Stress history/incremental

These latter curves are particularly important when they are obtained experimentally because they are less time consuming and require less specimen preparation than creep curves. Isochronous graphs at several time intervals can also be used to build up creep curves and indicate areas where the main experimental creep programme could be most profitably concentrated. They are also popular as evaluations of deformational behaviour because the data presentation is similar to the conventional tensile test data referred to in Section 2.3. It is interesting to note that the isochronous test method only differs from that of a conventional incremental loading tensile test in that (a) the presence of creep is recognised, and (b) the memory which the material has for its stress history is accounted for by the recovery periods. 

Note that the isochronous test method is quite similar to that of a conventional incremental loading tensile test and differs only in that the presence of creep is recognized and the memory of the material for its stress history is overcome by the recovery periods. Isochronous data are often presented on log-log scales because this provides a more precise indication of the nonlinearity of the data by yielding a straight-line plot of slope less than unity. 

If the material is assumed to remain isotropic after yield, then there is no dependence on the deformation or stress history. Furthermore, if we assume that the yield behaviour is independent of the hydrostatic component of stress, then the principal axes of the strain increment are parallel to the principal axes of the deviatoric stress tensor. 

Consolidation tests are commonly performed to (1) evaluate the compressibOity of soil samples for the calculation of foundation settlement (2) investigate the stress history of the soils at the boring locations to calculate settlement as weU as to select stress paths to perform most advanced strength tests (3) evaluate elastic properties from measured bulk modulus values and (4) evaluate the time rate of settlement. Consohdation test procedures also can be modified to evaluate if foundation soils are susceptible to coUapse or expansion, and to measure expansion pressures under various levels of confinement. Consohdation tests include incremental consohdation tests (which are performed at a number of discrete loads) and constant rate of strain (CRS) tests where load levels are constantly increased or decreased. CRS tests can generally be performed relatively quickly and provide a continuous stress-strain curve, but require more sophisticated equipment. 

After a time increment dt, the local stresses in the fibers and matrix can be updated to obtain (tr,-, e e,)t at any time t+ dt. Using this information, the composite stress, strain, and strain rate (ac, ec, ec), can be obtained from the constituent parameters (iterative computation, the creep behavior of the composite and constituents can be predicted for any loading history, including cyclic creep. 

In a broader unselected population referred for nuclear stress testing, Sharir et al. (6) found that the extent of reversible perfusion defect (as expressed by the summed difference score) was the best predictor of subsequent nonfatal myocardial infarction, and was best fit by an exponential curve. Among these patients, 26% had a history of myocardial infarction, and patients with nonischemic cardiomyopathies, valvular disease, or who underwent revascularization within 60 days were excluded. Importantly, even though ejection fraction most powerfully stratified the risk of cardiac death, in patients with an ejection fraction >30% the amount of perfusion defect provided incremental prognostic information. In patients with an ejection fraction of <30%, the rates of cardiac death were high (>4% per year) regardless of the amount of ischemia. 

This idea can be used to formulate an integral representation of linear viscoelasticity. The strategy is to perform a thought experiment in which a step function in strain is applied, e t) = Cq H t), where H t) is the Heaviside step function, and the stress response a t) is measured. Then a stress relaxation modulus can be defined by E t) = <7(t)/ o Note that does not have to be infinitesimal due to the assumed superposition principle. To develop a model capable of predicting the stress response from an arbitrary strain history, start by decomposing the strain history into a sum of infinitesimal strain increments ... 

Tensile tests were performed on neat epoxy resins In the following conditions as-cast, as-postcured, as-quenched, and aged at decade Increments from 10 to 10 minutes at 140°C In nitrogen while stored In darkness. A summary of the observed resin stress-strain behavior Is shown In Figure 2. As can be seen, the epoxy polymer was found to be extremely sensitive to thermal history. 

Pre-liquefaction coefficient of consolidation (c ) values for each specimen were calculated based on measured hydraulic conductivity (k) and volume compressibility (m ) data for virgin loading shown in Figure 4a. Post-liquefaction c, values were back-calculated using time histories of pore pressure dissipation and volume change measurements obtained during post-liquefaction dissipation tests for each incremental change in effective stresses. Back-calculations of c were... 

To generalize the viscoelastic response further to account for linear behavior under a changing history of applied stress, we consider the incremental strain response under an increment, da, in shear stress applied at a time t = u ... 

Boltzman Superposition Principle (3,10). This principle states that the stress at a given point in the polymer is a function of the entire strain history at that point. Therefore, to each strain term in equation 9 is added an integral that represents contributions to the stress at a given time from strain increments at earlier times. 

Suppose a material initially free of stress is subjected to a test in which a strain y(to) is suddenly imposed at t = 0 and maintained constant for a while. This is classical stress relaxation, and the stress will decay according to the material s time-dependent relaxation modulus Gr(t), that is, x(t) = Gr t)y to). Now, however, at time t, the strain is suddenly changed to a new level y ti), held there for a while, then at changed to 7( 2). and so on, as sketched in Figure 15.12a. What happens to the stress as a result of this strain history Well, way back in 1876, Boltzmann suggested that the stresses resulting from each individual strain increment should be linearly additive, that is,... 

The discussion that follows, of sound propagation in a lossy polymer, is limited to the case where the stress-strain relation in the polymer is linear. The effect of loss mechanisms on the mechanical response of polymers is included by modifying the stress-strain relations (eq. 9). At small strains, at which the behavior of the polymer is linear, the stress-strain relations are modified according to the Boltzman Superposition Principle (3,10). This principle states that the stress at a given point in the polymer is a function of the entire strain history at that point. Therefore, to each strain term in equation 9 is added an integral that represents contributions to the stress at a given time from strain increments at earlier times. 

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