Determining the Stress Intensity Factor by Using the Principle of Minimum Potential Energy

Chen Guang-zu

Volume 8 Issue 12

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1987 > 8(12): 1121-1129

Chen Guang-zu. Determining the Stress Intensity Factor by Using the Principle of Minimum Potential Energy[J]. Applied Mathematics and Mechanics, 1987, 8(12): 1121-1129.

Citation:

Chen Guang-zu. Determining the Stress Intensity Factor by Using the Principle of Minimum Potential Energy[J]. Applied Mathematics and Mechanics, 1987, 8(12): 1121-1129.

Citation:

Chen Guang-zu. Determining the Stress Intensity Factor by Using the Principle of Minimum Potential Energy[J]. Applied Mathematics and Mechanics, 1987, 8(12): 1121-1129.

PDF( 452 KB)

Determining the Stress Intensity Factor by Using the Principle of Minimum Potential Energy

Chen Guang-zu

Qinghua University, Beijing

Received Date: 1986-07-10
Publish Date: 1987-12-15

Abstract

Abstract

Expressing the total potential energy of the system of a cracked body П by Williams' infinite series solution of stress and displacement components containing coefficients A_n(n = 1,2,...), we obtain a set of simultaneous linear equations of unknown coefficients A_n by using the principle of minimum potential energy. When the set of equations is solved, the stress intensity factor K₁ can be easily determined. It is equal to √2πaA₁ Take a sample plate as an example. A single-edgc-cracked plate under tension, with the ratio of crack length to the width of the plate being 0.5 and the ratio of half plate height to the width of the plate being 2.0 and 2. 5, has been calculated. Only 20-30 coefficients are taken, and the errors in stress intensity factors are within 5%.

FullText(HTML)

References(5)

References

[1]	钱伟长,《弹性力学》,科学出版社(1956)
[2]	Williams,M.L.,On the stress distribution at the base of a stationary crack,J.Appl.Mech.,24(1957).
[3]	Cross,B.and J.E.Srawley,Stress-intensity factors for a single-edge-notch tension specimen by boundary collocation of a stress function,NASA,TN,D-2395(1964).
[4]	Keer,L.M.and J.M.Freedman,Tensile strip with edge crack:Int.J.Engng.Sci.,11(1973).
[5]	陈光祖,顾求林,确定应力强度因子的势能法,全国第三届断裂会议,南京(1981).

Relative Articles

[1]	LI Ya, YI Zhijian, WANG Min, SU Kang. The Stress Intensity Factor of a FiniteWidth Plate With a Mode-Ⅰ Center Crack Subjected to Uniform Stress on the Crack Surface Near the Crack Tip[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1083-1091. doi: 10.21656/1000-0887.410130
[2]	TONG Gusheng, HU Zongqi, XU Penghua. Study on Stress Intensity Factors of Concrete Beams With Sharp V Notches[J]. Applied Mathematics and Mechanics, 2018, 39(3): 300-310. doi: 10.21656/1000-0887.380159
[3]	XU Hua, XU De-feng, YANG Lü-feng. A Finite Element Method With Generalized DOFs for Stress Intensity Factors of Crack Groups[J]. Applied Mathematics and Mechanics, 2016, 37(10): 1039-1049. doi: 10.21656/1000-0887.370050
[4]	ZHOU Yan, ZHANG Cai-gui, YANG Jing-rui, WANG Qi-zhi. Comprehensive Calibration of the Stress Intensity Factor for the Holed Flattened Brazilian Disc With an Inner Single Crack or Double Cracks[J]. Applied Mathematics and Mechanics, 2015, 36(1): 16-30. doi: 10.3879/j.issn.1000-0887.2015.01.002
[5]	JIANG Shou-yan, DU Cheng-bin. Evaluation on Stress Intensity Factors at the Crack Tip Under Dynamic Loads Using Extended Finite Element Methods[J]. Applied Mathematics and Mechanics, 2013, 34(6): 586-597. doi: 10.3879/j.issn.1000-0887.2013.06.005
[6]	CHEN Ai-jun, CAO Jun-jun. Analysis of Dynamic Stress Intensity Factors of Three-Point Bend Specimen Containing Crack[J]. Applied Mathematics and Mechanics, 2011, 32(2): 194-201. doi: 10.3879/j.issn.1000-0887.2011.02.007
[7]	GAO Xin, WANG Han-gong, KANG Xing-wu. Dynamic Stress Intensity Factor and Dynamic Crack Propagation Characteristics of Anisotropic Material[J]. Applied Mathematics and Mechanics, 2008, 29(9): 1017-1027.
[8]	CHEN Ai-jun, ZENG Wen-ji. Weight Function for Stress Intensity Factors in Rotating Thick-Walled Cylinder[J]. Applied Mathematics and Mechanics, 2006, 27(1): 28-34.
[9]	LIU Dian-kui, CHEN Zhi-gang. Scattering of SH-Wave by Cracks Originating at an Elliptic Hole and Dynamic Stress Intensity Factor[J]. Applied Mathematics and Mechanics, 2004, 25(9): 958-966.
[10]	ZHONG Ming, ZHANG Yong-yuan. The Analysis of Dynamic Stress Intensity Factor for Semi-Circular Surface Crack Using Time-Domain BEM Formulation[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1211-1216.
[11]	TANG Ren-ji, TANG Xin-yan. Method to Calculate Bending Center and Stress Intensity Factors of Cracked Cylinder Under Saint-Venant Bending[J]. Applied Mathematics and Mechanics, 2001, 22(1): 71-78.
[12]	Qian Ren-gen, Shouetsu Itou. DynamicStress Intensity Factors around Two Cracks near an Interface of Two Dissimilar EIastic Half-PIanes under In-plane Shear Impact Load[J]. Applied Mathematics and Mechanics, 1995, 16(1): 61-72.
[13]	Chen Wei-jiang, Wang Kai, Tang Ren-ji. Stress Intensity Factors of the Eccentric and Edge Cracked Cylinders[J]. Applied Mathematics and Mechanics, 1993, 14(4): 289-294.
[14]	Wang Cheng-duan. Study of the Stress Intensity Factor of Preformed V Shape Fracture Tip[J]. Applied Mathematics and Mechanics, 1992, 13(5): 469-477.
[15]	Zhang Ning-sheng, Zhao Xue-ren, Hsueh Dah-wei. A Weighted Residual Method for Elastic-Plastic Analysis near a Crack Tip and the Calculation of the Plastic Stress Intensity Factors[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1055-1066.
[16]	Wang Yuan-han. Stress Intensity Factors of a Plate with Two Cracks Emanating from an Arbitrary Hole[J]. Applied Mathematics and Mechanics, 1990, 11(8): 677-686.
[17]	Ning Jie, Chien Wei-zang. Finite Element Method Combined with Dynamic Photoelastic Analysis to Determine Dynamic Stress-Intensity Factors[J]. Applied Mathematics and Mechanics, 1989, 10(10): 865-870.
[18]	Stress Intensity Factor Considering the Material Plasticity Limited in Scope[J]. Applied Mathematics and Mechanics, 1985, 6(11): 1019-1026.
[19]	Ouyang Chang, Zhou Shiao-kang. On Computations of Stress Intensity Factors for Stiffened Half-Planes with Imperfections and Cracks[J]. Applied Mathematics and Mechanics, 1985, 6(2): 121-133.
[20]	Zhou Cheng-fan, Guan Chang-wen. Stress Concentration and Stress Intensity Factors for an Infinite Plane with Several Rows of Elliptic Holes and Cracks[J]. Applied Mathematics and Mechanics, 1983, 4(6): 789-800.