Deformation Limit

As already mentioned, once a network is formed it is difficult to characterize because of its insolubility. It is possible, however, to obtain some indirect information on the likely 

In some cases, molecular weights were observed to increase by a factor of approximately 30. Similar extents of reaction for the corresponding difunctional-trifunctionai reactions would yield networks in which incompleteness of cross-linking would be negligibly small. 

The dependence of elastic properties in general on cross-link functionality is of considerable importance. Changes in p beyond the values 3 or 4, however, requires replacement of the type of reaction illustrated in Eq. (1) by one of greater versatility. Such studies are described in the following section and in Part VI. 

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Designing plastic Basically the general design criteria applicable to plastics are the same as those for metals at elevated temperature that is, design is based on (1) a deformation limit, and (2) a stress limit (for stress-rupture failure). There are, of course, cases where weight is a limiting factor and other cases where short-term properties are important. 

Response deformation limits are used to ensure that adequate response to blast loads is provided. These limits are based on the type of structure or component, construction materials used, location of the structure and desired protection level. 

Building Performance Requirements - Deformation Limits Damage level88 Medium, reference Appendix 5.B. 

Both Eqs (7.64) and (7.65) reduce to Eq. (7.48) in the small deformation limit (A 1). This simple additivity separates the crosslink and entanglement contributions to the stress and hence allows them to be determined... 

One complication is that the boundary conditions (4-264)-(4-266) must be applied at the bubble surface, which is both unknown [that is, specified in terms of functions R(t) and fn(9,tangent unit vectors n and t, that appear in the boundary conditions are also functions of the bubble shape. In this analysis, we use the small-deformation limit s 1 to simplify the problem by using the method of domain perturbations that was introduced earlier in this chapter. First, we note that the unit normal and tangent vectors can be approximated for small e in the forms... 

As expected, this is identical to the 0(8) approximation obtained for the small-deformation limit in the preceding part of this subsection, namely Eq. (6-239). 

Experimental determination of the contributions above those predicted by the reference phantom network model has been controversial. Experiments of Oppermann and Rennar (1987) on endlinked poly(dimethylsiloxane) networks, represented by the dotted points in Figure 4.4, indicate that contributions from trapped entanglements are significant for low degrees of end-linking but are not important when the network chains are shorter. Experimental results of Erman and Wagner (1980) on randomly crosslinked poly(ethyl acrylate) networks fall on the solid line and indicate that the observed high deformation limit moduli are within the predictions of the constrained-junction model. 

For RP-faced sandvdch structures the design approaches includes both the unique characteristics introduced by sandwich construction and the special behavior introduced by RP materials. The overall stiffness provided by the interaction of the faces, the core, and their interfaces must be sufficient to meet deflection and deformation limits set for the structures. Overall stiffness of the sandwich component is also a key consideration in design for general instability of elements in compression (Figure 7.47). 

Ultimately we note that the classical theory of mixtures presented here is used also for solids but with deformations limited on those only which may be described through density. 

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