Density effect on erosion mechanisms in silica-phenolic solid rocket motors insulations

Article ID: 3988

Keywords: silica-phenolic, Augmented Density-Erosion Model, Gibson-Ashby, spallation gap, insulation, recession rate

Abstract

The design of lightweight Internal Thermal Protection Systems (ITPS) for solid rocket motors is constrained by the non-linear degradation of erosion resistance at low densities. The primary motivation for this work is the discrepancy often observed between standard design models and flight data, specifically in regions of complex flow such as the aft-dome and submerged nozzle inlets. This study establishes a physics-based constitutive law to predict the transition from thermochemical ablation to mechanical spallation in silica-phenolic composites. Unlike semi-empirical correlations, we derive an Augmented Density-Erosion Model from first principles by coupling the energy conservation equation with Gibson-Ashby cellular solids mechanics. We analytically demonstrate that the mechanical erosion rate scales with density according to a power law (r˙∝ ρ^−β) , where the exponent β ≈ 1.5 corresponds to the fracture toughness scaling of open-cell porous foams. This theoretical framework resolves the "spallation gap", the under-prediction of recession by standard heat-of-ablation models (Q^∗) in low-density felts (ρ < 600 kg·m⁻³). The model is validated against historical firing data, demonstrating that the erosion mechanism shifts from energy-limited to strength-limited regimes as density decreases. Furthermore, we address the practical application of these findings by quantifying "danger zones" in density space for graded insulation architectures. This work provides propulsion designers with a rigorous methodology for determining safety margins in mass-critical motor stages, ensuring structural integrity is not compromised by the pursuit of weight reduction.