Strain-versus-time 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. 

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 ... 

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. 

SS Given a set of creep strain and time data, develop a spreadsheet that allows the user to generate a strain-versus-time plot and then compute the steady-state creep rate. 

Plastic deformation is commonly measured by measuring the strain as a function of time at a constant load and temperature. The data is usually plotted as strain versus time. Deformation strain can be measured under many possible loading configurations. Because of problems associated with the preparation and gripping of tensile specimens, plastic deformation data are often collected using bend and compression tests. 

A typical creep experiment involves measuring the extent of deformation, called the creep strain, e, over extended periods of time, on the order of thousands of hours, under constant tensile loads and temperature. The resulting plot of creep strain versus time (Figure 5.43) shows the resulting creep rate, e = dejdt, which is the slope of the... 

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. 

Plots of strain versus time for a creep experiment were shown previously in Figure 13-75 and in this constant load experiment the strain obtained from each of the components can be simply summed to give Equation 13-92 ... 

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. 

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. 

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))...

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. 

A typical creep curve (strain versus time) normally exhibits three distinct regions (Fignre 8.29) transient (or primary), steady-state (or secondary), and tertiary. Important design parameters available from such a plot include the steady-state creep rate (slope of the linear region) and rupture lifetime (Figure 8.29). 

The stress—relaxation process is governed by a number of different molecular motions. To resolve them, the thermally stimulated creep (TSCr) method was developed, which consists of the following steps. (/) The specimen is subjected to a given stress at a temperature T for a time /, both chosen to allow complete orientation of the mobile units that one wishes to consider. (2) The temperature is then lowered to Tq T, where any molecular motion is completely hindered then the stress is removed. (3) The specimen is subsequendy heated at a controlled rate. The mobile units reorient according to the available relaxation modes. The strain, its time derivative, and the temperature are recorded versus time. By mnning a series of experiments at different orientation temperatures and plotting the time derivative of the strain rate observed on heating versus the temperature, various relaxational processes are revealed as peaks (243). 

Figure 8.12 illustrates the general effect of creep, plotted as a function of log strain versus log time. Under applied load a sample gradually deforms until a critical time (tc) after which it deforms rapidly. If creep is allowed to go unchecked, the sample may break abruptly. 

Fig. 7 a and b. Scheme of the thermomechanical behaviour of a well phase-separated thermoelasto-plastic. Stress-strain (or time) curves. Plots of heat effects versus time. First loading (ABC) and unloading (CD) cycle. Second loading (AC) and unloading (CD) cycle. The yielding point occurs at B. AD indicates the residual deformation after the first cycle. AB on the dQ/dT-time curve is the endo-effect resulting from the initial small-strain deformation AB U9)... 

Fig. 5.3 Schematic showing the changes in strain rate and elastic/creep strains of the individual constituents that occur during creep of a composite, (a) Strain rate versus time, (b) strain rate versus in situ stress acting in the fibers and matrix. In both plots, the shadowed portions show the elastic strain components, which compensate the creep rate mismatch of the individual phases, such that the total creep rates of the constituents remain equal. The creep mismatch ratio (CMR) is discussed in Section 5.2.4. After Wu and Holmes.31...

As already mentioned by various authors [24, 25], it is found experimentally that at various shear strains, for polydisperse polymers, the logarithmic plots of G(t, y) versus time are only shifted vertically. This indicates that the nonlinear relaxation modxilus might be factorizable ... 

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