Email this article and Applied Mechanics
56, 4, pp. 915-925, Warsaw 2018
DOI: 10.15632/jtam-pl.56.4.915
Inclined surface cracks in a graded half-plane subjected to frictional sliding contact
ding frictional contact are investigated in this study. The problem is modelled via the finite
element method (FEM) under the plane strain assumption employing a newly developed di-
splacement boundary condition. The shear modulus of the half-plane is graded exponentially
through the thickness direction by means of the homogeneous finite element approach. The
augmented Lagrange algorithm is selected as an iterative contact solver. The mixed mode
stress intensity factors (SIFs) which are induced by the contact stresses are evaluated utili-
zing the Displacement Correlation Technique (DCT). The accuracy of the present procedure
is ensured comparing the SIF results to those calculated by an analytical method for verti-
cal surface cracks. Additional SIF curves are generated as functions of the crack inclination
in order to reveal the effects of non-homogeneity, punch location, crack length and friction
coefficient. The prominent conclusion of this study indicates that the crack orientation has
profound effects on the behavior of SIF curves, which has not been presented in any study
published so far. Hence, consideration of crack inclination is proved essential to successfully
predict fracture behavior of a graded medium under frictional contact.
References
ANSYS Inc., 2013, Ansys Basic Analysis Procedures Guide – Release 15, Ansys Inc., Canonsburg
Arslan O., 2017, Computational contact mechanics analysis of laterally graded orthotropic half-
planes, World Journal of Engineering, 14, 145-154
Dag S., 2001, Crack and contact problems in graded materials, Ph.D. Thesis, Lehigh University,
Bethlehem
Dag S., Apatay T., Guler M.A., Gulgec M., 2012, A surface crack in a graded coating
subjected to sliding frictional contact, Engineering Fracture Mechanics, 80, 72-91
Dag S., Erdogan F., 2002, A surface crack in a graded medium loaded by a sliding rigid stamp,
Engineering Fracture Mechanics, 69, 1729-1751
Dag S., Guler M.A., Yildirim B., Ozatag A.C., 2009, Sliding frictional contact between a
rigid punch and a laterally graded medium, International Journal of Solids and Structures, 46, 4038-4053
Dag S., Yildirim B. and Sarikaya D., 2007, Mixed-mode fracture analysis of orthotropic
functionally graded materials under mechanical and thermal loads, International Journal of Solids
and Structures, 44, 7816-40
El-Borgi S., Keer L., Wissem B.S., 2004, An embedded crack in a functionally graded coating
bonded to a homogeneous substrate under frictional Hertzian contact, Wear, 257, 760-776
El-Borgi S., Keer L., Wissem B.S., 2013, An embedded crack in a functionally graded ortho-
tropic coating bonded to a homogeneous substrate under frictional Hertzian contact, International
Journal of Solids and Structures, 50, 3898-3910
Faanes S., 1995, Inclined cracks in fretting fatigue, Engineering Fracture Mechanics, 80, 6, 71-82
Giner E., Sabsabi M., Rodenas J.J., Fuenmayor F.J., 2014, Direction of crack propagation
in a complete contact fretting-fatigue problem, International Journal of Fatigue, 58, 172-180
Hasebe N., Okumura M., Nakamura T., 1989, Frictional punch and crack in plane elasticity,
Journal of Engineering Mechanics, 115, 6, 1137-1149
Hills D.A., Nowell D., Sackfield A., 1993, Mechanics of Elastic Contacts, Butterworth-
-Heinemann, London
Jitcharoen J., Padture N.P., Giannakopoulos A.E., Suresh S., 1998, Hertzian-Crack
suppression in ceramics with elastic-modulus-graded surfaces, Journal of the American Ceramic
Society, 81, 9, 2301-2308
Jones R.M., 1998, Mechanics of Composite Materials, Taylor & Francis, Philadelphia
Kim J-H., Paulino G.H., 2003, Mixed-mode J-integral formulation and implementation using
graded elements for fracture analysis of nonhomogeneous orthotropic materials, Mechanics of Materials, 35, 107-128
Lawn B., 1998, Indentation of ceramics with spheres: a century after Hertz, Journal of the American
Ceramic Society, 81, 8, 1977-1994
Mijar A.R., Arora J.S., 2004, An augmented Lagrangian optimization method for contact
analysis problems, 1: formulation and algorithm, Structural Multidisciplinary Optimization, 28, 99-112
Perez N., 2004, Fracture Mechanics, Kluwer Academic Publishers, Boston
Santare M.H., Lambros J., 2000), Use of graded finite elements to model behavior of nonho-
mogeneous materials, Journal of Applied Mechanics, 67, 819-822
Sarikaya D., Dag S., 2016, Surface cracking in an orthotropic medium subjected to frictional
contact, International Journal of Solids and Structures, 90, 1-11
Surresh S., 2001, Graded materials for resistance to contact deformation and damage, Science, 292, 5526, 2447-2451
Zhang Y., 2012, Overview: damage resistance of graded ceramic restorative materials, Journal of
the European Ceramic Society, 32, 11, 2623-2632