Strain- versus-stress plot

FIGURE 11. Strain versus time plotted for a 2-D NicaIon /Al203 composite during thermal cycling between 1100 and 600°C in air with a simultaneously applied tensile stress. 

Figure 15.4 Comparative strain rate versus stress plot for silicon nitride ceramics crept under tension (solid symbols) and under compression (open symbols). The characteristic asymmetric behavior is clearly displayed. The experimental data are collected in Ref [9].

Figure 15.6 Experimental temperature-compensated strain rates versus stress plots for tensile creep of silicon nitride-based ceramics. The stress exponents n = 3 and n = 10 are...

Figure 15.14 Strain rate versus stress plots, at (n = 1) —> shear thickening (n < 1) transition, temperatures between 1500 and 1600°C,fora Note that the transition stress a is SiAION (83.73% Si3N4, 7.77% AIN, 3.73% approximately independent of the temperature.

For the geotextile to provide an effective reinforcement function, it should have not only a high tensile strength, but also a high tensile modulus so that its resistance to tensile loads generated within the soil occurs at sufficiently small strains to prevent excessive movement of the reinforced soil structure. It is self-evident that decreases in these properties with time (i.e. creep behaviour) must be low, and that the polymers used should have resistance to degradation by the soil. An estimate of the anticipated reduction in strength can be determined from an analysis of creep strain versus time plots for various stress levels and a suitable reduction factor applied. 

Generally, the corresponding creep strain versus time plots feature a sequence of three stages (1) of axial deformation for a test specimen under constant stress load ... 

Fig. 6.52 Strain rate versus stress plot. SP ybAlits, filled square 5G Mullite, open triangles 5C Mullite, filled triangles and 9G Mullite, open circles [40]. With kind permission of Elsevier...

Stress response t versus time for a step input in strain y. The Hookean solid (b) shows no stress relaxation the Newtonian fluid (c) relaxes as soon as the strain is constant, while the viscoelastic liquid or solid shows stress relaxation over a significant time. In a viscoelastic liquid the stress relaxes to zero, while for the viscoelastic solid it asymptotically approaches an equilibrium stress r,. A small overshoot is shown in the strain versus time plot (a). This is typical of actual control systems, which may require 0.01 second or more to stabilize (see Chapter 8). 

Concept Check 8.5 Superimpose on the same strain-versus-time plot schematic creep curves for both constant tensile stress and constant tensile load, and explain the differences in behavior. 

For a monolayer film, the stress-strain curve from Eqs. (103) and (106) is plotted in Fig. 15. For small shear strains (or stress) the stress-strain curve is linear (Hookean limit). At larger strains the stress-strain curve is increasingly nonlinear, eventually reaching a maximum stress at the yield point defined by = dT Id oLx x) = 0 or equivalently by c (q x4) = 0- The stress = where is the (experimentally accessible) static friction force [138]. By plotting T /Tlx versus o-x/o x shear-stress curves for various loads T x can be mapped onto a universal master curve irrespective of the number of strata [148]. Thus, for stresses (or strains) lower than those at the yield point the substrate sticks to the confined film while it can slip across the surface of the film otherwise so that the yield point separates the sticking from the slipping regime. By comparison with Eq. (106) it is also clear that at the yield point oo. 

Viscoelastic creep data can be presented by plotting the creep modulus (constant applied stress divided by total strain at a particular time) as a function of time [23-26], Below its critical stress, the viscoelastic creep modulus is independent of stress applied. A family of curves describing strain versus time response to various applied stress may be represented by a single viscoelastic creep modulus versus time curve if the applied stresses are below the material s critical stress value. 

F ure 3-14 Torque versus Time Plot with a Vane in Controlled Strain Operation Where the Maximum Torque is Used to Calculate the Yield Stress. 

The elongation in a sample is the extensional strain that has built up in a polymer undergoing tensile or pulling tests. It is usually reported as "elongation at break", the strain or distension that caused the polymer sample to snap. Modulus, G, is the proportionality eonstant between strain and stress in a sample. Mathematically, it is the slope of the plot of stress versus strain. 

The formation of an IKB can be divided into two stages, namely nucleation and growth [139]. The nucleation process is not well understood, but occasionally small plastic strains are required to nucleate them [140]. The present model considers IKB growth only from 2Pc to 2P the dislocation segment with radius 2Pc is presumed to pre-exist, or to be nucleated during pre-straining. The values of 2Pc are typically estimated from Eq. (6), assuming a = Ot, where Ot is a threshold stress. The latter is in turn obtained experimentally from Wj versus a plots [140]. 

The mechanical behaviour of polymeric materials is often characterised by their stress/strain properties. A tension stress is applied at a very slow rate to a piece of material, which usually has a standardised dumbbell shape, as illustrated in Figure 2.15. Elongation, i.e. strain, is measured until the sample breaks. The results are usually displayed as a plot of stress versus strain. The stress reported to the smallest section of the sample is expressed in newtons per square centimetre (N/cm ). The strain is usually expressed as the percentage of the original length of the sample (AL/L x 100). Some typical stress/ strain plots are shown in Figure 2.16. 

A typical jump test is shown in Fig. 9.44 of flow stress versus strain. The stress temperature is 1450 °C. The slopes of each line in Fig. 9.44b yield for m 0.5, meaning that the stress exponent of the strain rate is 2 this indicates the superplastic behavior of the zirconia-alumina-spinel composite under the test conditions of temperature and strain rate. In order to determine the activation energy, a plot of strain rate versus the inverse absolute temperature must be made (as in Fig. 9.44c). The average activation energy of PS-HEBM-SPS is 945 kJ/mol, which is much higher than that of the composite processed from nanopowder mixtures (622 kJ/mol). This should represent GBS, if the concept of superplasticity is the dominant mechanism of deformation. Table 9.1 summarizes the strain rates and various temperatures of two and/or three specimens. PS-SPS appears in the Table 9.1 as PS-SPS and is listed under column C. For the purpose of comparison, the flow-stress results for nanopowder mixtures are also listed in Table 9.1 and are smaller than those processed from PS powders with/without HEBM. 

In the abridged method of creep testing the tests are conducted at several different stress levels and at the contemplated operating temperature. The data are plotted as creep strain versus time for a family of stress levels, all run at constant temperature. The curves are plotted out to the laboratory test duration and then extrapolated to the required design life. 

Based on the load-strain and load-deflection measurements, PSZT exhibits non-linear stress-strain behavior. A plot of linear-elastically computed stress (or engineering stress) versus strain for poled-depoled specimens tested at room temperature, 75, 86, 105 and 120°C is shown in Fig. 3. Deviations from linear-elastic behavior initiate at a nominal stress level of approximately 20 30 MPa for specimens tested at room temperature and 10 20 MPa for specimens tested at an elevated temperature. Furthermore, the extent of non-linearity increases as the testing temperature increases. Conversion of the load-strain data to the true stress-strain behavior was achieved by implementing the approach first described by Nadai and adapted by Chen et al. ° The true compressive (o-c) and tensile stresses (at) were calculated as follows ... 

Creep tests are carried out by applying a weight or load to a polymer sample in a temperature-controlled environment. Most testing is carried out in tension, but compression, shear and flexure may be used if more applicable to service conditions. Creep testing can be carried out on some tensile testers, but, since data may need to be collected over periods of up to a year, dedicated equipment is normally used. Creep data will often be required over a wide range of conditions and test times. Five to ten different stress levels will be required to construct a family of creep curves, and elevated-temperature testing may also be required. Log-log plots of strain versus time are created and extrapolated to give curves to the time period required [25]. 

Fig. 15 Temperature dependence of creep. Stress is stepped between 2 and 10 MPa in a sample at 44 °C and 24 C. The 10 MPa stress is held for 10 min at 44 °C and 100 min at 24 °C, after which stress is returned to 2 MPa. The top plot is the strain versus time the bottom plot is the ratio of stress to strain over time (Reprinted from Madden et al. (2007))...

Stress relaxation for step squeezing of polystyrene at 180°C. (a) Stress versus time for increasing strain steps. Stress increases at short times, 2-10 ms because the plates take a finite time to close. The horizontal stress response signifies transducer overload. The rapid drop for strains e > 1 indicates loss of lubricant, (b) Stress relaxation data plotted as relaxation modulis. Solid line is the linear viscoelastic relaxation modulus calculated from shear dynamic data. Adapted from Soskey and Winter (1985). 

The creep modulus is directly affected by the increase in the level of stress and temperature. With the exception of extremely low strains around 1 percent or less, the creep modulus decreases as the amount of stress is increased. This effect is illustrated in Figure 2-32. In a very similar manner, as the temperature is increased, the creep modulus significantly decreases. Figure 2-33 shows the creep modulus versus time plotted at different temperatures. As one would expect, the combined effect of increasing stress level and temperature on creep modulus is much more severe and should not be overlooked. 

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