Elasto-Plastic Normal Contact of Three-Dimensional Fractal Surfaces Using Halfspace Theory

The elasto-plastic normal contact of fractal surfaces is investigated. To study the influence of several surface parameters like fractal dimension and resolution, the surfaces are numerically generated using a special form of the structure function which is motivated by measurements of real rough surfaces. The contact simulation uses an iterative elastic halfspace solution based on a variational principle. A simple modification allows also the approximative solution of elasto-plastic contact problems. The influence of different surface parameters is studied with respect to the load-area relationship and the load-gap relationship. The simulations show that for realistic surface parameters the deformation is always in the plastic range.

[1]  R. S. Sayles,et al.  Numerical Contact Model of a Smooth Ball on an Anisotropic Rough Surface , 1994 .

[2]  T. R. Thomas,et al.  Stiffness of Machine Tool Joints: A Random-Process Approach , 1977 .

[3]  R. Sayles,et al.  Surface topography as a nonstationary random process , 1978, Nature.

[4]  Michele Ciavarella,et al.  Elastic Multiscale Contact of Rough Surfaces: Archard’s Model Revisited and Comparisons With Modern Fractal Models , 2001 .

[5]  C. Roques-carmes,et al.  Fractal approach to two-dimensional and three-dimensional surface roughness , 1986 .

[6]  D. Whitehouse,et al.  Two-dimensional properties of random surfaces , 1982, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[7]  J. Greenwood,et al.  The Elastic Contact of Rough Spheres , 1967 .

[8]  P. Nayak,et al.  Random Process Model of Rough Surfaces , 1971 .

[9]  Thomas Farris,et al.  Spectral Analysis of Two-Dimensional Contact Problems , 1996 .

[10]  F. P. Bowden,et al.  A review of the friction of solids , 1958 .

[11]  Kai Willner.  Contact Laws for Rough Surfaces , 2000 .

[12]  J. Greenwood.  A unified theory of surface roughness , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[13]  D. Whitehouse,et al.  The properties of random surfaces of significance in their contact , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[14]  Alberto Carpinteri,et al.  Lacunarity of the Contact Domain Between Elastic Bodies with Rough Boundaries , 1998 .

[15]  F. F. Ling.  Scaling law for contoured length of engineering surfaces , 1987 .

[16]  J. Greenwood,et al.  The Contact of Two Nominally Flat Rough Surfaces , 1970 .

[17]  J. Oden,et al.  Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods , 1987 .

[18]  Yong Hoon Jang,et al.  Linear elastic contact of the Weierstrass profile† , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[19]  J. Archard.  Elastic deformation and the laws of friction , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  Ning Ren,et al.  Contact Simulation of Three-Dimensional Rough Surfaces Using Moving Grid Method , 1993 .

[21]  Ning Ren,et al.  The Effects of Surface Roughness and Topography on the Contact Behavior of Elastic Bodies , 1994 .

[22]  L. He,et al.  The fractal character of processed metal surfaces , 1997 .

[23]  B. Bhushan,et al.  Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces , 1990 .

[24]  Euripides S. Mistakidis,et al.  Fractal geometry in structures. Numerical methods for convex energy problems , 1994 .

[25]  J. Greenwood,et al.  Contact of nominally flat surfaces , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[26]  D. Whitehouse,et al.  Discrete properties of random surfaces , 1978, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[27]  T. L. Warren,et al.  Random Cantor set models for the elastic-perfectly plastic contact of rough surfaces , 1996 .

[28]  B. Bhushan,et al.  Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler , 1995 .

[29]  Kai Willner.  Surface Models For Contact Laws , 2001 .

[30]  A. Majumdar,et al.  Fractal characterization and simulation of rough surfaces , 1990 .

[31]  Takahisa Kato,et al.  An FFT-Based Method for Rough Surface Contact , 1997 .

[32]  Bharat Bhushan,et al.  Generalized fractal analysis and its applications to engineering surfaces , 1995 .

[33]  B. Bhushan,et al.  A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle , 1996 .

[34]  B. Bhushan,et al.  Fractal Model of Elastic-Plastic Contact Between Rough Surfaces , 1991 .