Quasi-static responses

Shock Response Versus Quasi-Static Response for Internal Blast. We noted earlier that internal detonations of high explosives within structures caused both initial and reflected shock loadings, plus longer term gas pressure loads called quasi-static pressures. Figure 11 is a reproduction of a pressure trace showing both phases of the loading. 

Material properties. In addition to the common knowledge that the materials must be stronger, tougher, and lighter [79], it is envisioned that the materials must be less stiff during impact so that the impact duration can be extended and the elastic wave will have sufficient time to reach and be reflected by the boundary many times for a quasi-static response, as discussed by Olsson [76]. However, this requirement is contradictory to the structural requirement that is, the material must be stiff to provide structural capacity. 

Target size. In order to ensure that the flexure stress wave and shear stress wave be transmitted and reflected many times by the boundary, and to homogenize the stresses sufficiently, a smaller sized target tends to result in a quasi-static response. 

The material behavior above-described refers to the quasi-static response. However, elastomers subjected to real world loading conditions possess fluid-like characteristics typical of a viscoelastic material. When loaded by means of a stepwise strain, they stress-relax, i.e., the reaction force resulting from the application of an initial peak falls to an asymptotic value, which is theoretically reached after an infinite time [69]. Moreover, if an external force is suddenly applied, creep is observed and the strain begins to change slowly towards a limiting value. 

Shock loading in most metals and alloys produces greater hardening than quasi-static deformation to the same total strain, particularly if the metal undergoes a polymorphic phase transition, such as is observed in pure iron [1]-[10]. Figure 6.1 compares the stress-strain response of an annealed... 

P.S. Follansbee and G.T. Gray III, The Response of Single Crystal and Polycrystal Nickel to Quasi-Static and Shock Deformation, in Advances in Plasticity 1989 (edited by A.S. Khan and M. Tokuda), Pergamon Press, Oxford, 1989, pp. 385-388. 

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. 

For porous catalyst pellets with practical loadings, this quantity is typically much larger than the pellet void fraction e, indicating that the dynamic behavior of supported catalysts il dominated by the relaxation of surface phenomena (e.g., 35, 36). This implies that a quasi-static approximation for Equation (1) (i.e., e = 0) can often be safely invoked in the transient modeling of porous catalyst pellets. The calculations showed that the quasi-static approximation is indeed valid in our case the model predicted virtually the same step responses, even when the value of tp was reduced by a factor of 10. 

As for the mechanical response of thin lipid films, surface pressure(fl)-surface area(A) characteristics of lipid monolayer at air/water interface have been well studied under quasi-static conditions. It has been established that different phases are observed for the ensemble of lipid molecules in a two-dimensional arrangement, similarly to the gas, liquid, and solid phases and some other intermediate phases as in three-dimensional molecular assemblies. 

Dynamic properties are more relevant than the more usual quasi-static stress-strain tests for any application where the dynamic response is important. For example, the dynamic modulus at low strain may not undergo the same proportionate change as the quasi-static tensile modulus. Dynamic properties are not measured as frequently as they should be simply because of high apparatus costs. However, the introduction of dynamic thermomechanical analysis (DMTA) has greatly widened the availability of dynamic property measurement. 

SFM s can be also classified according to static and dynamic operating modes. Under quasi-static conditions, the microscope measures the instantaneous response of the cantilever when it interacts with the sample. Dynamic SFM enables separation of the elastic and inelastic component in the cantilever deflection when the sample surface is exposed to a periodically varying stress field. The dynamic modes are useful for investigation of viscoelastic materials such as polymers and results in additional improvements in the signal-to-noise ratio. 

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. 

Nevertheless, the responses of the test molecules embedded to the proteins differ significantly from that in solution (see Fig. 11). The fluctuation correlation function amplitude is considerably larger in solution for small times, but it decays much more quickly, so that only a very small quasi-static inhomogeneity (0.1 ps 2) remains within the observation window available in this experiment (6 ps). A much larger inhomogeneity remains for even longer times in the case of a protein environment. This result is consistent with the interpretation of optical photon echoes in protein environment (22-25,27), where a quasi-static contribution of the energy gap correlation function has been observed up to 100 ps. 

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