Stress inhomogeneous

Bilgili E, Yepes J, Stephenson L, Johanson K, Scarlett B. 2004. Stress inhomogeneity in powder specimens tested in the Jenike shear cell Myth or fact Part. Part. System Charact. 21(4) 293-302. 

Vibrational Raman band intensities and frequencies are also dependent on temperature, applied pressure, and the intrinsic microstructure of the material. These second-order parameters may be extracted from measured spectra. Both X-ray diffraction lines and Raman bands from polycrystalline materials show increased broadening as the microcrystallite grain sizes decrease. In fact, for the hexagonal phase of BN, bandwidths vary linearly with the reciprocal grain size (13). Inherent stress in thin films is manifested in vibrational line shifts. Based on pressure-dependent measurements of vibrational frequencies in bulk solids, inherent stress and stress inhomogeneity can be determined in thin films. Since localized stress can influence the optical and electronic properties of a thin film, it appears to be an important parameter in film characterization studies. Vibrational features also exhibit temperature-dependent frequency shifts. Therefore, an independent measurement of temperature is sometimes necessary to deconvolute these effects. Reference to Figure 1 shows that the molecular temperature of a material may be determined from the Stokes/anti-Stokes... 

In all the above mentioned experiments, hydrostatic (i.e. isotropic) pressure was applied to materials. In high-pressure experiments, this is usually assumed to be the case, but it is true only when the stress environment is purely hydrostatic. In other cases the stress state of the sample should be described by stress tensors, which are very difficult to determine. The mean pressure could be some average of the normal stress components over the sample, but one cannot neglect the effects of shear stress, differential stress, and stress inhomogeneity on many physical properties [191]. Influence of different conditions of compression on has been studied in detail on the bcc to rhombohedral phase transition in vanadium. Under a non-hydrostatic compression the phase transition occurred at 30 GPa at ambient temperature and at 37 GPa at 425 K. Under quasi-hydrostatic compression in the Ar pressure medium, Ptr increased to 53 GPa. When Ne was used as the medium, Ptr increased to 61.5 GPa, still short of the ideal value of 65 GPa [192]. 

A conservative assumption is that O can be set equal to zero. When the stress O equals the characteristic strength O the faUure probabUity is 63.2%. Under conditions other than tensUe loading, the stress distribution in a body is inhomogeneous. To account for this, a loading factor k is used to calculate the effective volume under stress and kVreplaces V. 

Equations (2.9) and (2.10) are representative of all isotropic, homogeneous solids, regardless of the stress-strain relations of a solid. What is strongly materials specific and uncertain is the appropriate value for shear stress, particularly if materials are in an inelastic condition or anisotropic, inhomogeneous properties are involved. The limiting shear stress controlled by strength is termed r. ... 

Wave propagation in an inhomogeneous anisotropic material such as a fiber-reinforced composite material is a very complex subject. However, its study is motivated by many important applications such as the use of fiber-reinforced composites in reentry vehicle nosetips, heatshields, and other protective systems. Chou [6-56] gives an introduction to analysis of wave propagation in composite materials. Others have applied wave propagation theory to shell stress problems. 

However, the foregoing derivation is valid only for isotropic beams of rectangular cross section. For beams of nonrectangular cross section, the parabolic stress distribution is not correct. Also, for laminated beams, the parabolic distribution is most assuredly incorrect because of layer inhomogeneity. In fact, for laminated beams, we must expect different shapes of stress distribution in each layer as seen in Figure 6-19 for wide beams (there interpreted as cylindrical bending of a long strip, i.e., a special plate). 

The aspect of sample preparation and characterization is usually hidden in the smallprint of articles and many details are often not mentioned at all. It is, however, a very crucial point, especially with surface and interface investigations since there might be many unknown parameters with respect to surface contaminations, surface conformations, built-in stresses, lateral sample inhomogeneities, roughness, interfacial contact etc. This is in particular important when surfaces and interfaces are investigated on a molecular scale where those effects may be quite pronounced. Thus special care has to be taken to prepare well defined and artifact free specimens, which is of course not always simple to check. Many of these points are areas of... 

Iv) Shear stress and viscosity. As explained In Section 1 three Independent estimates of the shear stress can be made for this particular type of flow. For both systems they all agree within the limits of statistical uncertainty as shown In Table II. The shear stress In the micro pore fluid Is significantly lower than the bulk fluid, which shows that strong density inhomogeneities can induce large changes of the shear stress. 

The hydrodynamic forces acting on the suspended colloids determine the rate of cake buildup and therefore the fluid loss rate. A simple model has been proposed in literature [907] that predicts a power law relationship between the filtration rate and the shear stress at the cake surface. The model shows that the cake formed will be inhomogeneous with smaller and smaller particles being deposited as the filtration proceeds. An equilibrium cake thickness is achieved when no particles small enough to be deposited are available in the suspension. The cake thickness as a function of time can be computed from the model. 

Figure 12 shows the stress-strain curves of IER at various temperatures. A strain-induced reinforcing effect is not observed at temperatures above -10 °C. This fact may be due to network inhomogeneities caused by imperfect crosslinking. 

Inelastic deformation of any solid material is heterogeneous. That is, it always involves the propagation of localized (inhomogeneous) shear. The elements of this localized shear do not occur at random places but are correlated in a solid. This means that the shears are associated with lines rather than points. The lines may delineate linear shear (dislocation lines), or they may delineate rotational shear (disclination lines). The existence of correlation means that when shear occurs between a pair of atoms, the probability is high that an additional shear event will occur adjacent to the initial pair because stress concentrations will lie adjacent to it. This is not the case in a liquid where the two shear events are likely to be uncorrelated. 

The main drawback in this type of thermometry is the presence of spurious thermoelectric powers due to chemical inhomogeneity, stress in conductors, contact effects in switches if present, etc. 

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