Strain local

We first consider strain localization as discussed in Section 6.1. The material deformation action is assumed to be confined to planes that are thin in comparison to their spacing d. Let the thickness of the deformation region be given by h then the amount of local plastic shear strain in the deformation is approximately Ji djh)y, where y is the macroscale plastic shear strain in the shock process. In a planar shock wave in materials of low strength y e, where e = 1 — Po/P is the volumetric strain. On the micromechanical scale y, is accommodated by the motion of dislocations, or y, bN v(z). The average separation of mobile dislocations is simply L = Every time a disloca-... 

So, for given strain rate s and v (a function of the applied shear stress in the shock front), the rate of mixing that occurs is enhanced by the factor djhy due to strain localization and thermal trapping. This effect is in addition to the greater local temperatures achieved in the shear band (Fig. 7.14). Thus we see in a qualitative way how micromechanical defects can enhance solid-state reactivity. 

Plastic strain localization and mixing due to void collapse in porous materials works in the same way, with perhaps an even greater degree of actual mixing due to jetting, and other extreme conditions that can occur at internal free surfaces in shock-loaded solids. 

In the gut, many pathogens adhere to the gut wall and produce their toxic effect via toxins which pervade the surrounding gut wall or enter the systemic circulation. Vibrio cholerae and some enteropathic E. coli strains localize on the gut wall and produce toxins which increase vascular permeability. The end result is a hypersecretion of isotonic fluids into the gut lumen, acute diarrhoea and consequent dehydration which may be fatal in juveniles and the elderly. In all these instances, binding to epithelial cells is not essential but increases permeation ofthe toxin and prolongs the presence of the pathogen. 

In the case of filled systems, the two latter effects provide a substantial contribution to C2 compared with the influence of trapped entanglements [80]. For filled systems, the estimated or apparent crosslinking density can be analyzed with the help of the Mooney-Rivlin equation using the assumption that the hard filler particles do not undergo deformation. This means that the macroscopic strain is lower than the intrinsic strain (local elongation of the polymer matrix). Thus, in the presence of hard particles, the macroscopic strain is usually replaced by a true intrinsic strain ... 

In this relation, 2C2 provides a correction for departure of the polymeric network from ideality, which results from chain entanglements and from the restricted extensibility of the elastomer strands. For filled vulcanizates, this equation can still be applied if it can be assumed that the major function of the dispersed phase is to increase the effective strain of the rubber matrix. In other words, because of the rigidity of the filler, the strain locally applied to the matrix may be larger than the measured overall strain. Various strain amplification functions have been proposed. Mullins and Tobin33), among others, suggested the use of the volume concentration factor of the Guth equation to estimate the effective strain U in the rubber matrix ... 

Smectic A liquid crystals are known to be rather sensitive to dilatations of the layers. As shown in [34, 35], a relative dilatation of less than 10-4 parallel to the layer normal suffices to cause an undulation instability of the smectic layers. Above this very small, but finite, critical dilatation the liquid crystal develops undulations of the layers to reduce the strain locally. Later on Oswald and Ben-Abraham considered dilated smectic A under shear [36], When a shear flow is applied (with a parallel orientation of the layers), the onset for undulations is unchanged only if the wave vector of the undulations points in the vorticity direction (a similar situation was later considered in [37]). Whenever this wave vector has a component in the flow direction, the onset of the undulation instability is increased by a portion proportional to the applied shear rate. 

This study (34) implies that a right dispersion of rubber particles may permit optimum stress field overlap that affords lower craze-initiation stresses and therefore can rapidly dissipate the strain energy in the HIPS. A more homogeneous spatial distribution of rubber particles allow for a uniform development of crazes. Prevention of the strain localization phenomenon to avoid the detrimental situation, where crazes prefer to develop in certain areas and quickly lead to a catastrophic crack, could result in a larger total volume of crazed material. Further, Donald and Kramer (22) discovered no crazes nucleating from an isolated rubber particle with diameter smaller than 1 urn because of an insufficient size of stress-enhanced zone. Since Sample-A has a small average particle size it should contain a large number of small rubber particles. Two small rubber... 

The Doi-Edwards model has been extended to allow processes of primitive-path fluctuations, constraint release, and tube stretching. These extensions of the theory allow accurate prediction of many steady-state and time-dependent phenomena, including shear thinning, stress overshoots, and so on. Predictions of strain localization and slip at walls... 

Fig. 2.2. (A) Illustration of the source of statistical fine structure (SFS) using simulated absorption spectra with different total numbers of absorbers N, where a Gaussian random variable provides center frequencies for the inhomogeneous distribution. Traces (a) through (d) correspond to N values of 10, 100, 1,000, and 10,000, respectively, and the traces have been divided by the factors shown. For clarity, yjj = Fi/10. Inset several guest impurity molecules are sketched as rectangles with different local environments produced by strains, local electric fields, and other imperfections in the host matrix. (B) SFS detected by FM spectroscopy for pentacene in p-terphenyl at 1.4K, with a spectral hole at zero relative frequency for one of the two scans. Note the repeatable fine structure...

The nucleation of voids produce a decrease of the macroscopic response of the material, by continuing deformation, they growth and coalesh as a result of strain localization causing small increments, at every cycle, of crack tip extension. 

Sheet thinning (reduced thickness in the weld) was observed in the friction sir welds of the a-Ti alloy. The weld ultimate strength was calculated based on the original sheet thickness and not the reduced section in the weld region. The a-Ti tensile specimens failed in the weld region and the elongation to fracture was low due to strain localization in the weld accompanied by sheet thinning. 

Investigation of the deformation relief occurring on the surface of samples additionally subjected to by 15% strain after different number of compression steps have shown that plateau on the initial portion of strain curves is result of strain localization (Fig. 2a) in macro shear bands (MSB). Its appearance is result of scattering some dislocation boundaries onto individual dislocations (Baushinger effect) and formation of avalanche of mobile dislocations (Fig. 2b). So, in this case yield of titanium is controlled by substructure that, probably, leads to weak dependence of yield stress on strain. Macrobands formed at the beginning of the cycle of loading remain until the end of loading. So, plastic flow of titanium is localized. 

As a rule, crack resistance of coarse aggregate concrete is determined by nonequilibrium mechanical testing using samples with a cut that initiates a crack. Nonequilibrium tests are characterized by loss of the deformation process stability of the sample during the moment of strain localization at the maximum load, with corresponding dynamic development of the main crack [14], However, such tests conflict with the condition in Equation (3.11), since in these concretes the size of the prefracture zone is 100-300 mm. 

We describe the high pressure triaxial cell in which tests will be performed. Then we present the strain local measurements developed to identify and characterize the different mechanical stages that can be correlated to permeability evolution and in particular strain localization. The experimental procedure focused for materials having low permeability and hydromechanical coupling (i.e. effective stress has an important role) is described. Finally we present two materials involved in the SELFRAC project and with which we have to improve our experimental developments. 

Measuring radial and axial strains in several points of the specimen surface allows to detect with larger precision a possible loss of homogeneity of strains during loading. This is a way to detect a strain localization point on the q-E curve and to locate shear bands or fractures in the specimen. 

An experimental set up (high pressure triaxial cell and local strain measurement system) and an experimental procedure have been developed in order to quantify the permeability evolution with deviatoric stress on clays of very low permeability. Developed techniques have been improved on concrete and sandstone. We are able to detect with precision strain localization and we are able to measure with the pulse method, permeability, at different stages of loading. A testing program on both Boom Clay and Opalinus is in progress. 

Mechanical Properties. As noted previously, caution must be exercised when interpreting strain within weldments, due to the potential for strain localization in transverse tensile tests. However, yield and tensile strength results require no special consideration. Yield strength is often related to hardness, and based on the hardness curves typically obtained for 2024 Al, yield strength as well as fracture location should correlate with the lowest-hardness location in the W -hardness curve. Mechanical properties for 2024 Al have been reported in numerous publications as a function of FSW variables, including tool rotation rate, travel speed, and sheet thickness (Ref 2,4—8,11, 15). 

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