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Friction

pp 1–13 | Cite as

Analytical model of friction behavior during polymer scratching with conical tip

  • Chengkai Jiang
  • Han JiangEmail author
  • Jianwei Zhang
  • Guozheng Kang
Open Access
Research Article
  • 68 Downloads

Abstract

To investigate the effects of the contact geometry, interfacial friction, and substrate recovery on the behavior of polymer scratching using a conical tip, an analytical model is proposed. The normal stress acting on the contact surface between the tip and the substrate is described as a function of the included angle θ, representing the angle between two planes across the axis of the conical tip, and the attack angle β, representing the angle between the conical surface and the substrate material surface. The effects of the rear contact geometry on the scratch friction between the tip and substrate, represented by recovery angle φ, owing to the instantaneous elastic recovery of the polymer substrate, are also introduced. Validated by the experimental and numerical results from the literature, the proposed analytical model can describe well the scratch coefficient of friction (SCOF), which is defined as the ratio of the tangential force to the normal force. Meaningful guidance is provided to understand the scratch friction behavior.

Keywords

polymer scratch contact geometry elastic recovery scratch coefficient of friction 

References

  1. [1]
    Briscoe B J, Sinha S K. Scratch resistance and localised damage characteristics of polymer surfaces–a review. Materialwiss Werkst 34(10–11): 989–1002 (2003)Google Scholar
  2. [2]
    Jiang H, Browning R, Sue H–J. Understanding of scratchinduced damage mechanisms in polymers. Polymer 50(16): 4056–4065 (2009)Google Scholar
  3. [3]
    Dasari A, Yu Z–Z, Mai Y–W. Fundamental aspects and recent progress on wear/scratch damage in polymer nanocomposites. Mat Sci Eng R 63(2): 31–80 (2009)Google Scholar
  4. [4]
    Brostow W, Deborde J, Jaclewicz M, Olszynski P. Tribology with emphasis on polymers: friction, scratch resistance and wear. J Mater Educ 24(4–6): 119–132 (2003)Google Scholar
  5. [5]
    Jiang H, Cheng Q, Jiang C, Zhang J, Li Y. Effect of stick–slip on the scratch performance of polypropylene. Tribol Int 91: 1–5 (2015)Google Scholar
  6. [6]
    Barr C J, Wang L, Coffey J K, Daver F. Influence of surface texturing on scratch/mar visibility for polymeric materials: a review. J Mater Sci 52(3): 1221–1234 (2017)Google Scholar
  7. [7]
    Moghbelli E, Sun L, Jiang H, Boo W J, Sue H J. Scratch behavior of epoxy nanocomposites containing α–zirconium phosphate and core–shell rubber particles. Polym Eng Sci 49(3): 483–490 (2009)Google Scholar
  8. [8]
    Misra R, Hadal R, Duncan S. Surface damage behavior during scratch deformation of mineral reinforced polymer composites. Acta Mater 52(14): 4363–4376 (2004)Google Scholar
  9. [9]
    Briscoe B J, Evans P D, Pellilo E, Sinha S K. Scratching maps for polymers. Wear 200(1): 137–147 (1996)Google Scholar
  10. [10]
    An J, Kang B–H, Choi B–H, Kim H–J. Observation and evaluation of scratch characteristics of injection–molded poly (methyl methacrylate) toughened by acrylic rubbers. Tribol Int 77: 32–42 (2014)Google Scholar
  11. [11]
    Zhang J, Jiang H, Jiang C, Cheng Q, Kang G. In–situ observation of temperature rise during scratch testing of poly (methylmethacrylate) and polycarbonate. Tribol Int 95: 1–4 (2016)Google Scholar
  12. [12]
    Barr C J, Wang L, Coffey J K, Gidley A, Daver F. New technique for the quantification of scratch visibility on polymeric textured surfaces. Wear 384–385: 84–94 (2017)Google Scholar
  13. [13]
    Hossain M M, Jahnke E, Boeckmann P, Guriyanova S, Minkwitz R, Sue H–J. Effect of thermal history on scratch behavior of multi–phase styrenic–based copolymers. Tribol Int 99: 248–257 (2016)Google Scholar
  14. [14]
    Wee J–W, Park S–Y, Choi B–H. Observation and understanding of scratch behaviors of glass fiber reinforced polycarbonate plates with various packing pressures during the injection molding process. Tribol Int 90: 491–501 (2015)Google Scholar
  15. [15]
    Jiang H, Lim G, Reddy J, Whitcomb J, Sue H J. Finite element method parametric study on scratch behavior of polymers. J Polym Sci Pol Phys 45(12): 1435–1447 (2007)Google Scholar
  16. [16]
    Pelletier H, Gauthier C, Schirrer R. Influence of the friction coefficient on the contact geometry during scratch onto amorphous polymers. Wear 268(9): 1157–1169 (2010)Google Scholar
  17. [17]
    Hossain M M, Jiang H, Sue H–J. Effect of constitutive behavior on scratch visibility resistance of polymers—A finite element method parametric study. Wear 270(11): 751–759 (2011)Google Scholar
  18. [18]
    Hossain M M, Browning R, Minkwitz R, Sue H–J. Effect of asymmetric constitutive behavior on scratch–induced deformation of polymers. Tribol Lett 47(1): 113–122 (2012)Google Scholar
  19. [19]
    Van Breemen L, Govaert L, Meijer H. Scratching polycarbonate: A quantitative model. Wear 274: 238–247 (2012)Google Scholar
  20. [20]
    Aleksy N, Kermouche G, Vautrin A, Bergheau J–M. Numerical study of scratch velocity effect on recovery of viscoelastic–viscoplastic solids. Int J Mech Sci 52(3): 455–463 (2010)Google Scholar
  21. [21]
    Felder E, Bucaille J L. Mechanical analysis of the scratching of metals and polymers with conical indenters at moderate and large strains. Tribol Int 39(2): 70–87 (2006)Google Scholar
  22. [22]
    Gao W M, Wang L, Coffey J K, Daver F. Understanding the scratch behaviour of polymeric materials with surface texture. Materials & Design 146: 38–48 (2018)Google Scholar
  23. [23]
    Feng B. Tribology behavior on scratch tests: Effects of yield strength. Friction 5(1): 108–114 (2017)Google Scholar
  24. [24]
    Feng B, Chen Z. Tribology behavior during indentation and scratch of thin films on substrates: effects of plastic friction. AIP Advances 5(5): 057152 (2015)Google Scholar
  25. [25]
    Subhash G, Zhang W. Investigation of the overall friction coefficient in single–pass scratch test. Wear 252(1): 123–134 (2002)Google Scholar
  26. [26]
    Lafaye S, Gauthier C, Schirrer R. A surface flow line model of a scratching tip: apparent and true local friction coefficients. Tribol Int 38(2): 113–127 (2005)Google Scholar
  27. [27]
    Lafaye S, Gauthier C, Schirrer R. Analysis of the apparent friction of polymeric surfaces. J Mater Sci 41(19): 6441–6452 (2006)Google Scholar
  28. [28]
    Lafaye S, Gauthier C, Schirrer R. Analyzing friction and scratch tests without in situ observation. Wear 265(5): 664–673 (2008)Google Scholar
  29. [29]
    Komvopoulos K. Sliding friction mechanisms of boundarylubricated layered surfaces: Part II—Theoretical analysis. Tribol T 34(2): 281–291 (1991)Google Scholar
  30. [30]
    Jardret V, Zahouani H, Loubet J–L, Mathia T. Understanding and quantification of elastic and plastic deformation during a scratch test. Wear 218(1): 8–14 (1998)Google Scholar
  31. [31]
    Tayebi N, Conry T F, Polycarpou A A. Determination of hardness from nanoscratch experiments: Corrections for interfacial shear stress and elastic recovery. J Mater Res 18(09): 2150–2162 (2003)Google Scholar
  32. [32]
    Briscoe B, Biswas S, Sinha S, Panesar S. The scratch hardness and friction of a soft rigid–plastic solid. Tribol Int 26(3): 183–193 (1993)Google Scholar
  33. [33]
    Gauthier C, Lafaye S, Schirrer R. Elastic recovery of a scratch in a polymeric surface: experiments and analysis. Tribol Int 34(7): 469–479 (2001)Google Scholar
  34. [34]
    Pelletier H, Durier A–L, Gauthier C, Schirrer R. Viscoelastic and elastic–plastic behaviors of amorphous polymeric surfaces during scratch. Tribol Int 41(11): 975–984 (2008)Google Scholar
  35. [35]
    Bucaille J, Felder E, Hochstetter G. Mechanical analysis of the scratch test on elastic and perfectly plastic materials with the three–dimensional finite element modeling. Wear 249(5): 422–432 (2001)Google Scholar
  36. [36]
    Goddard J, Wilman H. A theory of friction and wear during the abrasion of metals. Wear 5(2): 114–135 (1962)Google Scholar
  37. [37]
    Lafaye S, Gauthier C, Schirrer R. The ploughing friction: analytical model with elastic recovery for a conical tip with a blunted spherical extremity. Tribol Lett 21(2): 95–99 (2006)Google Scholar
  38. [38]
    Lafaye S. True solution of the ploughing friction coefficient with elastic recovery in the case of a conical tip with a blunted spherical extremity. Wear 264(7): 550–554 (2008)Google Scholar
  39. [39]
    Ducret S, Pailler–Mattei C, Jardret V, Vargiolu R, Zahouani H. Friction characterisation of polymers abrasion (UHWMPE) during scratch tests: single and multi–asperity contact. Wear 255(7): 1093–1100 (2003)Google Scholar
  40. [40]
    Young D F, Munson B R, Okiishi T H, Huebsch W W. A brief introduction to fluid mechanics. John Wiley & Sons, 2010.Google Scholar
  41. [41]
    Xiong D, Ge S. Friction and wear properties of UHMWPE/Al2O3 ceramic under different lubricating conditions. Wear 250(1–12): 242–245 (2001)Google Scholar
  42. [42]
    Tong J, Ma Y, Jiang M. Effects of the wollastonite fiber modification on the sliding wear behavior of the UHMWPE composites. Wear 255(1–6): 734–741 (2003)Google Scholar
  43. [43]
    Zoo Y–S, An J–W, Lim D–P, Lim D–S. Effect of Carbon Nanotube Addition on Tribological Behavior of UHMWPE. Tribol Lett 16(4): 305–309 (2004)Google Scholar
  44. [44]
    Pan D, Kang G, Jiang H. Viscoelastic constitutive model for uniaxial time–dependent ratcheting of polyetherimide polymer. Polym Eng Sci 52(9): 1874–1881 (2012)Google Scholar
  45. [45]
    Jiang H, Zhang J, Kang G, Xi C, Jiang C, Liu Y. A test procedure for separating viscous recovery and accumulated unrecoverable deformation of polymer under cyclic loading. Polym Test 32(8): 1445–1451 (2013)Google Scholar
  46. [46]
    Jiang C K, Jiang H, Zhang J W, Kang G Z. A viscoelastic–plastic constitutive model for uniaxial ratcheting behaviors of polycarbonate. Polym Eng Sci 55(11): 2559–2565 (2015)Google Scholar
  47. [47]
    Brostow W, Hagg Lobland H E, Narkis M. Sliding wear, viscoelasticity, and brittleness of polymers. J Mater Res 21(9): 2422–2428 (2006)Google Scholar
  48. [48]
    Brostow W, Kovacevic V, Vrsaljko D, Whitworth J. Tribology of polymers and polymer–based composites. J Mater Educ 32(89): 273–290 (2010)Google Scholar
  49. [49]
    Kalogeras I M, Hagg Lobland H E. The Nature of the Glassy State: Structure and Glass Transitions. J Mater Educ 34(3–4): 69–94 (2012)Google Scholar

Copyright information

© The author(s) 2018

Open Access: The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (https://doi.org/creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Chengkai Jiang
    • 1
  • Han Jiang
    • 1
    Email author
  • Jianwei Zhang
    • 1
  • Guozheng Kang
    • 1
  1. 1.Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengduChina

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