用Wu-Carlsson解析权函数法（WFM）求得了无限板孔边径向单裂纹和对称双裂纹的高精度解析权函数（WF）。分别用Shivakumar-Forman和Newman的解及基于复变函数泰勒级数展开的数值权函数WCTSE法结果，通过对相应格林函数（GF）的逐点比较验证了本文解析权函数的精度。该权函数不但精度高，而且作为裂纹长度的连续函数，能够高效准确地求解任意长度（a/R≤2）裂纹在任意复杂载荷作用下的断裂力学关键参量；且孔边单/双裂纹问题的权函数的形式和推导方法完全相同。作为示例，用该解析权函数计算了孔边裂纹在裂纹嘴楔形载荷、裂纹面幂函数，以及圆孔冷挤压残余应力等多种载荷形式下的应力强度因子。
Highly accurate Weight Functions (WFs) for the radial crack(s) at a circular hole are derived by using the Wu-Carlsson analytical Weight Function Method (WFM). Accuracy of the WFs proposed is verified and validated point-by-point by using Green's Functions (GFs) of Shivakumar-Forman and Newman, and also the Weight function Complex Taylor Series Expansion (WCTSE) method. It is shown that the WFs proposed are not only highly accurate, but also, as a continuous function for crack length, enable determination of key mechanical parameters of cracks of any length (a/R ≤ 2) under arbitrary loadings with high efficiency and accuracy. A unified approach is adopted for the derivations and expressions of WFs for single/double hole-edge crack(s). The analytical WFs proposed are also used to calculate stress intensity factors for various load cases including wedge-splitting forces at the crack mouth, crack face power stresses, and residual stress fields induced by cold-working of the circular hole.
[1] 郦正能. 应用断裂力学[M]. 北京:北京航空航天大学出版社, 2012. LI Z N. Applied fracture mechanics[M]. Beijing:Beihang University Press, 2012(in Chinese).
[2] BUECKNER H F. A novel principle for the computation of stress intensity factors[J]. Zeitschrift fuer Angewandte Mathematik & Mechanik, 1970, 50:529-546.
[3] RICE J R. Some remarks on elastic crack-tip stress fields[J]. International Journal of Solids and Structures, 1972; 8:751-758.
[4] WU X R, CARLSSON A J. Weight functions and stress intensity factor solutions[M]. Oxford:Pergamon Press, 1991.
[5] FETT T, MUNZ D. Stress intensity factors and weight functions[M]. Southampton:Computational Mechanics Publications, 1997.
[6] GLINKA G, SHEN G. Universal features of weight functions for cracks in mode I[J]. Engineering Fracture Mechanics, 1991, 40:1135-1146.
[7] WU X R, TONG D H. Evaluation of various analytical weight function methods base on exact K-solutions of an edge-cracked circular disc[J]. Engineering Fracture Mechanics, 2018, 189:64-80.
[8] WU X R, TONG D H, ZHAO X C, et al. Review and evaluation of weight functions and stress intensity factors for edge-cracked finite-width plate[J]. Engineering Fracture Mechanics, 2018, 195:200-221.
[9] WAGNER D, MILLWATER H. 2D weight function development using a complex Taylor series expansion method[J]. Engineering Fracture Mechanics, 2012, 86:23-37.
[10] JING Z, WU X R. Wide-range weight functions and stress intensity factors for arbitrarily shaped crack geometries using complex Taylor series expansion method[J]. Engineering Fracture Mechanics, 2015, 138:215-232.
[11] ZHAO X C, WU X R, TONG D H.Weight functions and stress intensity factors for pin-loaded single-edge notch bend specimen[J]. Fatigue & Fracture of Engineering Materials & Structure, 2015, 38:1519-1528.
[12] SHIVAKUMAR V, FORMAN R G. Green's function for a crack emanating from a circular hole in an infinite sheet[J]. International Journal of Fracture, 1980, 16:305-316.
[13] NEWMAN J C, Jr. A nonlinear fracture mechanics approach to the growth of small cracks[C]//AGARD Conference Proceedings, 1983, 328:6.1-6.26.
[14] JIN X C, ZENG Y, DING S, et al. Weight function of stress intensity factor for symmetrical radial cracks emanating from hollow cylinder[J]. Engineering Fracture Mechanics, 2016, 159:144-154.
[15] JIN X C, ZENG Y, DING S, et al. Weight function of stress intensity factor for single radial crack emanating from hollow cylinder[J]. Engineering Fracture Mechanics, 2017, 170:77-86.
[16] 吴学仁. 冷挤压孔边残余应力场中裂纹的应力强度因子[J]. 航空学报, 1989, 10(9):A442-A447. WU X R. Residual stress intensity factors for radial cracks at the edge of a cold-worked hole[J]. Acta Aeronautica et Astronautica Sinica, 1989, 10(9):A442-A447(in Chinese).
[17] KIM J, HILL M R. Weight functions for a finite width plate with single or double radial cracks at a circular hole[J]. Engineering Fracture Mechanics, 2016, 168:112-130.
[18] XU W, WU X R, YU Y. A weight function method for mixed modes hole-edge cracks[J]. Fatigue & Fracture of Engineering Materials & Structure, 2018, 41(1):223-34.
[19] XU W, WU X R, YU Y. Weigh function, stress intensity factor and crack opening displacement solutions to periodic collinear edge hole cracks[J]. Fatigue & Fracture of Engineering Materials & Structure, 2017, 40(12):2068-2079.
[20] GREGORY R D. A circular disc containing a radial edge crack opened by a constant internal pressure[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1977, 81:497-521.
[21] MUSKHELISHVILI N I. Some basic problems of the mathematical theory of elasticity[M]. Goningen:P. Noordhoff Ltd., 1953:89-104.
[22] WU X R, ZHAO X C, XU W, et al. Discussions on weight functions and stress intensity factors for radial crack(s) emanating from a circular hole in an infinite plate[J]. Engineering Fracture Mechanics, 2018, 192:192-204.
[23] RICH D L, IMPELZZERI L F. Fatigue analysis of coldworked and interference fit fastener holes:ASTM STP-637[R]. West Conshohocken, PA:ASTM, 1977.
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