Abstract
Tunnels, pipelines, and other subterranean circular cavities are common components of modern infrastructure. In addition, seismic activities are common in many areas with pipelines, which may put these structures under unknown risk of fracture. A particular risk case of interest can be characterized as a plane strain problem with a circular cavity and crack in an infinite plane under antiplane stress. Antiplane, i.e., mode III, loading has seen less study relative to modes I and II due to the lower risk factor in structures that are especially vulnerable to fracture (e.g., in the automotive and aerospace industries), and the increase in complexity compared to modes I and II. The work here further explores this phenomenon on circular cavities, and particularly, the effect of non-radial cracks on the stress intensity factor via a parametric study. The study introduces a semi-analytical method and also uses commercial finite element software to further expand on the investigation.
Issue Section:
Research Papers
References
1.
Yokobori
, T.
, Kamei
, A.
, and Konosu
, S.
, 1971
, “Report of Research Institute for Strength and Fracture of Materials
,” Tohoku University
, Sendai, Japan
, 7
, p. 57
.2.
Yokobori
, T.
, Ichikawa
, M.
, Konosu
, S.
, and Takahashi
, R.
, 1972
, “Report of Research Institute for Strength and Fracture of Materials
,” Tohoku University
, Sendai, Japan
, 8
, p. 1
.3.
Tweed
, J.
, and Melrose
, G.
, 1989
, “Cracks at the Edge of an Elliptic Hole in Out of Plane Shear
,” Eng. Fract. Mech.
, 34
(3
), pp. 743
–747
. 4.
Sih
, G. C.
, 1963
, “Stress-Intensity Factors for Longitudinal Shear Cracks
,” AIAA J.
, 1
(10
), pp. 2387
–2388
. 5.
Rice
, J. R.
, 1966
, “Contained Plastic Deformation Near Cracks and Notches Under Longitudinal Shear
,” Int. J. Fract. Mech.
, 2
(2
), pp. 426
–447
. 6.
Rice
, J. R.
, 1968
, “Mathematical Analysis in the Mechanics of Fracture,” Fracture: An Advanced Treatise
, 2nd ed., H
. Liebowitz
, ed., Academic Press
, New York
, pp. 191
–311
.7.
Rice
, J. R.
, 1967
, “Stresses Due to a Sharp Notch in a Work Hardening Elastic-Plastic Material Loaded by Longitudinal Shear
,” ASME J. Appl. Mech.
, 34
(2
), pp. 287
–298
. 8.
Belytschko
, T.
, and Black
, T.
, 1999
, “Elastic Crack Growth in Finite Elements With Minimal Remeshing
,” Int. J. Numer. Methods Eng.
, 45
(5
), pp. 601
–620
. 9.
Moës
, N.
, Dolbow
, J.
, and Belytschko
, T.
, 1999
, “A Finite Element Method for Crack Growth Without Remeshing
,” Int. J. Numer. Methods Eng.
, 46
, pp. 131
–150
. 10.
Melenk
, J.
, and Babuška
, I.
, 1996
, “The Partition of Unity Finite Element Method: Basic Theory and Applications
,” Comput. Methods Appl. Mech. Eng.
, 39
(1–4
), pp. 289
–314
. 11.
Nagashima
, T.
, Omoto
, Y.
, and Tani
, S.
, 2003
, “Stress Intensity Factor Analysis of Interface Cracks Using X-FEM
,” Comput. Methods Appl. Mech. Eng.
, 56
(8
), pp. 1151
–1173
. 12.
Huynh
, D. B. P.
, and Belytschko
, T.
, 2009
, “The Extended Finite Element Method for Fracture in Composite Materials
,” Int. J. Numer. Methods Eng.
, 77
(2
), pp. 214
–239
. 13.
Javanmardi
, M. R.
, and Maheri
, M. R.
, 2019
, “Extended Finite Element Method and Anisotropic Damage Plasticity for Modelling Crack Propagation in Concrete
,” Finite Elem. Anal. Des.
, 165
, pp. 1
–20
. 14.
Roth
, S.-N.
, Léger
, P.
, and Soulaïmani
, A.
, 2020
, “Strongly Coupled XFEM Formulation for Non-planar Three-Dimensional Simulation of Hydraulic Fracturing With Emphasis on Concrete Dams
,” Comput. Methods Appl. Mech. Eng.
, 363
, p. 112899
. 15.
Zhuang
, Z.
, Liu
, Z.
, Cheng
, B.
, and Liao
, J.
, 2014
, Extended Finite Element Method
, Elsevier Science and Technology
, Waltham, MA
, p. 137
.16.
Liu
, X. Y.
, Xiao
, Q. Z.
, and Karihaloo
, B. L.
, 2004
, “XFEM for Direct Evaluation of Mixed Mode SIFs in Homogeneous and Bi-materials
,” Int. J. Numer. Methods Eng.
, 59
(8
), pp. 1103
–1118
. 17.
Areias
, P. M. A.
, and Belytschko
, T.
, 2005
, “Analysis of Three-Dimensional Crack Initiation and Propagation Using the Extended Finite Element Method
,” Int. J. Numer. Methods Eng.
, 63
(5
), pp. 760
–788
. 18.
Shen
, Y.
, and Lew
, A.
, 2010
, “An Optimally Convergent Discontinuous Galerkin-Based Extended Finite Element Method for Fracture Mechanics
,” Int. J. Numer. Methods Eng.
, 82
(6
), pp. 716
–755
. 19.
Marco
, M.
, Infante-García
, D.
, Belda
, R.
, and Giner
, E.
, 2020
, “A Comparison Between Some Fracture Modelling Approaches in 2D LEFM Using Finite Elements
,” Int. J. Fract.
, 223
(1–2
), pp. 151
–171
. 20.
Fries
, T.-P.
, and Belytschko
, T.
, 2010
, “The Extended/Generalized Finite Element Method: An Overview of the Method and Its Applications
,” Int. J. Numer. Methods Eng.
, 84
(3
), pp. 253
–304
. 21.
Westergaard
, H. M.
, 1939
, “Bearing Pressures and Cracks: Bearing Pressures Through a Slightly Waved Surface or Through a Nearly Flat Part of a Cylinder, and Related Problems of Cracks
,” ASME J. Appl. Mech.
, 6
(2
), pp. pp. A49
–A53
. 22.
Williams
, M. L.
, 1957
, “On the Stress Distribution at the Base of a Stationary Crack
,” ASME J. Appl. Mech.
, 24
(1
), pp. 109
–114
. 23.
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
. 24.
Isida
, M.
, and Tsuru
, H.
, 1981
, “A Circular Inclusion and an Arbitrary Array of Cracks in Infinite Body Under Antiplane Shear
,” Trans. Jpn. Soc. Mech. Eng., Ser. A
, 47
(420
), pp. 810
–817
. 25.
Tada
, H.
, Paris
, P. C.
, and Irwin
, G. R.
, 2000
, The Stress Analysis of Cracks Handbook
, 3rd ed., ASME Press
, New York
.Copyright © 2023 by ASME
You do not currently have access to this content.
