Stress/strain responses

Young s modulus can be deterrnined by measuring the stress—strain response (static modulus), by measuring the resonant frequency of the body... 

Shock loading in most metals and alloys produces greater hardening than quasi-static deformation to the same total strain, particularly if the metal undergoes a polymorphic phase transition, such as is observed in pure iron [1]-[10]. Figure 6.1 compares the stress-strain response of an annealed... 

Figure 6.3. Stress-strain response of shock-loaded 6061-T6 A1 as a function of peak shock pressure showing minimal shock strengthening.

Figure 6.14 shows the reload compressive stress-strain response of shock-loaded copper as a function of pulse duration [40]. For copper shock loaded to 10 GPa the yield strength is observed to increase with increasing pulse... 

Figure 6.14. Stress-strain response of copper shock loaded to 10 GPa as a function of duration.

Perhaps the most significant complication in the interpretation of nanoscale adhesion and mechanical properties measurements is the fact that the contact sizes are below the optical limit ( 1 t,im). Macroscopic adhesion studies and mechanical property measurements often rely on optical observations of the contact, and many of the contact mechanics models are formulated around direct measurement of the contact area or radius as a function of experimentally controlled parameters, such as load or displacement. In studies of colloids, scanning electron microscopy (SEM) has been used to view particle/surface contact sizes from the side to measure contact radius [3]. However, such a configuration is not easily employed in AFM and nanoindentation studies, and undesirable surface interactions from charging or contamination may arise. For adhesion studies (e.g. Johnson-Kendall-Roberts (JKR) [4] and probe-tack tests [5,6]), the probe/sample contact area is monitored as a function of load or displacement. This allows evaluation of load/area or even stress/strain response [7] as well as comparison to and development of contact mechanics theories. Area measurements are also important in traditional indentation experiments, where hardness is determined by measuring the residual contact area of the deformation optically [8J. For micro- and nanoscale studies, the dimensions of both the contact and residual deformation (if any) are below the optical limit. 

The Bowyer and Bader [96] methodology can be used to predict stress-strain response of short fiber-rein-forced plastics. The stress on the composite (cT( ) at a given strain can be computed by fitting the response to a form of Eq. (4) with two parameters, the fiber orientation factor (Cfl) and interfacial shear strength (t,). 

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... 

Berkovits, A., Relationship Between Fatigue Life in the Creep Fatigue Region Stress-Strain Response, NASA, 1988. 

The mechanical concepts of stress are outlined in Fig. 1, with the axes reversed from that employed by mechanical engineers. The three salient features of a stress-strain response curve are shown in Fig. la. Initial increases in stress cause small strains but beyond a threshold, the yield stress, increasing stress causes ever increasing strains until the ultimate stress, at which point fracture occurs. The concept of the yield stress is more clearly realised when material is subjected to a stress and then relaxed to zero stress (Fig. Ih). In this case a strain is developed but is reversed perfectly - elastically - to zero strain at zero stress. In contrast, when the applied stress exceeds the yield stress (Fig. Ic) and the stress relaxes to zero, the strain does not return to zero. The material has irreversibly -plastically - extended. The extent of this plastic strain defines the residual strain. 

The two features of elasticity and plasticity are the key features of stress-strain responses. The responses are dynamic and they may be totally or incompletely reversible, totally irreversible and also sensitive to various... 

The aim for tree breeders and forest managers is to define and grow a plantation which will be elastic in its response to the large stresses induced by high wind speeds. Petty Swain (1985) have established models of the stress-strain responses of forest trees which may be used to define the sizes and morphologies of trees, for a defined range of wind speeds and elastic responses. A typical response of a plantation grown spruce tree to wind speed is shown on Fig. 2. This is a classic stress/strain curve, with an... 

FIGURE 11.18 Tensile stress-strain responses of polypropylene/styrene-butadiene rubber (PP-SBR) blends at several ratios (where LL is linear low molecular weight LH is linear high molecular weight BL is branched low molecular weight and BH is branched high molecular weight). (From Cook, R.F., Koester, K.J., Macosko, C.W., and Ajbani, M., Polym. Eng. Sci., 45, 1487, 2005.)... 

The stress-strain response of ideal networks under uniaxial compression or extension is characterized as follows ... 

In Chapter 4, the response of these models to dynamic (i.e., sinusoidal) loads or strains is illustrated. In Chapter 5, the stress-strain response in constant rate experiments is described. Models with nonlinear springs and nonlinear dashpots (i.e., stress not proportional to strain or to strain rate)... 

Orientation effects are strongly coupled to nonlinear behavior, discussed in Section V, and the stress-strain response discussed in Chapter 5, Orientation makes an initially isotropic polymer anisotropic so that five or nine modulus/compliance values arc required to describe the linear response instead of two, as discussed in Chapter 2. For an initially anisotropic polymer the various modulus/compliance components can be altered by the orientation. It may not be necessary to know all components for an... 

ASTM D 3518 (1991). Practice for in-plane shear stress-strain response of unidirectional reinforced plastics. 

Petit, P.H. (1969). A simplified method of determining the in-plane shear stress-strain response of unidirectional composites. In Composite Materials Testing and Design, ASTM STP 460, ASTM, Philadelphia, PA, pp. 83-93. 

Figure 5.67 Influence of temperature on the stress-strain response of (a) cellulose acetate and (b) poly(methyl methacrylate). Reprinted, by permission, from J. M. G. Cowie, Polymers Chemistry Physics of Modem Materials, 2nd ed., p. 283. Copyright 1991 by J. M. G. Cowie.

Thus, this consideration shows that the thermoelasticity of the majority of the new models is considerably more complex than that of the phantom networks. However, the new models contain temperature-dependent parameters which are difficult to relate to molecular characteristics of a real rubber-elastic body. It is necessary to note that recent analysis by Gottlieb and Gaylord 63> has demonstrated that only the Gaylord tube model and the Flory constrained junction fluctuation model agree well with the experimental data on the uniaxial stress-strain response. On the other hand, their analysis has shown that all of the existing molecular theories cannot satisfactorily describe swelling behaviour with a physically reasonable set of parameters. The thermoelastic behaviour of the new models has not yet been analysed. 

Stern model in interface studies, 626 Stokes law, in emulsion creaming, 601 Storage, of emulsions, stability test, 591-594, 597-598, 604-606 Straight-phase HPLC, lipoxygenase activity measurement, 411-412 Strain response, see Stress/strain responses... 

Stress/strain responses, emulsion stability, 591 -592 (figs.)... 

Figure 5 shows the stress-strain responses of an MEA with Nation (NR-111) membrane tested at 25°C and with four RH levels. 

When an elastic material is stressed, there is an immediate strain response. The classical representation of stress strain response in a perfectly elastic material is schematically represented in Fig. 2.1. 

Fig. 2.7 Stress-Strain response for a viscoelastic material (Newtonian behavior). (From ref. [7])...

Fig. E11.2c Extensional stress-strain response of the PE-GMA, PE-MAH, and 256 multilayer films at 140°C and extension rate of 0.1 s. [Reproduced by permission from T. Saito and C. W. Macosko, Interfacial Cross-linking and Diffusion via Extensional Rheometry, Polym. Eng. Sci., 42, 1-9 (2002).]...

Another important result from the atomistic simulations was that the stress-strain response of a region of material around an interface that debonded could be represented by an elastic fracture analysis at the next higher size scale if the interface was assumed to be larger than 40 A. Hence, an elastic fracture criterion was used in the microscale finite element analysis, which focused on void-crack... 

Examples of the overall stress-strain response are summarized in Fig. 1.34. In practice, the stresses at which these cracks evolve may be larger, because the formation of cracks, at stresses above crT, depends on the availability of flaws in the 90° plies. 

Fig. 1.34 Simulated stress-strain response for a 2-D CMC subject to tunnel cracking.

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