An energy-based method for analyzing instrumented spherical indentation experiments

Wangyang Ni, Yang Tse Cheng, Che Min Cheng, David S. Grummon

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


Using dimensional analysis and finite element calculation, we studied spherical indentation in elastic-plastic solids with work hardening. We report two previously unknown relationships between hardness, reduced modulus, indentation depth, indenter radius, and work of indentation. These relationships, together with the relationship between initial unloading stiffness and reduced modulus, provide an energy-based method for determining contact area, reduced modulus, and hardness of materials from instrumented spherical indentation measurements. This method also provides a means for calibrating the effective radius of imperfectly shaped spherical indenters. Finally, the method is applied to the analysis of instrumented spherical indentation experiments on copper, aluminum, tungsten, and fused silica.

Original languageEnglish
Pages (from-to)149-157
Number of pages9
JournalJournal of Materials Research
Issue number1
StatePublished - Jan 2004

ASJC Scopus subject areas

  • Materials Science (all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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