A unified approach to failure and its application to highly filled polymers

Abstract

Two interrelated general approaches to the study of structural failure of highly filled polymeric materials, e.g., a solid propellant, are described. These consist of the macroscopic (thermodynamics and continuum mechanics) and microscopic (molecular model) methods of analysis in conjunction with solid propellant experimental data. The thermodynamic investigation indicates that propellant material under loading goes through stages of stable and unstable behavior which depend upon the rate at which work is absorbed and dissipated by the material. The instability point seems to correlate with results from subscale motors. The thermodynamic investigation is then extended by a functional analysis of failure treated from a viewpoint of continuum mechanics. Since fracture, per se, is a physical observable, it is represented by a “state vector” in n‐dimensional space. The number of dimensions of this space depends upon the basic variables involved in fracture. Since the correct failure criteria must be tensorally consistent with the tensor rank of fracture, distinct sets of functions can be applied to experimental data. The data are compared to the classical scalar functions of failure. They were obtained from uniaxial and biaxial creep and relaxation tests to failure, uniaxial and biaxial tension tests conducted under constant rates of loading and of strain, with and without superimposed hydrostatic pressure, and pure shear tests to failure. The correlation between the different types of induced failure is demonstrated through the microscopic approach by use of molecular models and the application of statistical mechanics.

Solid Propellant Structural Integrity Investigations: Dynamic Response and Failure Mechanisms

“…Crack velocities predicted by Equation (8) are of the order of 1.0 to 2.5 inches per minute, depending on crack length and test temperature, in excellent agreenment with the experimental observations.…”

“…9 ) if the outer supports are restrained from lateral motion. Specifically, it was found that the normal stress a y across the shear is proportional to the applied shear stress T. and is, approximately, ry t 0.3o (8) where 'to is the shear force divided by the total area.…”