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Stress-strain behavior plots

The stress-strain curves for the two commercial samples and the Bl through B4 samples are plotted in Figure 17.9. The samples Bl, B3, and B6 are plotted with the commercial silica samples, showing the similarity in the stress-strain behavior (Figure 17.9a). As the primary particle size and... [Pg.513]

FIGURE 31.13 (a) Plot showing the stress-strain behavior of various irradiated rubbers, (b) Plot showing the variation of tensile strength and modulus of rubbers irradiated with different doses, (c) Plot showing the variation of hysteresis loss, set, and elongation at break of irradiated fluorocarbon rubbers. (From Banik, I. and Bhowmick, A.K., Radial. Phys. Chem., 54, 135, 1999. With permission.)... [Pg.902]

Several stress-strain plots are shown in Fig. 1-10. Four important quantities characterize the stress-strain behavior of a polymer ... [Pg.33]

For both EPDM-LDH and XNBR-LDH nanocomposites, the various tensile properties are summarized in Table 13 and their typical stress-strain plots are shown in Fig. 58 [104]. In Fig. 58a, the gum vulcanizates of both rubber systems showed typical NR-like stress-strain behavior with a sharp upturn in the stress-strain plot after an apparent plateau region, indicating strain-induced crystallization. With the addition of LDH-C10 in the XNBR matrix, the stress value at all strains increased significantly, indicating that the matrix undergoes further curing (Fig. 58b). [Pg.161]

Other interesting features of elastomeric networks can be revealed using the plots of the reduced stress, crred = /( — -2) against inverse extension ratio 1. This can be analyzed from the stress-strain behavior described by a phenomenological expression suggested by Mooney [78] and Rivlin and Saunders [79] ... [Pg.300]

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. 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.
Young s Modulus. Young s moduli, E, for several resins are plotted vs. temperature in Fig. 7. Young s moduli were determined from stress-strain diagrams. At 4K, their values are within 10%. Therefore, the low-temperature values of E do not depend markedly on the detailed chemical structure. It must be emphasized that epoxy resins are energy-elastic and have a nearly linear stress-strain behavior to fracture at low temperatures. No rate dependence was found over several decades. This is not true for many high polymers, such as polyethylene (PE), which are not cross-linked. PE behaves viscoelastically, even at 4 K [%... [Pg.22]

Superposition techniques may also be used to correlate stress-strain behavior in the rubbery state. In their study of styrene-acrylonitrile copolymers filled with glass beads, Narkis and Nicolais (1971) obtained stress-strain curves at temperatures above 7. Stress-strain curves were plotted for different fractions of filler, and in terms of both the polymer and composite strain. At a given strain, the stress increased with increasing filler concentration, as expected. It was possible to shift curves of stress vs. polymer strain along the stress axis to produce a master curve (Figure 12.12). In addition to the empirical measurements, an attempt was made to calculate stress-strain curves from the strain-independent relaxation moduli (see Section 1.16 and Chapter 10) by integrating the following equation ... [Pg.395]

Fig. 8. (a) Stress-strain plot for a generalized Maxwell model to different strain rates, as depicted in figure. Plot shows nonlinear stress-strain behavior in spite of material model (Maxwell) following laws of linear viscoelasticity (see text), (b) Stress and strain data from different strain rates given in (a) divided by strain rate dy/dt, demonstrating that material model follows linear viscoelasticity (see text). [Pg.9078]

Figure 6. The initial slope of the toughness ratio versus the relative saturation strain, a, as a function of the initial hardening Ho/f-o, for a range of Poisson s ratio and m. The insert plots hysteresis loops in order to illustrate the dependence of the stress strain behavior on m. Figure 6. The initial slope of the toughness ratio versus the relative saturation strain, a, as a function of the initial hardening Ho/f-o, for a range of Poisson s ratio and m. The insert plots hysteresis loops in order to illustrate the dependence of the stress strain behavior on m.
Based on the load-strain and load-deflection measurements, PSZT exhibits non-linear stress-strain behavior. A plot of linear-elastically computed stress (or engineering stress) versus strain for poled-depoled specimens tested at room temperature, 75, 86, 105 and 120°C is shown in Fig. 3. Deviations from linear-elastic behavior initiate at a nominal stress level of approximately 20 30 MPa for specimens tested at room temperature and 10 20 MPa for specimens tested at an elevated temperature. Furthermore, the extent of non-linearity increases as the testing temperature increases. Conversion of the load-strain data to the true stress-strain behavior was achieved by implementing the approach first described by Nadai and adapted by Chen et al. ° The true compressive (o-c) and tensile stresses (at) were calculated as follows ... [Pg.576]

For most metallic materials, elastic deformation persists only to strains of about 0.005. As the material is deformed beyond this point, the stress is no longer proportional to strain (Hooke s law. Equation 6.5, ceases to be valid), and permanent, nonrecoverable, or plastic deformation occurs. Figure 6.10a plots schematically the tensile stress-strain behavior into the plastic region for a typical metal. The transition from elastic to plastic is a gradual one for most metals some curvature results at the onset of plastic deformation, which increases more rapidly with rising stress. [Pg.180]

Concept Check 6.3 Make a schematic plot showing the tensile engineering stress-strain behavior for a typical metal alloy to the point of fracture. Now superimpose on this plot a schematic compressive engineering stress-strain curve for the same alloy. Explain any differences between the two curves. [Pg.191]

Make schematic plots of the three characteristic stress-strain behaviors observed for polymeric materials. [Pg.581]

Figure 8 shows the temperature contour lines for the steady-state thermal analysis. Note the brick half-section was modeled with an element mesh of 9 elements across the width and 18 elements along the length. The element mesh chosen is typically based on the expected nonlinear stress-strain behavior of the refractory and the nonlinear compression-only behavior of the brick joint. In the case of castable systems, the circumferential width of the model is selected by trial solutions to determine the estimated maximum circumferential tensile stress that could be developed by the castable lining. Figure 8 is a line contour plot in which the letters on the contours represent a temperature at that location. Color contour plots are also available from most programs and provide a much better visualization of the temperature distribution, especially for more complicated temperature distributions. [Pg.381]

Fig. 21 is a plot that depicts the relative strengths of several features of a solder joint. In a properly fabricated joint, the intermetallic compounds are very strong and deform elastically, but should never fracture. In a tensile test, a properly formed high Pb/Sn solder joint always fails within the bulk solder which implies that the strengths of the interfaces depicted in Fig. 25 are greater than the strength of the solder. Note that the stress-strain behavior of only one interface is shown in Fig. 26. Although each interface shown in Fig. 25 exhibits a different stress-strain behavior, each must possess a tensile strength greater than the solder. If an interface in the structure is weaker than the solder, it will result in a brittle, planar failure in a tensile pull test. A change in fracture mode from plastic solder fracture to brittle elastic interface fracture is usually an indication that a terminal is defective. Lead-rich solders are usually weaker and more ductile than tin-based solders (Fig. 26). Fig. 21 is a plot that depicts the relative strengths of several features of a solder joint. In a properly fabricated joint, the intermetallic compounds are very strong and deform elastically, but should never fracture. In a tensile test, a properly formed high Pb/Sn solder joint always fails within the bulk solder which implies that the strengths of the interfaces depicted in Fig. 25 are greater than the strength of the solder. Note that the stress-strain behavior of only one interface is shown in Fig. 26. Although each interface shown in Fig. 25 exhibits a different stress-strain behavior, each must possess a tensile strength greater than the solder. If an interface in the structure is weaker than the solder, it will result in a brittle, planar failure in a tensile pull test. A change in fracture mode from plastic solder fracture to brittle elastic interface fracture is usually an indication that a terminal is defective. Lead-rich solders are usually weaker and more ductile than tin-based solders (Fig. 26).
The influence of the annealing process at a higher temperature was also studied, and important changes in the properties of a sample annealed at 55°C during 5 days (PTEB-CR sample) were observed [33]. The PTEB-CR specimens were stretched at 1 and 10 cm/min, but the behavior was similar in both cases. Typical stress-strain plots are shown in Fig. 14 for samples stretched at 23°C... [Pg.391]

Figure 3.3 shows representative stress-strain curves for a variety of polymeric materials. At normal use temperatures, such as room temperature, rigid polymers such as polystyrene (PS) exhibit a rapid increase in stress with increasing strain until sample failure. This behavior is typical of brittle polymers with weak interchain secondary bonding. As shown in the top curve in Figure 3.3, the initial stress-strain relation in such polymers is approximately linear and can be described in terms of Hooke s law, i.e., S = Ee, where E is Young s modulus, typically defined as the slope of the stress-strain plot. At higher stresses, the plot becomes nonlinear. The point at which this occurs is called the proportional limit. [Pg.39]

Let s start by looking at a simple polymer, polyethylene, that has a lot going on in its stress/strain plots (Figure 13-38). Flexible, semi-crystalline polymers such as this (where the T of the amorphous domains is below room temperature) usually display a considerable amount of yielding or cold-drawing, as long as they are not stretched too quickly. For small deformations, Hookean elastic-type behavior (more or less) is observed, but beyond what is called the yield point irreversible deformation occurs. [Pg.422]

FIGURE 12.11 Improvements of the mechanical properties of three-dimensional reinforced CMCs by hybrid infiltration routes (a) R.T. flexural stress-strain plots for a three-dimensional carbon fiber reinforced composite before and after cycles of infiltration (comparison between eight cycles with zirconium propoxide and fonr cycles pins a last infiltration with aluminum-silicon ester (b) plot of the mechanical strength as a fnnction of the final open porosity for composites and matrix of equivalent porosity, before and after infiltration (Reprinted from Colomban, R and Wey, M., Sol-gel control of the matrix net-shape sintering in 3D reinforced ceramic matrix composites, J. Eur. Ceram. Soc., 17, 1475, 1997. With permission from Elsevier) (c) R.T. tensile behavior (d) comparison of the R.T. mechanical strength after thermal treatments at various temperatures. (Reprinted from Colomban, R, Tailoring of the nano/microstructure of heterogeneous ceramics by sol-gel routes, Ceram. Trans., 95, 243, 1998. With permission from The American Ceramic Society.)... [Pg.106]

From a plot of true stress-true strain behavior on logarithmic coordinates K and n can be found where K is determined by extrapolating the curve to unit strain value while the /(is defined by the slope of the plastic region. [Pg.312]


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