International Journal of Fracture

, Volume 215, Issue 1–2, pp 39–48 | Cite as

The steady-state Archard adhesive wear problem revisited based on the phase field approach to fracture

  • Valerio Carollo
  • Marco PaggiEmail author
  • José Reinoso
Original Paper


The problem of adhesive wear is herein investigated in relation to periodic asperity junction models in the framework of the Archard interpretation suggesting that wear debris formation is the result of asperity fracture. To this aim, the phase field model for fracture is exploited to simulate the crack pattern leading to debris formation in the asperity junction model. Based on dimensional analysis considerations, the effect of the size of the junction length, the lateral size of the asperity, and the amplitude of the re-entrant corner angles \(\gamma \) and \(\beta \) defined by the junction geometry is examined in the parametric analysis. Results show that two failure modes are expected to occur, one with a crack nucleated at the re-entrant corner \(\gamma \), and another with a crack nucleated at the re-entrant corner \(\beta \), depending on the dominant power of the stress-singularity at the two re-entrant corner tips. Steady-state adhesive wear, where the initial asperity junction geometry is reproduced after debris formation, is observed for asperity junctions with \(\gamma = 45^\circ \), almost independently of the lateral size of the asperity and of the horizontal projection of the junction length.


Adhesive wear Steady-state conditions Phase field approach to fracture Nonlinear finite element method 



The authors would like to acknowledge Prof. D. A. Hills (University of Oxford) for useful discussion and suggestions on the problem of steady state wear. JR acknowledges the support of the projects funded by the Spanish Ministry of Economy and Competitiveness/FEDER (Projects MAT2015-71036-P and MAT2015-71309-P) and the Andalusian Government (Projects of Excellence Nos. TEP-7093 and P12-TEP-1050).


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.IMT School for Advanced StudiesLuccaItaly
  2. 2.Universidad de SevillaSevilleSpain

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