Strain direction

The refractograp of figure 4 shows highly oriented micro cracks of a polystyrene sample. The orientation of the cracks is perpendicular to the mechanical strain direction. The X-ray refracted intensitiy can be interpreted as crack density, i.e. the inner surfaces within a unit volume. Changing the tilt angle (of polystyrene and polystyrene blend samples) with respect to the primary beam leads to significantly different distributions of crack orientation (Fig. 5). 

A useful approximation of B for a conical hopper is B = 22f/a, where a is the bulk density of the stored product. The apparatus for determining the properties of solids has been developed and is offered for sale by the consulting firm of Jenike and Johansen, Winchester, Massachusetts, which also performs these tests on a contract basis. The flow-factor FF tester, a constant-rate-of-strain, direct-shear-type machine, gives the locus of points for the FF cui ve as well as ( ), the... 

The uniaxially elongated NR vulcanizate with a = 4.0 formed line stmctures with several micrometers in width along the strain direction, as shown in Figure 21.12. It was evident from the series of observations with different a that there was a strong dependence of a on line-width change (data not... 

Hydrogen exchange studies have been extended to laiger aromatic systems in which ring strain directed regioselectivity toward p-selectivity is also observed. See refs. 26,28-30. 

The transition state of singlet carbene cycloaddition to alkenes involves an electrophilic approach of the vacant p orbital to the n bond of alkenes. By contrast, the first step of the triplet addition process may involve the in-plane a orbital of the carbene. As in the case of C—H insertion (see Section 5.1), the difference in the transition structure between the singlet and triplet cycloaddition becomes important in the intramolecular process, especially when approach to a double bond is restricted by ring strain. Direct photolysis of ( )-2-(2-butenyl)phenyldiazomethane (99) in the presence of methanol gives l-ethenyl-l,la,6,6fl-tetrahydrocycloprop [fljindene [100, 29%, (E/Z)= 10 1] and l-(2-butenyl)-2-(methoxymethyl)benzene (101, 67%). Triplet-sensitized photolysis results in a marked increase in the indene (52%, EjZ) = 1.3.T) at the expense of the ether formation (4%) (Scheme 9.30). On the other hand, direct photolysis of phenyldiazomethane in an equimolar mixture of... 

For a material strained in one direction, one may check that At/l equals the only nonzero strain component, when the z-direction and the measuring direction are chosen along the strain direction. 

Transmission electron microscopy (TEM) and birefringence studies of strained and/ or fractured epoxies have revealed more direct experimental evidence that molecular flow can occur in these glasses. Films of DGEBA-DETA ( 11 wt.- % DETA) epoxies, 1 pm thick, were strained directly in the electron microscope and the deformation processes were observed in bright-field TEM 73 110). Coarse craze fibrils yielded in-homogeneously by a process that involved the movement of indeformable 6-9 tan diameter, highly crosslinked molecular domains past one another. The material between such domains yielded and became thinner as plastic flow occurred. 

The ratio of any value of the stress to the corresponding value of the strain is called the modulus. It is a direct measure of a material s resistance to deformation. Only in the low-strain region of the curve are the stress and strain directly proportional to one another. Therefore, only in this region is the modulus a constant. 

Acena, J.L. et al. Strain-Directed Bridge Cleavage of (Phenylsulfonyl)-7-oxabicyclo[2.2.1]heptane Derivatives Application to the Total Synthesis of Carba-a-DL-glucopyranose. 3.1 1992 [100]... 

With homogeneous strain, the deformation is proportionately identical for each volume element of the body and for the body as a whole. Hence, the principal axes, to which the strain may be referred, remain mutually perpendicular during the deformation. Thus, a unit cube (with its edges parallel to the principal strain directions) in the unstrained body becomes a rectangular parallelepiped, or parallelogram, while a circle becomes an ellipse and a unit sphere becomes a triaxial ellipsoid. Homogeneous strain occurs in crystals subjected to small uniform temperature changes and in crystals subjected to hydrostatic pressure. 

It should be noted that for a polycrystal composed of cubic crystalhtes, the Voigt and Reuss approximations for the bulk modulus are equal to each other, as they should be since the bulk modulus represents a volume change but not shape change. Therefore, in a cube the deformation along the principal strain directions are the same. Hence, Eqs. 10.39 and 10.40 are equal and these equations also hold for an isotropic body. The... 

Some methods introduce strain directly by generating the new C-C bond in the cyclization step [3]. Wurtz-type cyclizations (modification by Miiller-Roscheisen... 

Rothwell, Martinson and Gorman have studied the formation of stress induced crazes in polymethyl methacrylate. The sample was initially stressed and held at a strain of 3.5 %. Upon relaxation, SAXS-patterns of 1.5 s were recorded using a linear photodiode detector array. A sequence of selected curves recorded in a plane parallel to the strain direction is shown in Fig. 49. The peak at h = 0.014 is probably due to an... 

Fig. 49. Scattered x-ray intensity curves versus angle parameter h, for a poJymethyl methacrylate sample during relaxation at constant strain. Data for the curves were obtained at the indicated times after the initial deformation of 3.5% and in a plane parallel to the strain direction...

Fig. 9.20 Evolution of the G band as a function of uniaxial strain. The spectra are measured with incident light polarized along the strain direction, collecting the scattered light with no analyzer. The magnitudes of the strain, ranging from 0% to 0.8%, are indicated on the right side of the spectra [18]...

Table 6.1. Microhardness perpendicular to the chain orientation (strain) direction H , indentation anisotropy at room temperature (25°C) AH, X-ray crystallinity Wc(WAXS), percentage of a and modifications (according to Tashiro et al, 1980) and crystal hardness of homo-PBT He stretched at various strains, s. 

Figure 9.26 FT-IR polarization spectra (— parallel and ---perpendicular to the strain direction) measured with a singleelement detector of the whole area (a) and with one pixel in the matrix area (b) and island area (c) of the 50% elongated PHB/PLA (50/50wt%) blend film. Reproduced with permission from Ref [53] 2008, ACS Publications.

Amplification products were obtained only for Bacillus cereus out of the microorganisms reported in Table 6, allowing their application in the selective detection of B. cereus strains directly in foods. 

Figure 8.33. CDF —z(r) of PEE 1000/43 at e = 0.88. The long-period peaks are pointing upward (a) long period to the next neighbor in straining direction (b) stronger long period to the closest neighbor (in oblique direction)...

The pressure is defined as the rate of change of energy with strain normalized to cell volume. For the thermal contribution this can be calculated by applying small strains to the cell and recalculating the thermal contribution to the free energy, giving rise to the thermal pressure in each strain direction ... 

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