Applied strain rate

Various workers have used equation 8.8, or some modified version thereof, to compare observed with calculated crack velocities as a function of strain rate, but Fig 8.8 shows results from tests on a ferritic steel exposed to a carbonate-bicarbonate solution. The calculated lines move nearer to the experimental data as the number of cracks in equation 8.9 is increased, while the numbers of cracks observed varied with the applied strain rate, being about 100 for 4pp 10 s , but larger at slower 4pp and smaller at higher 4pp. 

The yield occurs when the product of the applied strain rate (e) and the global relaxation time reaches the order of unity, i.e., ex 1. Thus, we obtain... 

When the induced voltage Fopen is not completely in phase with the applied strain, or the induced current is not completely in phase with the applied strain rate (piezoelectric relaxation), the e-constant becomes a complex quantity as follows ... 

If the applied strain rate is equal to the rate of molecular jumps, then... 

Note that, since the stress-strain curves are dependent on the applied strain rate and the specimen temperature, both PED and AT], are functions of the strain, strain rate, and temperature. 

The change in the physical mechanism of deformation from elasticity, viscoelasticity to plasticity depends on the time scales in which the amorphous solid is measured and relaxed. The dependene of stress-strain relationship on relaxation time is conceptualized in Fig. 18, where the yield stress is defined. The yield occurs when the product of the relaxation time and the applied strain rate reaches a constant value [28, 38, 39]. Using Eq. (50) and replacing yield stress components ... 

Fig-1 Mechanical response of SAN to simple shear at an applied strain rate of 10 2/s and 10 4/s for isothermal or adiabatic conditions (solid and dashed lines, respectively). The temperature increase delays the hardening for a strain rate of 10 4/s which vanishes for 10 2/s. In this case, the material reaches the glass transition temperature and enters the rubbery state resulting in a small load-bearing capacity... 

Fig. 37a aad b. Schematic representatiaii of plastic flow for the 2-process model (a) yield stress vs. applied strain rate flk) creep strain rate Ep vs. applied stress... 

Sluckin adopted a quasi-equilibrium thermodynamic approach to understanding the effect of a strain rate field on the isotropic-anisotropic transition in polymer solutions. He derived a Clausius-Clapeyron-like equation which connects the shift in the critical polymer mole fraction C, and Cj, which are concentrations of isotropic and nematic phases, respectively, to the applied strain rate. 

Another example of a transient measurement is given in Figure 3.73. Figure 3.73(a) shows the start up of an imposed strain rate and the subsequent measurement of the stress build-up ((t" " (0) over time. Figure 3.73(b) shows the relaxation of an applied strain rate and the subsequent measurement of the stress decay (stress build-up for a polymer melt is shown in Figure 3.74. 

With regard to this latter point Brereton et al. point out that the integral equation predicts that the stress-maximum observed at strain-rates greater than ip, should be approximately linearly dependent on the logarithm of the applied strain-rate. Such a feature is in accord with yield-stress data at different temperatures for a wide range of isotropic polymers, in both tension and compression. Many workers have attempted to describe this linear dependence of the yield stress on log (strain-rate) in terms of various modifications of Eyring s theory of viscosity. For example the equation... 

Consider a cylindrical bar of homo-PS of diameter D that is to undergo plastic flow through crazing, subjected to an applied strain rate that is initially producing a purely elastic response in the absence of crazing, i.e.. 

However, amorphous water-soluble materials, such as food materials, deform viscoelastically. The deformation and relaxation behavior of such materials can be described by means of various viscoelastic models. Depending on the nature of the stress/strain applied, either the storage and loss modulus or the elasticity and the viscosity are included as material parameters in these models. These rheological material parameters depend on the temperature and the water content as well as on the applied strain rate. The viscoelastic deformation enlarges the contact area and decreases the distance between the particles (see Fig. 7.3). If the stress decreases once again, the achieved deformation is partially reversed (structural relaxation). 

Figure 1.18 Influence the slow strain rate technique and the applied potential on the ductility of 41% cold rolled and annealed AISI 304 S.S. at 1000 (7 for 24 hours. The applied strain rate was 5.5a 10 sec" (19).

The toughening effectiveness of impact modifiers of any kind in unsaturated polyester and vinyl ester resins will depend on the rate of impact or applied strain, atmospheric conditions (temperature, presence of solvents), and the toughness of the base resin. As the applied strain rate increases or the lest temperature decreases the effectiveness of the rubber additive may decrease. This is because the rubbery particles and the matrix resin b me more brittle under these conditions. As a result, when comparing toughness data from different sources, testing... 

Some data on scale failure have been determined experimentally and are illustrated in Fig. 2-26 for tensile stresses, which is regarded as the more critical situation. Figure 2-26 a shows the situations for an alumina scale on a high alloy steel and for a chromia former. Figure 2-26 b shows the results for nickel oxide on nickel. The data are plotted versus the applied strain rate at a variety... 

One of the main mechanical test results is given by Fig. 5-33 which shows the Cof-fin-Manson curves of three different materials. The following points can be observed at =2 X10" s (irrespective of the applied strain rate). 

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