An extended macroindentation method for determining the hardness of poorly compressible materials

Shubhajit Paul, Chenguang Wang, Changquan Calvin Sun

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Indentation hardness, H, is an important mechanical property that quantifies the resistance to deformation by a material. For pharmaceutical powders, H can be determined using a macroindentation method, provided they can form intact tablets suitable for testing. This work demonstrates a method for determining the hardness of problematic materials that cannot form suitable tablets for macroindentation. The method entails predicting the hardness of a given powder at zero porosity (H0) from those of microcrystalline cellulose and its binary mixture with the test compound using a power law mixing rule based on weight fraction. This method was found suitable for 13 binary mixtures. In addition, the H0 values derived by this method could capture changes due to different particle sizes of sucrose and sodium chloride. Furthermore, the derived H0 reasonably agreed with the single crystal indentation hardness of a set of 16 crystals when accounting for the effect of indentation condition and structural anisotropy. The mixture method thus extends the use of macroindentation for predicting indentation hardness of powders that cannot form intact tablets and, hence, their plasticity.

Original languageEnglish (US)
Article number122054
JournalInternational journal of pharmaceutics
StatePublished - Aug 25 2022

Bibliographical note

Funding Information:
We thank the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported within this paper ( The authors declare no competing interest.

Publisher Copyright:
© 2022 Elsevier B.V.


  • Indentation hardness
  • Mechanical property
  • Mixing rule
  • Tabletability

PubMed: MeSH publication types

  • Journal Article


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