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Meccanica

, Volume 53, Issue 9, pp 2411–2436 | Cite as

A computational study of the influence of surface roughness on material strength

  • Alison McMillan
  • Rhys Jones
  • Daren Peng
  • Gregory A. Chechkin
Article
  • 162 Downloads

Abstract

In machine component stress analysis, it usually assumed that the geometry specified in CAD provides a fair representation of the geometry of the real component. While in particular circumstances, tolerance information, such as minimum thickness of a highly stressed region, might be taken into consideration, there is no standard practice for the representation of surface quality. It is known that surface roughness significantly influences fatigue life, but for this to be useful in the context of life prediction, there is a need to examine the nature of surface roughness and determine how best to characterise it. Non-smooth geometry can be represented in mathematics by fractals or other methods, but for a representation to have a practical value for a manufactured component, it is necessary to accept that there is a lower limit to surface profile measurement resolution. Resolution and mesh refinement also play a part in any computational analysis undertaken to assess surface profile effects: in the analyses presented, a nominal axi-symmetric geometry has been taken, with a finite non-smooth region on the boundary. Various surface roughness representations are modelled, and the significance of the characterized surface roughness type is investigated. It is shown that the applied load gives rise to a nominally uni-axial stress state of 90% of the yield, although surface roughness features have the effect of modifying the load path, and give rise to localized regions of plasticity near to the surface. The material of the test model is assumed to be elasto-plastic, and the development and evolution of plastic zones formed within the geometry are shown for multiple load cycles.

Keywords

FEA Surface roughness Residual stress Fatigue strength Fractal Geometry 

Notes

Acknowledgements

Alison McMillan would like to acknowledge Wrexham Glyndwr University for the release from undergraduate teaching responsibilities, which has provided the time to write this work up. She would also like to acknowledge Chris Rodopoulos for his suggestions and numerous discussions around this topic. The contribution to this paper by GAC was partially supported by the Russian Foundation of Basic Researches (project 15-01-07920). No other external funding was received.

Compliance with ethical standards

Conflict of Interest Statement

The authors declare that they have no conflict of interest.

References

  1. 1.
    Ed Leach R (2013) Characterisation of areal surface texture. Springer, BerlinCrossRefGoogle Scholar
  2. 2.
    Wiśniewska, M (2014) The ISO 25178 standards for areal surface texture measurements: a critical appraisal. In: The challenges of contemporary science. Theory and applications. Fundacja na Rzecz Młodych Naukowców, Warsaw, Poland, pp 97–98Google Scholar
  3. 3.
    Department of Defense Joint Service Specification Guide, Aircraft Structures, JSSG-2006, October (1998)Google Scholar
  4. 4.
    EASA certification specifications and acceptable means of compliance for engines, CS-E, Amendment 4, 12 March 2015; sections AMC E 515 “Engine Critical Parts” and AMC E 650 “Vibration Surveys”Google Scholar
  5. 5.
    Saint-Venant AJCB (1855) Memoire sur la Torsion des Prismes. Mem Divers Savants 14:233–560Google Scholar
  6. 6.
    Love AEH (1944) A treatise on the mathematical theory of elasticity, 4th edn. Cambridge University Press, CambridgeMATHGoogle Scholar
  7. 7.
    Ainsworth M, Oden JT (2000) A priori error estimation in finite element analysis. Wiley Interscience, New YorkCrossRefMATHGoogle Scholar
  8. 8.
    Armstrong CG, McKeag RM, Ou H, Price MA (2000) Geometric processing for analysis. In: Geometric modeling and processing 200: theory and applications proceedings, February 2000Google Scholar
  9. 9.
    Robinson T, Armstong CG, Chua HS (2012) Strategies for adding features to CAD models in order to optimize performance. Struct Multidiscip Optim 46(3):415MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Hill R (1998) The mathematical theory of plasticity. Oxford University Press, OxfordMATHGoogle Scholar
  11. 11.
    Jones R, Molent L, Barter S, Matthews N, Tamboli D (2014) Supersonic particle deposition as a means for enhancing the structural integrity of aircraft structures. Int J Fatigue 68:260–268CrossRefGoogle Scholar
  12. 12.
    Bowden FP, Tabor D (1964) The friction and lubrication of solids. Oxford University Press, OxfordMATHGoogle Scholar
  13. 13.
    Yu G, Li H, Walker D (2011) Removal of mid spatial-frequency features in mirror segments. J Eur Opt Soc Rapid Publ 6:11044CrossRefGoogle Scholar
  14. 14.
    Curtis S, de los Rios ER, Rodopulos CA, Levers A (2003) Analysis of the effects of controlled shot peening on fatigue damage of high strength aluminium alloys. Int J Fatigue 25:59–66CrossRefGoogle Scholar
  15. 15.
    Mandelbrot BB (1982) The fractal geometry of nature. Freeman and Co, New YorkMATHGoogle Scholar
  16. 16.
    Carpinteri A, Spagnoli A (2004) A fractal analysis of size effect on fatigue crack growth. Int J Fatigue 26:125–133CrossRefMATHGoogle Scholar
  17. 17.
    Spagnoli A (2005) Self-similarity and fractals in the Paris range of fatigue crack growth. Mech Mater 37:519–529CrossRefGoogle Scholar
  18. 18.
    Jones R, Chen F, Pitt S, Paggi M, Carpinteri A (2016) From NASGRO to fractals: representing crack growth in metals. Int J Fatigue 82:540–549CrossRefGoogle Scholar
  19. 19.
    Molent L, Jones R (2016) A stress versus crack growth rate investigation (aka stress—cubed rule). Int J Fatigue 87:435–443CrossRefGoogle Scholar
  20. 20.
    http://www.iso.org/iso/home.html. Accessed 27 Feb 2017
  21. 21.
    de Berg M, Cheong O, van Kreveld M, Overmars M (2008) Computational geometry: algorithms and applications, 3rd edn. Springer, Berlin HeidelbergCrossRefMATHGoogle Scholar
  22. 22.
    Bakhvalov NS, Panasenko GP (1989) Averging processes in periodic media. Kluwer Aacdemic Publ, DordrechtMATHGoogle Scholar
  23. 23.
    Bensoussan A, Lions J-L, Papanicolau G (1978) Asymptotic analysis for periodic structures. North-Holland, AmsterdamGoogle Scholar
  24. 24.
    Chechkin GA, Piatnitkski AL, Shamaev AE (2007) Homogenization. Methods and applications. American Mathematical Society, ProvidenceCrossRefGoogle Scholar
  25. 25.
    Jikov VV, Kozlov SM, Oleinik OA (1994) Homogenization of differential operators and integral functionals. Berlin etc, Springer-VerlangCrossRefMATHGoogle Scholar
  26. 26.
    Marchenko VA, Khruslov EYa (2006) Homogenization of partical differential equations. Birkhäuser, BostonGoogle Scholar
  27. 27.
    Sánchez-Palencia E (1987) Homogenization techniques for composite media. Springer, BerlinCrossRefMATHGoogle Scholar
  28. 28.
    Belyaev AG, Piatnitski AL, Chechkin GA (1998) Asymptotic behaviour of a solution to a boundary value problem in a perforacted domain with oscillating boundary. Sib Math J 39(4):621–644 (translated in English from Sibirskii Matematicheskii Zhurnal 39(4):730–754Google Scholar
  29. 29.
    Chechkin GA, Friedman A, Piatnitkski AL (1999) The boundary value problem in domains with very rapidly oscillating boundary. J Math Anal Appl (JMAA) 231(1):213–234MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Amirat Y, Bodart O, Chechkin GA, Piatnitski AL (2011) Boundary homogenization in domains with randomly oscillating boundary. Stochastic Processes and their Applications 121(1):1–23MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Chechkin GA, Chechkina TP, D’Apice C, De Maio U, Mel’nyk TA (2009) Asymptotic analysis of a boundary value problem in a cascade thick junction with a random transmission zone. Appl Anal 88(10–11):1543–1562MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Chechkin GA, Chechkina TP, D’Apice C, De Maio U, Mel’nyk TA (2010) Homogenization of a 3D thick cascade junction with the random transmission zone periodic in one direction. Russ J Math Phys 17(1):35–55MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Chechkin GA, D’Apice C, De Maio U, Piatnitkski AL (2014) On the rate of convergence of solutions in domain with random multilevel oscillating boundary. Asymptot Anal 87(1–2):1–28MathSciNetMATHGoogle Scholar
  34. 34.
    ASTM (1998) Standard practice for conducting force controlled constant amplitude axial fatigue tests of metallic materials. ASTM E646, ConshohockenGoogle Scholar
  35. 35.
    Lai J, Huang H, Buising W (2016) Effects of microstructure and surface roughness on the fatigue strength of high-strength steels. Proc Struct Integr 2:1213–1220. (21st European conference fracture, EXF21, 20–24 June 2016, Catania)Google Scholar
  36. 36.
    Yuri T, Ono Y, Ogata T (2003) Effects of surface roughness and notch on fatigue properties for Ti-5Al-2.5Sn ELI alloy at cryogenic temperatures. Sci Technol Adv Mater 4:291–299CrossRefGoogle Scholar
  37. 37.
    Abaqus Manuals. Dassault Systèmes Simulia Corporation, ProvidenceGoogle Scholar
  38. 38.
    Brinckmann S, Van der Giessen E (2007) A fatigue crack initiation model incorporating discrete dislocation plasticity and surface roughness. Int J Fract 148:155–167CrossRefMATHGoogle Scholar
  39. 39.
    Vrac D, Sidjanin L, Balos S (2014) The effect of honing speed and grain size on surface roughness and material removal rate during honing. Acta Polytech Hung 11(10):163–175Google Scholar
  40. 40.
    Ali K, Peng D, Jones R, Singh RRK, Zhao XL, McMillan AJ, Berto F (2016) Crack growth in a naturally corroded bridge steel. Fatigue Fract Eng Mater Struct.  https://doi.org/10.1111/ffe.12568 Google Scholar
  41. 41.
    Jones R (2014) Fatigue crack growth and damage tolerance, invited review paper. Fatigue Fract Eng Mater Struct 37(5):463–483CrossRefGoogle Scholar
  42. 42.
    Jones R, Huang P, Peng D (2016) Crack growth from naturally occurring material discontinuities under constant amplitude and operational loads. Int J Fatigue 91:434–444CrossRefGoogle Scholar
  43. 43.
    Molent L, Jones R (2016) The influence of cyclic stress intensity threshold on fatigue life scatter. Int J Fatigue 82:748–756CrossRefGoogle Scholar
  44. 44.
    Berens AP, Hovey PW, Skinn DA (1991) Risk analysis for aging aircraft fleets—Volume 1: analysis. WL-TR-91-3066, Flight Dynamics Directorate, Wright Laboratory, Air Force Systems Command, Wright-Patterson Air Force Base, October 1991Google Scholar
  45. 45.
    Molent L, Barter SA, Wanhill RJH (2011) The lead crack fatigue lifing framework. Int J Fatigue 33:323–331CrossRefGoogle Scholar
  46. 46.
    Lemaitre J (1985) Coupled elasto-plasticity and damage constitutive equations. Comput Methods Appl Mech Eng 51:31–49ADSCrossRefMATHGoogle Scholar
  47. 47.
    Ed Leach R (2013) Characterisation of areal surface texture. Springer, BerlinCrossRefGoogle Scholar
  48. 48.
    Wiśniewska M (2014) The ISO 25178 standards for areal surface texture measurements: a critical appraisal. In: The challenges of conteporary science. Theory and applications, Fundacja na Rzecz Młodych Naukowców, Warsaw, Poland, pp 97–98Google Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Alison McMillan
    • 1
  • Rhys Jones
    • 2
  • Daren Peng
    • 2
  • Gregory A. Chechkin
    • 3
  1. 1.School of Applied Sciences, Computing and EngineeringWrexham Glyndwr UniversityWrexhamUK
  2. 2.Department of Mechanical and Aerospace EngineeringMonash UniversityClaytonAustralia
  3. 3.Department of Differential Equations, Faculty of Mechanics and MathematicsM. V. Lomonosov Moscow State UniversityMoscowRussian Federation

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