Intergranular strain

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. 

Voigt Model. According to Voigt the intergranular strain in the sample reference system is zero and then the strain tensor in the crystallite is identical with the macroscopic strain ... 

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. 

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... 

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. 

ABSTRACT In the present paper a multiphase model including a hypoplastic formulation of the solid phase is presented and its application to earthquake engineering problems discussed. The macroscopic soil model, which is based on the theory of porous media, comprises three distinct phases namely, solid, fluid and gas phase. For each of these the compressibility of the respective medium is taken into account in the mathematical formulation of the model. The solid phase is modelled using the hypoplastic constitutive equation including intergranular strain to allow for a realistic description of material behaviour of cohesionless soils even under cyclic loading. The model was implemented into the finite element package ANSYS via the user interface and also allows the simulation of soil-structure interaction problems. 

To overcome these problems, a multiphase model considering a hypoplastic approach including intergranular strain for the solid phase has been developed in this work. Due to its implementation into the finite element program ANSYS it also allows for soil-structure-interaction analyses within the existing finite element framework. In Holler Meskouris (2006), presented the application of the model to a soil-strncture interaction analysis of silos under dynamic excitation. 

Here Sij is an additional variable representing the intergranular strain. Its rate of change is determined from equation 31. 

Due to the hypoplastic formulation including intergranular strain, the model is capable of predicting soil behaviour even under cyclic loading and therefore offers... 

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). 

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