Exact analysis of the orientation-adjusted adhesive full stick contact of layered structures with the asymmetric bipolar coordinates

doi:10.1007/s10483-022-2860-9

Abstract

Abstract: The adhesion failure has become one dominant factor in determining the reliability and service life of miniaturized devices subject to loadings with arbitrary orientations. This article establishes an adhesive full stick contact model between an elastic half-space and a rigid cylinder loaded in any direction. Using the Papkovich-Neuber functions, the Fourier integral transform, and the asymmetric bipolar coordinates, the exact solution is obtained. Unlike the Johnson-Kendall-Roberts (JKR) model, the present adhesive contact model takes into account the effects of the load direction as well as the coupling of the normal and tangential contact stresses. Besides, it considers the full stick contact which has large values of the friction coefficient between contacting surfaces, contrary to the frictionless contact supposed in the JKR model. The result shows that suitable angles can be found, which makes the contact surfaces difficult to be peeled off or easy to be pressed into.

Key words: contact mechanics, adhesion, friction, Johnson-Kendall-Roberts (JKR) model, Fourier integral transform, exact solution

2010 MSC Number:

Pengxu GUO, Yueting ZHOU. Exact analysis of the orientation-adjusted adhesive full stick contact of layered structures with the asymmetric bipolar coordinates. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 883-898.

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References

[1] YAO, H., LI, P., CHENG, W., YANG, W., YANG, Z., ALI, H. P. A., GUO, H., and TEE, B. C. K. Environment-resilient graphene vibrotactile sensitive sensors for machine intelligence. ACS Materials Letters, 2(8), 986-992(2020)
[2] YAO, H., YANG, W., CHENG, W., TAN, Y. J., SEE, H. H., LI, S., ALI, H. P. A., LIM, B. Z. H., LIU, Z., and TEE, B. C. K. Near-hysteresis-free soft tactile electronic skins for wearables and reliable machine learning. Proceedings of the National Academy of Sciences of the United States of America, 117(41), 25352-25359(2020)
[3] ZHANG, T., ZHANG, Z., KIM, K. S., and GAO, H. An accordion model integrating self-cleaning, strong attachment and easy detachment functionalities of gecko adhesion. Journal of Adhesion Science and Technology, 28(3-4), 226-239(2014)
[4] PENA-FRANCESCH, A., AKGUN, B., MISEREZ, A., ZHU, W., GAO, H., and DEMIREL, M. C. Pressure sensitive adhesion of an elastomeric protein complex extracted from squid ring teeth. Advanced Functional Materials, 24(39), 6227-6233(2014)
[5] GUO, Y., ZHAO, H. P., FENG, X. Q., and GAO, H. On the robustness of spider capture silk's adhesion. Extreme Mechanics Letters, 29, 100477(2019)
[6] PENG, Z. and CHEN, S. Effect of bending stiffness on the peeling behavior of an elastic thin film on a rigid substrate. Physical Review E-Statistical, Nonlinear, and Soft Matter Physics, 91(4), 1-7(2015)
[7] PENG, Z., WANG, C., YANG, Y., and CHEN, S. Effect of relative humidity on the peeling behavior of a thin film on a rigid substrate. Physical Review E, 94(3), 1-10(2016)
[8] PENG, Z., YIN, H., YAO, Y., and CHEN, S. Effect of thin-film length on the peeling behavior of film-substrate interfaces. Physical Review E, 100(3), 32804(2019)
[9] YIN, H. B., LIANG, L. H., WEI, Y. G., PENG, Z. L., and CHEN, S. H. Determination of the interface properties in an elastic film/substrate system. International Journal of Solids and Structures, 191-192, 473-485(2020)
[10] HERTZ, H. On the contact of elastic solids. Journal für die Reine und Angewandte Mathematik, 92, 156-171(1881)
[11] JOHNSON, K. L., KENDALL, K., and ROBERTS, A. D. Surface energy and the contact of elastic solids. Proceedings of the Royal Society of London A:Mathematical and Physical Sciences, 324(1558), 301-313(1971)
[12] DERJAGUIN, B. V., MULLER, V. M., and TOPOROV, Y. P. Effect of contact deformations on the adhesion of particles. Journal of Colloid and Interface Science, 53(2), 314-326(1975)
[13] MAUGIS, D. Adhesion of spheres:the JKR-DMT transition using a dugdale model. Journal of Colloid and Interface Science, 150(1), 243-269(1992)
[14] GUO, X. and JIN, F. A generalized JKR-model for two-dimensional adhesive contact of transversely isotropic piezoelectric half-space. International Journal of Solids and Structures, 46(20), 3607-3619(2009)
[15] ZHOU, S. S., GAO, X. L., and HE, Q. C. A unified treatment of axisymmetric adhesive contact problems using the harmonic potential function method. Journal of the Mechanics and Physics of Solids, 59(2), 145-159(2011)
[16] WU, F., LI, X. Y., ZHENG, R. F., and KANG, G. Z. Theory of adhesive contact on multi-ferroic composite materials:spherical indenter. International Journal of Engineering Science, 134, 77-116(2019)
[17] JIN, F., TANG, Q., GUO, X., and GAO, H. A generalized Maugis-Dugdale solution for adhesion of power-law graded elastic materials. Journal of the Mechanics and Physics of Solids, 154, 104509(2021)
[18] ZHUPANSKA, O. I. Adhesive full stick contact of a rigid cylinder with an elastic half-space. International Journal of Engineering Science, 55, 54-65(2012)
[19] GOODMAN, L. E. Contact stress analysis of normally loaded rough spheres. Journal of Applied Mechanics, Transactions ASME, 29, 515-522(1962)
[20] SPENCE, D. A. Self similar solutions to adhesive contact problems with incremental loading. Proceedings of the Royal Society of London Series A:Mathematical and Physical Sciences, 305(1480), 55-80(1968)
[21] SPENCE, D. A. An eigenvalue problem for elastic contact with finite friction. Mathematical Proceedings of the Cambridge Philosophical Society, 73, 249-268(1973)
[22] SPENCE, D. A. The Hertz contact problem with finite friction. Journal of Elasticity, 5(3-4), 297-319(1975)
[23] ZHUPANSKA, O. I. and ULITKO, A. F. Contact with friction of a rigid cylinder with an elastic half-space. Journal of the Mechanics and Physics of Solids, 53(5), 975-999(2005)
[24] ZHUPANSKA, O. I. Axisymmetric contact with friction of a rigid sphere with an elastic half-space. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences, 465(2108), 2565-2588(2009)
[25] BORODICH, F. M. and GALANOV, B. A. Non-direct estimations of adhesive and elastic properties of materials by depth-sensing indentation. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences, 464(2098), 2759-2776(2008)
[26] BORODICH, F. M. Contact problems at nano/microscale and depth sensing indentation techniques. Materials Science Forum, 662, 53-76(2011)
[27] BORODICH, F. M. The Hertz-type and adhesive contact problems for depth-sensing indentation. Advances in Applied Mechanics, 47, 225-366(2014)
[28] BORODICH, F. M., GALANOV, B. A., and SUAREZ-ALVAREZ, M. M. The JKR-type adhesive contact problems for power-law shaped axisymmetric punches. Journal of the Mechanics and Physics of Solids, 68, 14-32(2014)
[29] GALIN. L. A. Contact Problems:the Legacy of L. A. Galin, Springer, New York (2008)
[30] BARBER, J. R. Contact Mechanics, Springer, Switzerland (2018)
[31] UFLYAND, Y. S. Survey of Articles on the Applications of Integral Transforms in the Theory of Elasticity, North Carolina State University at Raleigh, North Carolina (1965)
[32] LEBEDEV, N. N., SKALSKAYA, I. P., and UFLYAND, Y. S. Worked Problems in Applied Mathematics, General Publishing Company, Canada (1965)
[33] ERDELYI, A. Tables of Integral Transforms, Vol. 1, McGraw-Hill Book Company, New York (1954)
[34] CHEN, S. and GAO, H. Non-slipping adhesive contact of an elastic cylinder on stretched substrates. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences, 462(2065), 211-228(2006)
[35] CHEN, S. and GAO, H. Non-slipping adhesive contact between mismatched elastic spheres:a model of adhesion mediated deformation sensor. Journal of the Mechanics and Physics of Solids, 54(8), 1548-1567(2006)
[36] CHEN, S. H. and GAO, H. J. Non-slipping adhesive contact between mismatched elastic cylinders. International Journal of Solids and Structures, 44(6), 1939-1948(2007)
[37] MAUGIS, D. Contact, Adhesion and Rupture of Elastic Solids, Springer Science & Business Media, New York (2000)
[38] MCMEEKING, R. M., CIAVARELLA, M., CRICRÌ, G., and KIM, K. S. The interaction of frictional slip and adhesion for a stiff sphere on a compliant substrate. Journal of Applied Mechanics, Transactions ASME, 87(3), 1-7(2020)
[39] PENG, B., LI, Q., FENG, X. Q., and GAO, H. Effect of shear stress on adhesive contact with a generalized Maugis-Dugdale cohesive zone model. Journal of the Mechanics and Physics of Solids, 148, 104275(2021)
[40] BARQUINS, M. Adherence and rolling kinematics of a rigid cylinder in contact with a natural rubber surface. The Journal of Adhesion, 26(1), 1-12(1988)