Modulus defect

It is sometimes useful to define a term, known as the modulus defect. 

At very low speeds, the indentation probes primarily the response of the gel network and hence the measured hardness shows a strong dependence on the equilibrium modulus. Defects cause both the gel equilibrium modulus as well as the hardness to decrease. At fast measurement speeds, physical entanglements and viscous friction between polymer chains contribute substantially to the measured response. The measured hardness increases and becomes less dependent on the quality of the polymer network as quantified by the equilibrium modulus. 

Although Conrad et al. have frequently justified their results in terms of conventional lattice-defect theory (including the size-misfit and modulus-defect formalisms), they have gone on to consider the effects of chemical interaction between the solute and solvent atoms. In doing so, the interaction mechanism was deduced, with the aid of atomic-orbital theory, to take the form of covalent bonding between the interstitial atom and the... 

Secondly, the ultimate properties of polymers are of continuous interest. Ultimate properties are the properties of ideal, defect free, structures. So far, for polymer crystals the ultimate elastic modulus and the ultimate tensile strength have not been calculated at an appropriate level. In particular, convergence as a function of basis set size has not been demonstrated, and most calculations have been applied to a single isolated chain rather than a three-dimensional polymer crystal. Using the Car-Parrinello method, we have been able to achieve basis set convergence for the elastic modulus of a three-dimensional infinite polyethylene crystal. These results will also be fliscussed. 

Where is the ratio of the irradiated to unirradiated elastic modulus. The dislocation pinning contribution to the modulus change is due to relatively mobile small defects and is thermally annealable at 2000°C. Figure 13 shows the irradiation-induced elastic modulus changes for GraphNOL N3M. The low dose change due to dislocation piiming (dashed line) saturates at a dose <1 dpa. 

The actual experimental moduli of the polymer materials are usually about only % of their theoretical values [1], while the calculated theoretical moduli of many polymer materials are comparable to that of metal or fiber reinforced composites, for instance, the crystalline polyethylene (PE) and polyvinyl alcohol have their calculated Young s moduli in the range of 200-300 GPa, surpassing the normal steel modulus of 200 GPa. This has been attributed to the limitations of the folded-chain structures, the disordered alignment of molecular chains, and other defects existing in crystalline polymers under normal processing conditions. 

Observe that this is a geometric property, not to be confused with the modulus of the material, which is a material property. I, c, Z, and the cross-sectional areas of some common cross-sections are given in Fig. 3-1, and the mechanical engineering handbooks provide many more. The maximum stress and defection equations for some common beamloading and support geometries are given in Fig. 3-2. Note that for the T- and U-shaped sections in Fig. 3-1 the distance from the neutral surface is not the same for the top and bottom of the beam. It may occasionally be desirable to determine the maximum stress on the other nonneutral surface, particularly if it is in tension. For this reason, Z is provided for these two sections. 

In spite of the absence of periodicity, glasses exhibit, among other things, a specific volume, interatomic distances, coordination number, and local elastic modulus comparable to those of crystals. Therefore it has been considered natural to consider amorphous lattices as nearly periodic with the disorder treated as a perturbation, oftentimes in the form of defects, so such a study is not futile. This is indeed a sensible approach, as even the crystals themselves are rarely perfect, and many of their useful mechanical and other properties are determined by the existence and mobility of some sort of defects as well as by interaction between those defects. Nevertheless, a number of low-temperamre phenomena in glasses have persistently evaded a microscopic model-free description along those lines. A more radical revision of the concept of an elementary excitation on top of a unique ground state is necessary [3-5]. 

Regiodefects are less readily incorporated into crystallites than defect-free chain sequences. In semicrystalline polymers, increasing levels of misinsertion result in reduced crystallinity. This can affect numerous physical properties, resulting in reduced modulus, lower heat distortion temperature, and decreased tensile strength. 

Stereodefects reduce the overall regularity of an isotactic polymer chain and hinder its ability to crystallize. As the concentration of defects increases, the degree of crystallinity falls, resulting in reduced density, reduced melting temperatures, lower heat distortion temperatures, reduced modulus, and reduced yield stress. 

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