Elastic stress, experimental

If the elastic modulus is obtained from the slope of the elastic stress-strain curve, then we can evaluate the first term on the right-hand side in Equation (8.3) from experimental data elastic stress-strain curves. The second term on the right-hand side in Equation (8.3) can be evaluated from the product of the strain rate, which is set in a constant strain-rate experiment, and the viscosity. As we discussed in Chapter 3, the viscosity of a macromolecule is related to the shape factor v, therefore we can evaluate the second term on the right-hand side of Equation (8.3) from the product of the shape factor and the strain rate. 

According to Eqs. (13.145) and (13.148) the fracture stress in plane strain is a factor 1 /(1-v2) 1 /0.84 1.2 higher than in plane stress. Experimentally, however, the difference is much bigger. The reason for this discrepancy is that Griffith s equations were developed in linear fracture mechanics, which is based on the results of linear elasticity theory where the strains are supposed to be infinitesimal and proportional to the stress. 

A combination of Eqs. (13.167) and (13.168) yields the typical concave shape of the elastic stress-strain curve of well-oriented fibres. In Fig. 13.98 the calculated stress-strain curve is compared with the experimental curve at decreasing stress of a Twaron 1000 fibre. It shows almost elastic behaviour. By including the simple theory the tensile curve with yield can be calculated as shown in Fig. 13.99. 

Northolt and Van der Hout (1985) originally derived theoretical (and experimentally confirmed) expressions for the modulus and the elastic stress-strain relation for aramids and similar fibres. 

Hie core structures of dislocations are more important during ordinary dissolution than the elastic stress fields. While this conclusion might not be true for very low undersaturations, experimental evidence indicates that it is true for moderate undersaturations. Evidence indicates that dissolution inhibitors act by chemisorbing at specific surface sites namely, at kinks in crystallographic surface steps. 

In flow the challenge has been to write convincing equations that couple concentration and composition gradients to elastic stresses and the bulk flow field. When done within a two-fluid model for polymer solutions transitions in light-scattering patterns seen in experiment may be explained. Extensions to polymer blends are potential candidates as explanations of shear-induced shifts of the spinodal and biphasic islands seen experimentally. - ... 

It is straightforward to imagine protein conformational changes that couple to the stress of a frustrated monolayer elastic curvature. The experiments described in the preceding sections demonstrate that there is an energetically significant elastic stress locked into the leaflets of a lamellar bilayer near to a lamellar-nonlamellar phase transition. Experimentally, bilayers near to a lamellar-nonlamellar transition means that relatively... 

A comparison of both calculated from Equation (9.3) and experimental lAnI values as a function of A, for PMMA is shown in Figure 9.1. The calculations were conducted at Vp = Vbh, V(, ,p = Vd = 0 and k = 0, since the experimental data were obtained at 135 °C, i.e., at T > Tg (Tg 105 °C for PMMA [24]). This figure reveals sufficiently good mutual agreement of both data. A fractal conception of rubber-like elasticity has been put forward by Balankin [27]. The stress F depends on it from the modulus of elasticity stress E as ... 

In this expression, k is a constant equal to about 0.5 nm, corresponding to a mean intermolecular distance when only physical interactions (dispersive and acid-base interactions) are involved and Ef are the elastic moduli of the matrix and the fiber, respectively. This model is equivalent to that of Gent and Schultz [3,4] for a cylindrical geometry and in the case of pure elastic stress transfer between both materials. It is very well verified experimentally for various fiber-matrix systems. The infiuence of the formation of interfacial layers exhibiting mechanical behavior completely different from that of the bulk matrix has also been examined [31]. 

Figure 3. Indentation stress strain relationships for glass ceramic. Dashed line shows the expected Hertzian elastic response. Experimental results are shown for the coarse (10p.m grain size), medium (5 pm) and fine (2 jm) microstructures. The larger the grains, the more deviation from the elastic response.

In this equation, essentially similar to the condition for cracking of a lap joint or removal of a film by applying a compression (Fig. 10b), W is the work of adhesion, E is the Young modulus of the film, d its thickness and e the residual elastic strain (or o the elastic stress) in the coating. Experimental results confirmed this theory for elastomers adhering to glass. For biaxial tension, is replaced by cr ( 1 - v ), where v is the Poisson ratio. 

In AD2000 code [9], there is the possibility to evaluate the results of an FE analysis based on Chapter S4 Estimation of stresses based on computed and experimental strength analysis. Chapter S4 describes basically the elastic stress analysis method Stresses are determined using an elastic analysis, classified into categories, and limited to allowable values that have been conservatively established so that a plastic collapse will not occur for thick-walled components, the plastic analysis methods are more adequate. In Chapter S4 [9], there is no guideline for such an analysis, but the application is not forbidden. 

Fig. 1.13 S-N curve obtained for austenitic stainless steel type 304 B. S is the equivalent ideally elastic stress amplitude. Open circles are experimental data points...

A characteristic property of polymers is the ability to be stretched (strained) when a force is applied (stress). Experimental measurements of this ability is complicated by the fact that in practice, polymers are not highly ordered. The limiting elastic modulus (strain/stress) is inferred by measuring the moduli of polymers of increasing crystallinity, and extrapolating to 100% crystalline polymer. 

Theoretically, the dimensionality for elasticity, stress and hardness is identical in Pascal unit (energy density) but at different states. The ideal form represents the intrinsic property change without experimental artifacts being involved. However, the softening and the slope transition in the IHPR plastic deformation arises from the extrinsic competition between activation of and resistance to glide dislocations, which is absent in the elastic deformation in particular using the non-contact measurement such as SWA techniques and Raman measurements. 

Common experimental evidence shows that the viscosity of polymers varies as they flow. Under certain conditions however, elastic effects in a polymeric flow can be neglected. In these situations the extra stress is again expressed, explicitly, in terms of the rate of deformation as... 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

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