Elastic strain theory

Finally, there is experimental evidence that the thermal polymerization of some monomers with mismatches comparable to PTS cannot be described by the elastic strain theory... 

One of the shortcomings of the elastic strain theory which leaves room for further improvements is the fact that assumptions must be made about the individual initiation, propagation and termination steps which cannot be observed independently but are calculated from the overall reaction rate. 

The maximum elastic strain theory (St. Venant s theory) states that inception of failure is due if the largest local strain, 3, within the material exceeds somewhere a critical value e. The failure criterion, therefore, is derived as... 

It is consistent with the approximations of small strain theory made in Section A.7 to neglect the higher-order terms, and to consider the elastic moduli to be constant. Stated in another way, it would be inconsistent with the use of the small deformation strain tensor to consider the stress relation to be nonlinear. The previous theory has included such nonlinearity because the theory will later be generalized to large deformations, where variable moduli are the rule. 

To describe properties of solids in the nonlinear elastic strain state, a set of higher-order constitutive relations must be employed. In continuum elasticity theory, the notation typically employed differs from typical high pressure science notations. In the present section it is more appropriate to use conventional elasticity notation as far as possible. Accordingly, the following notation is employed for studies within the elastic range t = stress, t] = finite strain, with both taken positive in tension. 

Time dependence Viscoelastic deformation is a transition type behavior that is characterized by the occurrence of both elastic strain and time-dependent flow. It is the time dependence of the mechanical properties of plastics that makes the behavior of these materials difficult to analyze by mathematical theory. 

The deformation of a specimen during indentation consists of two parts, elastic strain and plastic deformation, the former being temporary and the latter permanent. The elastic part is approximately the same as the strain produced by pressing a solid sphere against the surface of the specimen. This is described in detail by the Hertz theory of elastic contact (Timoshenko and Goodier, 1970). 

In retrospect, it should not be surprising that a time independent theory modeled after elasticity theory does not apply to a plastic flow process. Elastic deformation is conservative with the work done on the material stored as elastic strain energy. Plastic deformation is non-conservative with the work done on the material dissipated as heat, or converted into internal defects... 

In textbooks, plastic deformation is often described as a two-dimensional process. However, it is intrinsically three-dimensional, and cannot be adequately described in terms of two-dimensions. Hardness indentation is a case in point. For many years this process was described in terms of two-dimensional slip-line fields (Tabor, 1951). This approach, developed by Hill (1950) and others, indicated that the hardness number should be about three times the yield stress. Various shortcomings of this theory were discussed by Shaw (1973). He showed that the experimental flow pattern under a spherical indenter bears little resemblance to the prediction of slip-line theory. He attributes this discrepancy to the neglect of elastic strains in slip-line theory. However, the cause of the discrepancy has a different source as will be discussed here. Slip-lines arise from deformation-softening which is related to the principal mechanism of dislocation multiplication a three-dimensional process. The plastic zone determined by Shaw, and his colleagues is determined by strain-hardening. This is a good example of the confusion that results from inadequate understanding of the physics of a process such as plasticity. 

Most of the experimental results on CJTE can be explained on the basis of molecular field theory. This is because the interaction between the electron strain and elastic strain is fairly long-range. Employing simple molecular field theory, expressions have been derived for the order parameter, transverse susceptibility, vibronic states, specific heat, and elastic constants. A detailed discussion of the theory and its applications may be found in the excellent review by Gehring Gehring (1975). In Fig. 4.23 various possible situations of different degrees of complexity that can arise in JT systems are presented. 

Buckingham theory and, 330 chain decomposition, 325 cooperative behavior of defects, 338 deuterium shifts, 361 dispersive interactions, 330 elastic strain, 333 electrostatic coupling, 352 exchange of positions, 351 heteroisotopic pairs, 348... 

During a collision, the colliding solids undergo both elastic and inelastic (or plastic) deformations. These deformations are caused by the changes of stresses and strains, which depend on the material properties of the solids and the applied external forces. Theories on the elastic deformations of two elastic bodies in contact are introduced in the literature utilizing Hertzian theory for frictionless contact and Mindlin s approach for frictional contact. As for inelastic deformations, few theories have been developed and the available ones are usually based on elastic contact theories. Hence, an introduction to the theories on elastic contact of solids is essential. 

In contrast, some theories consider the elastic strain energy field to be important. Dissolution in-hibitors appear to slow down dissolution by adsorbing at special surface sites namely, kinks in crystallographic steps. 

The effect of a dislocation line on dissolution nucleation has been attributed to the effect of their elastic strain energies on the chemical potential of the material nearby them (4). How ever this is a doubtful idea in both theory and practice. In theory the elastic energy of a screw dislocation line does not... 

The correlation between the effective strain of a polymer chain and its absorption energy, established from direct absorption measurements on stretched polymer fibres allows an independent determination of the length of the repeat unit as a function of X via optical absorption measurements Data obtained by this method display a systematic deviation from the theoretical plot (Fig. 7) as do data derived from resonant Raman measurements . This indicates that the agreement between experimental data and predictions of the elastic strain (ES)-theory is fulfilled only... 

The question of whether microhardness is a property related to the elastic modulus E or the yield stress T is a problem which has been commented on by Bowman Bevis (1977). These authors found an experimental relationship between microhardness and modulus and/or yield stress for injection-moulded semicrystalline plastics. According to the classical theory of plasticity the expected microindentation hardness value for a Vickers indenter is approximately equal to three times the yield stress (Tabor s relation). This assumption is only valid for an ideally plastic solid showing sufficiently large deformation with no elastic strains. PE, as we have seen, can be considered to be a two-phase material. Therefore, one might anticipate a certain variation of the H/ T 3 ratio depending on the proportion of the compliant to the stiff phase. 

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