Unique universal scaling in nanoindentation pop-ins

Yuji Sato,Shuhei Shinzato,Takahito Ohmura,Shigenobu Ogata,Takahiro Hatano

doi:10.1038/s41467-020-17918-7

Abstract

Power laws are omnipresent and actively studied in many scientific fields, including plasticity of materials. Here, we report the power-law statistics in the second and subsequent pop-in magnitudes during load-controlled nanoindentation testing, whereas the first pop-in is characterized by Gaussian-like statistics with a well-defined average value. The transition from Gaussian-like to power-law is due to the change in the deformation mechanism from dislocation nucleation to dislocation network evolution in the sharp-indenter induced abruptly decaying stress and dislocation density fields. Based on nanoindentation testing on the (100) and (111) surfaces of body-centered cubic (BCC) iron and the (100) surface of face-centered cubic (FCC) copper, the scaling exponents of the power laws were determined to be 5.6, 3.9, and 6.4, respectively. These power-law exponents are much higher than those typically observed in micro-pillar plasticity (1.0–1.8), suggesting that the nanoindentation plasticity belongs to a different universality class than the micro-pillar plasticity.

Highlights

Power laws are omnipresent and actively studied in many scientific fields, including plasticity of materials
Nanoindentation experiments are conducted on the 〈100〉- and 〈111〉-oriented surfaces ((100) and (111) surfaces) of body-centered cubic (BCC) iron (Fe) and the (100) surface of face-centered cubic (FCC) copper (Cu) at room temperature (300 K)
The first pop-in, which is indicated by a dark-blue solid arrow, was unique: it had the largest magnitude in terms of the displacement burst, Δh, of the pop-ins observed in each nanoindentation testing

Summary

Introduction

Power laws are omnipresent and actively studied in many scientific fields, including plasticity of materials. Based on nanoindentation testing on the (100) and (111) surfaces of body-centered cubic (BCC) iron and the (100) surface of face-centered cubic (FCC) copper, the scaling exponents of the power laws were determined to be 5.6, 3.9, and 6.4, respectively. 1234567890():,; Power laws are ubiquitous and actively studied in many fields of science, especially in statistical studies of the magnitudes of natural phenomena such as earthquakes[1] They are observed in the plasticity of micro- and nanoscale materials in mechanical testing[2,3,4,5,6,7,8,9,10]. Stochastic analyses of the pop-in magnitude are performed by defining the pop-in magnitude as the indenter displacement burst and as the drop of the contact stress between the indenter and target materials

Methods

Results

Conclusion