Concurrent and Hierarchical Multiscale Analysis for Layer-Thickness Effects of Nanoscale Coatings on Interfacial Stress and Fracture Behavior

To investigate the effects of coating layer thickness on stress and the debonding behavior near the interface of coating layer and substrate, multiscale analysis is a must since molecular dynamics (MD) simulations can only be performed on models with thicknesses of about tens of nanometers on common computers, but the real thicknesses of such layers are around 300–1200 nm. In this work, generalized particle dynamics (GP) modeling for Al coated on Fe is first developed by using an atomistic domain near the layer interface and having high-scale particles far from that region to reduce degrees of freedom. Results show that the thicker coatings experience lower local average shearing stresses for a given shear strain. However, it is found that when the layer thickness reaches a large value, further increase of the layer thickness will not greatly benefit the reduction of the stress, thereby not increasing the allowable load. This trend is consistent with the simulation for Al₂O₃ coated on Fe by a hierarchical multiscale analysis which is formulated by proposing a nanoscale-based key variable, G_db, called debonding energy density. This variable, defined by the debonding energy per unit area, is used to characterize material bonding strength in realizing that failure originates from the atomistic and nanoscale. The difference and connection of this low-scale fracture variable, G_db, with crack energy release rate, G_IC, in traditional fracture mechanics is illustrated and how G_db can be easily determined through atomistic simulation is exemplified. To make the new variable effective in engineering applications, G_db is used as input to a macroscopic scale finite element model. The obtained layer-thickness effect directly confirms the existence of a critical thickness, predicted by the GP method. This work is an effort in developing material failure theory from lower scales where material fracture originates but with applications in continuum scale via both hierarchical and concurrent multiscale analyses.