Optimization Development and Application of Lee-Tarver Reaction Rate Model

To address the shortcomings of the Lee-Tarver ignition and growth reaction rate equation, which comprises numerous parameters (15) and is difficult to calibrate, semi-periodic trigonometric functions were introduced to optimize the model. The new rate equation enhances the continuity of the ignition term, restricts the maximum value of the shape factors for the growth and completion terms to 1, mitigates the parameter compensation between the proportional coefficients (Grow1 and Grow2) and the shape factors, eliminates the reaction degree limit of the trinomial structure, reduces the number of parameters in the reaction rate equation to 10, thereby improving parameter calibration efficiency. Based on LS-Dyna, a secondary development was conducted for the improved ignition and growth model. Comparative calculations were performed to assess the shock initiation simulation results from the Lee-Tarver model and the optimized model, revealing highly consistent results for the internal pressure and reaction degree of the explosive, validating the correctness of the model development. Utilizing experimental data from explosive-driven metal plates, the parameters of the optimized ignition and growth model were calibrated with LS-OPT, and the sensitivity of the rate equation parameters was statistically analyzed to identify key parameters, providing a reference for further improving parameter calibration efficiency. Comparisons between experimental and simulated results of explosive-driven metal plates showed a simulation error of less than 3%, confirming the engineering validity of the calibrated parameters. Applying the improved ignition and growth model with safety experiments, the impact initiation response characteristics of ammunitions under bullet/fragment impact were investigated. Within 66 μs after bullet impact, the peak internal pressure of the explosive reached 0.145 Mbar (48.3% of the detonation pressure), indicating no detonation reaction occurred. Under fragment impact conditions, the peak internal pressure of the explosive was only 0.0079 Mbar, with the reaction degree near the impact point being higher than in other regions, but the maximum reaction degree was merely 0.01, confirming no detonation. The simulation results of the optimized model exhibited good consistency with experimental test results, validating the engineering applicability of the optimized and developed ignition and growth model.