Loading rate dependence

Fig. 9 Loading rate dependence of quasi-static fracture toughness values, determined by an FBA method and dynamic fracture toughness values, Kj, determined by the DKC method for Charpy type fracture specimens of (a) PC and (b) POM.

By contrast, for measurements carried out in situ at 330 K, no loading-rate dependence was observed for rates between 5 and 200 nN/s. This observation indicates that the corresponding experiment was carried out under quasiequilibrium conditions. These data obtained at 330 K are equivalent to those obtained at 301 K, but at a lower loading rate [135,139]. 

Fig. 3 Schematic view of the human vimentin protein and force-strain curves of coiled-coil intermediate filament under tensile loadings, (a) Schematic representation of vimentin structure, (b) Force-strain behaviors of a coiled-coil a-helical structures revealing the loading rate dependency of the molecular-level stiffness under tensile loading. (Reprinted from [66], with kind permission from Springer Science and Business Media), (c) a-p secondary structural transition of coiled-coil a-helix under tensile loading. (Reprinted from [67])...

Okubo, S., Fukui, K., Qi, Q. X. (2006). Uniaxial compression and tension tests of anthracite and loading rate dependence of peak strength. International Journal of Coal Geology, 68, 196-204. doi 10.1016/j.coal.2006.02.004... 

The strength and length scale of the hydrophobic interaction between hexadecane molecnles were also directly measured by SMFS. Hexadecane molecnles were tethered by flexible PEG linkers to AFM probes and substrates, and a layer of hydrophilic polymer was added to increase the accessibility of hydrophobic molecnles for the force spectroscopy measurements. A barrier was shown by the statistic analysis of the loading rate dependence of rnptnre forces the activation energy estimated from the dissociation rate was 41 6kJmol ... 

Constitutive relations (stress-strain relations) of materials are greatly dependent on stress and strain rates. Therefore, the dependency should he considered for precise simulation of impact phenomena. Constitutive relations and their loading-rate dependencies are shown in this section. 

In impact conditions, the loading rate is quite high, so that the plastic behavior of metals is much influenced. In order to describe the loading-rate dependency, several models have been presented. The Johnson-Cook model, shown in O Eq. 29.5, is a model by which Ludwik type hardening and loading-rate dependency can be expressed (Johnson and Cook 1983). 

Plastics are very often used in temperature ranges lower than their Tgs, so that then-constitutive relations used for analyses should be linear elastic. However, strictly speaking, then-moduli have a weak dependency to loading rates. If the dependency is a problem for impact analyses, the variation of moduli should be compensated. For this purpose, viscoelastic models are sometimes used to express the loading rate dependency (Sato and Ikegami 2000). 

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