The weight function method is a powerful method for the determination of key parameters of stress intensity factors and crack opening displacements that are fundamental for crack analyses in fracture mechanics. The method has a remarkable computational efficiency without compromising solution accuracy and is especially suited for cracks in real-world components with complex stress gradients. A critical issue for successful development and reliable application of the weight function method is how to achieve verifiable and high solution accuracy. This paper provides several reflections on the current state of the art in weight function methods, including a brief historical perspective and description of several analytical and numerical weight methods, with main focus on the two-dimensional (2D) analytical approaches. A variety of typical application examples are presented. A platform for point-by-point accuracy assessment by using the Green's functions is established on a completely independent numerical approach with validated accuracy. Rigorous and systematic verification of the accuracy levels of different 2D analytical weight function approaches are conducted using several benchmark crack geometries. The sources of inaccuracy of different analytical weight function methods are analysed. A brief account on weight function methods for analysing three-dimensional (3D) crack problems with arbitrary univariant and bivariant stress distributions is provided.

REFERENCES

1Irwin GR. Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech. 1957; 24: 361-364.
10.1115/1.4011547
Google Scholar
2Tada H, Paris PC, Irwin GR. The Stress Analysis of Cracks Handbook. Third ed. USA, New York: ASME Press; 2000.
10.1115/1.801535
Google Scholar
3Rooke DP, Cartwright DJ. Compendium of Stress Intensity Factors. England, London: H.M.S.O; 1976.
Google Scholar
4 Y Murakami (Ed). Stress Intensity Factors Handbook. England, Oxford: Pergamon Press; 1986.
Google Scholar
5Zerbst U, Vormwald M, Andersch C, et al. The development of a damage tolerance concept for railway components and its demonstration for a railway axle. Eng Fract Mech. 2005; 72: 209-239.
10.1016/j.engfracmech.2003.11.011
Web of Science® Google Scholar
6McClung RC, Lee Y-D, Cardinal JW, Guo Y (2013) The pursuit of K: Reflections on the current state-of-the-art in stress intensity factor solutions for practical aerospace applications. 27th ICAF: 1–18.
Google Scholar
7Bazant ZP, Planas J. Fracture and Size Effect. Boca Raton, Boston, London, New York, Washington D.C: CRC Press; 1997.
Google Scholar
8 NASGRO®. Fracture Mechanics and Fatigue Crack Growth Analysis Software, Version 7.0. NASA Johnson Space Center and Southwest Research Institute; 2012.
Google Scholar
9 DARWIN®. Design Assessment of Reliability With Inspection. DARWIN Theory, Version 6.1. Developed by Southwest Research Institute; 2008.
Google Scholar
10Wagner D, Millwater H. 2D weight function development using a complex Taylor series expansion method. Eng Fract Mech. 2012; 86: 23-37.
10.1016/j.engfracmech.2012.02.006
Web of Science® Google Scholar
11Matos PFP, Nowell D. On the accurate assessment of crack opening and closing stresses in plasticity-induced fatigue crack closure problems. Eng Fract Mech. 2007; 75: 1579-1601.
10.1016/j.engfracmech.2006.09.007
Web of Science® Google Scholar
12Bueckner H. A novel principle for the computation of stress intensity factors. Zeitschrift fuer Angewandte Mathematik & Mechanik. 1970; 50: 529-546.
Web of Science® Google Scholar
13Rice JR. Some remarks on elastic crack tip stress fields. Int J Solids Struct. 1972; 8: 751-758.
10.1016/0020-7683(72)90040-6
Web of Science® Google Scholar
14Pairs PC, McMeeking RM, Tada H. The weight function method for determining stress intensity factors, in Cracks and Fracture. ASTM STP. 1976; 601: 471-489.
Google Scholar
15Labbens R, Pellissier-Tanon A, Heliot J. Practical method for calculating stress intensity factors through weight functions, in mechanics of crack growth. ASTM STP. 1976; 590: 368-384.
Google Scholar
16Wu XR, Carlsson AJ. The generalized weight function method for crack problems with mixed boundary conditions. J Mech Phys Solids. 1983; 31: 485-497.
10.1016/0022-5096(83)90012-1
Web of Science® Google Scholar
17Aliabadi MH, Rooke DP, Cartwright DJ. An improved boundary element formulation for calculating stress intensity factors, application to aerospace structures. J Strain Anal Eng Des. 1987; 22: 203-207.
10.1243/03093247V224203
Web of Science® Google Scholar
18Andrasic CP, Parker AP (1980) Weight functions for cracked curved beam, “Numerical Methods in Fracture Mechanics” proceeding of the 2nd Int. Conf., University College, Swansea, UK.
Google Scholar
19Andrasic CP, Parker AP. Dimensionless stress intensity factors for cracked thick cylinders under polynomial crack face loading. Eng Fract Mech. 1984; 19: 187-193.
10.1016/0013-7944(84)90078-X
Web of Science® Google Scholar
20Tsai CH, Ma CC. Weight functions for cracks in finite rectangle plates. Int J Fract. 1989; 40: 43-63.
10.1007/BF01150865
Web of Science® Google Scholar
21Sham TL. A unified finite element method for determining weight functions in two and three dimensions. Int J Solids Struct. 1987; 23: 1357-1372.
10.1016/0020-7683(87)90002-3
Web of Science® Google Scholar
22Beghini M, Bertini L, Vitale E. A numerical approach for determining weight function in fracture mechanics. Int J Numer Methods Eng. 1991; 32: 595-607.
10.1002/nme.1620320309
Web of Science® Google Scholar
23Fett T, Pham VB, Bahr HA. Weight functions for kinked semi-infinite cracks. Eng Fract Mech. 2004; 71: 1987-1995.
10.1016/j.engfracmech.2003.10.003
Web of Science® Google Scholar
24Ince R. Determination of the fracture parameters of the double-K model using weight functions of split-tension specimens. Eng Fract Mech. 2012; 96: 416-432.
10.1016/j.engfracmech.2012.08.024
Web of Science® Google Scholar
25Fett T (1990) Stress intensity factors and weight functions for the edge cracked plate calculated by the boundary collocation method. KfK-Report 4791, Kernforschungszentrum Karlsruhe.
Google Scholar
26Xiao QZ, Karihaloo BL. Approximate Green's functions for singular and higher order terms of an edge crack in a finite plate. Eng Fract Mech. 2002; 69: 959-981.
10.1016/S0013-7944(01)00114-X
Web of Science® Google Scholar
27Kuna M. Finite Elements in Fracture Mechanics. Berlin, German: Springer; 2013.
10.1007/978-94-007-6680-8
Google Scholar
28Deng PR, Matsumoto T. Weight function determination for shear cracks in reinforced concrete beams based on finite element method. Eng Fract Mech. 2017; 177: 61-78.
10.1016/j.engfracmech.2017.03.046
Web of Science® Google Scholar
29Bueckner HF. Weight functions for the notched bar. ZAMM-J Appl Math Mech/Zeitschrift fur Angewandte Mathematik und Mechanik. 1971; 51: 97-109.
10.1002/zamm.19710510204
Web of Science® Google Scholar
30Orange TW. Crack shapes and stress intensity factors for edge-cracked specimens. ASTM STP. 1972; 513: 71-78.
Google Scholar
31Grandt AFJ. Stress intensity factors for some through-cracked fastener holes. Int J Fract. 1975; 11: 283-294.
10.1007/BF00038895
Web of Science® Google Scholar
32Orange TW. Wide-range weight functions for the strip with a single edge crack. ASTM STP. 1985; 868: 95-105.
Google Scholar
33Petroski HJ, Achenbach JD. Computation of the weight function from a stress intensity factor. Eng Fract Mech. 1978; 10: 257-266.
10.1016/0013-7944(78)90009-7
Web of Science® Google Scholar
34Görner F, Mattheck C, Morawietz P, Munz D. Limitations of the Petroski-Achenbach crack opening displacement approximation for the calculation of weight functions. Eng Fract Mech. 1985; 22: 269-277.
10.1016/S0013-7944(85)80029-1
Web of Science® Google Scholar
35Fett T. Limitations of the Petroski-Achenbach procedure demonstrated for a simple load case. Eng Fract Mech. 1988; 29: 713-716.
10.1016/0013-7944(88)90173-7
Web of Science® Google Scholar
36Niu X, Glinka G. On the “Limitations of the Petroski-Achenbach crack opening displacement approximation for the calculation of weight function”—do they really exist? Eng Fract Mech. 1987; 26: 701-706.
10.1016/0013-7944(87)90135-4
Web of Science® Google Scholar
37Wu XR. On the influence of reference load case on the crack face weight functions. Int J Fract. 1991; 48: 179-192.
10.1007/BF00036630
Web of Science® Google Scholar
38Brennan FP. Evaluation of stress intensity factors by multiple reference state weight function approach. Theor Appl Fract Mech. 1994; 20: 249-256.
10.1016/0167-8442(94)90017-5
Web of Science® Google Scholar
39Karihaloo B, Xiao QZ. Linear and non-linear fracture mechanics. In: I Milne, RO Ritchie, B Karihaloo, eds. Comprehensive Structural Integrity, Vol.2 (2.03). Pergamon: Elsevier; 2003: 81-212.
10.1016/B0-08-043749-4/02128-5
Google Scholar
40Fett T, Bahr HA. Mode I stress intensity factors and weight functions for short plates under different boundary conditions. Eng Fract Mech. 1999; 62: 593-606.
10.1016/S0013-7944(99)00014-4
Web of Science® Google Scholar
41Wu XR. Analytical wide-range weight functions for various finite cracked bodies. Eng Anal Bound Elem. 1992; 9: 307-322.
10.1016/0955-7997(92)90016-Z
Web of Science® Google Scholar
42Glinka G, Shen G. Universal features of weight functions for cracks in mode I. Eng Fract Mech. 1991; 40: 1135-1146.
10.1016/0013-7944(91)90177-3
Web of Science® Google Scholar
43Fett T. Direct determination of weight functions from reference loading cases and geometrical conditions. Eng Fract Mech. 1992; 42: 435-444.
10.1016/0013-7944(92)90165-B
Web of Science® Google Scholar
44Wu XR, Carlsson AJ. Weight functions and stress intensity factor solutions. Oxford, UK: Pergamon Press; 1991.
Google Scholar
45Fett T, Munz D. Stress intensity factors and weight functions. Southampton, UK: Computational Mechanics Publications; 1997.
Google Scholar
46Shen G, Glinka G. Determination of weight functions from reference stress intensity factors. Theor Appl Fract Mech. 1991; 15: 237-245.
10.1016/0167-8442(91)90022-C
Web of Science® Google Scholar
47Ojdrovic RP, Petroski HJ. Weigh t functions from multiple reference states and crack profile derivatives. Eng Fract Mech. 1991; 39: 105-111.
10.1016/0013-7944(91)90026-W
Web of Science® Google Scholar
48Jing Z, Wu XR. Wide-range weight functions and stress intensity factors for arbitrarily shaped crack geometries using complex Taylor series expansion method. Eng Fract Mech. 2015; 50: 215-232.
10.1016/j.engfracmech.2015.03.006
Web of Science® Google Scholar
49Xu W, Wu XR, Wang H. Weight functions and strip yield solution for two equal-length collinear cracks in an infinite sheet. Eng Fract Mech. 2011; 78: 2356-2368.
10.1016/j.engfracmech.2011.05.007
Web of Science® Google Scholar
50Wu XR, Xu W. Strip yield crack analysis for multiple site damage in infinite and finite panels—a weight function approach. Eng Fract Mech. 2011; 78: 2585-2596.
10.1016/j.engfracmech.2011.06.016
Web of Science® Google Scholar
51Xu W, Wu XR. Weight functions and strip-yield model analysis for three collinear cracks. Eng Fract Mech. 2012; 85: 73-87.
10.1016/j.engfracmech.2012.02.009
Web of Science® Google Scholar
52Xu W, Wang H, Wu XR e. A novel method for residual strength prediction for sheets with multiple site damage: methodology and experimental validation. Int J Solids Struct. 2014; 51: 551-565.
10.1016/j.ijsolstr.2013.10.012
CAS Web of Science® Google Scholar
53Xu W, Wu XR, Yu Y. Weight function, stress intensity factor and crack opening displacement solutions to periodic hole-edge cracks. Fatigue Fract Eng Mater Struct. 2017; 40: 2068-2079.
10.1111/ffe.12626
Web of Science® Google Scholar
54Liu ZX, Xu W, Yin Y, Wu XR. Weight functions and stress intensity factors for two unequal-length collinear cracks in an infinite sheet. Eng Fract Mech. 2019; 209: 173-186.
10.1016/j.engfracmech.2019.01.025
Web of Science® Google Scholar
55Orynyak IV, Borodii MV, Torop VM. Approximate construction of a weight function for quarter-elliptical, semi-elliptical and elliptical cracks subjected to normal stresses. Eng Fract Mech. 1994; 49: 143-151.
10.1016/0013-7944(94)90118-X
Web of Science® Google Scholar
56Orynyak IV, Borodii MV. Point weight function method application for semi-elliptical mode I cracks. Int J Fract. 1994; 70: 117-124.
10.1007/BF00034135
Web of Science® Google Scholar
57Lee YD, McClung RC, Chell GG. An efficient stress intensity factor solution scheme for corner cracks at holes under bivariant stressing. Fatigue Fract Eng Mater Struct. 2008; 31: 1004-1016.
10.1111/j.1460-2695.2008.01292.x
Web of Science® Google Scholar
58Zhao XC (2017) Wide-range point weight function method for three-dimensional cracks in complex stress fields. PhD thesis (in Chinese), AECC Beijing Institute of Aeronautics Materials.
Google Scholar
59Dempsey JP, Mu Z. Weight function for an edge-cracked plate. Eng Fract Mech. 2014; 132: 93-103.
10.1016/j.engfracmech.2014.10.023
Web of Science® Google Scholar
60Ribeiro RL, Hill MR. A benchmark fracture mechanics solution for a two-dimensional eigenstrain problem considering residual stress, the stress intensity factor, and superposition. Eng Fract Mech. 2016; 163: 313-326.
10.1016/j.engfracmech.2016.06.007
Web of Science® Google Scholar
61Kim J, Hill MR. Weight functions for a finite width plate with single or double radial cracks at a circular hole. Eng Fract Mech. 2016; 168: 112-130.
10.1016/j.engfracmech.2016.10.002
Web of Science® Google Scholar
62Ball DL. The influence of residual stress on the design of aircraft primary structure. J ASTM Int. 2010; 5(4): 1-18.
Google Scholar
63Ball DL, etc JLABRJ. A detailed evaluation of the effects of bulk residual stress on fatigue in Aluminum. Adv Mat Res, Vols. 2014; 891-892: 1205-1211.
10.4028/www.scientific.net/AMR.891-892.1205
Google Scholar
64Zhang J, Victor CL. Simulation of crack propagation in fiber-reinforced concrete by fracture mechanics. Cem Concr Res. 2004; 34: 333-339.
10.1016/j.cemconres.2003.08.015
CAS Web of Science® Google Scholar
65Xu W, Rao DY, Wu XR, Tong DH, Zhao XC. Accurate mixed modes weight functions and stress intensity factors for center- and edge-cracked circular disk with consideration of friction. Submitted to. Int J Fract. 2019.
PubMed Web of Science® Google Scholar
66Fett T, Mattheck C, Munz D. Approximate weight function for 2D and 3D-problems. Eng Anal Bound Elem. 1989; 6: 48-63.
10.1016/0955-7997(89)90042-8
Web of Science® Google Scholar
67Wu XR, Tong DH. Evaluation of various analytical weight function methods base on exact K-solutions of an edge-cracked circular disc. Eng Fact Mech. 2018; 189: 64-80.
10.1016/j.engfracmech.2017.09.024
Web of Science® Google Scholar
68Wu XR, Tong DH, Zhao XC, Xu W. Review and evaluation of weight functions and stress intensity factors for edge-cracked finite-width plate. Eng Fact Mech. 2018; 195: 200-221.
10.1016/j.engfracmech.2018.04.001
Web of Science® Google Scholar
69Xu W, Zhang C, Wu XR, Yu Y. Some important solutions to crack problems for orthotropic composites by using analytical weight function method. Submitted to. Int J Solids Struct. 2019.
PubMed Google Scholar
70Lorenzo JM, Cartwright DJ, Aliabadi MH. Boundary-element weight-function analysis for crack-surface displacements and strip-yield cracks. Eng Anal Bound Elem. 1994; 13: 283-289.
10.1016/0955-7997(94)90054-X
Web of Science® Google Scholar
71John R, Kaldon SG, Johnson DA, Coker D. Weight function for a single edge cracked geometry with clamped ends. Int J Fract. 1985; 72: 145-158.
10.1007/BF00042825
Web of Science® Google Scholar
72Buchanan DJ, John R, Johnson DA. Determination of crack bridging stresses from crack opening displacement profiles. Int J Fract. 1997; 87: 101-117.
10.1023/A:1007495331890
CAS Web of Science® Google Scholar
73Jones IS. A wide range weight function for a single edge cracked geometry with clamped ends. Int J Fract. 1997; 89: 1-18.
10.1023/A:1007463205924
Web of Science® Google Scholar
74Dempsey JP, Mu Z. Weight function for an edge-cracked rectangular plate. Eng Fract Mech. 2014; 132: 93-103.
10.1016/j.engfracmech.2014.10.023
Web of Science® Google Scholar
75Dempsey JP, Adamson RM, Defranco SJ. Fracture analysis of base-edge-cracked reverse-tapered plates. Int J Fract. 1995; 69: 281-294.
10.1007/BF00037379
Web of Science® Google Scholar
76Adamson RM, Dempsey JP, Mulmule SV. Fracture analysis of semi-circular and semi-circular-bend geometries. Int J Fract. 1996; 77: 213-222.
10.1007/BF00018778
Web of Science® Google Scholar
77Lee HY, Hong CS. A new weight function approach using indirect boundary integral method. Eng Fract Mech. 1995; 52: 1087-1105.
10.1016/0013-7944(95)00055-Z
Web of Science® Google Scholar
78Wu XH, Bowen P. Fatigue crack growth resistance of unidirectional fiber reinforced Titanium metal-matrix composites under transverse loading. Metall Mater Trans A. 2000; 31: 2083-2092.
10.1007/s11661-000-0236-6
Web of Science® Google Scholar
79Ismonov S, Daniewicz SR. Simulation and comparison of several crack closure assessment methodologies using three-dimensional finite element analysis. International Journal of Fatigue. 2010; 32: 1322-1329.
10.1016/j.ijfatigue.2010.01.016
Web of Science® Google Scholar
80Ball DL, Watton JD (2011) Fatigue life variability in large aluminum forgings with residual stress, 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Denver, Colorado, USA.
Google Scholar
81 R6: Assessment of the integrity of structures containing defects. British Energy Generation Ltd, Revision 4, 2009.
Google Scholar
82 Guide to methods for assessing the acceptability of flaws in metallic structures, BS 7910:2013+A1:2015. BSI Standards Publication. The British Standards Institution 2015.
Google Scholar
83Zerbst U, Schodel M, Webster S, Ainsworth R. Fitness-for-service fracture assessment of structures containing cracks—a workbook based on European SINTAP/FITNET procedure. 1st ed. Elsevier Ltd; 2007.
Google Scholar
84Zerbst U, Schwalbe K-H, Anisworth RA. An overview of failure assessment methods in codes and standards. In: I Milne, RO Ritchie, B Karihaloo, eds. Comprehensive Structural Integrity, Vol.7 (7.01). Pergamon: Elsevier; 2003: 1-48.
10.1016/B0-08-043749-4/07053-1
Google Scholar
85Dillstrom P, Gunnars J, Unge P, Mangard D (2018) Procedure for Safety Assessment of Components with Defects. Handbook Edition 5. Report number: 2018:18 ISSN: 2000–0456. Swedish Radiation Safety Authority.
Google Scholar
86McClung RC, Lee Y-D, Tschopp JA, Srivatsa SK, Leverant GR, Waldhart CJ, Jameel MA, Enright MP, Millwater HR, Lehmann DJ, Huyse L, Fitch SHK, Dubke JP (2008) Turbine Rotor Material Design—Phase II. DOT/FAA/AR-07/13.
Google Scholar
87Kumar S, Barai SV. Determining the double-K fracture parameters for three-point bending notched concrete beams using weight function. Fatigue Fract Eng Mater Struct. 2010; 33: 645-660.
10.1111/j.1460-2695.2010.01477.x
Web of Science® Google Scholar
88Tada H, Paris PC, Irwin GR. The Stress Analysis of Cracks Handbook. First ed. Pennsylvania, Hellertown: Del Research Corp; 1973.
Google Scholar
89Wu XR, Zhao XC, Xu W, Tong DH. Discussions on weight functions and stress intensity factors for radial crack(s) emanating from a circular hole in an infinite plate. Eng Fact Mech. 2018; 192: 192-204.
10.1016/j.engfracmech.2018.02.001
Web of Science® Google Scholar
90Cruse TA, Raveendra ST. A general solution procedure for fracture mechanics weight function evaluation based on the boundary element method. Comput Mech. 1988; 3: 157-166.
10.1007/BF00297442
Google Scholar
91Aliabadi MH, Cartwright DJ, Rooke DP. Fracture mechanics weight functions by the removal of singular fields using boundary element analysis. Int J Fract. 1989; 40: 271-284.
10.1007/BF00963661
Web of Science® Google Scholar
92Wen PH, Aliabadi MH, Rooke DP. Application of weight function method to elastodynamic fracture mechanics. Int J Fract. 1996; 76: 193-206.
10.1007/BF00048286
Web of Science® Google Scholar
93Wen PH, Aliabadi MH, Rooke DP. Mixed-mode weight functions in three-dimensional fracture mechanics: dynamic. Eng Fract Mech. 1998; 59: 577-587.
10.1016/S0013-7944(97)00156-2
Web of Science® Google Scholar
94Kaya AC, Erdogan F. Stress intensity factors and COD in an orthotropic strip. Int J Fract. 1980; 16: 171-190.
10.1007/BF00012620
Web of Science® Google Scholar
95Jin X, Zeng Y, Ding S, et al. Weight function of stress intensity factor for single radial crack emanating from hollow cylinder. Eng Fract Mech. 2017; 170: 77-86.
10.1016/j.engfracmech.2016.11.031
Web of Science® Google Scholar
96Shivakumar V, Forman RG. Green's function for a crack emanating from a circular hole in an infinite sheet. Int J Fract. 1980; 16: 305-316.
10.1007/BF00018234
Web of Science® Google Scholar
97Hill MR, Kim J (2016) Weight functions for a finite width plate with a radial crack at a circular hole, 2016 AFGROW Workshop.
Google Scholar
98Wigglesworth LA. Stress distribution in a notched plate. Mathematika. 1957; 4: 76-96.
10.1112/S002557930000111X
Google Scholar
99Gregory RD. The spinning circular disc with a radial edge crack; an exact solution. Int J Fract. 1989; 41: 39-50.
10.1007/BF00014836
Web of Science® Google Scholar
100Gregory RD. A circular disc containing a radial edge crack opened by a constant internal pressure. Math Proc Camb Philos Soc. 1977; 81: 497-521.
10.1017/S030500410005355X
Web of Science® Google Scholar
101Li J, Wang X, Tan CL. Weight functions for the determination of stress intensity factor and T-stress for edge-cracked plates with built-in ends. Int J Press Vessel Pip. 2004; 81: 285-296.
10.1016/j.ijpvp.2003.12.013
Web of Science® Google Scholar
102Babolian E, Masouri Z. Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions. J Comput Appl Math. 2008; 220: 51-57.
10.1016/j.cam.2007.07.029
Web of Science® Google Scholar
103Schajer GS, Prime MB. Use of inverse solutions for residual stress measurements. J Eng Mater Technol. 2006; 128: 375-382.
10.1115/1.2204952
Web of Science® Google Scholar
104Cruse TA, Besuner PM. Residual life prediction for surface cracks in complex structural details. J Aircr. 1975; 12: 369-375.
10.2514/3.44458
Google Scholar
105Xu RX, Wu XR. A weight function approach to stress-intensity factors for half-elliptical surface cracks in cylindrical pressure vessels subjected to thermal shock. Int J Press Vessel Pip. 1989; 39: 375-391.
10.1016/0308-0161(89)90108-7
Web of Science® Google Scholar
106Shen G, Glinka G. Weight functions forr a surface semi-elliptical crack in a finite plate. Theor Appl Fract Mech. 1991; 15: 247-255.
10.1016/0167-8442(91)90023-D
Web of Science® Google Scholar
107Glinka G. Development of Weight Functions and Computer Integration Procedures for Calculating Stress Intensity Factors Around Cracks Subjected to Complex Stress Fields. SaFFD, Inc. Prepared for Analytical Services & Materials, Inc; 1996.
Google Scholar
108Zhao W, Wu XR, Yan MG. Weight function method for three dimensional crack problems-I. Basic formulation and application to an embedded elliptical crack in finite plates. Eng Fract Mech. 1989; 34: 593-607.
10.1016/0013-7944(89)90122-7
Web of Science® Google Scholar
109Zhao W, Wu XR, Yan MG. Weight function method for three dimensional crack problems-II. Application to surface cracks at a hole in finite thickness plates under stress gradients. Eng Fract Mech. 1989; 34: 609-624.
10.1016/0013-7944(89)90123-9
Web of Science® Google Scholar
110Fujimoto WT, (1976) Determination of crack growth and fracture toughness parameters for surface flaws emanating from fastener holes. In: Proceedings AIAA/ASME/SAE 17th Structure, Structural Dynamics and Material Conference, King of Prussia, PA, 1976: 522–531.
Google Scholar
111Zhao, W, Sutton, MA, Shvakumar, KN, Newman, JC, Jr. Stress intensity factors for surface and corner cracks emanating from a wedge-loaded hole. FAA/NASA International Symposium on Advanced Structural Integrity Methods for Airframe Durability and Damage Tolerance. Hampton, Virginia, USA, May 1994. NASA Conference Publication 3274.
Google Scholar
112Zhao W, Wu XR. Stress intensity factor evaluation by weight function for surface crack in edge notch. Theor Appl Fract Mech. 1990; 13: 225-238.
10.1016/0167-8442(90)90090-M
Web of Science® Google Scholar
113Zhao W, Wu XR. Stress intensity factors for corner cracks at a semi-circular notch under stress gradients. Fatigue Fract Eng Mater Struct. 1990; 13: 347-360.
10.1111/j.1460-2695.1990.tb00606.x
Web of Science® Google Scholar
114Zhao W, Newman JC, Sutton MA, Shivakumar KN, Wu XR. Stress intensity factors for surface cracks at a hole by a three-dimensional weight function method with stresses from the finite element method. Fatigue Fract Eng Mater Struct. 1998; 21: 229-239.
10.1046/j.1460-2695.1998.00015.x
Web of Science® Google Scholar
115Bakuckas JG. Comparison of boundary correction factor solutions for two symmetric cracks in a straight-shank hole. Eng Fract Mech. 2001; 68: 1095-1106.
10.1016/S0013-7944(01)00013-3
Web of Science® Google Scholar
116Daniewiz SR, Aveline CR. Strip-yield and finite element analysis of part-through surface flaws. Eng Fract Mech. 2000; 67: 21-39.
10.1016/S0013-7944(00)00032-1
Web of Science® Google Scholar
117Guagliano M, Vergani L. Mode I stress intensity factors for curved cracks in gears by a weight functions method. Fatigue Fract Eng Mater Struct. 2001; 24: 41-52.
10.1046/j.1460-2695.2001.00360.x
CAS Web of Science® Google Scholar
118Zhao XC, Wu XR, Newman JC Jr, Tong DH. Stress intensity factors for surface cracks in single-edge notch bend specimen by a three-dimensional weight function method. Fatigue Fract Eng Mater Struct. 2016; 39: 1407-1418.
10.1111/ffe.12458
Web of Science® Google Scholar
119Zhao XC, Wu XR, Newman JC Jr, Tong DH. Stress intensity factors for corner cracks in single-edge notch bend specimen by a three-dimensional weight function method. Fatigue Fract Eng Mater Struct. 2017; 40: 277-287.
10.1111/ffe.12496
Web of Science® Google Scholar
120Oore M, Burns DJ. Estimation of stress intensity factors for embedded irregular cracks subjected to arbitrary normal stress fields. J Press Vessel Technol. 1980; 102: 202-211.
10.1115/1.3263321
Web of Science® Google Scholar
121McClung RC, Enright MP, Lee Y-D, Huyse LJ (2004) Efficient fracture design for complex turbine engine components, Proceedings of ASME Turbo Expo 2004, Power for Land, Sea and Air. June 14-17, 2004, Vienna, Austria.
Google Scholar
122Raju IS, Newman JC Jr. Stress intensity factors for internal and external surface cracks in cylindrical vessels. J Press Vessel Technol. 1982; 104: 293-298.
10.1115/1.3264220
Web of Science® Google Scholar
123Ghajar R, Googarchin HS. General point weight function for semi-elliptical crack in finite thickness plates. Eng Fract Mech. 2013; 109: 33-44.
10.1016/j.engfracmech.2013.06.007
Web of Science® Google Scholar
124Wu XR, Tong DH, Xu W, Zhao XC. Weight Functions in Fracture Mechanics: Theory and Applications. Beijing, China: Aviation Press; 2019 (in Chinese).
Google Scholar

Citing Literature

Volume42, Issue9

Special Issue:Advances in Fatigue and Fracture ‐ Celebrating the 40th Anniversary of FFEMS

September 2019

Pages 2017-2042

A review and verification of analytical weight function methods in fracture mechanics

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A review and verification of analytical weight function methods in fracture mechanics

Abstract

REFERENCES

Citing Literature

References

Related

Information