Stress-strain data for

Table 2-3 Examples of room temperature tensile stress-strain data for several plastics and other materials...

FIGURE 6.1 A set of consistent stress-strain data for P-plastomers with ethylene content between 8.2 wt% (highest) and 16.0 wt% (lowest). The data for P-plastomers with intermediate composition is intermediate within these extremes. 

Table IV lists the mechanical stress-strain data for a series of hybrid TEOS-PTMO materials containing different levels of Ti-isop in the starting reaction mixture. These materials, with the exception of the first one, were all made using a modified reaction scheme (see experimental section) in order to incorporate the titanium into the network. The starting reaction mixtures in all cases contained 50% by weight of the glass precursors (TEOS and Ti-isop) and 50% by weight of PTMO(2000) (endcapped with triethoxysilane). One set of samples without titanium was made in order to compare the effects of the reaction scheme on the observed mechanical properties.

Figure 11 shows plots according to equation(lO) of stress-strain data for triol-based polyester networks formed from the same reactants at three initial dilutions (0% solvent(bulk), 30% solvent and 65% solvent). Only the network from the most dilute reactions system has a strictly Gaussian stress-strain plot (C2 = 0), and the deviations from Gaussian behaviour shown by the other networks are not of the Mooney-Rivlin type. As indicated previously, they are more sensibly interpreted in terms of departures of the distribution of end-to-end vectors from Gaussian form. 

Studies have been made of the elastic (time-independent) properties of single-phase polyurethane elastomers, including those prepared from a diisocyanate, a triol, and a diol, such as dihydroxy-terminated poly (propylene oxide) (1,2), and also from dihydroxy-terminated polymers and a triisocyanate (3,4,5). In this paper, equilibrium stress-strain data for three polyurethane elastomers, carefully prepared and studied some years ago (6), are presented along with their shear moduli. For two of these elastomers, primarily, consideration is given to the contributions to the modulus of elastically active chains and topological interactions between such chains. Toward this end, the concentration of active chains, vc, is calculated from the sol fraction and the initial formulation which consisted of a diisocyanate, a triol, a dihydroxy-terminated polyether, and a small amount of monohydroxy polyether. As all active junctions are trifunctional, their concentration always... 

Calculations of cross-link density from stress-strain and volume-swelling measurements on supercontracted wool fibers immersed in solutions of LiBr (Haly, 1963a) gave values differing by factors of 3 to 4 from those calculated from the supercontraction data of Crewther (1964b). When extrapolated to zero disulfide content, the stress-strain data for wool fibers (Haly, 1963a) suggested that the cross-link density of the... 

Fig. 17a-d. Tensile stress-strain data for a) homopolystyrene b) original HIPS sample c) sample with large particles d) sample with small particles... 

Fig. 4 Tensile stress/strain data for the epoxy adhesives at specified average strain rates, at 23°C (a) XD1493 (b) XD4600 .

Tensile Properties. Stress-strain data for the M-E-23/25-48 series is shown in Figure 16. Elongations at break drop rapidly with lower DBTDL concentrations. Young s modulus was measured at about 42 MPa (6,000 psi). Similar results were obtained in samples of the M-B-40/15-49 series where Young s modulus in this case was ca. 60MPa (8,700 psi). 

Figures 13.16 and 13.17 are plots of the compressive stress-strain data for two amorphous and two crystalline polymers, respectively, while Figure 13.18 shows tensile and compressive stress-strain behavior of a normally brittle polymer (polystyrene). The stress-strain curves for the amorphous polymers are characteristic of the yield behavior of polymers. On the other hand, there are no clearly defined yield points for the crystalline polymers. In tension, polystyrene exhibited brittle failure, whereas in compression it behaved as a ductile polymer. The behavior of polystyrene typifies the general behavior of polymers. Tensile and compressive tests do not, as would normally be expected, give the same results. Strength and yield stress are generally higher in compression than in tension.

Figure 13.16 Compressive stress-strain data for two amorphous poiymers poiyvinyi chioride (PVC) and cellulose acetate (CA). (From Kaufman, H.S. and Falcetta, J.J., Eds., Introduction to Polymer Science and Technology, John Wiley Sons, New York, 1977. With permisson.)...

Two basically different stress-strain behaviors were observed. In Fig. 3, the 300 and 4.2 K stress-strain data for sample A-18 are shown on two different scales. Note the plastic behavior from almost zero strain, the high strain to failure, and the 50% increase in tensile strength from 300 to 4.2 K. Figure 4 illustrates... 

Frew, D. J., Forrestal, M. J., Chen, W. (2001). A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock materials. Experimental Mechanics, 41, 40-46. doi 10.1007/BF02323102... 

FIGURE 29.2. Comparison of typical stress-strain data for PDMS rubber [39] in a Mooney-Rivlin plot with Neo-Hookean and Mooney-Rivlin strain energy function descriptions. (See text for discussion). 

Table 20.9 Non-linearity by least squares analysis of stress strain data for single filaments, tows and unidirectional composites under the conditions of zero stress at zero strain...

This is a useful result, as it means that stress-strain data for load-unload cycles may be used to separate out bond-stretching and conformational contributions to the stress [61]. Thus we may evaluate them as follows, applying equation (4.16) to loading and unloading, and making use of equation (4.17), for any value of elongation where the above restrictions apply (particularly where stress transients can... 

Here X = L/Lo is the extension ratio of the sample. Note that the corresponding strain is = (L -Lo) /To = A - 1. The proportional factor G is the shear modulus of the sample. Equation (4) describes small deformation uniaxial data on polymer networks quite well. With a fit of experimental stress-strain data for low extensions it is possible to predict crosslink properties because the classical models show that the shear modulus G is proportional to both temperature and crosslink density Vc ... 

An alternative model which also describes stress-strain data for larger deformation is presented by the Mooney-Rivlin equation [40, 41], The equation describes the rubber elasticity of a polymer network on the basis that the elastomeric sample is incompressible and isotropic in its unstrained state and that the sample behaves as Hookean solid in simple shear. In a Mooney-Rivlin plot of a uniaxial deformation, the experimental measured stress cr, divided by a factor derived from classical models, is plotted as function of the reciprocal deformation 1/A ... 

The design engineer of plastic component parts needs more than just shortterm stress-strain data for anticipating long-term deformation behavior. For example, the useful service lifetime of the molded part is curtailed by onset of... 

Mechanical Properties. The tensile stress-strain behavior of ethylene-co-styrene polymers, including the effects of crystallinity and molecular weight, has been extensively reported and analyzed. Figure 5 presents tensile stress-strain data for a series of copolymers differing primarily in styrene content. The copolymers generally exhibit large strain at ruptiu e, and have been foimd to show uniform deformation behavior (46). 

Figure 3.11 Stress-strain data for natural rubber according to Mullins. The solid line is calculated by the Edwards and Vilgis theory using the parameters NcksT —1.2 MPa, NsksT — 2.1 MPa, t] = 0.2, a = = 7.5. (Reproduced with permission from Edwards and Vilgis,...

Figure 11-133. Tensile stress-strain data for Du Font s Zytel 101 nylon at 23°C (73 F).

Collecting stress-strain data for cyclic fatigue in the axial direction and recording the reduction in stiffness in both axial and circumferential directions it was possible to relate the effects of damage to the equivalent moduli A of the pipe to their undamaged values A by... 

Two techniques, direct shear and torsion, were used to test foam samples in shear as shown in Figs. 8.11 and 8.12. Tensile and shear stress strain data for HlOO foam are shown in Figs. 8.13 and 8.14, respectively. The initial slopes in those figures correspond to = 60 MPa and G = 21 MPa. Note that those values are averaged over a scatter of about 6%. It was also noted that stiffnesses increase monotoiucally toward the center of a 25 mm thick foam slab. 

Treloar, L.R.G. (1944) Stress-strain data for vulcanised rubber under various types of deformation. Trans. Faraday Soc., 40, 59. 

To return linear viscoelasticity, it is required that g(e) approaches unity for small strain. The stress-strain data for Smith s SBR vulcanisate rubber material are plotted in Figure 11.3(a). Log stress against log time plots were obtained for fixed strains and, as shown in Figure 11.3(b), form parallel linear relationships. This suggests via Equation (11.7) that the quantity g(e)/e is independent of time. It was found that for extension ratios up to 2, g(e) = 1 provided that a is understood to denote the true stress. At higher strains, the empirical function... 

The short-term stress-strain data for a plastic are of limited use and should only be used for preselection of material. In reality, plastic components are seldom designed for and subjected to such high levels of strain as applied in short-term tests. The product failure is brittle in nature. The longterm creep and fatigue properties are more important for structural applications. 

Plasticity. A number of authors, Ref 12 to 18, have reported on the stress-strain response of the Sn-Ag-Cu alloys. Unfortunately, most of the reported data are limited in either temperature range or strain rate, or both. Tests performed at slower strain rates tend to capture creep effects that are reflected in lower moduli, yield, and ultimate strengths when compared with faster strain rates. In particular. Ref 12,15, and 18 examine the effects of strain rate on the stress strain curve for the Sn-Ag-Cu alloy. The choice of stress-strain data for modeling purposes is governed by the choice of failure theory. When plasticity is combined with creep in the finite element analysis, the plasticity, i.e., the stress-strain data, should not include creep effects. Data obtained with strain rates of approximately 0.01/s or greater are recommended. In the case... 

References 9 and 12 present stress-strain data for the temperature range — 25 to 125 C (- 13 to 257 °F) at a consistent strain rate of 4.2 X 10 /s. The author has demonstrated success producing fatigue life predictions on leaded solder interconnects using the Coffin-Manson relation and Cole s data (Ref 19) which was taken at a similar strain rate, 6 X 10 /s. Reference 9 data is shown in Fig. 8 and used in select analysis examples that follow. Note that the elastic modulus at - 25 °C (- 13 °F) is lower than that at 25 °C (77 °F). Elastic modulus usually increases with decreasing temperature. Vianco notes that the material response may transition from linear elastic to elastic-plastic at 25 °C (77 °F) and the higher temperature data may reflect the simultaneous effects of work hardening and... 

Table 6.3 Tensile Stress-Strain Data for Several Hypothetical Metals to Be Used with Concept Checks 6.2 and 6.4...

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