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Background <p>Indentation size effect phenomenon (ISE – dependence of measured hardness numbers on imprint size) was widely studied, but the nature of data scattering remains insufficiently studied in the series of indentations.</p> Objective <p>This study investigates the influence of microstructure in single-phase polycrystalline materials on data scattering associated with ISE, covering microhardness to conventional hardness penetration depths.</p> Methods <p>Seven grades of structural steel and alloys with varying treatments and microstructures (austenitic, ferritic, bainitic, and martensitic; nine materials total) were subjected to force-controlled Vickers indentations at multiple load levels. Hardness values were treated as stochastic parameters, fitted to a Weibull distribution with probe-number-dependent parameters. A specific data processing technique eliminated this dependence, yielding saturation values (asymptotic to infinite probes).</p> Results <p>The mathematical expectation (mean hardness) exhibited weak size dependence, showing both normal and reverse ISE. The Weibull form factor (governing data scatter) was strongly size-dependent, demonstrating bilinear behavior in double logarithmic coordinates with imprint diagonal to grain size ratio as abscissa. A nonlocal continuum plasticity model based on stochastic nature of plastic flow was proposed to explain this behavior.</p> Conclusions <p>In single-phase polycrystalline materials, data scatter is a geometric effect governed solely by the imprint diagonal-to-grain size ratio (or prior austenite grain size). This phenomenon is material-independent under conditions of isotropy and absent extrinsic gradients of microstructure.</p>

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Experimental Insights into Reproducibility of Microhardness Tests of Polycrystalline Metals

  • 期刊论文

  • 发表日期：

    2025年12月4日

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  • S.P. Samoilov,
  • Y.E. Kapelyushin,
  • T. Sonar

摘要

Background

Indentation size effect phenomenon (ISE – dependence of measured hardness numbers on imprint size) was widely studied, but the nature of data scattering remains insufficiently studied in the series of indentations.

Objective

This study investigates the influence of microstructure in single-phase polycrystalline materials on data scattering associated with ISE, covering microhardness to conventional hardness penetration depths.

Methods

Seven grades of structural steel and alloys with varying treatments and microstructures (austenitic, ferritic, bainitic, and martensitic; nine materials total) were subjected to force-controlled Vickers indentations at multiple load levels. Hardness values were treated as stochastic parameters, fitted to a Weibull distribution with probe-number-dependent parameters. A specific data processing technique eliminated this dependence, yielding saturation values (asymptotic to infinite probes).

Results

The mathematical expectation (mean hardness) exhibited weak size dependence, showing both normal and reverse ISE. The Weibull form factor (governing data scatter) was strongly size-dependent, demonstrating bilinear behavior in double logarithmic coordinates with imprint diagonal to grain size ratio as abscissa. A nonlocal continuum plasticity model based on stochastic nature of plastic flow was proposed to explain this behavior.

Conclusions

In single-phase polycrystalline materials, data scatter is a geometric effect governed solely by the imprint diagonal-to-grain size ratio (or prior austenite grain size). This phenomenon is material-independent under conditions of isotropy and absent extrinsic gradients of microstructure.