Fracture-mode map of brittle coatings: Theoretical development and experimental verification

Chong He, Zhaoqian Xie, Zhenbin Guo, Haimin Yao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)


Abstract Brittle coatings, upon sufficiently high indentation load, tend to fracture through either ring cracking or radial cracking. In this paper, we systematically study the factors determining the fracture modes of bilayer material under indentation. By analyzing the stress field developed in a coating/substrate bilayer under indentation in combination with the application of the maximum-tensile-stress fracture criterion, we show that the fracture mode of brittle coatings due to indentation is determined synergistically by two dimensionless parameters being functions of the mechanical properties of coating and substrate, coating thickness and indenter tip radius. Such dependence can be graphically depicted by a diagram called 'fracture-mode map', whereby the fracture modes can be directly predicated based on these two dimensionless parameters. Experimental verification of the fracture-mode map is carried out by examining the fracture modes of fused quartz/cement bilayer materials under indentation. The experimental observation exhibits good agreement with the prediction by the fracture-mode map. Our finding in this paper may not only shed light on the mechanics accounting for the fracture modes of brittle coatings in bilayer structures but also pave a new avenue to combating catastrophic damage through fracture mode control.
Original languageEnglish
Article number2667
Pages (from-to)19-35
Number of pages17
JournalJournal of the Mechanics and Physics of Solids
Publication statusPublished - 30 Jun 2015


  • Cracking morphology
  • Hertzian fracture
  • Laminated materials
  • Thin film

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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