Microscopic stresses

In our current model, the stress is assumed to be constant over the element (i.e., the stress is treated as piecewise constant on the macroscopic scale). We therefore assign the macroscopic stress a value equal to the spatial average of the microscopic stress ... 

It is known that for a materials with two or more phases the stress field is the superposition of stresses at two levels Macroscopic stresses which exist between the different layers and result from the internal force balance through the whole material. Microscopic stresses which appear between grains or phases in the material. Thus, the micro residual stresses stemming from the two-phase system have to be added to the results from finite element analysis (where only macro residual stresses are determined) allowing direct comparison with the total stresses experimentally measured. Figure 9 shows the macro residual surface stresses from the numerical analysis for the two and three layer specimens. One can see that the results from X-ray measurements agree fairly well with the predicted values. 

Microscopic stresses are found inside individual splats and are generated due to the gradient of the coefficient of thermal expansion (CTE) between the hot particle and the cooler substrate. 

Raman photoluminescence piezospectroscopy of bone, teeth and artificial joint materials has been reviewed by Pezzotti (2005) with emphasis placed on confocal microprobe techniques. Characteristic Raman spectra were presented and quantitative assessments of their phase structure and stress dependence shown. Vibrational spectroscopy was used to study the microscopic stress response of cortical bone to external stress (with or without internal damages), to define microscopic stresses across the dentine - enamel junction of teeth under increasing external compressive masticatory load and to characterise the interactions between prosthetic implants and biological environment. Confocal spectroscopy allows acquisition of spatially resolved spectra and stress imaging with high spatial resolution (Green etal., 2003 Pezzotti, 2005 Munisso etal., 2008). 

Luo, D., Wang, W. X., and Takao, Y. Effects of the distribution and geometry of carbon nanotubes on the macroscopic stiffness and microscopic stresses of nanocomposites. Comp Sci and Tech., 67,2947-2958 (2007). 

In general, one can say if the filler particles are well dispersed and have diameters between 20 nm and 80 nm, they will reinforce the matrix. Larger particles will act as microscopic stress concentrators and will lower the strength of the polymer component. 

Defect t5q>es frequently relate to the mechanism causing the indication. Many NDT methods have an intrinsic sensitivity for specific types of indications. Examples are ( ) ultrasonic C-scans sensitive to boundaries between materials of different acoustic impedance (eg, voids, delaminations), (2) X-ray radiography sensitive to variations in density (eg, inclusion of foreign objects, voids), and (5) acoustic emission sensitive to microscopic stress release (eg, crack growth). 

Wunderlich Bernhard. Effect of decoupling of molecular segments, microscopic stress-transfer and confinement of the nanophases in semicrystalline polymers. Macromol. Rapid Commun. 26 no. 19 (2005) 1521-1531. 

The best compromise of proton conductivity and stability is achieved at intermediate lEC and moderate water uptake. Insufficient water content extinguishes the bulk-water-like proton mobility. Excessive swelling is a problem, as well. It reduces the steady-state performance as a result of proton dilution. Moreover, excessive swelling increases the microscopic stress on polymer fibrils, rendering PEMs with high lEC more prone to mechanical degradation. 

Crystallinity associated with the local ordering of polytetrafluoroethylene (PTFE) backbones is deemed an important PEM property in view of mechanical and thermal stability. The degree of crystallinity has an impact on microscopic stress-strain... 

FIGURE 2.20 Microscopic stress versus strain relation. Elastic pressure is depicted as a function of the swelling parameter r] for the three scenarios of pore wall deformation, discussed in this section. They correspond to isotropic deformation (Equation 2.33), anisotropic deformation (Equation 2.34), and elongation (Equation 2.35). 

Relations between and r], discussed in this section, are illustrated in Figure 2.20. All three deformation scenarios predict that P decreases in the limit of dehydration. At zero swelling, that is, for t] = 0, they approach P = 0. These characteristics of microscopic stress versus strain relations are in qualitative agreement with experimental observations (Freger, 2002 Silberstein, 2008). The shear modulus G of polymer walls is related to Young s modulus Ehy E = 2(1 v)G, with a value of y = 0.5 proposed for Poisson s ratio in Choi et al. (2005). 

By way of concluding remarks, let us reiterate the limitations of the theory presented here. The ensemble averages of the microscopic stress tensors appearing in the equations of motion Eqs. (12) and (13) were... 

In order to link the macro- and micro-problems, the boundary conditions on the RVE must ensure that the macroscopic stress power is equal to the average microscopic stress power, that is, they must satisfy Hill s condition [17] ... 

In a partially or nonoriented system, the microscopic axial stresses are larger than Oq by a factor of up to E/Ej where E is the longitudinal modulus of elasticity of the sub volume containing the elastic element. If all sub volumes of a sample behave identically, then E is the longitudinal modulus of the (partially) oriented sample. Naturally the largest axial stresses are experienced by those elements oriented in the direction of uniaxial stress. In a completely oriented system E and E are equal by definition, and macroscopic and microscopic stress (in the direction of orientation) are equal also. 

The total pressure is the average of the diagonal part of the microscopic stress tensor,... 

The force exerted by the fluid on a particle follows from integrating the total microscopic stress (pressure plus viscous stress) over the particle surface. Since the microscopic detail is lost from the description, closure relations need to be used that related the force to macroscopic quantities. It is customary to split the total fluid-to-particle force into different contributions. These... 

Here, the total force that a particle appUes to the fluid is computed by integrating the total microscopic stress, over the particle surface. 

The expression for the microscopic stress used was the one for incompressible fluids. For a compressible fluid, a contribution related to the divergence of the compressibility enters and the bulk viscosity comes into play. In the case of an incompressible hquid, we have V =0. At a macro-... 

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