Strain sensitive response of filled elastomers

The strain dependence of the elastic and the anelastic behavior of filled elastomers is discussed in the light of recent experiments on carbon-black filled rubber as well as on sodium chloride filled polyurethane. The latter experiments suggest that the apparent creep of filled elastomers is the manifestation of the gradual change of the elastic moduli resulting from the loss with strain of effective filler matrix interaction, rather than a truly viscoelastic phenomenon. N recent years linear viscoelastic analysis of an assumedly homogeneous, isotropic and thermorheologically simple medium has been accepted as a standard procedure for evaluating the structural integrity of solid-propellant rocket motors.1 Although it is generally recognized that, on the microscale, the solid propellant is neither continuous nor homogeneous, the previously mentioned idealization is assumed to be "permissible with important exceptions, such as stress induced anisotropy and fracture origins," on the basis of the purported similarity of the effect of microstructure in such materials with those in "concrete, asphalt or for that matter metals7' (Ref. 1, p. 785). Coupling this assumption with the desire to introduce the "least amount of analytical complexity," the way is opened for the application of the classical methods of linear viscoelastic analysis using the various well established procedures of material characterization and the "correspondence principle" between elastic and linear viscoelastic solutions of boundary value problems, the implicit assumption being that the relevant range of structural performance coincides, for all practical purposes, with the range of infinitesimal or, at least, of very small strains. Once these premises of the structural integrity analysis have been accepted, the further development is exclusively concerned with increasingly sophisticated analytical methods within the given framework, with their computerization and with increasingly elaborate generalizations. Unfortunately, the assumptions which have produced an accessible analytical theory have, at the same time, dissociated the analytical results from reality, simply because they have become irrelevant to the principal engineering purpose of the analysis, which is a realistic evaluation of structural integrity. The main reason for this dissociation is the fact that the highly filled elastomeric propellant can be represented by the linear viscoelastic medium only within the range of infinitesimal strains, which is not the range that is of particular relevance in structural integrity evaluation. The structurally relevant strain ranges are those of a) shorttime straining with strain rates of the order of up to 10 in./ in./sec during firing and flight, with maximum strains at the inner bore of the order of 10 to 60% reached in tens of milliseconds, b) of thermal strain cycling at rates of the order of 10~3 to 10~ 5 in./in./sec and maximum strains in the one to several percent range, and c) of long-time storage strains of a similar order of magnitude but considerably lower strain rates and material degradation. Although in materials other than solid propellants, the structural integrity analysis of which requires the consideration of