Texture measurements stress strain

Elastic (shear) modulus measurements were carried out on cylindrical gel samples using a TA.XT2I HR Texture Analyser (Stable Micro Systems, UK). Swollen networks were uniaxially compressed (at constant volume) between two parallel flat plates. The stress-strain isotherms were determined in the range of deformation ratio 0.7 < < 1. 

Texture has a number of component attributes, and some of them can be assessed by mechanical means. The texture or firmness of cooked potatoes is evaluated by subjecting each sample to a compression test using a universal testing machine equipped with a load cell. Cooked potato cylinders are compressed in a single-cycle compression-decompression test. Uniaxial compression is measured with an Instron machine with a lOON load cell. Measurements are performed on hot potato cylinders (depth 12 mm, height 10 mm) from 15 potatoes immediately after cooking, at a deformation rate of 20 mm/min. Stress and strain at fracture are calculated by the Instron series IX version 7.40 software and means of 15 repetitions are calculated. 

General methodology includes preparation of the solid texture. The measurement techniques may be the application of forces such as pure stress (also strain), shear, or their combinations and the measurement of the resistance to this procedure (Table III). Also used are special methods such Table III. Measurable Properties of Texture... 

The compression of uniform samples to the point where the force exceeds the structural capacity causes it to permanently deform and essentially break (4). A typical load-deformation curve can be used to derive values for yield stress, yield strain, and compressive yield work, and depending on the linearity of the onset of compression, a compressive modulus may be obtained (4). These measurements can be used to provide an index of hardness for fats, which have been successfully correlated to the textural attributes of hardness and spreadability obtained through sensory evaluation (4). Unfortunately, these tests are destructive in nature and yield minimal information about the native microstructure of the system. 

Sometimes the dependence of the measured strain on sin T becomes strongly nonlinear, especially in metals after plastic deformation, and cannot be explained by the texture or by the stress gradient effect. In general. Equations (84) are too restrictive because they do not take into account the plastically induced part of the strain and stress. They must be replaced by the exact Equations (73) ... 

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. 

In Nylon, where the plane-strain texture is less perfect than that in HDPE, such measurements can be made more readily, as Fig. 9.16 shows, with continuity of the data across zero normal stress without a break. 

In general, SMPF is perceived as a two-phase composite material with a crystalline phase mixed with an amorphous phase. A multiscale viscoplasticity theory is developed. The amorphous phase is modeled using the Boyce model, while the crystalline phase is modeled using the Hutchinson model. Under an isostrain assumption, the micromechanics approach is used to assemble the microscale RVE. The kinematic relation is used to link the micro-mechanics constitutive relation to the macroscopic constitutive law. The proposed theory takes into account the stress induced crystallization process and the initial morphological texture, while the polymeric texture is updated based on the apphed stresses. The related computational issue is discussed. The predictabihty of the model is vahdated by comparison wifli test results. It is expected that more accurate measurement of the stress and strain in the SMPF with large deformation may further enhance the predictability of the developed model. It is also desired to reduce the number of material parameters in the model. In other words, a deeper understanding and physics based theoretical modeling are needed. 

Rheology is the study of flow of matter and deformation and these techniques are based on their stress and strain relationship and show behavior intermediate between that of solids and liquids. The rheological measurements of foodstuffs can be based on either empirical or fundamental methods. In the empirical test, the properties of a material are related to a simple system such as Newtonian fluids or Hookian solids. The Warner-Bratzler technique is an empirical test for evaluating the texture of food materials. Empirical tests are easy to perform as any convenient geometry of the sample can be used. The relationship measures the way in which rheological properties (viscosity, elastic modulus) vary under a... 

The chapter begins with an overview of elastic anisotropy in crystalline materials. Anisotropy of elastic properties in materials with cubic symmetry, as well as other classes of material symmetry, are described first. Also included here are tabulated values of typical elastic properties for a variety of useful crystals. Examples of stress measurements in anisotropic thin films of different crystallographic orientation and texture by recourse to x-ray diffraction measurements are then considered. Next, the evolution of internal stress as a consequence of epitaxial mismatch in thin films and periodic multilayers is discussed. Attention is then directed to deformation of anisotropic film-substrate systems where connections among film stress, mismatch strain and substrate curvature are presented. A Stoney-type formula is derived for an anisotropic thin film on an isotropic substrate. Anisotropic curvature due to mismatch strain induced by a piezoelectric film on a substrate is also analyzed. 

Stresses produced in sol-gel-derived films modify the lattice parameters of the film and its orientation or texture. These effects are clearly observed in the X-ray diffraction (XRD) patterns of Figure 27.16 [55]. The XRD pattern of a (Ca, Pb) TiOs perovskite thin film on a Pt-coated silicon substrate shows a textured film with a (100) preferred orientation and with the cell parameters for the perovskite indicated in Table 27.5. When this film is electrolytically separated from the substrate, it recovers the random orientation of the ceramic powder and its preferred orientation disappears observe the lattice parameters and strains measured in a (Ca, Pb)TiOs thin film on the substrate and this film is separated from the substrate in comparison with those of the bulk ceramic (Table 27.5) [55]. 

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