Isotropic hardening curve characterization by the resultant profile of ball indentation tests

  • L. Q. Machado
  • L. MalcherEmail author
Technical Paper


Traditionally, the material’s stress–strain relationship is acquired from uniaxial testing, which is widely used to describe its behavior under plastic deformation. When it comes to traditional hardness tests, such as in the Brinell, Knoop, Rockwell, and Vickers, they have been mostly used as a way to assess the capability a material has to resist plastic deformation. The technique developed and presented here has gone beyond that by determining other material properties in addition to hardness. This is performed by relating the applied load to the resultant indentation profile impressed in the material. Similar approaches have been devised aided by instrumented indentation devices. However, the methodology presented here does not require the use of such a device. It considers that the use of three configurations of the Brinell hardness test is enough to represent the material behavior within the boundaries of the plastic deformation experienced by it. Therefore, it is simpler than the usual approaches in this aspect. On the other hand, the indentation profile is also assessed along with the load–depth information obtained for each of those configurations. For that, a multi-image analysis of the indention impressions is performed in a confocal laser microscope. The indentation profile informs the amount of pile-up/sink-in experienced by the material. These phenomena are directly related to the strain hardening of the material and therefore influence the description of the plastic stress–strain curve. The extracted profiles are used as a reference with which the predicted output of repeated FEM modeling is compared. In this process, several trial stress–strain curves are provided to minimize the discrepancy between numerical and experimental data in an iterative FEM modeling of the indentation process. The process runs until reaching the established tolerance and thus providing the hardening parameters that best fit the experimental data. The SAE 1524 is analyzed in the present work employing the Kleinermann–Ponthot constitutive hardening model, which is composed of four parameters. It is shown that the determined parameters conform closely to the experimental data. Therefore, the procedure is viable for the material characterization task.


Parameter identification Indentation test Indentation multi-image analysis Stress–strain curve 



The authors acknowledge the Department of Mechanical Engineering of the University of Brasília and CNPq for providing them all the necessary to develop this research. Lucival Malcher would also like to acknowledge the support from the Brazilian Council for the Scientific and Technological Development—CNPq (contract 311933/2018-1).


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of TechnologyUniversity of BrasíliaBrasíliaBrazil

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