Abstract
The dynamic contact mechanics of isotropic elastic coating bonded to homogeneous substrate was examined. The coating is indented by a sliding rigid punch of a cylindrical profile. The rigid punch moves over the coating at a steady subsonic speed. To determine contact stresses, an analytical method based on the singular integral equation technique is put forward. Governing partial differential equations are derived considering general theory of elastodynamics. The influences of dimensionless punch speed, mass density ratio, shear modulus, coefficient of friction, relative coating thickness and Poisson’s ratio on contact stresses and contact related parameters were found. Comparison of the contact stresses computed by elastodynamic and elastostatic theories clearly shows that the relative difference between these two results is quite remarkable. Hence, in sliding contact problems incorporating punches with relatively high speed, elastodynamic theory is required to find more realizable stress results.
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References
S. Hogmark, S. Jacobson and M. Larsson, Design and evaluation of tribological coatings, Wear, 246 (2000) 20–33.
K. L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, UK. (1985).
D. M. Burmister, The general theory of stresses and displacements in layered systems, J. Appl. Phys., 16 (1945) 89–94.
W. T. Chen, Computation of stresses and displacements in a layered elastic medium, Int. J. Engng. Sci., 9 (1971) 775–800.
W. T. Chen and P. A. Engel, Impact and contact stress analysis in multilayer media, Int. J. Solids Struct., 8 (1972) 1257–1281.
P. K. Gupta and J. A. Walowit, Contact stresses between and elastic cylinder and a layered elastic solid, ASME J. Lub. Tech., 96 (1974) 250–257.
C. H. Kuo and L. M. Keer, Contact stress analysis of a layered transversely isotropic half-space, ASME J. Tribol., 114 (2) (1992) 253–261.
K. Komvopoulos, Finite element analysis of a layered elastic solid in normal contact with a rigid surface, ASME J. Tribol., 110 (3) (1988) 447–485.
E. R. Kral and K. Komvopoulos, Three dimensional finite element analysis of surface deformation and stresses in an elastic-plastic layered medium subjected to indentation and sliding contact loading, ASME J. Appl. Mech., 63 (1996) 365–375.
E. R. Kral, K. Komvopoulos and D. B. Bogy, Finite element analysis of repeated indentation of an elastic-plastic layered medium by a rigid sphere, Part I: Surface results, ASME J. Appl. Mech., 62 (1995a) 20–28.
E. R. Kral, K. Komvopoulos and D. B. Bogy, Finite element analysis of repeated indentation of an elastic-plastic layered medium by a rigid sphere, Part II: Subsurface results, ASME J. Appl. Mech., 62 (1995b) 29–42.
M. Shakeri, A. Sadough and S. R. Ahmadi, Elastic stress analysis of bi-layered isotropic coatings and substrate subjected to line scratch indentation, J. Mat. Processing Tech., 196 (2008) 213–221.
M. R. Lovell, Analysis of contact between transversely isotropic coated surfaces: Development of stress and displacement relationships using FEM, Wear, 214 (1998) 165–174.
C. Morrow and M. Lovell, Numerical contact analysis of transversely isotropic coatings, Wear, 236 (1999) 360–367.
Z. Shi and S. Ramalingam, Stresses in coated solids due to normal and shear tractions on an elliptical region, Surf. Coating Technol., 138 (2001) 192–204.
M. Kot, Contact mechanics of coating-substrate systems: Monolayer and multilayer coatings, Archives of Civil and Mechanical Engineering, 12 (2012) 464–470.
S. J. Cole and R. S. Sayles, A numerical model for the contact of layered elastic bodies with real rough surfaces, ASME J. Tribol., 114 (2) (1992) 334–340.
K. S. Lee, Effect of elastic modulus mismatch on the contact crack initiation in hard ceramic coating layer, KSME International J., 17 (12) (2003) 1928–1937.
K. Komvopoulos, Subsurface crack mechanisms under indentation loading, Wear, 199 (1996) 9–23.
K. Komvopoulos and S.-S. Cho, Finite element analysis of subsurface crack propagation in a half-space due to a moving asperity contact, Wear, 209 (1997) 57–68.
H. Djabella and R. D. Arnell, Finite element analysis of the contact stresses in elastic coating substrate under normal and tangential load, Thin Solid Films, 223 (1993) 87–97.
K. Aslantas and S. Tasgetiren, Debonding between coating and substrate due to rolling-sliding contact, Materials and Design, 23 (2002) 571–576.
J.-J. Kang, B.-S. Xu, H.-D. Wang and C.-B. Wang, Influence of contact stress on rolling contact fatigue of composite ceramic coatings plasma sprayed on a steel roller, Tribol. Int., 73 (2014) 47–56.
L. Lee, P. Behera, K. R. Sriraman and R. R. Chromic, The effect of contact stress on the sliding wear behavior of Zn-Ni electrodeposited coatings, Wear, 400–401 (2018) 82–92.
H. J. Choi, On the plane contact problem of a functionally graded elastic layer loaded by a frictional sliding flat punch, J. of Mechanical Science and Technology, 23 (2009) 2703–2713.
M. A. Guler and F. Erdogan, The frictional sliding contact problems of rigid parabolic and cylindrical stamps on graded coatings, Int. J. Mech. Sci., 49 (2007) 161–182.
R. Goltsberg and I. Etsion, Contact area and maximum equivalent stress in elastic spherical contact with thin hard coating, Tribol. Int., 93 (2016) 289–296.
I. N. Sneddon, Stress produced by a pulse of pressure moving along the surface of a semi-infinite solid, Rendiconti del Circolo Matematico di Palermo, 2 (1952) 57–62.
J. Cole and J. Huth, Stresses produced in a half plane by moving loads, ASME J. Appl. Mech., 25 (1958) 433–436.
A. C. Eringen and E. S. Suhubi, Elastodynamics, Academic Press, New York, USA, 2 (1975).
H. G. Georgidas and J. R. Barber, Steady-state transonic motion of a line load over an elastic half-space: The corrected cole/huth solution, ASME J. Appl. Mech., 60 (1993) 772–774.
A. Verrujit and C. C. Cordova, Moving loads on an elastic half-plane with hysteretic damping, ASME J. Appl. Mech., 68 (2001) 915–922.
Y. T. Zhou, K. Y. Lee and Y. H. Jang, Influences of the moving velocity and material property on frictionless contact problem of orthotropic materials indented by a moving punch, Arch. Mech., 65 (3) (2013) 195–217.
Y. T. Zhou, K. Y. Lee and Y. H. Jang, Indentation theory orthotropic materials subjected to a frictional moving punch, Arch. Mech., 66 (2) (2014) 71–94.
Y. T. Zhou and K. Y. Lee, Dynamic behavior of a moving frictional punch over the surface of anisotropic materials, Appl. Math. Model., 38 (2014) 2311–2327.
Y. T. Zhou and T. W. Kim, Frictional moving contact over the surface between a rigid punch and piezomagnetic materials - Terfanol-D as example, Int. J. Solids Struct., 50 (2013) 4030–4042.
M. N. Balci and S. Dag, Dynamic frictional contact problems involving elastic coatings, Tribol. Int., 124 (2018) 70–92.
F. Erdogan, Mixed boundary value problems in mechanics, S. Nemat-Nasser (Ed.), Mechanics Today, Pergamon Press, New York, 4 (1978) 1–86.
N. I. Muskhelishvili, Singular Integral Equations, Noordhoff, Groningen, The Netherlands (1953).
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Recommended by Associate Editor Heung Soo Kim
Mehmet N. Balci is a Ph.D. candidate in Mechanical Engineering at Middle East Technical University (METU), Turkey. His research interests are analytical methods in engineering, finite element method, contact mechanics of coated and layered structures.
Serkan Dag received his B.S. and M.S. in Mechanical Engineering from Middle East Technical University (METU), Turkey. Then, he received his Ph.D. from Lehigh University, USA. He is a Full Professor in Mechanical Engineering at Middle East Technical University (METU), Turkey. His research interests are in the fields of solid mechanics, mechanics of micro-nano structures, fracture mechanics, contact mechanics, computational and analytical methods.
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Balci, M.N., Dag, S. Mechanics of dynamic contact of coated substrate and rigid cylindrical ended punch. J Mech Sci Technol 33, 2225–2240 (2019). https://doi.org/10.1007/s12206-019-0425-8
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DOI: https://doi.org/10.1007/s12206-019-0425-8