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A receding contact analysis for an elastic layer reinforced with a functionally graded coating and pressed against a half-plane

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Abstract

We aim to analyze the receding contact mechanics of an elastic layer reinforced by a functionally graded coating, pressed against a half-plane substrate as an integral assembly. The graded reinforcement is modeled by an inhomogeneous medium whose shear modulus is allowed to vary exponentially. A smooth receding contact is arisen due to the normal tractions applied over a finite segment of the reinforcement surface. The primary goal of this study is the determination of both the receding contact pressure and the extent of receding contact along the assembly and substrate interface. Using both an analytical and a finite element method solves the problem. In the former approach, Fourier integral transforms help convert the problem into a singular integral equation of Cauchy type, which is numerically integrated with Gauss-Chebyshev quadrature. In the numerical approach, multiple homogeneous layers approximate the graded coating. The stresses at those nodes lying on sublayer interfaces are averaged over their surrounding elements for guaranteeing the continuity in stress field. Very good agreements are found between the results obtained from the two methods. Extensive parametric case studies reveal that material properties, loading configuration, and geometric parameters all play important roles in the determination of both the contact pressure distribution and the length of contact. These receding contact properties can therefore be optimized as desired by appropriately varying the influential parameters. Both the solution methodologies and the numerical results presented in this work can provide some useful guidelines on the better design of multilayered functionally graded structures.

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References

  1. S. D. Conzone, D. P. Butt and A. H. Bartlett, Joining MoSi2 to 316L stainless steel, J. Mater. Sci., 32 (1997) 3369–3374.

    Article  Google Scholar 

  2. K. J. Jobin, M. N. Abhilash and H. Murthy, A simplified analysis of 2D sliding frictional contact between rigid indenters and FGM coated substrates, Tribol. Int., 108 (2017) 174–185.

    Article  Google Scholar 

  3. C.-H. Yang, W.-N. Ma, D.-W. Ma, Q. He and J.-L. Zhong, Analysis of the low velocity impact response of functionally graded carbon nanotubes reinforced composite spherical shells, J. Mech. Sci. Technol, 32 (2018) 2681–2691.

    Article  Google Scholar 

  4. S. Suresh, M. Olsson, A. Giannakopoulos, N. Padture and J. Jitcharoen, Engineering the resistance to sliding-contact damage through controlled gradients in elastic properties at contact surfaces, Acta Mater., 47 (1999) 3915–3926.

    Article  Google Scholar 

  5. H. J. Choi, On the plane contact problem of a functionally graded elastic layer loaded by a frictional sliding flat punch, J. Mech. Sci. Technol, 23 (2009) 2703–2713.

    Article  Google Scholar 

  6. M. A. Güler and F. Erdogan, Contact mechanics of graded coatings, Int. J. Solids Struct., 41 (2004) 3865–3889.

    Article  MATH  Google Scholar 

  7. S. Chen, C. Yan, P. Zhang and H. Gao, Mechanics of adhesive contact on a power-law graded elastic half-space, J. Mech. Phys. Solids, 57 (2009) 1437–1448.

    Article  MathSciNet  MATH  Google Scholar 

  8. X. Guo, F. Jin and H. Gao, Mechanics of non-slipping adhesive contact on a power-law graded elastic half-space, Int. J. Solids Struct., 48 (2011) 2565–2575.

    Article  Google Scholar 

  9. L. L. Ke and Y. S. Wang, Two-dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties, Int. J. Solids Struct., 43 (2006) 5779–5798.

    Article  MATH  Google Scholar 

  10. T.-J. Liu, Y.-S. Wang and C. Zhang, Axisymmetric frictionless contact of functionally graded materials, Arch. Appl. Mech., 78 (2008) 267–282.

    Article  MATH  Google Scholar 

  11. J. A. Garrido and A. Lorenzana, Receding contact problem involving large displacements using the BEM, Eng. Anal. Bound. Elem., 21 (1998) 295–303.

    Article  MATH  Google Scholar 

  12. E. Graciani, V. Mantic, F. Paŕ0is and A. Blázquez, Weak formulation of axi-symmetric frictionless contact problems with boundary elements: Application to interface cracks, Comput. Struct., 83 (2005) 836–855.

    Article  Google Scholar 

  13. S. Dag and K. A. Ilhan, Mixed-mode fracture analysis of orthotropic functionally graded material coatings using analytical and computational methods, J. Appl. Mech.-ASME, 75 (2008) 7816–7840.

    Article  Google Scholar 

  14. S. Dag, M. A. Güler, B. Yildirim and A. C. Ozatag, Sliding frictional contact between a rigid punch and a laterally graded elastic medium, Int. J. Solids Struct., 46 (2009) 4038–4053.

    Article  MATH  Google Scholar 

  15. M. N. Balci, S. Dag and B. Yildirim, Subsurface stresses in graded coatings subjected to frictional contact with heat generation, J. Therm. Stresses, 40 (2016) 517–534.

    Article  Google Scholar 

  16. M. A. Güler, Y. F. Gülver and E. Nart, Contact analysis of thin films bonded to graded coatings, Int. J. Mech. Sci., 55 (2012) 50–64.

    Article  Google Scholar 

  17. M. A. Güler, A. Kucuksucu, K. B. Yilmaz and B. Yildirim, On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium, Int. J. Mech. Sci., 120 (2017) 12–29.

    Article  Google Scholar 

  18. R. Jahedi, S. Adibnazari and G. H. Farrahi, Performance analysis of functionally graded coatings in contact with cylindrical rollers, Adv. Mech. Eng. (2014) 1–12.

    Google Scholar 

  19. M. Turan, G. Adıyaman, V. Kahya and A. Birinci, Axisymmetric analysis of a functionally graded layer resting on elastic substrate, Struct. Eng. Mech., 58 (2016) 423–442.

    Article  Google Scholar 

  20. B. Yildirim, S. Dag and F. Erdogan, Three dimensional fracture analysis of FGM coatings under thermo mechanical loading, Int. J. Fracture, 132 (2005) 371–397.

    Article  MATH  Google Scholar 

  21. M. N. Abhilash and H. Murthy, Finite element analysis of 2-D elastic contacts involving FGMs, Int. J. Comput. Methods Eng. Sci. Mech., 15 (2014) 253–257.

    Article  Google Scholar 

  22. S. El-Borgi, R. Abdelmoula and L. Keer, A receding contact plane problem between a functionally graded layer and a homogeneous substrate, Int. J. Solids Struct., 43 (2006) 658–674.

    Article  MATH  Google Scholar 

  23. M. Rhimi, S. El-Borgi, S. W. Ben and F. B. Jemaa, A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate, Int. J. Solids Struct., 46 (2009) 3633–3642.

    Article  MATH  Google Scholar 

  24. M. Rhimi, S. El-Borgi and N. Lajnef, A double receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate, Mech. Mater., 43 (2011) 787–798.

    Article  Google Scholar 

  25. S. El-Borgi, S. Usman and M. A. Güler, A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate, Int. J. Solids Struct., 51 (2014) 4462–4476.

    Article  Google Scholar 

  26. J. Yan and X. Li, Double receding contact plane problem between a functionally graded layer and an elastic layer, Eur. J. Mech. A-Solids, 53 (2015) 143–150.

    Article  MathSciNet  MATH  Google Scholar 

  27. İ. Çömez, S. El-Borgi, V. Kahya and R. Erdöl, Receding contact problem for two-layer functionally graded media indented by a rigid punch, Acta. Mech., 227 (2016) 2493–2504.

    Article  MathSciNet  MATH  Google Scholar 

  28. J. Yan and C. Mi, Double contact analysis of multilayered elastic structures involving functionally graded materials, Arch. Mech., 69 (2017) 199–221.

    MathSciNet  Google Scholar 

  29. J. Yan and C. Mi, On the receding contact between an in-homogeneously coated elastic layer and a homogeneous half-plane, Mech. Mater., 112 (2017) 18–27.

    Article  Google Scholar 

  30. Z. Liu, J. Yan and C. Mi, On the receding contact between a two-layer inhomogeneous laminate and a half-plane, Struct. Eng. Mech., 66 (2018) 329–341.

    Google Scholar 

  31. I. Argatov, Solution of the plane hertz problem, J. Appl. Mech. Tech. Phys., 42 (2001) 1064–1072.

    Article  MathSciNet  MATH  Google Scholar 

  32. F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Q. Appl. Math., 29 (1972) 525–534.

    Article  MathSciNet  MATH  Google Scholar 

  33. E. Jen and R. Srivastav, Solving singular integral equations using Gaussian quadrature and overdetermined systems, Comput. Math. Appl., 9 (1983) 625–632.

    Article  MathSciNet  MATH  Google Scholar 

  34. Z. Liu, On the numerical simulation of receding contact in multilayered elastic structures, Master Thesis, Southeast University (2018).

  35. I. Argatov, Frictionless and adhesive nanoindentation: Asymptotic modeling of size effects, Mech. Mater., 42 (2010) 807–815.

    Article  Google Scholar 

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Acknowledgments

This work was supported by the National Natural Science Foundation of China [grant number 11872149], the Natural Science Foundation of Jiangsu Province [grant number BK20161411], the National Key R&D Program of China [grant number 2017YFC0702800], and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering, Southeast University, Nanjing, Jiangsu, China

    Jie Yan & Changwen Mi

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  1. Jie Yan
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  2. Changwen Mi
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Correspondence to Changwen Mi.

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Recommended by Associate Editor Heung Soo Kim

Jie Yan received her Ph.D degree from School of Civil Engineering at the Southeast University in December 2018. Her research interests include contact mechanics, singular integral equations and complex analysis.

Changwen Mi is currently a Full Professor of Engineering Mechanics at the Southeast University, China. He received his Ph.D. in solid mechanics from the University of Wyoming in 2006 and a M.S. in precision instruments and machinery from the University of Science and Technology of China in 2003, respectively. He was a Research Scientist at the University of Wyoming and Arizona State University from 2007 until 2010 when he joined the Southeast University as a faculty member.

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Yan, J., Mi, C. A receding contact analysis for an elastic layer reinforced with a functionally graded coating and pressed against a half-plane. J Mech Sci Technol 33, 4331–4344 (2019). https://doi.org/10.1007/s12206-019-0829-5

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  • DOI: https://doi.org/10.1007/s12206-019-0829-5

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