Numerical modelling of shock-induced chemical reactions (SICR) in reactive powder mixtures using smoothed particle hydrodynamics (SPH)

Abstract

Shock compaction of reactive powder mixtures to synthesize new materials is one of the oldest material processing techniques and has been studied extensively by several researchers over the past few decades. The quantitative connection between the shock energy imparted and the extent of reaction that can be completed in the small time window associated with the passage of the shock wave is complicated and depends on a large variety of parameters. In particular, our understanding of the complex interplay between the thermo-elasto-viscoplastic behaviour of the granular constituents and their temperature dependent, diffusion-limited reaction mechanism may be enriched through careful numerical simulations. A robust numerical model should be able to handle extremely large deformations coupled with diffusion mediated fast reaction kinetics. In this work, a meshfree discrete particle numerical method based on smoothed particle hydrodynamics (SPH) to simulate shock-induced chemical reactions (SICR) in reactive powder mixtures is proposed. We present a numerical strategy to carry out reactions between reactant powder particles and partition the obtained products between the particles in a manner that accounts for the requirement that the total mass of the entire system remains constant as the reactions occur. Instead of solving the reaction–diffusion problem, we propose a ‘pseudo-diffusion’ model in which a distance dependent reaction rate constant is defined to carry out chemical reaction kinetics. This approach mimics the actual reaction–diffusion process at short times. Our numerical model is demonstrated for the well-studied reaction system Nb + 2Si NbSi2. The predicted mass fractions of the product obtained from the simulations are in agreement with experimental observations. Finally, the effects of impact speed, particle arrangement and mixing ratio on the predicted product mass fractions are discussed.