Yield strain stress-time curves

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)... 

One way to obtain long-term information is through the use of the time-temperature-superposition principle detailed in Chapter 7. Indeed, J. Lohr, (1965) (the California wine maker) while at the NASA Ames Research Center conducted constant strain rate tests from 0.003 to 300 min and from 15° C above the glass transition temperature to 100° C below the glass transition temperature to produce yield stress master curves for poly(methyl methacrylate), polystyrene, polyvinyl chloride, and polyethylene terephthalate. It should not be surprising that time or rate dependent yield (rupture) stress master curves can be developed as yield (rupture) is a single point on a correctly determined isochronous stress-strain curve. Whether linear or nonlinear, the stress is related to the strain through a modulus function at the yield point (mpture) location. As a result, a time dependent master curve for yield, rupture, or other failure parameters should be possible in the same way that a master curve of modulus is possible as demonstrated in Chapter 7 and 10. 

Generally large yield stress effects were dominant in the nematic melts, but they were strongly pre-history dependent. A three region flow curve for 15 mol % modified poly(pheny1-1,4-phenylene terephthalate) was probably due to a not completely molten system. Dynamic viscosity measurements showed strong pseudoplastic behaviour. Strain and time dependence phenomena were not observed. 

The stress-strain-time data can be plotted as creep curves of strain vs. log time (Fig. 3.10 top view). Different methods are also used to meet specific design requirements. Examples of methods include creep curves at constant times to yield isochronous stress versus strain curves or at a constant strain, giving isometric stress versus log-time curves, as shown in the bottom views in Fig. 3.10. 

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

As a pipeline is heated, strains of such a magnitude are iaduced iato it as to accommodate the thermal expansion of the pipe caused by temperature. In the elastic range, these strains are proportional to the stresses. Above the yield stress, the internal strains stiU absorb the thermal expansions, but the stress, g computed from strain 2 by elastic theory, is a fictitious stress. The actual stress is and it depends on the shape of the stress-strain curve. Failure, however, does not occur until is reached which corresponds to a fictitious stress of many times the yield stress. 

As shown in Sect. 2, the fracture envelope of polymer fibres can be explained not only by assuming a critical shear stress as a failure criterion, but also by a critical shear strain. In this section, a simple model for the creep failure is presented that is based on the logarithmic creep curve and on a critical shear strain as the failure criterion. In order to investigate the temperature dependence of the strength, a kinetic model for the formation and rupture of secondary bonds during the extension of the fibre is proposed. This so-called Eyring reduced time (ERT) model yields a relationship between the strength and the load rate as well as an improved lifetime equation. 

The isochronous stress-strain curves for the creep of PP bead foams (254) were analysed to determine the effective cell gas pressure po and initial yield stress do as a function of time under load (Figure 11). po falls below atmospheric pressure after 100 second, and majority of the cell air is lost between 100 and 10,000 s. Air loss is more rapid than in extruded PP foams, because of the small bead size and the open channels at the bead boundaries, do reduces rapidly at short yield times <1 second, due to proximity of the glass transition, and continues to fall at long times. 

In the category of deformation properties the phenomena of stress-strain behaviour, modulus and yield, stress relaxation and creep have been discussed already in Chap. 13. Here we want to give special attention to the long-term deformation properties. For a good design we need sufficiently reliable creep data (or stress-strain curves as a function of time and temperature). 

Representative stress-strain curves for the various materials, rates, and temperatures are shown in Figure 6. Tests were replicated from two to five times in general these replications had very high reproducibility in yield values. Values at fracture, especially fracture strain, showed much more scatter. Accordingly the yield values of the unmodified material, which are really fracture values, also contained more scatter. (In the plots of yield values to follow, the data symbols lie over all of the replication values unless the values are sufficiently spaced to permit another symbol.)... 

Both destructive and nondestructive measurements can be done on an Instron Material Tester. In this system, the sample is loaded in a test cell, and the compression or tension force is measured when the upper part of the cell is moved over a given distance (time). Within the elastic limit of the gel, the elastic modulus E (or gel strength) is obtained from the initial slope of the nondestructive stress/strain curve additional deformation results in the breakage of the sample, giving the characteristic parameters—yield stress and breaking strain. 

Constant stress (creep) measurements A constant is stress is applied to the system and the strain y or compliance J (y/a) is followed as a function of time. By measuring creep curves at increasing stress values, it is possible to obtain the residual (zero-shear) viscosity ri 6) and the critical stress that is, the stress above which the structure starts to break down. <7 is sometimes referred to as the true yield value. 

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