||Study of An Elasto-plastic Microcontact Model For Evaluating Elastic Recovery
||Department of Aeronautics & Astronautics (on the job class)
asperity height distributions
Normally, in statistical contact analyses, asperity height distributions are assumed to follow a Gaussian distribution. However, engineered surfaces are frequently non-Gaussian, depending upon the material and surface state being evaluated. When two surfaces experience contact deformations, the original topographies of the surfaces vary with different loads, and the deformed topographies of the surfaces after unloading and elastic recovery are different from those of two contacting surfaces under a constant load.
Keywords: micro-contact, skewness, kurtosis, asperity height distributions.
All engineered surfaces are microscopically rough, and a contact behavior between two such surfaces is related to the asperities on the surfaces. This characterization is very important to the study of interfacial phenomena, such as friction, thermal and electrical contact resistance. The study of the deformation behavior of contact asperities and accurate modeling of rough surfaces is important in order to discuss contact problems as well.
MATERIALS AND METHODS
A theoretical method is proposed in the present study to discuss the variations of the topographies of the surfaces for two contact conditions. The profile of the probability density function (PDF) of asperity height is sharp if it is obtained from the surface contacts under a normal load. If the material initial plasticity index is small, the PDF of asperity height of a contact surface after elastic recovery is close to that before contact.
RESULTS AND DISCUSSION
The probability density function of asperity heights in the non-Gaussian form before the deformations is determined by the initial skewness and the initial kurtosis only. After the deformations, the skewness and the kurtosis no longer remain unchanged, but vary with the interference formed by a rigid, smooth surface in contact with a rough surface. The profile of the g(z*) function becomes steep and sharp as the d*value decreases to a sufficiently small value. When d*<0.5, the calculation of integrating g(z*) is hard to converge unless the error tolerance is enlarged. If the tolerance is loosened, the behavior of the integration of g(z*) demonstrated in the case of d*<0.5 shows a big difference in its characteristic from that demonstrated in the case of d^>0.5. Therefore, the lower bound of d* was set to be 0.5 in the present study. Apart from the initial skewness and initial kurtosis, the mean separation between two contact surfaces is also an important factor in the variations of g(z*). The topography of the rough surface will be changed when two surfaces are subjected to contact deformations. The skewness and kurtosis parameters in the non-Gaussian probability density function vary with the mean separation of two contact surfaces. In the present study, these two parameters can be evaluated under the condition of either two contact surfaces under a constant load or the rough surface after elastic recovery. By fixing the contact loads of two surfaces, the negative magnitude of skewness for the surface contacts under a constant load is lowered by increasing the initial skewness of the rough surface. The behavior of kurtosis due to the change in the dimensionless contact load is exactly opposite to that demonstrated in the skewness parameter. If the initial values of skewness and kurtosis are given, the kurtosis value evaluated for the surface contacts under a constant normal load is lowered by decreasing the contact load of two contact surface. The kurtosis value evaluated at the same contact load is lowered by increasing the negative magnitude of the initial skewness. However, the effect of the initial skewness magnitude on the skewness after elastic recovery is exactly opposite to the effect on the skewness created at the contact of a constant load if they are evaluated at the dimensionless contact load. This feature is related to the magnitude of the plasticity index. A relatively high possibility of elastic recovery generally occurs at the contact surface with a small plasticity index. In addition, the degree of the elastic recovery corresponding to a surface with a small initial skewness is always higher than that exhibited in a surface with a large initial skewness. We find the effect of a small plasticity index and a surface with a small initial skewness makes the skewness (negative magnitude) after the elastic recovery be overtaken by the combined effect of the same plasticity index and a large initial skewness. The influence of different initial skewnesses on the contact load or the contact area exhibited in the present model is obviously smaller than that exhibited in the case of assuming constant-skewness and constant-kurtosis.
However, the PDF of asperity height of a contact surface after elastic recovery is closer to that of a contact surface under a normal load if a large initial plasticity index is assumed. How the influence of the dimensionless contact load, the initial skewness, and the initial plasticity index of the rough surface, are investigated on the basis of the topography models mentioned above. The behavior exhibited in the model of the invariant PDF is different from the present model.
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-3 研究目的與內容 4
第二章 基本理論 7
2-1 應用統計理論分析微接觸行為 7
2-2 粗糙峰彈性接觸變形 8
2-3 粗糙峰完全塑性接觸變形 9
2-4 粗糙峰彈塑性接觸變形 9
2-5 粗糙峰高度機率密度分佈函數 11
2-6 粗糙峰接觸負載及接觸面積 15
第三章 彈性回復微接觸之統計理論模型 20
3-1 兩平面接觸時粗糙峰高度分佈機率密度函數的變化 20
3-2 粗糙峰經彈性回復後高度分佈機率密度函數的變化 24
第四章 結果與討論 29
第五章 結論 34
Liu, G., Wang, Q. J., and Lin, C., 1999, “A Survey of Current Models for Simulating the Contact between Rough Surfaces,” STLE Tribology Transactions, 42, pp. 581-591.
Bhushan, B., 1996, “Contact Mechanics of Rough Surfaces in Tribology: Single Asperity Contact,” Tribology Letters, 4, pp. 1-35.
Bhushan, B., 1998, “Contact Mechanics of Rough Surfaces in Tribology: Multiple Asperity Contact,” Tribology International, 34, pp. 299-305.
Greenwood, J. A., Williamson, J.B.P., 1966, “Contact of Nominally Flat Surfaces,” Proceedings of Royal Society of London, Series A, 295, pp. 300-319.
Zhuravlev, V. A., 1940, “On Question of Theoretical Justification of the Amontons-Coulomb Law for Friction of Unlubricated Surfaces,” Zh. Tekh. Fiz., 10, pp. 1447-1452.
Jamari, J., Schipper, D.J., Deformation due to contact between a rough surface and Asmoothball Wear, 2007, 262, pp. 138–145.
Wang, S. Development of theoretical contact width formulas and a numerical model for curved rough surfaces. Journal of Tribology—Transactions of the ASME 2007; 129: 735–42.
Carbone, G, Bottiglione, F., “Asperity Contact Theories: Do they predict linearity between contact area and load?” Journal of the Mechanics and Physics of Solids 2008, 56, pp. 2555–2572.
Li L., Etsion I., Talke FE., “Elastic–Plastic Spherical Contact Modeling Including Roughness Effects.” Tribology Letters 2010, 40, pp. 357–363.
Bryant, M.J., Evans H.P., Snidle R.W., “Plastic Deformation in Rough Surface Line Contact-a Finite Element Study.” Tribology International 2012, 46, pp. 269–78.
Greenwood, J. A., Tripp, J. H., 1967, “The Elastic Contact of Rough Spheres,” ASME Journal of Applied Mechanics, 34, pp. 153-259.
Whitehouse, D. J., Archard, J. F., 1970, “The Properties of Random Surfaces of Significance in Their Contact,” Proceedings of Royal Society of London,3Series A, 316, pp. 97-121.
Hisakado, T., 1974, “Effects of Surface Roughness on Contact between Solid Surfaces,” Wear, 28, pp. 217-234.
Bush, A.W., Gibson, R.D., Thomas, T.R., 1975, “The Elastic Contact of a Rough Surface,” Wear, 35, pp. 87-111.
Bush, A.W., Gibson, R.D., Keogh G.P., 1979, “Strongly Anisotropic Rough Surface,” ASME Journal of Lubrication Technology, 101, pp. 15-20.
Greenwood, J.A., Wu J.J., 2001, “Surface Roughness and Contact: An Apology,” Meccanica, 36, pp. 617-630.
Williamson, J.B.P., 1968, “Topography of Solid Surfaces,” in Interdisciplinary Approach to Friction and Wear, P. M. Ku, ed., SP-181, NASA Special Publication, NASA, Washington, DC, pp. 85-142.
Whitehouse, D. J., 1994, Handbook of Surface Metrology, Institute of Physics Publishing, Bristol, UK.
Stout, K. J., Davis, E. J., and Sullivan, P. J., 1990, Atlas of Machined Surfaces, Chapman and Hall, London.
Whitehouse, D. J., 2003, Handbook of Surface and Nanometrology, Institute of Physics Publishing, Bristol, pp. 99.
McCool, J. I., 1992, “Non-Gaussian Effects in Microcontact,” Int. J. Mach. Tools Manuf., 32, No. 1, pp. 115-123.
McCool, J. I., 2000, “Extending the Capability of the Greenwood Williamson Microcontact Model,” ASME J. Tribology, 122, pp. 496-502.
Yu, N., Polycarpou, A. A., 2002, “Contact of Rough Surfaces With Asymmetric Distribution of Asperity Heights,” ASME J. Tribology, 124, pp. 367-376.
Yu, N., Polycarpou, A. A., 2004, “Combining and Contacting of Two Rough Surfaces with Asymmetric Distribution of Asperity Heights,” ASME J. Tribology, 126, pp. 225-232.
Yu, N., Polycarpou, A. A., 2004, “Extracting Summit Roughness Parameters From Random Gaussian Surfaces According for Asymmetry of the Summit Heights,” ASME J. Tribol., 126, pp. 761-766.
Kotwal, C. A., Bhushan, B., 1996, “Contact Analysis of non-Gaussian Surfaces for Minimum Static and Kinetic Friction and Wear,” Tribology Transactions, 39, pp. 890-898.
Cohen, D., Kligerman, Y., Etsion, I. : The effect of surface roughness on static friction and junction growth of an elastic–plastic spherical contact. J. Tribology. Trans. ASME 131, 021404 (2009)
Li, L., Etsion, I., Talke, F.E.: Contact area and static friction of rough surfaces with high plasticity index. J. Tribology. Trans. ASME 262, 138–145 (2010)
Chung, J. C., Lin, J. F., 2005, “Variation in Fractal Properties and non-Gaussian Distributions of Microcontact between Elastic-Plastic Rough Surfaces with Mean Surface Separation,” accepted by ASME Journal of Applied Mechanics, in press.
Othmani, A., Kaminsky, C., 1998, “Three Dimensional Fractal Analysis of Sheet Metal Surfaces,” Wear, 214, pp. 147-150.
Johnson, K. L., 1985,Contact Mechanics. Cambridge, Cambridge University.
Chang, W. R., Etsion, I., Bogy, D. B., 1987, “An Elastic-Plastic Model for the Contact of Rough Surfaces,” ASME Journal of Tribology, 109, pp. 257-263.
Tabor, D., 1951, The Hardness of Metals, Oxford, Oxford University.
Chang, W. R., Etsion, I., Bogy, D. B., 1988, “Static Friction Coefficient Model for Metallic Rough Surfaces,” ASME Journal of Tribology, 110, pp. 57-63.
Kogut, L., Etsion, I., 2002, “Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat,” ASME Journal of Applied Mechanics, 69, pp. 657-62.
Thomas, T. R., 1982, ROUGH SURFACES, Longman Inc., New York.
Nayak, P. R., 1971, “Random process model of rough surfaces,” J. Lubr. Technol., 93, pp. 398-407.
Kogut, L., Etsion, I., 2003, “A Finite Element Based Elastic-Plastic Model for the Contact of Rough Surfaces,” STLE Tribology Transactions, 46, pp. 383-390.
Gibra, I. N., 1973, Probability and Statistical Inference for Scientists and Engineers, Prentice-Hall Inc., Englewood Cliffs, NJ.
Zhao, Y., Chang, L., 2001, “A Model of Asperity Interactions in Elastic-Plastic Contact of Rough Surfaces,” ASME Journal of Tribology, 123, pp. 857-864.
Nuri, K. A., and Halling, J., 1975, “The Normal Approach between Rough Flat Surface in Contact,” Wear, 32, pp. 81-93.