Multi-scale modelling of fatigue crack propagation due to liquid droplet impingement

Abstract

We develop a sequential multi-scaling framework for studying the problem of fatigue crack propagation due to liquid droplet impingement. The scope is limited to a hypothetical material and a hypothetical liquid. The multi-scaling is achieved by handshaking the atomistic scale molecular dynamics (MD) simulations with the continuum scale smoothed particle hydrodynamics (SPH). The handshaking, in turn, is performed by evaluating the material, the fracture and the loading properties from MD simulations, and using them as inputs in the continuum scale SPH model. Due to the qualitative agreement of the pressure developed in the fluid and the substrate between the MD simulations and already published results, the liquid droplet impact in SPH is simulated through appropriate surface stresses. Further, we incorporate the pseudo-spring approach within the SPH model to develop a methodology for studying mixed-mode fatigue crack propagation. Our methodology provides good agreement with the existing literature for several cases. Lastly, we calculate the fatigue life of an edge-cracked specimen due to liquid droplet impingement.