Tensile stress softening

In Fig. 20 we show a theoretical dispersion plot using these parameters and a tensile stress = 2.7 x 10 dyn/cm. Due to the symmetry of the modes at X the stress tensor tpy does not affect the surface eigenmodes at this symmetry point. In addition, we have softened the intralayer force constant 4>ii in the first layer by about 10%. With these parameters, we find good agreement between experimental data and theoretical dispersion curves. 

TMA measures the mechanical response of a polymer looking at (1) expansion properties including the coefficient of linear expansion, (2) tension properties such as measurement of shrinkage and expansion under tensile stress, i.e., elastic modulus, (3) volumetric expansion, i.e., specific volume, (4) single-fiber properties, and (5) compression properties such as measuring the softening or penetration under load. 

An important feature of filled elastomers is the stress softening whereby an elastomer exhibits lower tensile properties at extensions less than those previously applied. As a result of this effect, a hysteresis loop on the stress-strain curve is observed. This effect is irreversible it is not connected with relaxation processes but the internal structure changes during stress softening. The reinforcement results from the polymer-filler interaction which include both physical and chemical bonds. Thus, deforma-tional properties and strength of filled rubbers are closely connected with the polymer-particle interactions and the ability of these bonds to become reformed under stress. 

It is demonstrated that the quasi-static stress-strain cycles of carbon black as well as silica filled rubbers can be well described in the scope of the theoretic model of stress softening and filler-induced hysteresis up to large strain. The obtained microscopic material parameter appear reasonable, providing information on the mean size and distribution width of filler clusters, the tensile strength of filler-filler bonds, and the polymer network chain density. In particular it is shown that the model fulfils a plausibility criterion important for FE applications. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. 

Molecular mechanisms for stress-softening are also discussed. It is shown that this phenomenon is not related to the chain slippage or to a conversion of a "hard" adsorbed phase to a soft one. The obtained results assume that the stress-softening in silicon rubbers is caused by two possible reasons changes in the positions of filler particles relative to the direction of stretching at the first deformation and by a re-distribution of the topological hindrances. It is shown that the tensile strength at break as a fiinction of temperature is closely related to the chain dynamics at the elastomer-filler interface. 

A molecular model is proposed for the explanation of the temperature dependence of stress-strain characteristics such as, e.g., the modulus, the stress-softening and the tensile streilgth at break for filled PDMS. The model emphasizes the importance of the following molecular parameters ... 

FIG. 5.3. Shows tlie effect of applying local heat to a thin slice of glass tube. At a radial section opposite the heated spot, compressive shesses are set up in the outer layer of glass, and tensile stresses are set up in the inner layer, as shown in (a). These stresses disappear when the heated spot begins to soften. Wlien tlie glass is allowed to cool the heated spot contracts and sets up compressive stresses in the... 

It is well known that the tensile strength of carbon black filled hydrocarbon rubbers increases with black structure at elevated temperatures, but not at room temperature or below (175). Since primary structure in carbon black increases modulus, hysteresis, and stress-softening (Section VII), an increase of the strength with structure might be expected on consideration of Eq. (32). The conditions under which tensile strength becomes independent of carbon black structure correspond to the regime... 

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