Elastic modulus experimental values

The comparison of experimental i and calculated according to the equation (12) elasticity modulus values for the studied HDPE has been adduced in Fig. 9.1. As one can see, the good correspondence between theoiy and experiment is obtained (the average discrepancy between E and E7 does not exceed 6%, that is, comparable with an error of elasticity modulus experimental determination). 

As the estimations have shown [26], the theoretical values E E7) are a little smaller than elasticity modulus experimental magnitudes. This assumes one more structural factor availability, influencing on the value E. This factor can be traditional macromolecular binary hooking network, which can... 

The estimation of the elasticity modulus theoretical values of according to Equations 6.6 and 6.7 shows good correspondence with experimental values of E... 

Frenkel S computed the force required to shear two planes of atoms past each other in a perfect crystal and showed that the critical yield stress (or elastic limit) is of the order G/ln, where G is the shear modulus. Experimental values of the elastic limit are 1(X)-1(K)0 times smaller than the above estimate. By considering the form of the interatomic forces and other configurations of mechanical stability, the theoretical shear strength could be reduced to G/30, still well above the observed values in ordinary materials. It is now firmly established that crystalline imperfections, such as dislocations, microscopic cracks, and surface irregularities, are primarily the reasons for the observed mechanical weakness of crystalline solids. This aspect of the mechanical behavior of solids, including a discussion of strengthening mechanisms, is discussed in Volume 2, Chapter 7. In this section the chemical and structural aspects of mechanical behavior, i.e., bonding and crystal structure, are emphasized. 

The calculated and experimental values of the equilibrium lattice constant, bulk modulus and elastic stiffness constants across the M3X series are listed in Table I. With the exception of NiaGa, the calculated values of the elastic constants agree with the experimental values to within 30 %. The calculated elastic constants of NiaGa show a large discrepancy with the experimental values. Our calculated value of 2.49 for the bulk modulus for NiaGa, which agrees well with the FLAPW result of 2.24 differs substantially from experiment. The error in C44 of NiaGe is... 

To determine the crosslinking density from the equilibrium elastic modulus, Eq. (3.5) or some of its modifications are used. For example, this analysis has been performed for the PA Am-based hydrogels, both neutral [18] and polyelectrolyte [19,22,42,120,121]. For gels obtained by free-radical copolymerization, the network densities determined experimentally have been correlated with values calculated from the initial concentration of crosslinker. Figure 1 shows that the experimental molecular weight between crosslinks considerably exceeds the expected value in a wide range of monomer and crosslinker concentrations. These results as well as other data [19, 22, 42] point to various imperfections of the PAAm network structure. 

Table 10-3 Comparison of theoretically possible and actual experimental values for modulus of elasticity and tensile strength of various materials...

From these definitions one may corroborate the intention of HTS in chemistry and materials science. The total speed-up factor of this part of the R D (Research and Development) process, as stated earlier, is between 5 and 50, but contrary to most of the pharma applications true (semi-) quantitative answers will result. As a result, this approach is essentially applicable in any segment of R D. On the other hand, this approach requires methods of experimentation that have almost the same if not the same accuracy as in the traditional one-experiment-at-the time approach. This is key as (i) in process optimisation accuracy is key and (ii) in research, also in academic research, accuracy is important as some polymer properties do not span a wide range of values (e.g., the elastic modulus of amorphous polymers) or may depend critically on molecular weight distribution or molecular order. 

The experimental results have approximately the same shapes but are generally lower in value than the results obtained from Equation 1. The shape is a result of the stress being a function of the coefficient of expansion and the elastic modulus of the epoxy. The lower values indicate that the stress change predicted from the equation is larger than that of the experimental data. Again, it is the samples with the lower Tgs and moduli at high temperatures that are closest to the equation results. 

Fig. 20. Calculated and experimental (dotted and solid curves respectively) values of (1) elastic modulus (E) and (2) ultimate compression strength (crj versus phenolic microsphere concentration (C) in an epoxy syntactic foam at 23 °C 162)...

In addition to strength and WOF of FMs, the elastic behavior of these architectures should be considered. Simple brick models were proposed to accurately predict elastic properties of FMs [1, 24], Figure 1.8 shows the elastic modulus versus orientation for uniaxially aligned Si3N4/BN FMs with experimentally measured values, indicating that there is very good agreement between experiment and prediction. This prediction can be used for FMs with multiaxial architectures. 

Elastic and viscous stress-strain curves can be experimentally determined from incremental stress-strain curves measured on samples of different tendons. Typical elastic and viscous stress-strain curves for rat tail and turkey tendons are shown in Figures 7.4 and 7.5. For both types of tendons the curves at high strains are approximately linear. As we discuss in Chapter 8, the elastic modulus can be calculated for collagen, because most of the tendon is composed of collagen and water, by dividing the elastic slope by the collagen content of tendon. When this is done the value of the elastic modulus of collagen in tendon is somewhere between 7 and 9 GPA. 

QCM-D measurements that include dissipation allow a more accurate estimate of mass changes through application of Voigt model that takes into account the viscoelastic properties of the system. Modeling software QTools supphed by Q-Sense uses the full thick layer expressions to model the response. Here, this program has been used to estimate the mass, thickness, viscosity, and shear elastic modulus of the adsorbed pectin layer on BSA surface, with a best fit between the experimental and model/and D values. 

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... 

The question of whether microhardness is a property related to the elastic modulus E or the yield stress T is a problem which has been commented on by Bowman Bevis (1977). These authors found an experimental relationship between microhardness and modulus and/or yield stress for injection-moulded semicrystalline plastics. According to the classical theory of plasticity the expected microindentation hardness value for a Vickers indenter is approximately equal to three times the yield stress (Tabor s relation). This assumption is only valid for an ideally plastic solid showing sufficiently large deformation with no elastic strains. PE, as we have seen, can be considered to be a two-phase material. Therefore, one might anticipate a certain variation of the H/ T 3 ratio depending on the proportion of the compliant to the stiff phase. 

Figure 17. Variations of bulk properties derived from variations of the individual elastic constants of stishovite. (a) Bulk modulus (K) and shear modulus (G). Solid lines are the average of Reuss and Voigt limits the latter are shown as dotted lines (Voigt limit > Reuss limit), (b) Velocities of P (top) and S (lower) waves through a poly crystalline aggregate of stishovite. Circles indicate experimental values obtained by Li et al. (1996) at room pressure and 3GPa. After Carpenter et al. (2000a).

Fig.5 shows the calculated curvature and temperature evolution for an FGM deposit with thickness of about 180 im, which is consistent with the experimental results shown in Fig.4 except for the transient oscillations. Fig.6 (a) shows the calculated stress distributions in 2-layer and FGM deposits. The gradual stress variation in the FGM can be observed. In Fig.6 (b) effects of model parameters such as the substrate temperature and elastic modulus of YPSZ on the stress distribution in 2-layer deposits are demonstrated. As the substrate temperature is raised from 600 to 825K, the tensile stress in the NiCrAlY layer is significantly reduced. If a value of elastic modulus of 190GPa of a dense bulk material was used, the compressive residual stress in the YPSZ is excessively overestimated. This example clearly demonstrates the importance of using realistic values for modeling thermal and mechanical behavior of sprayed deposits. 

Figure 19 shows the dependence of the apparent elastic modulus on the quantity D. For the sake of comparison, results of compression measurements performed on both isotropic and anisotropic samples are shown. The composites contain Fe304 filler particles with concentration of 30wt%. In the case of isotropic samples, the apparent elastic modulus increases slightly within the experimental error of 5%. For anisotropic samples, the apparent modulus increases significantly under deformation up to the value D = 0.85. Above this value, the modulus does not change notably. 

---