Self-affine surface morphology of plastically deformed metals

TL;DR

This study reveals that plastically deformed metals develop self-affine surface roughness over a wide scale range, with a stable Hurst exponent around 0.75, modeled as fractional Brownian motion, indicating a fractal strain distribution.

Contribution

It provides the first comprehensive analysis of self-affine surface morphology in metals across multiple scales using combined microscopy techniques.

Findings

Surface roughness develops self-affine characteristics over 10 nm to 2 mm scales.

Hurst exponent decreases then stabilizes at approximately 0.75 with increasing strain.

Surface profiles can be modeled as fractional Brownian motion.

Abstract

We analyze the surface morphology of metals after plastic deformation over a range of scales from 10 nm to 2 mm, using a combination of atomic force microscopy and scanning white-light interferometry. We demonstrate that an initially smooth surface during deformation develops self-affine roughness over almost four orders of magnitude in scale. The Hurst exponent $H$ of one-dimensional surface profiles is initially found to decrease with increasing strain and then stabilizes at $H \approx 0.75$. By analyzing their statistical properties we show that the one-dimensional surface profiles can be mathematically modelled as graphs of a fractional Brownian motion. Our findings can be understood in terms of a fractal distribution of plastic strain within the deformed samples.