Energy dissipation Shear yielding

Both massive voiding and shear yielding dissipate energy however, shear yielding is often favored over voiding, especially under uniaxial stress, elevated... 

This model was introduced by Neville and Hunter (13,14) for the case of sterically stabilized dispersions which have undergone reversible flocculation. It is assumed that the major contribution to the excess energy dissipation in such pseudoplastic systems comes from the need to provide energy from the shear field to separate contacting particles. Under these conditions, the extrapolated yield value is given by the expression (13,32,33),... 

Integrating over the hysteresis loop between the compression and decompression curves in Figure 19 yields the amount of energy dissipated through the reversible bond formation/dissociation process. Unfortunately, it is not possible to determine the contribution of these transitions to the friction of phosphate films because such a calculation would require knowledge of the number of similar instabilities that occur per sliding distance, which is certainly beyond the limits of first-principles calculations. Nonetheless, the results do indicate that pressure- and shear-induced chemical reactions can contribute to the friction of materials. 

The second model introduced by Hunter and cowor)ters (20,21) is the elastic floe model. In this case, the structural units (which persist at high shear rates) are assumed to be small floes of particles (called floccules) which are characterised by the ability of the particle structure to trap some of the dispersion medium. In this energy dissipation is considered to arise from two processes, namely the viscous flow of the suspension medium around the floes (which are the basic flow units) and the energy involved in stretching the floes to brealc the floe doublets apart so that the amount of structure in the system is preserved inspite of the floc-floc collision. This model gives the following expression for the yield value. 

Opp is the longitudinal to longitudinal or p to p-wave" scattering cross section of an isolated scatterer. At low frequencies it is primarily associated with the monopole scattering mode. Ops is the mode conversion or longitudinal to shear wave or p to s-wave cross section. It is primarily associated with the dipole mode at low frequencies, oa is the absorption cross section which describes energy dissipation inside viscoelastic inclusions (embedded in an otherwise elastic matrix material). It is active in all modes of excitation. Combining Equation 29 and 30 yields... 

There are indications that correlation in scatterer responses and interactions between scatterers may not be important generally, even at moderately high volume concentrations of scatterers (33.34). Equations like Equation 29 should therefore yield useful qualitative information about the low frequency structure in c and a over extended ranges of values of < ), depending in the particular system under consideration. A study of the cross sections adds further information about the types of waves scattered (longitudinal or shear) and the relative importance of energy dissipation by the inclusions ... 

Shear yielding in the bulk of the material is incorporated through the constitutive law presented in the previous section. The definition of the plastic strain rate CP together with the expression for the driving stress 6 specifies the energy dissipation rate per unit volume G D< = /2tY . The energy balance in the material can then be written as... 

The possible development of gradients in the components of the interfacial stress tensor due to flow of an adjacent fluid implies that the momentum flux caused by the the flow of liquid at one side of the interface does not have to be completely transported across the interface to the second fluid but may (partly or completely) be compensated in the interface. The extent to which this is possible depends on the rheological properties of the interface. For small shear stresses the interface may behave elastically or viscoelastically. For an elastic interfacial layer the structure remains coherent the layer will only deform, while for a viscoelastic one it may or may not start to flow. The latter case has been observed for elastic networks (e.g. for proteins) that remciln intact, but inside the meshes of which liquid can flow leading to energy dissipation. At large stresses the structure may yield or fracture (collapse), leading to an increased flow. 

Shear yielding is well established as the principal deformation mechanism and source of energy dissipation in both uiunodified and rubbo -toughened epoxy resins [2,3,27,83,121]. As molecular mobility in the epoxy resin network chains decreases, the ability of the matrix to deform by shear yielding is reduced. This is the reason why epoxy resins become both more brittle and more difficult to toughen as the epoxy resin crosslink density increases and/or as the network chains increase in rigidity, e.g. by use of highly aromatic epoxy resin monomers (see Section 19.7.1.1). 

Interfacial adhesion is the adhesion in which interfaces between phases or components are maintained by intermolecular forces, chain entanglements, or both, across the interfaces. Interfacial adhesion between rubber and PMMA must be sufficient to permit the effective transfer of stress to the rubber particles and also to provide multiple sites for crazing and localized shear yielding for effective impact energy dissipation. 

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