Dilatational strain

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

Physical Effects of Filler. Dispersion of any hard particulate matter in a soft matrix will yield a composite with quite different properties. The two main causes for these effects are load sharing of the filler particles and strain dilatation of filled elastomers. 

Predictions of the mechanical response of filled elastomers are further aggravated by the phenomenon of strain dilatation. As soon as dilatation commences, the tensile stress lag behind elongation, the degree of dilatation for a given composite being roughly a measure for the deviation from the expected mechanical response. Dilatation increases with particle size and volume fraction of filler—it decreases somewhat if the filler is bonded to the matrix. Farris (16,17) showed that dilatation can account well for the mechanical behavior of solid propellants and his equation ... 

Figure 1. The stress-strain dilatational behavior of three highly filled elastomers...

Figure 3. The stress-strain dilatational behavior of a 63.5 vol % filled elastomer at a series of hydrostatic pressures at a high strain rate...

Here/o (=/i of equation 49 of Chapter 11) is the fractional free volume at zero strain. For reasonable values of parameters near Tg, it can be estimated that a tensile strain of 1% would shift the time scale by about one logarithmic decade. In a simpler formulation, the ratio j6ty/j8 may be taken as unity. Experiments of this sort have been report for poly(methyl methacrylate), copolymers consisting largely of polyacrylonitrile, polycarbonate, and an acrylonitrile-butadiene-styrene copolymer blend the effects of strain dilatation on tensile stress relaxation, torsional stress relaxation, and combined tensile and torsional stress relaxation have been compared. - ... 

Dehnung extension, expansion, elongation (Verdehnung) strain (Dilatation) dilatation, dilation... 

This hydrostatic application of stress -p, where p is called the pressure, generates a volumetric strain (dilatation)... 

To demonstrate that propellants are non-linear materials even at small strains, one need only check the superposition principle experimentally. In the range of small strains below detectable dewetting or volumetric dilatation [6,9-11], most propellants have a relaxation that is independent of strain and in general closely obey the scalar multiplication homogeneity rule. Yet this relaxation modulus cannot be used to accurately predict the response due to other isothermal, low rate, small strain inputs. To demonstrate the inadequacies of linear viscoelastic predictions on solid propellants, laboratory tests where superposition is applicable can be performed. Figure 6.1 illustrates the stress-strain-dilatational behavior of a typical composite propellant. The dilatation-strain behavior is caused by vacuole formation within the microstructure... 

A wide variety of nonnewtonian fluids are encountered industrially. They may exhibit Bingham-plastic, pseudoplastic, or dilatant behavior and may or may not be thixotropic. For design of equipment to handle or process nonnewtonian fluids, the properties must usually be measured experimentally, since no generahzed relationships exist to pi e-dicl the properties or behavior of the fluids. Details of handling nonnewtonian fluids are described completely by Skelland (Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967). The generalized shear-stress rate-of-strain relationship for nonnewtonian fluids is given as... 

F(FG = normal (shear) component of force A = area u(w) = normal (shear) component of displacement o-(e ) = true tensile stress (nominal tensile strain) t(7) = true shear stress (true engineering shear strain) p(A) = external pressure (dilatation) v = Poisson s ratio = Young s modulus G = shear modulus K = bulk modulus. 

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

The radial (diametrical strain) will be the same as the circumferential strain e2. For any shell of revolution the dilation can be found by substituting the appropriate expressions for the circumferential and meridional stresses in equation 13.36. 

It can be seen by examination of equations 13.7 and 13.9, that for equal stress in the cylindrical section and hemispherical head of a vessel the thickness of the head need only be half that of the cylinder. However, as the dilation of the two parts would then be different, discontinuity stresses would be set up at the head and cylinder junction. For no difference in dilation between the two parts (equal diametrical strain) it can be shown that for steels (Poisson s ratio = 0.3) the ratio of the hemispherical head thickness to cylinder... 

The idea is simple consider a polycrystalline material that is subjected to locally varying strain. Then every crystal is probing its local strain by small compression or expansion of the lattice constant. The superposition of all these dilated lattices makes the observable line profiles - and as a function of order their breadth has to increase linearly. According to Kochendorfer the polycrystalline material becomes inhomogeneous or heterogeneous . 

Animal models have established that infections can induce autoimmune disease. For example, coxsackievirus B3 infection of susceptible strains of mice results in inflammation in the heart that resembles the myocarditis and dilated cardiomyopathy that occurs in humans.28 44 The same disease can be induced by injecting mice with cardiac myosin mixed with adjuvant, thereby reproducing the disease in the absence of virus infection, indicating that an active viral infection is not necessary for the development of autoimmune disease.9 29 44 Likewise, a number of autoimmune diseases can be... 

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