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Research Papers: Friction and Wear

Efficient Steady-State Computation for Wear of Multimaterial Composites

[+] Author and Article Information
Florian Feppon

Centre de Mathématiques Appliquées,
École polytechnique,
Route de Saclay,
Palaiseau 91128, France
e-mail: florian.feppon@polytechnique.edu

Mark A. Sidebottom

Department of Mechanical
Engineering and Mechanics,
Lehigh University,
Bethlehem, PA 18015

Georgios Michailidis

SIMaP-Université de Grenoble, INPG,
1130 rue de la Piscine,
St. Martin d'Hères 38402, France

Brandon A. Krick

Assistant Professor
Department of Mechanical
Engineering and Mechanics,
Lehigh University,
Bethlehem, PA 18015

Natasha Vermaak

Assistant Professor
Department of Mechanical
Engineering and Mechanics,
Lehigh University,
Bethlehem, PA 18015

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 8, 2015; final manuscript received October 16, 2015; published online February 18, 2016. Assoc. Editor: Min Zou.

J. Tribol 138(3), 031602 (Feb 18, 2016) (10 pages) Paper No: TRIB-15-1247; doi: 10.1115/1.4031993 History: Received July 08, 2015; Revised October 16, 2015

Traditionally, iterative schemes have been used to predict evolving material profiles under abrasive wear. In this work, more efficient continuous formulations are presented for predicting the wear of tribological systems. Following previous work, the formulation is based on a two parameter elastic Pasternak foundation model. It is considered as a simplified framework to analyze the wear of multimaterial surfaces. It is shown that the evolving wear profile is also the solution of a parabolic partial differential equation (PDE). The wearing profile is proven to converge to a steady-state that propagates with constant wear rate. A relationship between this velocity and the inverse rule of mixtures or harmonic mean for composites is derived. For cases where only the final steady-state profile is of interest, it is shown that the steady-state profile can be accurately and directly determined by solving a simple elliptic differential system—thus avoiding iterative schemes altogether. Stability analysis is performed to identify conditions under which an iterative scheme can provide accurate predictions and several comparisons between iterative and the proposed formulation are made. Prospects of the new continuous wear formulation and steady-state characterization are discussed for advanced optimization, design, manufacturing, and control applications.

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Figures

Grahic Jump Location
Fig. 1

Representation of the wear model coupling the evolution of contact pressure and the surface topography. (a) Nonuniform wear in heterogeneous materials. In this example, the wear rate of material B, Kb, would be less than that of material A. (b) Schematic of elastic foundation model relating pressure and topography.

Grahic Jump Location
Fig. 2

Schematic of the computational domain, Ω. The domain is occupied by two materials (A, B) with the wear coefficient rates Ka > Kb.

Grahic Jump Location
Fig. 3

(a) An in-plane distribution of materials (see Sec. 5, H = L). For this distribution, the wear profile is computed and plotted along the dotted-dashed line in (a) with two CFL values: CFL = 2.5 (b) and CFL = 0.45 (c). A CFL constant greater than one is subject to potential numerical instability issues. Note the difference in scale between (b) and (c).

Grahic Jump Location
Fig. 4

(a) A first example in-plane distribution of materials with (H = L) and (b) a schematic of the corresponding 3D steady-state profile computed by solving Eq. (20). The material with wear coefficient, Kb, is indicated in black. (c) Along the dotted-dashed line in (a), comparisons are shown of the evolving worn profile (dashed line, z, Eq. (13)) and the steady-state (solid-line, z̃, Eq. (22)) profile at several iterations of the finite-difference scheme (Eq. (13)).

Grahic Jump Location
Fig. 5

(a) A second example in-plane distribution of materials (H = L) with (b) a schematic of the 3D steady-state profile computed by solving Eq. (20). The material with wear coefficient, Kb, is indicated in black. (c) Along the dotted-dashed line in (a), comparisons are shown of the evolving worn profile (dashed line, z, Eq. (13)) and the steady-state (solid-line, z̃, Eq. (22)) profile at several iterations of the finite-difference scheme (Eq. (13)).

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