Stress-strain curve, quasi-static

Stress softening 7, 59, 77 Stress-strain curve, quasi-static 78 —, cycle 69, 76-78... 

Gray and Follansbee [44] quasi-statically tested OFE copper samples that had been shock loaded to 10 GPa and pulse durations of 0.1 fis, 1 /rs, and 2 fus. The quasi-static stress-strain curves are shown in Fig. 7.10 with the response of annealed starting copper included for comparison. The yield strength of shock-loaded copper is observed to increase with pulse duration, as the work-hardening rate is seen to systematically decrease. 

The success of the developed model in predicting uniaxial and equi-biaxi-al stress strain curves correctly emphasizes the role of filler networking in deriving a constitutive material law of reinforced rubbers that covers the deformation behavior up to large strains. Since different deformation modes can be described with a single set of material parameters, the model appears well suited for being implemented into a finite element (FE) code for simulations of three-dimensional, complex deformations of elastomer materials in the quasi-static Emit. 

Beside the consideration of the up-cycles in the stretching direction, the model can also describe the down-cycles in the backwards direction. This is depicted in Fig. 47a,b for the case of the S-SBR sample filled with 60 phr N 220. Figure 47a shows an adaptation of the stress-strain curves in the stretching direction with the log-normal cluster size distribution Eq. (55). The depicted down-cycles are simulations obtained by Eq. (49) with the fit parameters from the up-cycles. The difference between up- and down-cycles quantifies the dissipated energy per cycle due to the cyclic breakdown and re-aggregation of filler clusters. The obtained microscopic material parameters for the viscoelastic response of the samples in the quasi-static limit are summarized in Table 4. 

Quasi-static deformation 63 —, stress-strain curve 78... 

Figure 13.13. Compressive stress-strain curves of native silica (SiOx and X-SiOx) and polyurea-crosslinked vanadia (VO and X-VOx) aerogels. Bulk densities SiOx - 0.213 gcm X-SiOx- 0.548 gcm VOx-0.121 gcm and X-VOx 0.430 gcm . A. Quasi-static compression of SiOx at a strain rate of 9 x 10 " s at 23°C X-SiOx at 5 x 10 s at 23°C and X-SiOx at 5 x 10 s at —196°C inset same curves plotted using a different scale. B. Quasi-static compression of yO iat a strain rate of 9 x 10 s at 23°C X-VOx nt 5 x 10 s at 23°C and X-VOx at 5 x 10 s at — 196°C inset up to 10% compressive strain.

Fig. 29. Resolved yield stresses of single-crystal Mo obtained at ambient pressure (solid circles and solid lines) and at 225 GPa (solid squares and dashed lines). Except for the estimated point at 225 GPa and 300 K (see text), the remaining results were obtained from the stress-strain curves in Fig. 28 obtained at a strain rate of Is . For comparison, ambient temperature and pressure experimental data points from the Seeger group [70,71] and the Aono group [79] at lower quasi-static strain rates are also shown.

Fig. 10.5. Stretching curve measured for PEVA12 with a strain rate ch = 0.005 s (continuous line). Quasi-static stress-strain relationship (squares) [124]...

A subtraction of the total amount of stress decay, Aazz(t oo), from the respective initial stresses measmed along the stretching curve gives the stress-true strain relationship associated with the limit of zero strain rates, i.e., under quasi-state conditions. The quasi-static stress-strain relationship obtained in this manner for PEVA12 is included in Fig. 10.5. 

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