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Research Articles

Adhesive Contact of Elastic-Plastic Layered Media: Effective Tabor Parameter and Mode of Surface Separation

[+] Author and Article Information
Z. Song

Research Assistant

K. Komvopoulos

Professor
Fellow ASME
e-mail: kyriakos@me.berkeley.edu
Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720

1Corresponding author.

Manuscript received June 17, 2012; final manuscript received July 29, 2012; accepted manuscript posted online September 6, 2012; published online January 25, 2013. Assoc. Editor: Nick Aravas.

J. Appl. Mech 80(2), 021022 (Jan 25, 2013) (9 pages) Paper No: JAM-12-1239; doi: 10.1115/1.4007543 History: Received June 17, 2012; Revised July 29, 2012; Accepted September 06, 2012

Adhesive contact of a rigid sphere with a layered medium consisting of a stiff elastic layer perfectly bonded to an elastic-plastic substrate is examined in the context of finite element simulations. Surface adhesion is modeled by nonlinear spring elements obeying a force-displacement relation governed by the Lennard–Jones potential. Adhesive contact is interpreted in terms of the layer thickness, effective Tabor parameter (a function of the layer thickness and Tabor parameters corresponding to layer and substrate material properties), maximum surface separation, layer-to-substrate elastic modulus ratio, and plasticity parameter (a characteristic adhesive stress expressed as the ratio of the work of adhesion to the surface equilibrium distance, divided by the yield strength of the substrate). It is shown that surface separation (detachment) during unloading is not encountered at the instant of maximum adhesion (pull-off) force, but as the layered medium is stretched by the rigid sphere, when abrupt surface separation (jump-out) occurs under a smaller force (surface separation force). Ductile- and brittle-like modes of surface detachment, characterized by the formation of a neck between the rigid sphere and the layered medium and a residual impression on the unloaded layered medium, respectively, are interpreted for a wide range of plasticity parameter and maximum surface separation. Numerical results illustrate the effects of layer thickness, bulk and surface material properties, and maximum surface separation (interaction distance) on the pull-off and surface separation forces, jump-in and jump-out contact instabilities, and evolution of substrate plasticity during loading and unloading. Simulations of cyclic adhesive contact demonstrate that incremental plasticity (ratcheting) in the substrate is the most likely steady-state deformation mechanism under repetitive adhesive contact conditions.

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Figures

Grahic Jump Location
Fig. 7

(a) Surface force P¯ versus surface separation δ¯ during loading (solid lines) and unloading (dashed lines) and (b) residual surface height h¯r versus radial distance r¯ for elastic-plastic layered medium, El/Es = 10, β = 6.67, t¯ = 8, and δ¯max = 3.33, 10, and 16.7

Grahic Jump Location
Fig. 6

(a) Surface force P¯ versus surface separation δ¯ during loading (solid lines) and unloading (dashed lines) and (b) residual surface height h¯r versus radial distance r¯ for elastic-plastic layered medium, El/Es = 10, β = 33.3, t¯ = 8, and δ¯max = 3.33, 10, and 16.7. (Pull-off force P¯off and separation force P¯sep are defined in (a).)

Grahic Jump Location
Fig. 5

Substrate effect θ versus center layer deflection ξ for elastic layered medium having a wide range of El/Es

Grahic Jump Location
Fig. 4

Substrate effect θ versus layer thickness t¯ for elastic layered medium with El/Es in the range of 2.5–40

Grahic Jump Location
Fig. 3

Center deflection before surface separation h¯o versus Tabor parameter μ for homogeneous elastic half-space

Grahic Jump Location
Fig. 1

(a) Schematic showing a rigid sphere of radius R in close proximity with a layered medium consisting of an elastic layer of thickness t and an elastic-plastic substrate (center deflection ho is due to an adhesion (attractive) surface force) and (b) finite element mesh of the layered medium, showing the nonlinear spring elements used to model interfacial adhesion

Grahic Jump Location
Fig. 8

Residual center height h¯o,r versus maximum surface separation δ¯max for elastic-plastic layered medium, El/Es = 10, β = 3.33–33.3, and t¯ = 8

Grahic Jump Location
Fig. 9

(a) Surface force P¯ versus surface separation δ¯ during loading (solid lines) and unloading (dashed lines) and (b) residual surface height h¯r versus radial distance r¯ for elastic-plastic layered medium, El/Es = 10, β = 1.67, 6.67, and 33.3, t¯ = 8, and δ¯max = 10

Grahic Jump Location
Fig. 2

Pull-off force P¯off versus layer thickness t¯ for a layered medium consisting of an elastic layer of El = 20 GPa and a rigid substrate

Grahic Jump Location
Fig. 10

(a) Surface force P¯ versus surface separation δ¯ during loading (solid lines) and unloading (dashed lines) and (b) residual surface height h¯r versus radial distance r¯ for elastic-plastic layered medium, El/Es = 2.5, 10, and 40, β = 33.3, t¯ = 8, and δ¯max = 10

Grahic Jump Location
Fig. 11

Contours of equivalent plastic strain ɛ¯p after complete unloading for elastic-plastic layered medium, El/Es = 2.5, 10, and 40, β = 33.3, t¯ = 8, and δ¯max = 10

Grahic Jump Location
Fig. 12

(a) Surface force P¯ versus surface separation δ¯ during loading (solid lines) and unloading (dashed lines) and (b) residual surface height h¯r versus radial distance r¯ for elastic-plastic layered medium, El/Es = 10, β = 33.3, t¯ = 4, 8, and 16, and δ¯max = 10

Grahic Jump Location
Fig. 13

Surface force P¯ versus surface separation δ¯ during loading (solid lines) and unloading (dashed lines) for four consecutive loading cycles, elastic-plastic layered medium, El / Es = 10, β = 6.67 and 33.3, t¯ = 8, and δ¯max = 10

Grahic Jump Location
Fig. 14

Depth distributions of equivalent plastic strain ɛ¯p along the axis of symmetry (r¯ = 0) for four consecutive loading/unloading cycles, elastic-plastic layered medium, El/Es = 10, β = 6.67 and 33.3, t¯ = 8, and δ¯max = 10

Grahic Jump Location
Fig. 15

Radial distributions of equivalent plastic strain ɛ¯p along the layer/substrate interface (z¯ = –8) for four consecutive loading/unloading cycles, elastic-plastic layered medium, El/ Es = 10, β = 6.67 and 33.3, t¯ = 8, and δ¯max = 10

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