Exponent for Hall–Petch behaviour of ultra-hard multilayers

Abstract

Elastically inhomogeneous multilayer films are being exploited for use as ultra-hard coatings. These films exhibit a strong dependence between the compositional wavelength of the film, Λ, and the hardness, H=KΛ^−a+H₀ where the scaling exponent a depends on the elastic properties of the individual layers (shear moduli and Poisson ratios). The dislocation pileup model can explain this trend and form a bridge between the microscopic strength of multilayer interfaces and the macroscopic strength of the multilayer. A semianalytic solution to the pileup model of multilayer strength is presented. All parameter dependencies are solved analytically except a single dimensionless coefficient which is found from numerical simulation. The predictions are compared to data from a 2D discrete dislocation model and to experimental Cu/Ni data. Coefficients and exponents are given for some additional material systems.

Acknowledgements

The author would like to acknowledge the financial support of the Penn State University Department of Engineering Science and Mechanics and AFRL/MLBT. Additionally, conversations with P. Hazzeldine, S. Basu and L. Fang have been extremely useful. The author would like to thank L. Fang for helping to prepare useful data, particularly table 1. Finally, the comments and suggestions by the anonymous referee have been very useful.

This material is based in part on research sponsored by AFRL/MLBT, 2941 P Street, Room 136, WPAFB, OH 45433-7750 under agreement number F33615-03-2-5035. The US Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of AFRL/MLBT, 2941 P Street, Room 136, WPAFB, OH 45433-7750 or the US Government.