Abstract
This article deals with the interaction between a cracked hole and a line crack under uniform heat flux. Using the principle of superposition, the original problem is converted into three particular cracked hole problems: the first one is the problem of the hole with an edge crack under uniform heat flux, the second and third ones are the problems of the hole under distributed temperature and edge dislocations, respectively, along the line crack surface. Singular integral equations satisfying adiabatic and traction free conditions on the crack surface are obtained for the solution of the second and third problems. The solution of the first problem, as well as the fundamental solutions of the second and third, is obtained by the complex variable method along with the rational mapping function approach. Stress intensity factors (SIFs) at all three crack tips are calculated. Interestingly, the results show that the interaction between the cracked hole and the line crack under uniform heat flux can lead to the vanishing of the SIFs at the hole edge crack tip. The fact has never been seen for the case of a cracked hole and a line crack under remote uniform tension.
Similar content being viewed by others
References
O.L. Bowie (1956) ArticleTitleAnalysis of an infinite plate containing radial cracks originating at the boundary of an internal circular hole Journal of Mathematical Physics 35 60–71 Occurrence Handle0072.18904 Occurrence Handle78155
C.K. Chao J.Y. Lee (1996) ArticleTitleInteraction between a crack and a circular elastic inclusion under remote uniform heat flow International Journal of Solids and Structures 33 3865–3880 Occurrence Handle0920.73285
Y.Z. Chen N. Hasebe (1992) ArticleTitleAn alternative Fredholm integral equation approach for multiple crack problem and multiple rigid line problem in plane elasticity Engineering Fracture Mechanics 43 257–268 Occurrence Handle1992EnFM...43..257C
F. Erdogan (1969) ArticleTitleApproximate solution of systems of singular integral equations AISM Journal of Applied Mathematics 17 1041–1059 Occurrence Handle10.1137/0117094 Occurrence Handle0187.12404 Occurrence Handle261294
F. Erdogan G.P. Gupta (1972) ArticleTitleOn the numerical solution of singular integral equations Quarter Applied Mathematics 29 525–534 Occurrence Handle0236.65083 Occurrence Handle408277
A.H. Florence J.N. Goodier (1960) ArticleTitleThermal stresses due to disturbance of uniform heat flow by an insulated ovaloid hole ASME Journal of Applied Mechanics 27 635–639 Occurrence Handle0102.18903 Occurrence Handle127036
J. Han N. Hasebe (2001) ArticleTitleThermal stress problem for mixed heat conduction boundary around an arbitrarily shaped hole with crack under uniform heat flux Journal of Thermal Stresses 24 725–735
N. Hasebe S. Inohara (1980) ArticleTitleStress analysis of a semi-infinite plate with an oblique edge crack Ingenieur Archive 49 51–62 Occurrence Handle0426.73089
N. Hasebe M. Ueda (1980) ArticleTitleCrack originating from a corner of a square hole Engineering Fracture Mechanics 13 913–923
N. Hasebe A. Tomida T. Nakamura (1988) ArticleTitleThermal stresses of a cracked circular hole due to uniform heat flux Journal of Thermal Stresses 11 381–391
N. Hasebe K. Yoshikawa M. Ueda T. Nakamura (1994a) ArticleTitlePlane elastic solution for the second mixed boundary value problem and its application Archive of Applied Mechanics 64 295–306 Occurrence Handle0808.73010
N. Hasebe T. Nakamura Y. Ito (1994b) ArticleTitleAnalysis of the second mixed boundary value problem for a thin plate ASME Journal of Applied Mechanics 61 555–559 Occurrence Handle0811.73032 Occurrence Handle10.1115/1.2901495
N. Hasebe Y.Z. Chen (1996) ArticleTitleStress intensity solutions for the interaction between a hole edge crack and a line crack International Journal of Fractures 77 351–366
Hasebe, N. and Han, J.J. (2001). Interaction between elliptic hole and crack in thin plate under uniform bending heat flux. Proceedings of the 23rd International Conference on the Boundary Element Method 3-12.
N. Hasebe X.F. Wang M. Kondo (2003a) ArticleTitleInteraction between crack and arbitrarily shaped hole with stress and displacement boundaries International Journal of Fracture 119 83–102
N. Hasebe X.F. Wang M. Kondo (2003b) ArticleTitleGreen’s functions for plane problem under various boundary conditions and applications International Journal of Solids and Structures 40 5037–5049 Occurrence Handle1059.74008
Muskhelishvili, N.I. (1963). Some Basic Problems of Mathematical Theory of Elasticity. Noordhoff, Netherlands.
J. Schijve (1983) ArticleTitleStress intensity factors of hole edge cracks Comparison between one crack and two symmetric cracks. International Journal of Fractures 23 111–115
J. Tweed D.P. Rooke (1973) ArticleTitleThe distribution of stress near the tip of a radial crack at the edge of a circular hole International Journal of Engineering Science 11 1185–1195 Occurrence Handle0267.73064
K. Yoshikawa N. Hasebe (1999) ArticleTitleGreen’s function for a heat source in an infinite region with an arbitrarily shaped hole ASME Journal of Applied Mechanics 66 204–210 Occurrence Handle1690119 Occurrence Handle10.1115/1.2789147
X. Zhang N. Hasebe (1993) ArticleTitleBasic singular solutions for a cracked circular hole in an infinite medium Archive of Applied Mechanics 63 505–512 Occurrence Handle0785.73062
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vinh, P.C., Hasebe, N., Wang, XF. et al. Interaction between a cracked hole and a line crack under uniform heat flux. Int J Fract 131, 367–384 (2005). https://doi.org/10.1007/s10704-004-7138-3
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10704-004-7138-3