Viscous energy dissipation treatments

Majerus (61, 62) has approached the failure behavior of highly filled polymers by a thermodynamic treatment in which the ability to resist rupture is related to the propellant s ability to absorb and dissipate energy at a certain rate. An energy criterion which requires failure to be a function of both stress and strain was originally stated by Griffith (36) for brittle materials and later adapted to polymers by Rivlin and Thomas (80). Williams (115) has applied an energy criterion to viscoelastic materials such as solid propellants where appropriate terms are included for viscous energy dissipation. 

The loss factor tau 5 expresses which compoueut is dominant—the elastic or the viscous one. It defines the ratio of the energy dissipated to the energy stored elastically. Some refer to this as internal friction (Blanter et al. 2007). Details on the mathematical data treatment performed to deduce E E" and tan5 can be found in certain references (Chartoff et al. 2009 Mano et al. 2002). 

Mackenzie and Shuttleworth (MS) analyzed [24] the shrinkage rate of a spherical shell according to Frenkel s rnethod. The shell, shown in Fig. 6, can be used to represent the densification of a body containing spherical pores. The dimensions of the shell are chosen so that the central void occupies the same volume fraction as the pores in the sintering body. This is a much more elegant treatment than the analysis of the coalescence of spheres, because the shell remains spherical as it shrinks. Exact expressions can be written for the change in surface area and the energy dissipated in viscous flow as the shell contracts. The result is... 

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