Indentation Response of Power and Sigmoid Functionally Graded PSZ/NiCrAlY Composites

M. A. Eltaher*, A. Wagih

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Owing to their superior mechanical properties, functionally graded materials (FGMs) are currently applicable for many tribological systems, which increased the need for a rapid prediction tool of the hardness and wear behavior of these materials. To this end, this paper aims to present empirical equations to predict the residual indentation deformation for the PSZ/NiCrAlY composite FGM that could give a rapid indication on the material hardness and wear rates at different indentation loads. The empirical equations were derived for two common gradient laws, power (P-FGM) and sigmoid (S-FGM), based on numerical results obtained and validated with experimental results in this study. The numerical results were obtained by simulating indentation experiments using commercial finite element software considering the gradient of all the elastic and plastic material properties. The influence of the gradient index, gradient law and indentation displacement on the force-indentation response, contact pressure distribution, plastic stains, contact surface profile evolutions, and the residual indentation deformations were studied. The results showed that contact force and contact pressure were larger for P-FGM than S-FGM for all the gradient indices. The residual indentation deformation is larger for S-FGM than P-FGM for all the gradient indices due to the higher PSZ ceramic phase at the contact area for P-FGM than S-FGM. The residual indentation deformation of the FGM was normalized with respect to its value for the pure matrix based on the finite element results that highlighted the independence of this ratio on the indentation load. Finally, empirical equations were derived to predict the residual indentation deformation for the PSZ/NiCrAlY composite FGM with respect to the gradient index for both the gradient laws, power and sigmoid functions.

Original languageEnglish (US)
Article number2250026
JournalInternational Journal of Applied Mechanics
Issue number4
StatePublished - May 1 2022

Bibliographical note

Funding Information:
This study was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under Grant no. G-53-135-1442. The authors, therefore, acknowledge with thanks DSR for technical and financial support.

Publisher Copyright:
© 2022 World Scientific Publishing Europe Ltd.


  • empirical indentation forms
  • finite element method
  • homogenization
  • PSZ/NiCrAlY composite
  • sigmoid/power FG substrate

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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