting the measured strain pole distributions ( h(y)). The SODF fully describe the strain and stress state of the sample. 

Caustic embrittlement corrosion (caustic induced, stress corrosion cracking), which occurs as an intergranular form of corrosion where localized stresses and strains are present (and some silicate, which acts as a general corrosion inhibitor that protects grains at the expense of the grain boundaries). 

Superplastic ceramics deform without necking and fail by intergranular cracks that propagate perpendicular to the applied tensile axis. Grain size has been considered as a critical factor in superplasticity. In Fig. 8.88, fracture strain is indicated as a function of flow stress in FG ceramics, while the strain-rate sensitivity, m, remains high. In Fig. 8.88, various ceramics are plotted, (the reader is referred to the original works) ... 

The strain rate, as a function of applied stress, is shown in Fig. 9.33 for the steady-state creep rates of both the monolith and the nanocomposite ceramics. It may be observed that the creep rate of the nanocomposite is about three orders of magnitude lower than that of the monohth under tension, and three to four orders of magnitude lower under flexure. One of the most characteristic changes in microstmctures during creep is the rotation of the intergranular sihcon-carbide particles, accompanied by GBS and small cavity formation around the particles. This may be seen in Fig. 9.34a. 

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