Investigation of Stress in the Perforated Plate with the Presence of Edge Crack
Subject Areas : Analytical and Numerical Methods in Mechanical Design
1 - Department of Mechanical Engineering, Khorramabad Branch, Islamic azad university, Khorramabad, Iran
Keywords: failure, edge crack, Inglis formula, stress field,
Abstract :
The phenomenon of failure in objects is one of the major issues that human beings have been facing for a long time, and because of advances in technology in the present age, this issue is more important than in the past.All engineering materials, on the other hand, have tiny cracks from which failure begins.Therefore, estimating the residual life of thin plates made from these materials and used in space and offshore structures requires knowledge of the stress distribution due to cracking in these components. Because of the singularity of the crack tip due to large stresses, the presence of a relatively small crack can lead to a hazardous situation. Therefore, this area should be given more attention.In this research, using the Inglis formula and considering the correction coefficient of the compensatory free surface, the value of the stress coefficient for edge crack is obtained. Then, by replacing the new stress coefficient in Westergaard formula, we calculate the stress field of Mode I (Opening mode) and Mode II (sliding mode) in the perforated plane containing the edge crack. Finally, we examine the effects of various parameters such as loading angle, crack length and hole radius on the values obtained for stress in both modes by plotting.
[1] Abdelmoula, R., Semani, K., & Li, J. (2007). Analysis of cracks originating at the boundary of a circular hole in an infinite plate by using a new conformal mapping approach. Applied mathematics and computation, 188(2), 1891-1896.
[2] Batista, M. (2011). On the stress concentration around a hole in an infinite plate subject to a uniform load at infinity. International Journal of Mechanical Sciences, 53(4), 254-261.
[3] Boström, L. A. (1989). The Dugdale model used for short radial cracks emanating from a circular hole in an infinite sheet. Engineering fracture mechanics, 34(4), 823-829.
[4] Bowie, O. L. (1956). Analysis of an infinite plate containing radial cracks originating at the boundary of an internal circular hole. Journal of mathematics and physics, 35(1-4), 60-71.
[5] Du, Y., Liu, S., Duan, S., & Li, Y. (2013). Electro-elastic fields of piezoelectric materials with an elliptic hole under uniform internal shearing forces. Chinese Journal of Mechanical Engineering, 26(3), 454-461.
[6] Gdoutos, E. E. (2020). Fracture mechanics: an introduction (Vol. 263). Springer Nature.
[7] Guo, J. H., & Liu, G. T. (2008). Analytic solutions to problem of elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals. Applied Mathematics and Mechanics, 29(4), 485-493.
[8] Guo, J., & Liu, G. (2007). Stress analysis for an elliptical hole with two straight cracks. 力学学报, 23(5), 699-703.
[9] Guo, J.-H., et al., The behavior of two non-symmetrical permeable cracks emanating from an elliptical hole in a piezoelectric solid. European Journal of Mechanics-A/Solids, 2010. 29(4): p. 654-663
[10] Guo, J.-H., et al., Exact solutions for anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material. International Journal of Solids and Structures, 2009. 46(21): p. 3799-3809
[11] Huaimin, G., Guanting, L., & Jiandong, P. (2007). Stress analysis of an ellipse hole with a straight edge-crack by complex variable method. ACTA MECHANICA SOLIDA SINICA-CHINESE EDITION-, 28(3), 308.
[12] Inglis, C.E., Stresses in a plate due to the presence of cracks and sharp corners. Trans Inst Naval Archit, 1913. 55: p. 219-241.
[13] Isida, M., Chen, D. H., & Nisitani, H. (1985). Plane problems of an arbitrary array of cracks emanating from the edge of an elliptical hole. Engineering fracture mechanics, 21(5), 983-995.
[14] Kim, J., & Hill, M. R. (2016). Weight functions for a finite width plate with single or double radial cracks at a circular hole. Engineering Fracture Mechanics, 168, 112-130.
[15] Kolosov, G. V. (1909). On the application of complex function theory to a plane problem of the mathematical theory of elasticity (Orig Russian) (Doctoral dissertation, Doctoral thesis, University of Yuriew, Yuriew Publ Co).
[16] Lin, S., & Hills, D. A. (1996). Stress intensity factors for cracks emanating from a semicircular notch in a half-plate. The Journal of Strain Analysis for Engineering Design, 31(6), 433-439.
[17] Liu, S. H., Li, Y. Q., & Shen, Y. M. (2012). The electro-elastic fields of piezoelectric materials with an elliptic hole [J]. Engineering Mechanics, 29(12), 45-50.
[18] Liu, S., & Duan, S. (2014). Analytical solutions of cracks emanating from an elliptical hole under shear. Chinese Journal of Aeronautics, 27(4), 829-834.
[19] Liu, S., Qi, Y., Feng, D., Shi, X., & Wan, T. (2012). Numerical analysis of crack emanating from elliptical hole. Jixie Gongcheng Xuebao(Chinese Journal of Mechanical Engineering), 48(20), 83-87.
[20] Liu, S., Shen, Y., & Liu, J. (2012). Exact solutions for piezoelectric materials with an elliptic hole or a crack under uniform internal pressure. Chinese Journal of Mechanical Engineering, 25(4), 845-852.
[21] Liu, S., & Duan, S. (2014). Analytical solutions of cracks emanating from an elliptic hole in an infinite plate under tension. Chinese Journal of Mechanical Engineering, 27(5), 1057-1063.
[22] Miao, C., Wei, Y., & Yan, X. (2013). Interactions of two collinear circular hole cracks subjected to internal pressure. Applied Mathematics and Computation, 223, 216-224.
[23] Miao, C., Wei, Y., & Yan, X. (2015). A numerical analysis of a center circular-hole crack in a rectangular tensile sheet. Applied Mathematics and Computation, 250, 356-367.
[24] Muskhelishvili, N. I. (1966). Some Basic Problems of Mathematical Elasticity Theory [in Russian] Nauka.
[25] Muskhelishvili, N. I. (2013). The fundamental law of the theory of elasticity. The basic equations. In Some Basic Problems of the Mathematical Theory of Elasticity: Fundamental Equations Plane Theory of Elasticity Torsion and Bending (pp. 52-84). Dordrecht: Springer Netherlands.
[26] Newman, J. C. (1971). An improved method of collocation for the stress analysis of cracked plates with various shaped boundaries. National Aeronautics and Space Administration.
[27] Nisitani, H., & Isida, M. (1973). Stress intensity factor for the tension of an infinite plate having an elliptical hole with two cracks emanating from its apexes. Trans. Japan Soc. Mech. Eng, 39(317), 7-14.
[28] Norio, H., & Jiro, I. (1978). A crack originating from a triangular notch on a rim of a semi-infinite plate. Engineering Fracture Mechanics, 10(4), 773-782.
[29] Savin, G. N. (1961). Stress concentration around holes. (No Title).
[30] Sharma, D. S. (2012). Stress distribution around polygonal holes. International Journal of Mechanical Sciences, 65(1), 115-124.
[31] Shivakumar, V., & Forman, R. G. (1980). Green's function for a crack emanating from a circular hole in an infinite sheet. International Journal of Fracture, 16, 305-316.
[32] Theocaris, P. S., & Petrou, L. (1986). Stress distributions and intensities at corners of equilateral triangular holes. International Journal of Fracture, 31, 271-289.
[33] Tweed, J., & Rooke, D. P. (1979). The stress intensity factor for a crack at the edge of a loaded hole. International Journal of solids and structures, 15(11), 899-906.
[34] Tweed, J., & Rooke, D. P. (1973). The distribution of stress near the tip of a radial crack at the edge of a circular hole. International Journal of Engineering Science, 11(11), 1185-1195.
[35] Yan, X. (2004). Analysis for a crack emanating from a corner of a square hole in an infinite plate using the hybrid displacement discontinuity method. Applied Mathematical Modelling, 28(9), 835-847.
[36] Yan, X. (2005). Stress intensity factors for cracks emanating from a triangular or square hole in an infinite plate by boundary elements. Engineering Failure Analysis, 12(3), 362-375.
[37] Yang, J., Zhou, Y. T., Ma, H. L., Ding, S. H., & Li, X. (2017). The fracture behavior of two asymmetrical limited permeable cracks emanating from an elliptical hole in one-dimensional hexagonal quasicrystals with piezoelectric effect. International Journal of Solids and Structures, 108, 175-185.
