Wedge Specimens Under Simultaneous Straining and Cooling

This study is a continuation of the earlier study regarding uniaxial samples under simultaneous straining and cooling. The objective of this study was to extend the constitutive model application to specimens with multi-axial stress state. An ad hoc nonlinear viscoelastic constitutive model that is based on the cumulative damage of the propellant under load is applied. Cumulative damage parameters of the propellant were determined under five different temperature conditions with 75° and 20°F temperature extremes. The analysis is conducted on real times at the imposed temperatures without assuming timetemperature equivalence. A number of tests were performed using 3-D analog specimens subjected to low straining and cooling rates, and other tests to high straining and cooling rates. INTRODUCTION AND APPROACH Past effort to predict the stresses in a subscale motor that is subjected to a simultaneous straining and cooling test showed the predicted stresses to be smaller than the measured values by a factor of more than two. The analysis method was based on a linear elastic and also on a linear viscoelastic constitutive model. It was concluded that the problem lies in the propellant complex thermo-rheological behavior (i.e., the timetemperature equivalence based on the simple thermorheological behavior used in the linear viscoelastic model) is not applicable. Rigorous nonlinear viscoelastic (NLVE) solution, in particular with regard to prediction of propellant responses to simultaneous straining and cooling, is not yet obvious. The subject is part of the study in the Service Life Prediction Technology (SLPT) program. Awaiting the SLPT outcome and parallel to that effort, an interim ad hoc NLVE solution is proposed. Unlike the rigorous NLVE model, the proposed model is based on the assumption that the NLVE stress-strain relation is due to the load-induced micro-damage in the propellant. The physics of the damage is not well defined, but its intensity has been quantified as a damage measure or norm in terms of Lebesque integrals of stress (NG) and of strain (Ne),