Determination of hardness-strength and -flow behavior relationships in bulged aluminum alloys and verification by FE analysis on Rockwell hardness test

  • Amir Asgharzadeh
  • Sobhan Alah Nazari Tiji
  • Rasoul Esmaeilpour
  • Taejoon Park
  • Farhang PourboghratEmail author


Determination of mechanical properties in bulged specimens has its own challenges due to their nonhomogeneous geometry. In the present study, a set of empirical hardness-strength-hardening law correlations is proposed to estimate the flow behavior of the bulged specimens. To do so, comprehensive empirical strength-hardness correlations applicable for all aluminum alloys were developed by collecting datasets from 16 individual studies. These relationships were then compared with hardness/strength experimental data obtained from heat-treated AA6061 and AA7075 tubular specimens. Then, a set of empirical models was developed to calibrate the coefficients of the Holloman and Voce type hardening laws by utilizing the measured hardness and strength values. Finally, to assure the validity of the proposed model, Rockwell hardness test, conducted on the bulged AA6061 and AA7075, was simulated. To do so, the generated flow behavior of bulged specimens based on hardness measurement was used as input plastic flow data in Abaqus commercial FE software, and the indentation geometry on bulged Al specimens were then compared to the experiments. Comprehensive linear and second-degree polynomial relationships were regressed on compiled data for ultimate tensile and yield strengths, respectively. Reasonable agreement was achieved between hardness-strength relationships obtained for all Al alloys and processed AA6061 and AA7075 tubular samples, confirming that these relationships are applicable for any Al alloys regardless of product type and process design. Finally, although both Holloman and Voce type hardening laws gave reasonable estimation of flow behavior in Al tubular specimens particularly at high strain values, Voce model provided a better estimation in comparison to Holloman hardening law. The FE analysis of Rockwell hardness test confirmed that the proposed hardness-strength-hardening law relationship based on Voce type hardening rule was sufficiently accurate in predicting the flow curve in bulged 6061 and 7075 Al alloys.


Aluminum alloys Bulged specimen Hardness test Hardness-strength-hardening law correlation Finite element analysis 



The authors wish to thank the U.S. Department of Energy for the support of this project through the DOE award DE-FG02-13ER41974 and DOE DE-EE000597, with United States Automotive Materials Partnership LLC (USAMP).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Amir Asgharzadeh
    • 1
  • Sobhan Alah Nazari Tiji
    • 1
  • Rasoul Esmaeilpour
    • 1
  • Taejoon Park
    • 1
  • Farhang Pourboghrat
    • 1
    • 2
    Email author
  1. 1.Department of Integrated Systems EngineeringThe Ohio State UniversityColumbusUSA
  2. 2.Department of Mechanical and Aerospace EngineeringThe Ohio State UniversityColumbusUSA

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