Strain crystallinity, dependence

An experimental relationship between the microhardness and elastic modulus (E) has been found for various PE materials with different crystallinity values (Flores et al.., 2000). It is important to realize that microhardness - the plastic deformation of crystals at high strains - primarily depends on the average thickness and perfection of the nanocrystals, whereas in the case of the modulus, the elastic response at low strains is dictated by the cooperative effects of both microphases, the crystalline lamellae and the amorphous layer reinforced by tie molecules. The... 

Nonlinear viscoelasticity is the behavior in which the relationship of stress, strain, and time are not linear so that the ratios of stress to strain are dependent on the value of stress. (The Boltzmann superposition principle does not hold). Such behavior is very common in plastic systems, non-linearity being found especially at high strains or in crystalline plastics. 

The major uses of XRD are identification of crystalline phases, determination of strain, crystalline orientation and size, epitaxial relationship, and the accurate determination of atomic positions (better then in electron diffraction). Because of the strong Z dependence of X-ray scattering, light elements are difficult to deal with, particularly in the presence of heavy elements. 

Other phases of Ca-P than ACP reveal a crystalline structure with characteristic peaks on XRD analysis. There is a broad range in crystal morphology depending on composition and preparation characteristics such as temperature, pH, impurity, and the presence of macromolecules. Impurities, as commonly occur in bone mineral, greatly influence crystallinity (reflecting crystal size and crystal strain) but depend on the type of substitution. For example, type B carbonated apatite (CO3 for PO4 substitution) has a lower crystallinity and increased solubility, whereas F substitution (F for OH) give the opposite effects due to a better fit of the F ion in the apatite crystal structure. 

Two principal approaches have been used to model the yield behaviour of polymers. The first approach addresses the temperature and strain-rate dependence of the yield stress in terms of the Eyring equation for thermally activated processes [39]. This approach has been applied to many amorphous and crystalline polymers (see Section 12.5.1) and links have been established with molecular relaxation processes determined by dynamic mechanical and dielectric measurements and with non-linear viscoelastic behaviour determined by creep and stress relaxation. The Eyring approach assumes that the yield process is velocity controlled, i.e. the yield process relates to existing thermally activated processes that are accelerated by the application of the yield stress to the point where the rate of plastic deformation reaches the applied macroscopic strain rate. This approach has... 

Ductile deformation requires an adequate flexibility of polymer chain segments in order to ensure plastic flow on the molecular level. It has been long known that macromoleculai- chain mobility is a crucial factor decisive for either brittle or ductile behavior of a polymer [93-95]. An increase in the yield stress of a polymer with a decrease of the temperature is caused by the decrease of macromoleculai chain mobility, and vice versa the yield stress can serve as a qualitative measure of macromolecular chain mobility. It was shown that the temperature and strain rate dependencies of the yield stress are described in terms of relaxation processes, similarly as in linear viscoelasticity. Also, the kinetic elements taking pai-t in yielding and in viscoelastic response of a polymer are similar segments of chains, part of crystallites, fragments of amorphous phase. However, in crystalline polymei-s above their glass transition temperature the yield stress is determined by the yield stress required for crystal deformation... 

Modified ETEE is less dense, tougher, and stiffer and exhibits a higher tensile strength and creep resistance than PTEE, PEA, or EEP resins. It is ductile, and displays in various compositions the characteristic of a nonlinear stress—strain relationship. Typical physical properties of Tef2el products are shown in Table 1 (24,25). Properties such as elongation and flex life depend on crystallinity, which is affected by the rate of crysta11i2ation values depend on fabrication conditions and melt cooling rates. 

For a fiber immersed in water, the ratio of the slopes of the stress—strain curve in these three regions is about 100 1 10. Whereas the apparent modulus of the fiber in the preyield region is both time- and water-dependent, the equiUbrium modulus (1.4 GPa) is independent of water content and corresponds to the modulus of the crystalline phase (32). The time-, temperature-, and water-dependence can be attributed to the viscoelastic properties of the matrix phase. 

The thorough and persistent work on precursor decay (the dependence of Hugoniot elastic limit on propagation distance) of Duvall s Washington State University group was successful in demonstrating that precursor attenuation was due to both stress relaxation and hydrodynamic attenuation. Typical data on crystalline LiF is shown in Fig. 2.7. Observed plastic strain... 

Mechanical properties of plastics are invariably time-dependent. Rheology of plastics involves plastics in all possible states from the molten state to the glassy or crystalline state (Chapter 6). The rheology of solid plastics within a range of small strains, within the range of linear viscoelasticity, has shown that mechanical behavior has often been successfully related to molecular structure. Studies in this area can have two objectives (1) mechanical characterization of... 

Crazing. This develops in such amorphous plastics as acrylics, PVCs, PS, and PCs as creep deformation enters the rupture phase. Crazes start sooner under high stress levels. Crazing occurs in crystalline plastics, but in those its onset is not readily visible. It also occurs in most fiber-reinforced plastics, at the time-dependent knee in the stress-strain curve. 

Microindentation hardness normally is measured by static penetration of the specimen with a standard indenter at a known force. After loading with a sharp indenter a residual surface impression is left on the flat test specimen. An adequate measure of the material hardness may be computed by dividing the peak contact load, P, by the projected area of impression1. The hardness, so defined, may be considered as an indicator of the irreversible deformation processes which characterize the material. The strain boundaries for plastic deformation, below the indenter are sensibly dependent, as we shall show below, on microstructural factors (crystal size and perfection, degree of crystallinity, etc). Indentation during a hardness test deforms only a small volumen element of the specimen (V 1011 nm3) (non destructive test). The rest acts as a constraint. Thus the contact stress between the indenter and the specimen is much greater than the compressive yield stress of the specimen (a factor of 3 higher). 

The physical and chemical characteristics of zinc oxide powders are known to affect cement formation (Smith, 1958 Norman et al., 1964 Crisp, Ambersley Wilson, 1980 Prosser Wilson, 1982). The rate of reaction depends on the source, preparation, particle size and surface moisture of the powder. Crystallinity and lattice strain have also been suggested as factors that may change the reactivity of zinc oxide powders towards eugenol (Smith, 1958). 

The diffraction lines due to the crystalline phases in the samples are modeled using the unit cell symmetry and size, in order to determine the Bragg peak positions 0q. Peak intensities (peak areas) are calculated according to the structure factors Fo (which depend on the unit cell composition, the atomic positions and the thermal factors). Peak shapes are described by some profile functions 0(2fi—2fio) (usually pseudo-Voigt and Pearson VII). Effects due to instrumental aberrations, uniform strain and preferred orientations and anisotropic broadening can be taken into account. 

Their crystallization behavior compares with natural rubber, as follows (1) their rate of crystallization is more rapid and (2) their amount of crystallinity is temperature dependent, but considerably less strain dependent. These experimental rubbers have excellent green strength and building tack. 

Figure 18 shows the percent crystallinity obtained by birefringence measurements for NR at various elongations as a function of temperature. The relative shapes of the curves in this Figure show the pronounced temperature and strain dependence on the strain induced crystallization of NR. Of particular importance is the relatively high amounts of crystallinity that develop at room temperature. 

Figure 19 shows the temperature dependence of the percent crystallinity for high trans SBR, prepared with a Ba-Li catalyst and containing 757. trans-1,4 content with 14 wt.7. styrene, at 3 extension ratios. The percent crystallinity that develops is temperature dependent, there being an increase in the amount of crystallinity with a decrease in temperature. However, the amount of crystallinity that develops is essentially independent of strain. The amount of crystallinity that develops at room temperature, regardless of the level of strain, is extremely small ( 9) ... 

LDPE affect the dynamic mechanical, as well as other material properties of these polymers. The similarity of the temperature dependence of E between our toluene cast HB film and the quenched LDPE (both of 40% crystallinity) in Figure 14A as compared to our quenched HB film (% crystallinity 30%) is another indication of the importance of the level of crystallinity on properties. (This topic has already been discussed in some length in the section on stress-strain behavior). 

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