Strain response

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

A number of other indifferent stress rates have been used to obtain solutions to the simple shear problem, each of which provides a different shear stress-shear strain response which has no latitude, apart from the constant Lame coefficient /r, for representing nonlinearities in the response of various materials. These different solutions have prompted a discussion in the literature regarding which indifferent stress rate is the correct one to use for large deformations. 

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. 

Creep and Recovery Behaviour. Plastics exhibit a time-dependent strain response to a constant applied stress. This behaviour is called creep. In a similar fashion if the stress on a plastic is removed it exhibits a time dependent recovery of strain back towards its original dimensions. This is illustrated in... 

The most characteristic features of viscoelastic materials are that they exhibit a time dependent strain response to a constant stress (creep) and a time dependent stress response to a constant strain (relaxation). In addition when the... 

The simplest theoretical model proposed to predict the strain response to a complex stress history is the Boltzmann Superposition Principle. Basically this principle proposes that for a linear viscoelastic material, the strain response to a complex loading history is simply the algebraic sum of the strains due to each step in load. Implied in this principle is the idea that the behaviour of a plastic is a function of its entire loading history. There are two situations to consider. 

The predicted strain variation is shown in Fig. 2.43(b). The constant strain rates predicted in this diagram are a result of the Maxwell model used in this example to illustrate the use of the superposition principle. Of course superposition is not restricted to this simple model. It can be applied to any type of model or directly to the creep curves. The method also lends itself to a graphical solution as follows. If a stress is applied at zero time, then the creep curve will be the time dependent strain response predicted by equation (2.54). When a second stress, 0 2 is added then the new creep curve will be obtained by adding the creep due to 02 to the anticipated creep if stress a had remained... 

Fig. 2.44(b) Predicted strain response using Boltzmann s superposition principle... 

Show that for a viscoelastic material in which the modulus is given by (t) = At ", there will be a non-linear strain response to a linear increase in stress with time. 

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... 

Recovery is the strain response that occurs upon the removal of a stress or strain. The mechanics of the recovery process are illustrated in Fig. 2-34, using an idealized viscoelastic model. The extent of recovery is a function of the load s duration and time after load or strain release. In the example of recovery behavior shown in Fig. 2-34 for a polycarbonate at 23°C (73°F), samples were held under sustained stress for 1,000 hours, and then the stress was removed for the same amount of time. The creep and recovery strain measured for the duration of the test provided several significant points. 

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

Fig. 5. E.coU recA y.lux strain response on AR action (horizontal axis - concentration, M) the number of survived cells (A), the absolute intensity of bioluminescence (B), the relative...

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... 

The response of productivity to stress (Fig. 5) has the same form as the strain response (Fig. 1) and emphasises the major concern of agriculture and ecology in defining and (usually) reducing the plastic residual strain, the permanent productivity reduction. 

Table 10.4 summarizes the consistent responses, per Equation 10.1, of three elastomers that have been found to produce significantly large strain response. ... 

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... 

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