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<p>This study presents a rapid method to identify the yield stress (<i>σ</i><sub><i>y</i></sub>) and the work hardening exponent (<i>n</i>) which define the work hardening behavior of metallic materials using spherical instrumented indentation. The advantage of the proposed method is that it relies solely on the use of F-h indentation load curves, which are easy to obtain. The technique combines inverse analysis with a precomputed database of finite element simulations, avoiding time-consuming computations during optimization. Numerical indentation curves are generated from a database using an interpolation method, and mechanical parameters (<i>σ</i><sub><i>y</i></sub>, <i>n</i>) are identified by minimizing the error between experimental and numerical curves using the Nelder–Mead algorithm. It is shown that, for a given indentation depth, the evolution of the logarithm of the load is approximately linear with respect to the strain hardening exponent <i>n</i> and the <i>K</i> parameter which is defined by the authors as equal to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(( {1 - n} )\ln ( {^{{\sigma _y}}{/_E}} )\)</EquationSource> </InlineEquation>. This allows the use of a small database composed of a limited number of materials, which is therefore easy to establish. On the other hand, to improve robustness, we define a new method to determine the representative strain-stress points which are obtained from Hessian matrix of the residual function. In order to determine various representative points this process is repeated over different portions of the indentation curve, allowing the reconstruction of the strain hardening law using Hollomon’s model. The presented method is applied on one aluminum alloy, three low-alloy steels and one high-alloy steel, which present quenched and tempered or globalized microstructures. The obtained results are consistent with tensile tests except for the aluminum alloy which present an anisotropic microstructure. The approach proposed in this article provides a rapid and reliable tool for mechanical characterization, particularly suited to industrial applications. This approach, based on a nearly non-destructive technique, will be particularly useful due to its relative simplicity in preparing the material to be tested and its ability to test parts on site for which tensile tests are difficult or even impossible to perform.</p>

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Identification of work hardening laws by spherical indentation of metallic materials by rapid inverse analysis from a database

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Mohammad Mahdi Semnani Rahbar,
  • Raphael Omran,
  • Xavier Hernot,
  • Olivier Bartier,
  • Romaric Collet,
  • Daniel Maisonnette,
  • Gerard Mauvoisin

摘要

This study presents a rapid method to identify the yield stress (σy) and the work hardening exponent (n) which define the work hardening behavior of metallic materials using spherical instrumented indentation. The advantage of the proposed method is that it relies solely on the use of F-h indentation load curves, which are easy to obtain. The technique combines inverse analysis with a precomputed database of finite element simulations, avoiding time-consuming computations during optimization. Numerical indentation curves are generated from a database using an interpolation method, and mechanical parameters (σy, n) are identified by minimizing the error between experimental and numerical curves using the Nelder–Mead algorithm. It is shown that, for a given indentation depth, the evolution of the logarithm of the load is approximately linear with respect to the strain hardening exponent n and the K parameter which is defined by the authors as equal to \(( {1 - n} )\ln ( {^{{\sigma _y}}{/_E}} )\) . This allows the use of a small database composed of a limited number of materials, which is therefore easy to establish. On the other hand, to improve robustness, we define a new method to determine the representative strain-stress points which are obtained from Hessian matrix of the residual function. In order to determine various representative points this process is repeated over different portions of the indentation curve, allowing the reconstruction of the strain hardening law using Hollomon’s model. The presented method is applied on one aluminum alloy, three low-alloy steels and one high-alloy steel, which present quenched and tempered or globalized microstructures. The obtained results are consistent with tensile tests except for the aluminum alloy which present an anisotropic microstructure. The approach proposed in this article provides a rapid and reliable tool for mechanical characterization, particularly suited to industrial applications. This approach, based on a nearly non-destructive technique, will be particularly useful due to its relative simplicity in preparing the material to be tested and its ability to test parts on site for which tensile tests are difficult or even impossible to perform.