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Research Papers

Asymptotic Stress Fields for Complete Contact Between Dissimilar Materials

[+] Author and Article Information
Kisik Hong

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: kisik@umich.edu

M. D. Thouless

Professor
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125;
Department of Materials Science and
Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: thouless@umich.edu

Wei Lu

Professor
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: weilu@umich.edu

J. R. Barber

Professor
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: jbarber@umich.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 24, 2018; final manuscript received September 28, 2018; published online October 18, 2018. Assoc. Editor: Shengping Shen.

J. Appl. Mech 86(1), 011009 (Oct 18, 2018) (6 pages) Paper No: JAM-18-1488; doi: 10.1115/1.4041618 History: Received August 24, 2018; Revised September 28, 2018

We investigate the influence of material dissimilarity on the traction fields at the corners of a contact between an elastic right-angle wedge and an elastic half-plane. The local asymptotic fields are characterized in terms of the properties of the leading eigenvalue for cases of slip and stick as a function of the Dundurs bimaterial parameters α and β, and the coefficient of friction f. Permissible values of α and β are partitioned into two possible ranges, one where behavior is qualitatively similar to the case where the indenting wedge is rigid [α = 1] and the other where behavior is similar to the case where the materials are the same [α = β = 0]. The results give insight into the high local stresses at the edge of a contact between elastically dissimilar bodies and can also be used to evaluate the effectiveness of mesh refinement in corresponding finite element models.

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References

Williams, M. L. , 1952, “ Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension,” ASME J. Appl. Mech., 19(4), pp. 526–528. http://resolver.caltech.edu/CaltechAUTHORS:20140730-111744170
Churchman, C. M. , and Hills, D. A. , 2006, “ General Results for Complete Contacts Subject to Oscillatory Shear,” J. Mech. Phys. Solids, 54(6), pp. 1186–1205. [CrossRef]
Karuppanan, S. , Churchman, C. M. , Hills, D. A. , and Giner, E. , 2008, “ Sliding Frictional Contact Between a Square Block and an Elastically Similar Half-Plane,” Eur. J. Mech., 27(3), pp. 443–459. [CrossRef]
Churchman, C. M. , and Hills, D. A. , 2006, “ Slip Zone Length at the Edge of a Complete Contact,” Int. J. Solids Struct., 43(7–8), pp. 2037–2049. [CrossRef]
Kim, H. K. , Hills, D. A. , and Paynter, R. J. , 2014, “ Asymptotic Analysis of an Adhered Complete Contact Between Elastically Dissimilar Materials,” J. Strain Anal., 49(8), pp. 607–617. [CrossRef]
Cox, B. , 1990, “ Pellet-Clad Interaction (PCI) Failures of Zirconium Alloy Fuel Claddinga Review,” J. Nucl. Mater., 172(3), pp. 249–292. [CrossRef]
Dundurs, J. , 1969, “ Discussion of Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading,” ASME J. Appl. Mech., 36(3), pp. 650–652. [CrossRef]
Gdoutos, E. E. , and Theocaris, P. S. , 1975, “ Stress Concentrations at the Apex of a Plane Indenter Acting on an Elastic Half-Plane,” ASME J. Appl. Mech., 42(3), pp. 688–692. [CrossRef]
Comninou, M. , 1976, “ Stress Singularity at a Sharp Edge in Contact Problems With Friction,” Z. Für Angew. Math. und Phys. ZAMP, 27(4), pp. 493–499. [CrossRef]
Bogy, D. B. , 1971, “ Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles Under Surface Tractions,” ASME J. Appl. Mech., 38(2), pp. 377–386. [CrossRef]
Flicek, R. C. , Ramesh, R. , and Hills, D. A. , 2015, “ A Complete Frictional Contact: The Transition From Normal Load to Sliding,” Int. J. Eng. Sci., 92, pp. 18–27. [CrossRef]
Spence, D. A. , 1973, “ An Eigenvalue Problem for Elastic Contact With Finite Friction,” Proc. Cambridge Philos. Soc., 73(1), pp. 249–268. [CrossRef]
Barber, J. R. , Davies, M. , and Hills, D. A. , 2011, “ Frictional Elastic Contact With Periodic Loading,” Int. J. Solids Struct., 48(13), pp. 2041–2047. [CrossRef]
Comninou, M. , and Dundurs, J. , 1982, “ An Educational Elasticity Problem With Friction—Part 2: Unloading for Strong Friction and Reloading,” ASME J. Appl. Mech., 49(1), pp. 47–51. [CrossRef]
Turner, J. R. , 1979, “ The Frictional Unloading Problem on a Linear Elastic Half-Space,” IMA J. Appl. Math., 24(4), pp. 439–469. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) A quarter-plane (right-angle wedge) indenting a half-plane and (b) Sign convention for normal traction p and shear traction q. At a trailing edge, q = fp, and at a leading edge, q = –fp.

Grahic Jump Location
Fig. 2

Characteristics of the first slip eigenvalue λ1(s) (trailing edge—leading edge) with different friction coefficients: (a) f = 0.2, (b) f = 0.4, (c) f = 0.6, and (d) f = 0.8

Grahic Jump Location
Fig. 3

Lowest eigenvalue versus friction coefficient for contact between elastically similar materials (α = β = 0)

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Fig. 4

Partition of the Dundurs parallelogram

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Fig. 5

Contour plots of the critical friction coefficients: (a) fc and (b) fa

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