Double strain rate

Studies of stress overshoot on sudden imposition of constant rate of strain include Osaki, etal. 0) and Inoue, etal. ). Osaki, etal. also report the time dependence of N. Inoue, et al. note a potential artifact perturbing stress measurements, namely shear-induced phase separation. Representative experiments on double strain rates are presented by Oberhauser, et al. 2) and by Wang and Wang(13). The observed stress has a complex time dependence including overshoot and undershoot ... 

In a recent attempt to bring an engineering approach to multiaxial failure in solid propellants, Siron and Duerr (92) tested two composite double-base formulations under nine distinct states of stress. The tests included triaxial poker chip, biaxial strip, uniaxial extension, shear, diametral compression, uniaxial compression, and pressurized uniaxial extension at several temperatures and strain rates. The data were reduced in terms of an empirically defined constraint parameter which ranged from —1.0 (hydrostatic compression) to +1.0 (hydrostatic tension). The parameter () is defined in terms of principal stresses and indicates the tensile or compressive nature of the stress field at any point in a structure —i.e.,... 

Materials can show linear and nonlinear viscoelastic behavior. If the response of the sample (e.g., shear strain rate) is proportional to the strength of the defined signal (e.g., shear stress), i.e., if the superposition principle applies, then the measurements were undertaken in the linear viscoelastic range. For example, the increase in shear stress by a factor of two will double the shear strain rate. All differential equations (for example, Eq. (13)) are linear. The constants in these equations, such as viscosity or modulus of rigidity, will not change when the experimental parameters are varied. As a consequence, the range in which the experimental variables can be modified is usually quite small. It is important that the experimenter checks that the test variables indeed lie in the linear viscoelastic region. If this is achieved, the quality control of materials on the basis of viscoelastic properties is much more reproducible than the use of simple viscosity measurements. Non-linear viscoelasticity experiments are more difficult to model and hence rarely used compared to linear viscoelasticity models. 

It is clear from this work that most of the published values of and Gjc for rubber-tou ened plastics refer to plane-stress fracture. Measurements have been made on a variety of pdymers using SEN, double cantilever beam (DCB) and Charpy impact specimens. Figure 13 shows the results of one such study by Kobayashi and Broutman l, who used DCB specimens to measure C/c in AMBS polymers over a range of cr k speeds. The two most prominent features of the results are the rapid rise in Qc with rubber content, and the fall in Gx( at high crack eeds. Both effects are predicted by Eq. (8) the yield stress decreases with increas-in% rubber phase volume, so that the size of the plastic zone at the crack tip increases similarly, increating crack speed (and therefore strain rate at the crack tip) increases yield stress and reduces the size of the plastic zone. Thus the yield stress is die link between rubber phase volume and fracture resistance. 

Thin films with a thickness of 50 pm of a commercially available PS-PB-PS triblock copolymer (e.g. from BASF, 74% PS, 26% PB) are prepared by solution casting from a 3% solution in toluene onto TEFLON -foil, which is placed in a precleaned petri-dish. The solvent is slowly evaporated over a period of 2 weeks. Residual solvent is then removed and films are annealed under reduced pressure in a vacuum oven at 120°C (48 h). Finally, the films are removed from the support and are uniaxially stretched at a constant strain rate of 0.1 s 1 beyond the yield point at room temperature. ARM investigations are carried out on prestretched samples that are mechanically clamped or fixated by double-sided sticky tape onto the AFM sample holder. 

As discussed in Sect. 4, in the fluid, MCT-ITT flnds a linear or Newtonian regime in the limit y 0, where it recovers the standard MCT approximation for Newtonian viscosity rio of a viscoelastic fluid [2, 38]. Hence a yrio holds for Pe 1, as shown in Fig. 13, where Pe calculated with the structural relaxation time T is included. As discussed, the growth of T (asymptotically) dominates all transport coefficients of the colloidal suspension and causes a proportional increase in the viscosity j]. For Pe > 1, the non-linear viscosity shear thins, and a increases sublin-early with y. The stress vs strain rate plot in Fig. 13 clearly exhibits a broad crossover between the linear Newtonian and a much weaker (asymptotically) y-independent variation of the stress. In the fluid, the flow curve takes a S-shape in double logarithmic representation, while in the glass it is bent upward only. 

Figure 2b presents the plots of the flow stress taken at =50% as a function of initial strain rate at 450°C in a double logarithmic scale. The strain rate sensitivity coefficient m>0.3 was observed in all the strain rate range examined both for the ECAE and hot rolled (RD) conditions. The flow stress was lower and the strain rate sensitivity was higher in the ECAE condition as compared to the hot rolled one. 

Intermediate Response. Figure 6 is a double logarithmic plot of o/e vs. time in seconds at three different strain rates for the samples as a function of H O content. To extend the time scale and to correlate results at various , we have used the reduced-variables procedure shown to be applicable in describing the viscoelastic response of rubbery materials (8) as well as of several glassy polymers (6). (To compensate for the effect of different e we plot a/e vs. e/e the latter is simply the time, t.) Superposition over the entire time scale for 0% H2O (upper curve) is excellent except for times close to the fracture times of the materials tested e higher strain rates. For example, a deviat ipn occurs at 10 sec for the material at e = 3.3 x 10 sec... 

Figure 6. Double logarithmic plot of stress/strain rate vs. time (sec) for PMMA at three strain rates for samples of (upper curve) — 0% HtO (middle curve) 0.6% HtO (lower curve) 2.2% HtO. Upper curve displaced up by 0.5 log unit lower curve displaced down by 0.5 log unit.

O90ni Onishi, P., Hashemi, S. Effect of fibre concentration and strain rate on mechanical properties of single-gated and double-gated injection-moulded short glass fibre-reinforced polypropylene copolymer composites. J. Mater. Sci. 44 (2009) 3445-3456. 

The necking phenomenon observed upon stretching a polymer film at a constant temperature is a well-known consequence of a negative feedback loop driven by the interplay between the increase in temperature associated with the sample deformation and its glassification caused by the heat exchange with the environment (55). Oscillatory behavior and period-doubling in the stress resulting from a constant strain rate have been experimentally observed. 

Clearly, the homogeneous deformation response shown in Fig. 12.17 also applies in inhomogeneous flow where notches and other local strain concentrations are present. There, through the double effect of enhancement of the local strain hardening and of the strain rate, global embrittlement will result. 

Figure 12.10 Flow number and strain rate for the twin screw extruder, (a) single-flighted (b) double-flighted (c) triple-flighted...

Figures 12.10(a-c) shows that the flow number distribution for the single- and double-flighted screws are nearly identical, whereas, the triple-flighted screw produces mainly shear flow due to the small gaps that are present with this geometry. Interestingly, the geometry that created the highest volumetric strain rate was the double-flighted screw, which is the most commonly used screw geometry for twin screw extruders.

Fig. 26. Effect of strain rate on the stress-time (double logarithmic plot) behavior for a concentrated polymer solution, showing the increasing strength of the stress overshoot phenomenon with increasing strain rate. After Zapas and Phillips (81), with permission.

N. W. J. Brooks, R. A. Duckett, and I. M. Ward, Modeling of Double Yield Points in Polyethylene Temperature and Strain Rate Dependence J. Rheol. 39, 425-436 (1995). 

Zirconium and its alloys are susceptible to stress corrosion cracking (SCC) in such environments as Fe - or Cu -containing chloride solution, CH3OH -H hahdes, concentrated HNO3, halogen vapors, and liquid mercury or cesium [4,5]. Common test methods, e.g., U-bend, C-ring, split ring, direct tension, double cantilever, and slow strain rate tension, have been used to determine zirconium s susceptibility to SCC. 

Of the large number of SSC test methods that have been used to evaluate materitils for this service, five have survived uniaxial load tensile test. Shell bent beam test, C-ring test, double-cantilever-beam test, and slow strain rate test. The first four of these are incorporated in NACE Test Method for Laboratory Testing of Materials for Resistance to Sulfide Stress Cracking in HjS Environments (TM0177). Following are comments on these methods [3]. 

DCB double cantilever beam m strain rate sensitivity factor... 

As we have seen, the strain rate dependence does suggest that yield behaviour often indicates the presence of two thermally activated processes, as discussed above. In some cases, notably polyethylene, a double yield point is observed. Ward and co-workers [64], Seguala and Darras [65] and Gupta and Rose [66] concur that these two deformation processes are essentially interlamellar shear and intra lamellar shear (or c-slip). They are akin to the dynamic mechanical relaxation processes identified in Chapter 10.7.1 for the specially oriented PE sheets, and Seguala and Darras have related them to the a and o 2 transitions reported by Takayanagi [67]. This establishes a direct link between yield and viscoelastic behaviour. 

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