Interfacial contact stiffness of fractal rough surfaces

Dayi Zhang, Ying Xia, Fabrizio Scarpa, Jie Hong*, Yanhong Ma

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

44 Citations (Scopus)
353 Downloads (Pure)


In this work we describe a theoretical model that predicts the interfacial contact stiffness of fractal rough surfaces by considering the effects of elastic and plastic deformations of the fractal asperities. We also develop an original test rig that simulates dovetail joints for turbo machinery blades, which can fine tune the normal contact load existing between the contacting surfaces of the blade root. The interfacial contact stiffness is obtained through an inverse identification method in which finite element simulations are fitted to the experimental results. Excellent agreement is observed between the contact stiffness predicted by the theoretical model and by the analogous experimental results. We demonstrate that the contact stiffness is a power law function of the normal contact load with an exponent α within the whole range of fractal dimension D(1 < D < 2). We also show that for 1 < D < 1.5 the Pohrt-Popov behavior (α = 1/(3-D)) is valid, however for 1.5 < D < 2, the exponent α is different and equal to 2(D-1)/D. The diversity between the model developed in the work and the Pohrt-Popov one is explained in detail.

Original languageEnglish
Article number12874
Number of pages9
JournalScientific Reports
Publication statusPublished - 9 Oct 2017


  • Applied physics
  • Mechanical engineering
  • Nonlinear phenomena
  • Surfaces, interfaces and thin films


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