Strain shear zone dependence

Depending on the polymer chemical structure and MW and on the deformation conditions (temperature and strain rate), two types of deformation heterogeneities are observed crazes and shear deformation zones. 

It is usual to assume that the shear yield stress has the same temperature dependence and strain rate dependence as the flow stress of the polymer in the active zone of the craze, i.e., n, = n, and in fact usually one go even further and sets How-... 

The response of unvulcanized black-filled polymers (in the rubbery zone) to oscillating shear strains (151) is characterized by a strong dependence of the dynamic storage modulus, G, on the strain amplitude or the strain work (product of stress and strain amplitudes). The same behavior is observed in cross-linked rubbers and will be discussed in more detail in connection with the dynamic response of filled networks. It is clearly established that the manyfold drop of G, which occurs between double strain amplitudes of ca. 0.001 and 0.5, is due to the breakdown of secondary (Van der Waals) filler aggregation. In fact, as Payne (102) has shown, in the limit of low strain amplitudes a storage modulus of the order of 10 dynes/cm2 is obtained with concentrated (30 parts by volume and higher) carbon black dispersions made up from low molecular liquids or polymers alike. Carbon black pastes from low molecular liquids also show a very similar functional relationship between G and the strain amplitude. At lower black concentrations the contribution due to secondary aggregation becomes much smaller and, in polymers, it is always sensitive to the state of filler dispersion. 

The selection of the dominant deformation mechanism in the matrix depends not only on the properties of this matrix material but also on the test temperature, strain rate, as well as the size, shape, and internal morphology of the rubber particles (BucknaU 1977, 1997, 2000 Michler 2005 Michler and Balta-Calleja 2012 Michler and Starke 1996). The properties of the matrix material, defined by its chemical structure and composition, determine not rally the type of the local yield zones and plastic deformation mechanisms active but also the critical parameters for toughening. In amorphous polymers which tend to form fibrillated crazes upon deformation, the particle diameter, D, is of primary importance. Several authors postulated that in some other amorphous and semiciystalline polymers with the dominant formation of dUatational shear bands or extensive shear yielding, the other critical parameter can be the interparticle distance (ID) (the thickness of the matrix ligaments between particles) rather than the particle diameter. 

The stress-strain curves simulate a homogeneous deformation process of the polymer. However, on the microscale above the linear part of the stress-strain curve (see Fig. 1.15, curves (b), (c), (d)), localized heterogeneous deformation mechanisms occur. Depending on the polymer chemical structure and entanglement molecular weight Mg and on the deformation conditions (temperature and strain rate), several types of heterogeneous deformation are observed micro plastic zones, crazes, deformation zones, and shear bands. Their main features are sketched in Fig. 1.18. 

The dependence of the non-Newtonian viscosity jj on shear rate at relatively low shear rates is a property which can be classed with viscoelastic behavior in the terminal zone, since it reflects long-range conHgurational motions which are influenced by entanglements to the maximum degree. As pointed out in Chapter 10, the characteristic time r, which specifies the onset of non-Newtonian, behavior with increasing shear rate is closely related to the terminal viscoelastic relaxation time. (In this discussion of shear viscosity, the subscript 21 will be omitted from stress [Pg.380]

The critical strain energy release rates measured in each test are shown in Fig. 15. The fracture toughness measured decreases as the mode II fracture component increased in the tests for this particular material system. This mode mixity dependence of the fracture toughness of adhesively bonded joints apparently is in contrast with the observations of other researchers for other material systems [49-54]. This contradiction can be explained through analyzing the locus of failure. As discussed in Swadener and Liechti [52] and Swadener et al. [53], the locus of failure in their studies was independent of the fracture mode mixity, and the size of the plastic deformation zone at the crack tip increased with the fracture mode mixity. This increased plastic zone was shown to be responsible for a shear-induced toughening mechanism, which consequently, caused the fracture toughness to increase with the mode II components in their studies. In this study, however, as... 

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