Advertisement

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

  • Valerio Carollo
  • Marco Paggi
  • José Reinoso
Original Paper
  • 15 Downloads

Abstract

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.

Keywords

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

Notes

Acknowledgements

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).

References

  1. Aghababaei R, Warner DH, Molinari JF (2016) Critical length scale controls adhesive wear mechanisms. Nat Commun 7:11816CrossRefGoogle Scholar
  2. Aldakheel F, Mauthe S, Miehe C (2014) Towards phase field modeling of ductile fracture in gradient-extended elastic–plastic solids. Proc Appl Math Mech 14:411–412CrossRefGoogle Scholar
  3. Alessi R, Marigo JJ, Maurini C, Vidoli S (2017) Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: one-dimensional examples. Int J Mech Sci.  https://doi.org/10.1016/j.ijmecsci.2017.05.047
  4. Archard J (1953) Contact and rubbing of flat surfaces. J Appl Phys 24(8):981–988CrossRefGoogle Scholar
  5. Arnell R, Davies P, Halling J, Whomes T (1991) Tribology. Principles and design applications. Macmillian Education Ltd, LondonGoogle Scholar
  6. Bhushan B (2000) Modern tribology handbook. CRC Press, Boca RatonCrossRefGoogle Scholar
  7. Borden M, Hughes T, Landis C, Anvari A, Lee I (2016) A phase-field formulation for fracture in ductile materials: finite deformation balance law derivation, plastic degradation, and stress triaxiality effects. Comput Methods Appl Mech Eng 312:130–166CrossRefGoogle Scholar
  8. Bourdin B, Francfort GA, Marigo JJ (2008) The variational approach to fracture. J Elast 91(1):5–148CrossRefGoogle Scholar
  9. Brockley CA, Fleming GK (1965) A model junction study of severe metallic wear. Wear 8(5):374–380CrossRefGoogle Scholar
  10. Buckley DH (1981) Surface effects in adhesion, friction, wear, and lubrication, vol 5. Elsevier, AmsterdamGoogle Scholar
  11. Carpinteri A, Paggi M (2007) Analytical study of the singularities arising at multi-material interfaces in 2D linear elastic problems. Eng Fract Mech 74(1):59–74CrossRefGoogle Scholar
  12. Chung KH, Kim DE (2003) Fundamental investigation of micro wear rate using an atomic force microscope. Tribol Lett 15(2):135–144CrossRefGoogle Scholar
  13. Freddi F, Royer-Carfagni G (2011) Variational fracture mechanics to model compressive splitting of masonry-like materials. Ann Solid Struct Mech 2(2–4):57–67CrossRefGoogle Scholar
  14. Gotsmann B, Lantz MA (2008) Atomistic wear in a single asperity sliding contact. Phys Rev Lett 101(12):125,501CrossRefGoogle Scholar
  15. Greenwood JA, Tabor D (1955) Deformation properties of friction junctions. Proc Phys Soc Sect B 68(9):609CrossRefGoogle Scholar
  16. Hesch C, Franke M, Dittmann M, Temizer I (2016) Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems. Comput Methods Appl Mech Eng 301:242–258CrossRefGoogle Scholar
  17. Hills DA, Paynter RJH, Nowell D (2010) The effect of wear on nucleation of cracks at the edge of an almost complete contact. Wear 268(7–8):900–904CrossRefGoogle Scholar
  18. Holm R (2013) Electric contacts: theory and application. Springer, New YorkGoogle Scholar
  19. Kayaba T, Kato K (1979) The analysis of adhesive wear mechanism by successive observations of the wear process in SEM. Wear Mater 110:45–56Google Scholar
  20. Kim HK, Hills DA, Paynter RJH (2014) Asymptotic analysis of an adhered complete contact between elastically dissimilar materials. J Strain Anal Eng Des 49(8):607–617CrossRefGoogle Scholar
  21. Lubarda VA, Krajcinovic D, Mastilovic S (1994) Damage model for brittle elastic solids with unequal tensile and compressive strengths. Eng Fract Mech 49(5):681–697CrossRefGoogle Scholar
  22. Miehe C, Hofacker M, Welschinger F (2010a) A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199(45):2765–2778CrossRefGoogle Scholar
  23. Miehe C, Welschinger F, Hofacker M (2010b) Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int J Numer Methods Eng 83(10):1273–1311CrossRefGoogle Scholar
  24. Miehe C, Hofacker M, Schaenzel LM, Aldakheel F (2015) Phase field modeling of fracture in multi-physics problems. Part II. Brittle-to-ductile failure mode transition and crack propagation in thermo-elastic–plastic solids. Comput Methods Appl Mech Eng 294:486–522CrossRefGoogle Scholar
  25. Miehe C, Aldakheel F, Teichtmeister S (2017) Phase-field modeling of ductile fracture at finite strains: a robust variational-based numerical implementation of a gradient-extended theory by micromorphic regularization. Int J Numer Methods Eng 111:816–863CrossRefGoogle Scholar
  26. Mugadu A, Hills DA, Limmer L (2002a) An asymptotic approach to crack initiation in fretting fatigue of complete contacts. J Mech Phys Solids 50(3):531–547CrossRefGoogle Scholar
  27. Mugadu A, Hills DA, Nowell D (2002b) Modifications to a fretting-fatigue testing apparatus based upon an analysis of contact stresses at complete and nearly complete contacts. Wear 252(5):475–483CrossRefGoogle Scholar
  28. Paggi M, Carpinteri A (2008) On the stress singularities at multimaterial interfaces and related analogies with fluid dynamics and diffusion. Appl Mech Rev 61(2):020801CrossRefGoogle Scholar
  29. Paggi M, Reinoso J (2017) Revisiting the problem of a crack impinging on an interface: a modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model. Comput Methods Appl Mech Eng 321:145–172CrossRefGoogle Scholar
  30. Porter MI, Hills DA (2002) Note on the complete contact between a flat rigid punch and an elastic layer attached to a dissimilar substrate. Int J Mech Sci 44(3):509–520CrossRefGoogle Scholar
  31. Rabinowicz E, Tanner R (1966) Friction and wear of materials. J Appl Mech 33:479CrossRefGoogle Scholar
  32. Seweryn A, Molski K (1996) Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions. Eng Fract Mech 55(4):529–556CrossRefGoogle Scholar
  33. Stachowiak G, Batchelor AW (2013) Engineering tribology. Butterworth-Heinemann, OxfordGoogle Scholar
  34. Vahdat V, Grierson DS, Turner KT, Carpick RW (2013) Mechanics of interaction and atomic-scale wear of amplitude modulation atomic force microscopy probes. ACS Nano 7(4):3221–3235CrossRefGoogle Scholar
  35. Williams ML (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J Appl Mech 19(4):526–528Google Scholar
  36. Zhong J, Shakiba R, Adams JB (2013) Molecular dynamics simulation of severe adhesive wear on a rough aluminum substrate. J Phys D Appl Phys 46(5):055,307CrossRefGoogle Scholar
  37. Zienkiewicz OC, Taylor RL (2000) The finite element method: solid mechanics, vol 2. Butterworth-Heinemann, OxfordGoogle Scholar
  38. Ziman JM (1962) Electrons in metals: a short guide to the Fermi surface. Contemp Phys 4(2):81–99CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

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

Personalised recommendations