Glass stress-strain behavior

Several experiments will now be described from which the foregoing basic stiffness and strength information can be obtained. For many, but not all, composite materials, the stress-strain behavior is linear from zero load to the ultimate or fracture load. Such linear behavior is typical for glass-epoxy composite materials and is quite reasonable for boron-epoxy and graphite-epoxy composite materials except for the shear behavior that is very nonlinear to fracture. 

The strength of the fiber-matrix interface is one of the key parameters responsible for the stress-strain behavior and damage tolerance of ceramic composites. Two different types of tests are available to measure the fiber-matrix interfacial properties in fiber-reinforced ceramic composites. The first is based on an indentation technique to either push the individual fiber into or through the matrix. The second test method relies on pulling a single fiber out of a matrix. These methods have been compared59 to one another for a glass matrix material, and yield similar results. 

Thermosets are polymeric materials which when heated form permanent network structures via the formation of intermolecular crosslinks. Whether the final product has a glass transition temperature, Tg, above or below room temperature, and therefore normally exists as an elastomer or a glass, it is, strictly speaking, a thermo-set. In practice, however, thermosets are identified as highly crosslinked polymers that are glassy and brittle at room temperature. These materials typically exhibit high moduli, near linear elastic stress-strain behavior, and poor resistance to fracture. 

FIGURE 15.12 (a) Comparison of the stress-strain behavior of the three grades of Kevlar, (b) Comparison of the tenacity of Kevlar fibers with glass, steel, polyester, and nylon as a function of percentage strain. (From Tanner, D. et al.. The Kevlar story, Angew. Chem. Int. Eld. Engl. Adv. Mater., 28, 649, 1989. With permission from Verlag Chemie.)... 

Substantial yielding can occur in response to loading beyond the ductility limit of approximate proportionality of most stress-to-strain in URPs. This action is referred to as ductility. Most RPs does not exhibit such behavior. However, the absence of ductility does not necessarily result in brittleness or lack of flexibility. For example, glass fiber-TS polyester RPs do not exhibit ductility in their stress-strain behavior, yet they are not brittle, have good flexibility, and do not shatter upon impact (Chapter 7). The RPs do not shatter upon impact like sheet glass. 

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 ... 

The effect of temperature on tensile stress-strain behavior of PSF is depicted in Figure 4. The resin continues to exhibit useful mechanical properties at temperatures up to 160°C imder prolonged or repeated thermal exposure. This temperature Umit is extended to about 180°C in PES and PPSF. The tensile and flexin-al properties as well as resistance to cracking in chemical environments can be substantially enhanced by the addition of fibrous reinforcements such as chopped glass fiber. Mechanical properties at room temperatme for glass fiber-reinforced polysulfone, polyethersulfone, and polyphenylsulfone are shown in Table 5. 

Avoiding structural failure can depend in part on the ability to predict performance for all types of materials (plastics, metals, glass, and so on). Design engineers have developed sophisticated computer methods for calculating stresses in complex structures using different materials. These computational methods have replaced the oversimplified models of materials behavior relied upon previously. The result is early comprehensive analysis of the effects of temperature, loading rate, environment, and material defects on structural reliability. This information is supported by stress-strain behavior data collected in actual materials evaluations (see Chapters 3-5). 

Fedors and Landel [103] point out that stress-strain behavior of swollen elastomers can be determined experimentally more conveniently by measurements in uniaxial compression than uniaxial extension. In extension, strains of the order of a few hundred percent are required whereas, in compression, strains of the order of only a few percent provide sufficient data for analysis. SBR-glass bead composites cured by means of dicumyl peroxide were used for stress-strain measurements to estimate the concentration of the eftective network chains per unit volume of ttie whole rubber. It was found that with decreasing volume fraction of the composite, tire effective network density decreased linearly at first and then rather rapidly in an unexpected and inexplicable manner. 

Boyce, M.C., Socrate, M. and Liana, P.G. (2000) Constitutive model for the finite deformation stress-strain behavior of poly(ethylene terephthalate) above the glass transition. Polymer, 41, 2183. 

Venkatai aman K S and Narayanan K S (1998) Energetics of collision between grinding media in ball mills and mechanochemical effects. Powder Technol 96 190-201. Nicolais L and Narkis M (1971) Stress-strain behavior of styrene-acryloiiitrile/glass bead composites in the glass region, Polym Eng Sci 11 194-199. 

Natural rubber (NR)-rectorite nanocomposite was prepared by co-coagulating NR latex and rectorite aqueous suspension. The TEM and XRD were employed to characterize the microstructure of the nanocomposite. The results showed that the nanocomposite exhibited a higher glass transition temperature, lower tan d peak value, and slightly broader glass transition region compared with pure NR. The gas barrier properties of the NR-rectorite nanocomposites were remarkably improved by the introduction of nano scale rectorite because of the increased tortuosity of the diffusive path for a penetrant molecule. The nanocomposites have a unique stress-strain behavior due to the reinforcement and the hindrance of rectorite layers to the tensile crystallization of NR [36]. 

The past decade has seen steadily growing activity in the detailed atomistic modeling of polymer melts and glasses using energy minimisation and molecular dynamics simulation.These studies have been aimed at achieving an atomistic level understanding of a variety of physical properties such as stress-strain behavior, diffusion of small solute molecules and local chain motions. Because of its relative simplicity, polyethylene has come under a... 

To give an example of what can be achieved in such simulations we discuss below the stress-strain behavior as observed in simulations of the model PE I of polyethylene at a range of temperatures in the glass and melt. The sample size was 1000 monomers formed into a single linear chain as described in Section 5.4. The coohng curve for these samples is shown in... 

Figure 12.31 Typical stress-strain behavior to fracture for aluminum oxide and glass.

D.R. Oakley and B.A. Proctor, Tensile stress-strain behavior of glass fiber reinforced cement composites , in A. Neville (ed.) Fibre Reinforoed Cement and Conorete, The Construction Press, Lancaster, England, 1975, pp. 347-359. 

Table 15.4 shows the work recoveiy of some fibers under different strains and in different humidities. Inorganic fibers, such as glass, have very high work recovery at a low strain of 1%. However, they break at moderate and high strains, and no work recoveiy can be measured. The work recovery of polymer fibers is lower than their elastic (strain) recoveiy due to the non-linear stress-strain behavior. In addition, the work recovery also is affected by both strain and humidify. 

---