Boundary element method for the frictionless arc-shaped crack closure problem

Ru-Min Chao, Cheng Hung Chang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper deals with the closure problem of the arc-shaped crack in an infinite isotropic elastic media under unidirectional loading condition. Part of the arc-shaped crack surfaces will be in contact under certain loading orientations according to Toya (J. Mech. Phys. Solids, 1974, 22, 325-48), Chao & Laws (Q. J. Mech. Appl. Meth., 1992, 45(4), 629-40), and Chao & Rau (Engng Fract. Mech., 1995, 50(1), 121-30), who solved the problem by means of the complex variable method or the superposition of dislocations. The boundary element method will be used in this analysis. We first verified the contact results of a single arc-shaped crack with the solution given by Chao and Rau (Engng Fract. Mech., 1995, 50(1), 121-30). Then the solution corresponding to loading orientation w = 90° is given, which is the case of opened crack tips but crack closure at the middle part of the crack surface. Finally, the two symmetric arc-shaped cracks problem is discussed. It is believed that Tada et al., (The Stress Analysis of Cracks Handbook, Del Res. Corp., 1985) not only neglects the closure effect of the two symmetric arc-shaped cracks, but also contains an error in the calculation of the KI stress intensity factor.

Original languageEnglish
Pages (from-to)245-252
Number of pages8
JournalEngineering Analysis with Boundary Elements
Volume17
Issue number3
DOIs
Publication statusPublished - 1996 Apr 1

Fingerprint

Crack Closure
Crack closure
Boundary element method
Boundary Elements
Crack
Arc of a curve
Cracks
Surface Crack
Closure
Contact
Complex Variable Method
Stress Analysis
del operator
Crack Tip
Stress Intensity Factor
Dislocation
Superposition
Stress analysis
Stress intensity factors
Crack tips

All Science Journal Classification (ASJC) codes

  • Analysis
  • Engineering(all)
  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{2f1cf795c37a415f9d0c8f24210f6c56,
title = "Boundary element method for the frictionless arc-shaped crack closure problem",
abstract = "This paper deals with the closure problem of the arc-shaped crack in an infinite isotropic elastic media under unidirectional loading condition. Part of the arc-shaped crack surfaces will be in contact under certain loading orientations according to Toya (J. Mech. Phys. Solids, 1974, 22, 325-48), Chao & Laws (Q. J. Mech. Appl. Meth., 1992, 45(4), 629-40), and Chao & Rau (Engng Fract. Mech., 1995, 50(1), 121-30), who solved the problem by means of the complex variable method or the superposition of dislocations. The boundary element method will be used in this analysis. We first verified the contact results of a single arc-shaped crack with the solution given by Chao and Rau (Engng Fract. Mech., 1995, 50(1), 121-30). Then the solution corresponding to loading orientation w = 90° is given, which is the case of opened crack tips but crack closure at the middle part of the crack surface. Finally, the two symmetric arc-shaped cracks problem is discussed. It is believed that Tada et al., (The Stress Analysis of Cracks Handbook, Del Res. Corp., 1985) not only neglects the closure effect of the two symmetric arc-shaped cracks, but also contains an error in the calculation of the KI stress intensity factor.",
author = "Ru-Min Chao and Chang, {Cheng Hung}",
year = "1996",
month = "4",
day = "1",
doi = "10.1016/S0955-7997(96)00018-5",
language = "English",
volume = "17",
pages = "245--252",
journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Limited",
number = "3",

}

Boundary element method for the frictionless arc-shaped crack closure problem. / Chao, Ru-Min; Chang, Cheng Hung.

In: Engineering Analysis with Boundary Elements, Vol. 17, No. 3, 01.04.1996, p. 245-252.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Boundary element method for the frictionless arc-shaped crack closure problem

AU - Chao, Ru-Min

AU - Chang, Cheng Hung

PY - 1996/4/1

Y1 - 1996/4/1

N2 - This paper deals with the closure problem of the arc-shaped crack in an infinite isotropic elastic media under unidirectional loading condition. Part of the arc-shaped crack surfaces will be in contact under certain loading orientations according to Toya (J. Mech. Phys. Solids, 1974, 22, 325-48), Chao & Laws (Q. J. Mech. Appl. Meth., 1992, 45(4), 629-40), and Chao & Rau (Engng Fract. Mech., 1995, 50(1), 121-30), who solved the problem by means of the complex variable method or the superposition of dislocations. The boundary element method will be used in this analysis. We first verified the contact results of a single arc-shaped crack with the solution given by Chao and Rau (Engng Fract. Mech., 1995, 50(1), 121-30). Then the solution corresponding to loading orientation w = 90° is given, which is the case of opened crack tips but crack closure at the middle part of the crack surface. Finally, the two symmetric arc-shaped cracks problem is discussed. It is believed that Tada et al., (The Stress Analysis of Cracks Handbook, Del Res. Corp., 1985) not only neglects the closure effect of the two symmetric arc-shaped cracks, but also contains an error in the calculation of the KI stress intensity factor.

AB - This paper deals with the closure problem of the arc-shaped crack in an infinite isotropic elastic media under unidirectional loading condition. Part of the arc-shaped crack surfaces will be in contact under certain loading orientations according to Toya (J. Mech. Phys. Solids, 1974, 22, 325-48), Chao & Laws (Q. J. Mech. Appl. Meth., 1992, 45(4), 629-40), and Chao & Rau (Engng Fract. Mech., 1995, 50(1), 121-30), who solved the problem by means of the complex variable method or the superposition of dislocations. The boundary element method will be used in this analysis. We first verified the contact results of a single arc-shaped crack with the solution given by Chao and Rau (Engng Fract. Mech., 1995, 50(1), 121-30). Then the solution corresponding to loading orientation w = 90° is given, which is the case of opened crack tips but crack closure at the middle part of the crack surface. Finally, the two symmetric arc-shaped cracks problem is discussed. It is believed that Tada et al., (The Stress Analysis of Cracks Handbook, Del Res. Corp., 1985) not only neglects the closure effect of the two symmetric arc-shaped cracks, but also contains an error in the calculation of the KI stress intensity factor.

UR - http://www.scopus.com/inward/record.url?scp=0030114084&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030114084&partnerID=8YFLogxK

U2 - 10.1016/S0955-7997(96)00018-5

DO - 10.1016/S0955-7997(96)00018-5

M3 - Article

AN - SCOPUS:0030114084

VL - 17

SP - 245

EP - 252

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

IS - 3

ER -