Stress-strain behavior plastics

The properties of the lamina constituents, the fibers and the matrix, have been only briefly discussed so far. Their stress-strain behavior is typified as one of the four classes depicted in Figure 1-8. Fibers generally exhibit linear elastic behavior, although reinforcing steel bars in concrete are more nearly elastic-pertectly plastic. Aluminum, as well as... 

Let s address the issue of nonlinear material behavior, i.e., nonlinear stress-strain behavior. Where does this nonlinear material behavior come from Generally, any of the matrix-dominated properties will exhibit some degree of material nonlinearity because a matrix material is generally a plastic material, such as a resin or even a metal in a metal-matrix composite. For example, in a boron-aluminum composite material, recognize that the aluminum matrix is a metal with an inherently nonlinear stress-strain curve. Thus, the matrix-dominated properties, 3 and Gj2i generally have some level of nonlinear stress-strain curve. 

This stress-strain behavior is consistent with the optic metallographic data which evidenced partial redistribution of hydrogen over the powder particles when the compacting temperature was increased to 400°C and uniform hydrogen distribution on additional annealing or during plastic deformation at T > 500°C. 

Brittleness Brittle materials exhibit tensile stress-strain behavior different from that illustrated in Fig. 2-13. Specimens of such materials fracture without appreciable material yielding. Thus, the tensile stress-strain curves of brittle materials often show relatively little deviation from the initial linearity, relatively low strain at failure, and no point of zero slope. Different materials may exhibit significantly different tensile stress-strain behavior when exposed to different factors such as the same temperature and strain rate or at different temperatures. Tensile stress-strain data obtained per ASTM for several plastics at room temperature are shown in Table 2-3. 

Test rate and property The test rate or cross-head rate is the speed at which the movable cross-member of a testing machine moves in relation to the fixed cross-member. The speed of such tests is typically reported in cm/min. (in./min.). An increase in strain rate typically results in an increase yield point and ultimate strength. Figure 2-14 provides examples of the different test rates and temperatures on basic tensile stress-strain behaviors of plastics where (a) is at different testing rates per ASTM D 638 for a polycarbonate, (b) is the effects of tensile test-... 

The stress-strain behavior of plastics in flexure generally follows from the behavior observed in tension and compression for either unreinforced or reinforced plastics. The flexural modulus of elasticity is nominally the average between the tension and compression moduli. The flexural yield point is generally that which is observed in tension, but this is not easily discerned, because the strain gradient in the flexural RP sample essentially eliminates any abrupt change in the flexural stress-strain relationship when the extreme fibers start to yield. 

The majority of tests to evaluate the characteristics of plastics are performed in tension or flexure hence, the compressive stress-strain behavior of many plastics is not well described. Generally, the behavior in compression is different from that in tension, but the stress-strain response in compression is usually close enough to that of tension so that possible differences can be neglected (Fig. 2-19). The compression modulus is not always reported, since defining a stress at... 

This information is supported by stress-strain behavior data collected in actual materials evaluations. With computers the finite element method (FEA) has greatly enhanced the capability of the structural analyst to calculate displacement, strain, and stress values in complicated plastic structures subjected to arbitrary loading conditions (Chapter 2). FEA techniques have made analyses much more precise, resulting in better and more optimum designs. 

When compared to unreinforced plastics, the analysis and design of RPs is simpler in some respects and perhaps more complicated in others. Simplifications are possible since the stress-strain behavior of RPs is frequently... 

Figures 4 and 5 show the stress-strain behavior of reinforced elastomers and toughened plastics, respectively. In each case, the corresponding homopolymers are included for comparison. In...

FIGURE 14.6 Typical stress-strain behavior for fibers, plastics, and elastomers. 

FIGURE 14.9 Influence of temperature on the stress-strain behavior of a sample of poly(methyl methacrylate). (Modeled after Carswell, T.S. and Nason, H.K. Effects of Environmental Conditions on the Mechanical Properties of Organic Plastics, 1944. Copyright, ASTM, Philadelphia, PA. With permission.)... 

Fig. 10.60 Compressive stress-strain behavior of PS and LLDPE at 25°C and crosshead speed of 25.4 mm/min. At a compressive stress level of 20 MPa the deformation of the soft LLDPE is large, in the dissipative region and nearly twenty times the PS deformation, which is of the order of 0.04, in the elastic nondissipative range. [Reprinted by permission from B. Qian, D. B. Todd, and C. G. Gogos, Plastic Energy Dissipation (PED) and its Role in Heating/Melting of Single Component Polymers and Multi-component Polymer Blends, Adv. Polym. Techn., 22, 85-95 (2003).]...

We will use readily available plastic films to demonstrate stress-strain behavior. Students should be able to relate the physical behavior of thin films to the concepts of orientation and crystallinity. They should be able to explain terms such as cold drawing, yielding, and machine and transverse directions. 

Butter, and other unctuous materials, may be qualitatively described by a modified Bingham body (Elliott and Ganz, 1971 Elliott and Green, 1972), which consists of viscous, plastic and elastic elements in series. The stress-strain behavior for the model proposed by Elliot and Ganz (1971) is shown in Figure 7.12B. Diener and Heldman (1968) proposed a more complex model to describe how butter behaves when a low level of strain is applied. The model consists of plastic and viscous elements in parallel, coupled in series with a viscous element in parallel with a combination of a viscous and an elastic element. Figure 7.12C shows the stress-strain curve for... 

A plastic material is defined as one that does not undergo a permanent deformation until a certain yield stress has been exceeded. A perfectly plastic body showing no elasticity would have the stress-strain behavior depicted in Figure 8-15. Under influence of a small stress, no deformation occurs when the stress is increased, the material will suddenly start to flow at applied stress a(t (the yield stress). The material will then continue to flow at the same stress until this is removed the material retains its total deformation. In reality, few bodies are perfectly plastic rather, they are plasto-elastic or plasto-viscoelastic. The mechanical model used to represent a plastic body, also called a St. Venant body, is a friction element. The... 

Figure 10.2. Stress-strain behavior. With elastic (reversible) deformation, stress and strain are linearly proportional in most materials (exceptions include polymers and concrete). With plastic (permanent) deformation, the stress-strain relationship is nonlinear.

Before concluding this discussion of cell walls, we note that the case of elasticity or reversible deformability is only one extreme of stress-strain behavior. At the opposite extreme is plastic (irreversible) extension. If the amount of strain is directly proportional to the time that a certain stress is applied, and if the strain persists when the stress is removed, we have viscous flow. The cell wall exhibits intermediate properties and is said to be viscoelastic. When a stress is applied to a viscoelastic material, the resulting strain is approximately proportional to the logarithm of time. Such extension is partly elastic (reversible) and partly plastic (irreversible). Underlying the viscoelastic behavior of the cell wall are the crosslinks between the various polymers. For example, if a bond from one cellulose microfibril to another is broken while the cell wall is under tension, a new bond may form in a less strained configuration, leading to an irreversible or plastic extension of the cell wall. The quantity responsible for the tension in the cell wall — which in turn leads to such viscoelastic extension — is the hydrostatic pressure within the cell. 

The influence of temperature on the stress-strain behavior of polymers is generally opposite to that of straining rates. This is not surprising in view of the correspondence of time and temperature in the linear viscoelastic region (Section I l.5.2.iii). The curves in Fig. 11-23 are representative of the behavior of a partially crystalline plastic. 

Polymers which yield extensively under stress exhibit nonlinear stress-strain behavior. This invalidates the application of linear elastic fracture mechanics. It is usually assumed that the LEFM approach can be used if the size of the plastic zone is small compared to the dimensions of the object. Alternative concepts have been proposed for rating the fracture resistance of tougher polymers, like polyolelins, but empirical pendulum impact or dart drop tests are deeply entrenched forjudging such behavior. 

An effort to investigate the kinematics of plastic deformation in glassy atactic polypropylene was presented by Mott, Argon, and Suter.Using an atomistic simulation for strains up to 20%, the authors observed that the plastic rearrangement of the structure was revealed in the microstructural stress—strain behavior (i.e., smooth reversible portions bounded by irreversible sharp drops in the stress values). 

The load-displacement curves for C(T) tests of the neat EpoxyH were almost linear until the final unstable fracture. The fracture toughness value in 77K-LNj was 210 J/m and that in RT-air was 120 J/m. Thus the toughness increased by 1.8 times by changing the test environment from RT-air to 77K-LN. Brown and co-workers have found that amorphous polymers crazed in 77K-LNj, but not in a helium or vacuum at about 78K [20-22]. They have also reported that the stress-strain behavior of all polymers, amorphous and crystalline, is affected by at low temperatures [22]. Kneifel has reported that the fracture toughness of epoxy in 77K-LNj is higher than that in RT-air and 5K, and that the reason for this is the reduced notch effect by plastic deformation [23]. Then, the increase of the fracture toughness of the neat EpoxyH in this study is probably caused by the similar effect. 

Figure 4. Model of elastic-plastic, stress-strain behavior of the epoxy resin.

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