Deformations strong

LDA and HDA were interpreted to be similar to two limiting structural states of supercooled liquid water up to pressures of 0.6 GPa and down to 208 K. In this interpretation, the liquid structure at high pressure is nearly independent of temperature, and it is remarkably similar to the known structure of HDA. At a low pressure, the liquid structure approaches the structure of LDA as temperature decreases [180-182]. The hydrogen bond network in HDA is deformed strongly in a manner analogous to that found in water at high temperatures, whereas the pair correlation function of LDA is closer to that of supercooled water [183], At ambient conditions, water was suggested to be a mixture of HDA-like and LDA-like states in an approximate proportion 2 3 [184-186],... 

In this type of supramolecular organization, the dendritic core deforms strongly with increasing generation number, since the layer spacing remains... 

Optically undeformed or weakly deformed [ [ Strong undulatory extinction... 

The rate of sample deformation is also an important factor in defining the hysteresis response surface. As shown by Gorce [291], the rate of sample deformation strongly influences the extent energy dissipation processes. 

VVuv (ffl). Within the series, one tenn dominates, for example, the n 2 term for ethylene. Ethylene strongly resists torsional deformation to any angle other than 0 and 7t (180") (Fig. 4-10). 

For large deformations or for networks with strong interactions—say, hydrogen bonds instead of London forces—the condition for an ideal elastomer may not be satisfied. There is certainly a heat effect associated with crystallization, so (3H/9L) t. would not apply if stretching induced crystal formation. The compounds and conditions we described in the last section correspond to the kind of system for which ideality is a reasonable approximation. 

Knitted fabrics are produced from one set of yams by looping and interlocking processes to form a planar stmcture. The pores in knitted fabrics are usually not uniform in size and shape, and again depend largely on yam dimensions and on the numerous variables of the knitting process. Knitted fabrics are normally quite deformable, and again physical properties are strongly dependent on the test direction. 

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

Deformation Under Loa.d. The mechanical behavior of coal is strongly affected by the presence of cracks, as shown by the lack of proportionahty between stress and strain in compression tests or between strength and rank. However, tests in triaxial compression indicate that as the confirming pressure is increased different coals tend to exhibit similar values of compressive strength perpendicular to the directions of these confining pressures. Except for anthracites, different coals exhibit small amounts of recoverable and irrecoverable strain underload. 

Examination of the microstructure of the cavitated surface will commonly disclose evidence of deformation such as twins (Neumann hands) in carbon steel and general cold working in other metals (Case History 12.6). Damage from cavitation can be differentiated from attack by a strong mineral acid, which can produce a similar surface appearance, by observing the highly specific areas of attack characteristic of cavitation. Acid attack is typically general in its extent (Case History 12.6). 

As with any constitutive theory, the particular forms of the constitutive functions must be constructed, and their parameters (material properties) must be evaluated for the particular materials whose response is to be predicted. In principle, they are to be evaluated from experimental data. Even when experimental data are available, it is often difficult to determine the functional forms of the constitutive functions, because data may be sparse or unavailable in important portions of the parameter space of interest. Micromechanical models of material deformation may be helpful in suggesting functional forms. Internal state variables are particularly useful in this regard, since they may often be connected directly to averages of micromechanical quantities. Often, forms of the constitutive functions are chosen for their mathematical or computational simplicity. When deformations are large, extrapolation of functions borrowed from small deformation theories can produce surprising and sometimes unfortunate results, due to the strong nonlinearities inherent in the kinematics of large deformations. The construction of adequate constitutive functions and their evaluation for particular... 

It should be noted that the normality conditions, arising from the work assumption applied to inelastic loading, ensure the existence and uniqueness of solutions to initial/boundary value problems for inelastic materials undergoing small deformations. Uniqueness of solutions is not always desirable, however. Inelastic deformations often lead to instabilities such as localized deformations. It is quite possible that the work assumption, which is essentially a stability postulate, is too strong in these cases. Normality is a necessary condition for the work assumption. Instabilities, while they may occur in real deformations, are therefore likely to be associated with loss of normality and violation of the work assumption. 

A ubiquitous feature accompanying large deformations in inelastic materials is the appearance of various instabilities. For example, plastic deformation may lead to shear banding, and the development of damage frequently leads to the formation of fault zones. As remarked in Section 5.2.7, normality conditions derived from the work assumption may imply stability which is too strong for such cases. Physical instabilities are likely to be associated with loss of normality and violation of the work assumption. 

---