Quasi stress-strain curve

In the plastic region, ASME uses quasi-stress-strain curves similar to those in Fig. 8.11 to determine plastic buckling. These curves are plotted on log-log graphs with a factor of safety of two for stress. Because the stress-strain curves differ for different temperatures, a number of curves for different temperatures are plotted in Fig. 8.11. Hence, allowable stress is given by... 

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... 

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

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.

Figure 1 shows the results obtained during successive cycles of increasing shear strain (as measured at the outer cylinder surface). Hourly three stages in deformation behaviour can be distinguished In the quasi linear part of the stress-strain curves, the sample volume contracted approximately proportionally to the applied strain. Then, the absolute slopes of both stress and relative volume as function of strain decreased simultaneously. Stress remained virtually constant for the largest strains whereas volume increased again. 

A. C. Fischer Cripps and B. R. Lawn, Indentation stress strain curves for quasi ductile ceramics, Acta Mater. 44(2), 519 527 (1996). 

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.

Figure 5 shows stress-stain curve of a ceUular PP film determined by the method mentioned above. The strain of die foam displays a quasi-instantaneous elastic response with a strain 5 % (Dansachmiiller et al. 2005). 

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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