High Deformation Limit

Stress-strain data in elongation are mast conveniently interpreted in terms of the reduced stress or modulus defined by  

The resulting values of [f ] are then generally plotted against reciprocal elongation, as suggested by the semiempirical equation of Mooney and Rivlin  

The values of the high deformation modulus 2 Q for an end-linked -functional network may be interpreted using the equation  

Most of the pertinent experimental results have been obtained using PDMS model networks and typical results obtained on such tetrafunctional networks in the author s laboratory are shown in Fig. 1. In it, values of A4 are presented as a function of the volume fraction V2c of polymer in the system during the cross-linking procedure. If the reaction were incomplete in the undiluted state, A4 should show a marked dependence on V2C through its effect on the concentrations and mobilities of the reactants. The values of A4 show no trend whatever with decrease in V2c, which argues strongly that the end- 

The corresponding results for the trifunctional PDMS networks are presented in Fig. The values of A3 are also found to be essentially independent of V2c. but again somewhat exceed the predicted value, which is 1/3. The experimental value of the ratio A3/A4 characterizing the dependence of the high deformation modulus on cro -link functionality for this very limited range in 0 is thus 0.67 it is in essentially exact agreement with the theoretical value of 

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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. 

There has been the question why the TPV materials with ductile thermoplastic matrix display rubber elasticity. Several models have been suggested to answer this question (41 7). Inoue group first analyzed the origin of mbber elasticity in TPVs (43). They constructed a two-dimensional model with four EPDM mbber inclusions in ductile PP matrix and carried out the elastic-plastic analysis on the deformation mechanism of the two-phase system by finite-element method (FEM). The FEM analysis revealed that, even at highly deformed states at which almost the whole matrix has been yielded by the stress concentration, the ligament matrix between mbber inclusions in the stretching direction is locally preserved within an elastic limit and it acts as an in-situ formed adhesive for interconnecting mbber particles. 

Ductile properties such as crack pattern and deformations prefiguring the nearing failure are important characteristics regarding the fracture behavior of structural concrete members. The tests demonstrated that in general TRC members have a distinctive ductile behavior although the stress-strain-behavior of the fabrics is linear-elastic until a brittle tensile failure. While the deformations under service loads (SLS) are rather small, the load-bearing behavior of the specimens is characterized by a distinctive stabilized crack pattern as well as high deformations in ultimate limit state (ULS) of L/30 - L/20. 

When whiskers exceed the elastic limit they behave in one of three ways (I) they fracture by a cleavage (2) they show an important but strongly localized plastic deformation (3) they creep. Very thin copper and iron whiskers with high elastic limits fracture in a more or less brittle manner as is the case for materials that are normally brittle. The sudden release of large amounts of elastically stored energy produces high... 

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