Stress-strain behavior systems

Table 10-56 gives values for the modulus of elasticity for nonmetals however, no specific stress-limiting criteria or methods of stress analysis are presented. Stress-strain behavior of most nonmetals differs considerably from that of metals and is less well-defined for mathematic analysis. The piping system should be designed and laid out so that flexural stresses resulting from displacement due to expansion, contraction, and other movement are minimized. This concept requires special attention to supports, terminals, and other restraints. 

The general stress-strain behavior of our HBIB series has some similarity to those of the SBS block copolymers.(4) However, there are two prime differences between these two systems. 

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). 

The nano modified PDMS systems discussed have properties that enable a more confident prediction of ageing trends. The properties of the carborane modified system change in a linear fashion with radiation dose as opposed to the nonlinear trend observed for conventional particulate filled PDMS. The silica and carbon nano tubular systems display simplified mechanical properties. The reduction in Mullins effect or move to a more linear, less complex stress strain behavior, allows increased accuracy in property measurements. 

Figure 15. Stress-strain behavior of a typicai eiastic system, inciuding (A) yieid point, (B) eiastic iimit, (C) irreversibie deformation, and (D) fracture.

Stress is related to strain through constitutive equations. Metals and ceramics typically possess a direct relationship between stress and strain the elastic modulus (2) Polymers, however, may exhibit complex viscoelastic behavior, possessing characteristics of both liquids and solids (4.). Their stress-strain behavior depends on temperature, degree of cure, and thermal history the behavior is made even more complicated in curing systems since material properties change from a low molecular weight liquid to a highly crosslinked solid polymer (2). ... 

These properties are among the most important factors for the design of plastic parts and systems. In this section data for stress-strain behavior of PTFE in different modes and conditions are presented. Stress-strain curves for polytetrafluoroethylene are shown in Figs. 3.6 and 3.7 at various temperatures. 

Thermal Properties - Properties related to the effects of heat on physical systems such as materials and heat transport. The effects of heat include the effects on stmcture, geometry, performance, aging, stress-strain behavior, etc. 

A rigid foam is defined as one in which the polymer matrix exists in the crystalline state or, if amorphous, is below its Tg. Following from this, a flexible cellular polymer is a system in which the matrix polymer is above its Tg. According to this classification, most polyolefins, polystyrene, phenolic, polyycarbonate, polyphenylene oxide, and some polyurethane foams are rigid, whereas rubber foams, elastomeric polyurethanes, certain polyolefins, and plasticized PVC are flexible. Intermediate between these two extremes is a class of polymer foams known as semirigid. Their stress-strain behavior is, however, closer to that of flexible systems than to that exhibited by rigid cellular polymers. 

Figure 5.16 Stress-strain behavior for standard linear solid subjected to a sinusoidal stress. The system is elastic with a high modulus at very high frequencies and a lower modulus at low frequencies. At intermediate frequencies, hysteresis develops and the loss passes through a maximum.

The stress-strain behavior of ceramic polycrystals is substantially different from single crystals. The same dislocation processes proceed within the individual grains but these must be constrained by the deformation of the adjacent grains. This constraint increases the difficulty of plastic deformation in polycrystals compared to the respective single crystals. As seen in Chapter 2, a general strain must involve six components, but only five will be independent at constant volume (e,=constant). This implies that a material must have at least five independent slip systems before it can undergo an arbitrary strain. A slip system is independent if the same strain cannot be obtained from a combination of slip on other systems. The lack of a sufficient number of independent slip systems is the reason why ceramics that are ductile when stressed in certain orientations as single crystals are often brittle as polycrystals. This scarcity of slip systems also leads to the formation of stress concentrations and subsequent crack formation. Various mechanisms have been postulated for crack nucleation by the pile-up of dislocations, as shown in Fig. 6.24. In these examples, the dislocation pile-up at a boundary or slip-band intersection leads to a stress concentration that is sufficient to nucleate a crack. 

In this section, stress-strain behavior of typical rubber-plastic systems at low and high (impact) rates of static testing and under low-frequency... 

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