Volume 19, Issue 1 (2019)                   Modares Mechanical Engineering 2019, 19(1): 21-28 | Back to browse issues page

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Ghajar R, Hajimohamadi M. Determination of Stress Intensity Factor for Unequal Cracks Emanating from a Quasi-square Hole under Shear. Modares Mechanical Engineering. 2019; 19 (1) :21-28
URL: http://journals.modares.ac.ir/article-15-21030-en.html
1- Applied Mechanics Department, Mechanical Engineering Faculty, K. N. Toosi University of Technology, Tehran, Iran , ghajar@kntu.ac.ir
2- Applied Mechanics Department, Mechanical Engineering Faculty, K. N. Toosi University of Technology, Tehran, Iran
Abstract:   (203 Views)
In the different applications of thin plats in engineering industrial, some holes are created in the structure that can have different shapes such as circular, elliptical, and quasi-square. When the plate is subjected to loading, stress concentration around the hole causes the crack initiation in these areas that can results in a catastrophic failure. In this paper, mode II stress intensity factor (SIF) for two unequal aligned cracks emanating from a circle or a quasi-square hole in an infinite plane was investigated. The complex variable theory of Muskhelishvili and conformal mapping method were used. To obtain mapping function, Schwarts Christoffel integral was combined with some simple mapping functions. Accordingly, a new mapping function is presented and approximated to the sum of series expansion. Using this approximate mapping, SIF is calculated with high accuracy. Surfaces of the cracks and hole are traction-free. The plane is subjected to the pure shear at infinity. The analytical results are in good agreement with the literature. The obtained stress intensity factors have good accuracy for small cracks. The equation presented in this paper is applicable to the length of the different cracks and calculates the intensity coefficients of mode II for very small cracks with high accuracy. Results show that the shape of the hole is important only for the small cracks.
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Received: 2018/05/19 | Accepted: 2018/09/17 | Published: 2019/01/1
* Corresponding Author Address: Room 636, No 7, Pardis Street, Mollasadra Avenue, Vanak Square, Tehran, Iran. Postal Code: 1999143344

1. Muskhelishvili NI. Some basic problems of the mathematical theory of elasticity. Berlin: Springer; 1977. [Link] [DOI:10.1007/978-94-017-3034-1]
2. Savin GN. Stress concentration around holes. Oxford: Pergamon Press; 1961. [Link]
3. Durelli AJ, Rajaiah K. Quasi-square hole with optimum shape in an infinite plate subjected to in-plane loading. Journal of Mechanical Design. 1981;103(4):866-870. [Link] [DOI:10.1115/1.3254999]
4. Simha KRY, Mohapatra SS. Stress concentration around irregular holes using complex variable method. Sadhana. 1998;23(4):393-412. [Link] [DOI:10.1007/BF02745750]
5. Louhghalam A, Igusa T, Park C, Choi S, Kim K. Analysis of stress concentrations in plates with rectangular openings by a combined conformal mapping - finite element approach. International Journal of Solids and Structures. 2011;48(13):1991-2004. [Link] [DOI:10.1016/j.ijsolstr.2011.03.005]
6. Sharma DS. Stress distribution around polygonal holes. International Journal of Mechanical Sciences. 2012;65(1):115-124. [Link] [DOI:10.1016/j.ijmecsci.2012.09.009]
7. Lu AZ, Xu Z, Zhang N. Stress analytical solution for an infinite plane containing two holes. International Journal of Mechanical Sciences. 2017;128-129:224-234. [Link] [DOI:10.1016/j.ijmecsci.2017.04.025]
8. Bowie OL. Analysis of an infinite plate containing radial cracks originating at the boundary of an internal circular hole. Studies in Applied Mathematics. 1956;35(1-4):60-71. [Link]
9. Newman JC, United States National Aeronautics and Space Administration, Langley Research Center. An improved method of collocation for the stress analysis of cracked plates with various shaped boundaries. Washington D C: National Aeronautics and Space Administration; 1971. [Link]
10. Nisitani H, Isida M. Stress intensity factor for the tension of an infinite plate containing an elliptical hole with two symmetrical edge cracks. Transactions of the Japan Society of Mechanical Engineers. 1973;39(317):7-14. [Japanese] [Link]
11. Hasebe N, Horiuchi Y. Stress analysis for a strip with semi-elliptical notches or cracks on both sides by means of rational mapping function. Ingenieur Archiv. 1978;47(3):169-179. [Link] [DOI:10.1007/BF01047408]
12. Hasebe N, Ueda M. Crack originating from a corner of a square hole. Engineering Fracture Mechanics. 1980;13(4):913-923. [Link] [DOI:10.1016/0013-7944(80)90021-1]
13. Hasebe N, Chen YZ. Stress intensity solutions for the interaction between a hole edge crack and a line crack. International Journal of Fracture. 1996;77(4):351-366. [Link] [DOI:10.1007/BF00036252]
14. Yan X. A numerical analysis of cracks emanating from a square hole in a rectangular plate under biaxial loads. Engineering Fracture Mechanics. 2004;71(11):1615-1623. [Link] [DOI:10.1016/j.engfracmech.2003.08.005]
15. Yan X. A numerical analysis of cracks emanating from an elliptical hole in a 2-D elasticity plate. European Journal of Mechanics A Solids. 2006;25(1):142-153. [Link] [DOI:10.1016/j.euromechsol.2005.06.005]
16. Philipps AG, Karuppanan S, Churchman CM, Hills DA. Crack tip stress intensity factors for a crack emanating from a sharp notch. Engineering Fracture Mechanics. 2008;75(18):5134-5139. [Link] [DOI:10.1016/j.engfracmech.2008.08.002]
17. Zhao J, Xie L, Liu J, Zhao Q. A method for stress intensity factor calculation of infinite plate containing multiple hole-edge cracks. International Journal of Fatigue. 2012;35(1):2-9. [Link] [DOI:10.1016/j.ijfatigue.2011.06.001]
18. Liu S, Duan S. Analytical solutions of cracks emanating from an elliptical hole under shear. Chinese Journal of Aeronautics. 2014;27(4):829-834. [Link] [DOI:10.1016/j.cja.2014.06.007]
19. Miao C, Wei Y, Yan X. Two collinear square-hole cracks in an infinite plate in tension. Theoretical and Applied Fracture Mechanics. 2015;75:32-38. [Link] [DOI:10.1016/j.tafmec.2014.10.004]
20. Ghajar R, Hajimohamadi M. Analytical calculation of stress intensity factors for unequal cracks emanating from a circular hole in infinite plane. Amirkabir Journal of Mechanical Engineering. 2017 Mar. [Persian] [Link]
21. Hajimohamadi M, Ghajar R. An analytical solution for the stress field and stress intensity factor in an infinite plane containing an elliptical hole with two unequal aligned cracks. Applied Mathematics and Mechanics. 2018;39(8):1103-1118. [Link] [DOI:10.1007/s10483-018-2356-6]

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