The mixed boundary problems for finite plates with one crack or two collinear cracks are studied. Complex stress functions that satisfy the equilibrium equations and compatibility conditions in the cracked plate as well as the stress condition on crack surfaces are presented. Four models, that is, a square plate with one crack or with two collinear cracks and an airfoil-shaped plate with one crack or with two collinear cracks, are established. The unknown coefficients of the complex stress functions are determined by using boundary collocation method (BCM). The effects of crack orientation, crack distance, and boundary condition on SIFs are investigated by combining with BCM, and the corresponding photoelastic experiments are conducted. The test results generally agree with the BCM calculation results. 1. Introduction Finite plates with fixed and loaded combination boundary are frequently encountered in engineering practice, such as cantilever beams and aircraft airfoils. In both cases, part of the structures is fixed and the upper face of the cantilever or the windward side of the airfoil will be subjected to load. If such structures contain a crack or multicracks, how to evaluate their stability and strength is a significant subject because the strength of cracked structures is immensely dependent on the geometrical configuration, loading condition, and the crack behavior. In order to precisely predict the stability of the structures of cracked finite plates with mixed boundary condition, it is imperative to implement theoretical and experimental studies so as to obtain the dominative parameters that control the structure stability and, furthermore, to predict engineering disasters. Varied solutions to stress intensity factors for crack problems are generally in three different ways, namely, analytic, numerical, and experimental methods. For many plane problems, the SIFs can be found in the handbook [1, 2]. Muskhelishvili [3] established the fundamental equations in terms of complex functions to solve many plane problems. Jing [4] reviewed the numerical methods in literature and listed many available numerical methods, outstanding issues and potential future developments in this field. Marakami [5] used the finite element method to determine the stress intensity factors for a plate with single crack. Zhu et al. [6–11] investigated the effect of crack orientations on SIFs for cracks subjected to uniform load and proposed a brief formula of SIF based on BCM calculation results.Yavuz et al.[12] analyzed the interaction of multiple crack configuration
References
[1]
G. C. Sih, Handbook of Stress Intensity Factors, Leheigh University, Bethlehem, Pa, USA, 1973.
[2]
H. Tada, P. C. Paris, and G. R. Irwin, The Stress Analysis of Cracks Handbook, Del Research Corp, Hellertown, Penn, USA, 1973.
[3]
N. I. Muskhelishvili, Some Basic Problems of Mathematical Theory of Elasticity, Noordhoff Press, Amsterdam, The Netherland, 1953.
[4]
L. Jing, “A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering,” International Journal of Rock Mechanics and Mining Sciences, vol. 40, no. 3, pp. 283–353, 2003.
[5]
Y. Murakami, “A simple procedure for the accurate determination of stress intensity factors by finite element method,” Engineering Fracture Mechanics, vol. 8, no. 4, pp. 643–655, 1976.
[6]
Z. M. Zhu, S. C. Ji, and H. P. Xie, “An improved method of collocation for the problem of crack surface subjected to uniform load,” Engineering Fracture Mechanics, vol. 54, no. 5, pp. 731–741, 1996.
[7]
Z. M. Zhu, H. Xie, and S. C. Ji, “The mixed boundary problems for a mixed mode crack in a finite plate,” Engineering Fracture Mechanics, vol. 56, no. 5, pp. 647–655, 1997.
[8]
Z. M. Zhu, L. Wang, B. Mohanty, and C. Huang, “Stress intensity factor for a cracked specimen under compression,” Engineering Fracture Mechanics, vol. 73, no. 4, pp. 482–489, 2006.
[9]
Z. M. Zhu, “New biaxial failure criterion for brittle materials in compression,” Journal of Engineering Mechanics, vol. 125, no. 11, pp. 1251–1258, 1999.
[10]
Z. M. Zhu, “Evaluation of the range of horizontal stresses in the earth's upper crust by using a collinear crack model,” Journal of Applied Geophysics, vol. 88, pp. 114–121, 2013.
[11]
Z. M. Zhu, Y. Wang, Z. Zhou, B. Li, and H. Xie, “New fracture criterion for brittle materials under compression,” Journal of Sichuan University, vol. 40, no. 5, pp. 13–21, 2008.
[12]
A. K. Yavuz, S. L. Phoenix, and S. C. TerMaath, “An accurate and fast analysis for strongly interacting multiple crack configurations including kinked (V) and branched (Y) cracks,” International Journal of Solids and Structures, vol. 43, no. 22-23, pp. 6727–6750, 2006.
[13]
Y. Z. Chen, N. Hasebe, and K. Y. Lee, Multiple Crack Problems in Elasticity, Witpress, Southampton, NY, USA, 2003.
[14]
Z. M. Zhu, “An alternative form of propagation criterion for two collinear cracks under compression,” Mathematics and Mechanics of Solids, vol. 14, no. 8, pp. 727–746, 2009.
[15]
Y. H. Wang, L. G. Tham, P. K. K. Lee, and Y. Tsui, “A boundary collocation method for cracked plates,” Computers and Structures, vol. 81, no. 28-29, pp. 2621–2630, 2003.
[16]
W. C. Jin, Z. M. Zhu, and M. Z. Gao, “A general method to determine the stress intensity factor of multiple collinear cracks,” Mathematics and Mechanics of Solids, vol. 18, no. 4, pp. 397–408, 2012.
[17]
J. C. Newman, “An improved method of collocation for the stress analysis of cracked plate with various shaped boundaries,” NASA TN-D-6376, National Aeronautics and Space Administration, Washington, DC, USA, 1971.
