Citation:  Wang Zhiqiang, Cai Lixun, Huang Maobo. Full solution for characterizing stress fields near the tip of modeI crack under plane and powerlaw plastic conditions. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 95112 doi: 10.6052/0459187922360 
[1] 
Cherepanov GP. The propagation of cracks in a continuous medium. J Appl Math Mech, 1967, 31(3): 503512 doi: 10.1016/00218928(67)900342

[2] 
Rice JR. A path independent integral and the approximate analysis of concentration by notches and cracks. Int J Appl Mech, 1968, 35: 379386 doi: 10.1115/1.3601206

[3] 
Hutchinson JW. Singular behavior at the end of a tensile crack in a hardening material. J Mech Phys Solids, 1968, 16: 1331 doi: 10.1016/00225096(68)900148

[4] 
Rice JR, Rosengren GF. Plane strain deformation near a crack tip in a powerlaw hardening material. J Mech Phys Solids, 1968, 16: 112 doi: 10.1016/00225096(68)900136

[5] 
Shih CF. Tables of HutchinsonRiceRosengren singular field quantities. Brown University Materials Research Laboratory Rep. MRL E147, 1983

[6] 
Betegon C, Hancock J. Twoparameter characterization of elasticplastic cracktip fields. Int J Appl Mech, 1991, 58: 104113 doi: 10.1115/1.2897135

[7] 
Sharma SM, Aravas N. Determination of higherorder terms in asymptotic elastoplastic crack tip solutions. J Mech Phys Solids, 1991, 39: 10431072 doi: 10.1016/00225096(91)90051O

[8] 
Chao YJ, Yang S, Sutton M. On the fracture of solids characterized by one or two parameters: theory and practice. J Mech Phys Solids, 1994, 42(4): 629647 doi: 10.1016/00225096(94)900558

[9] 
Nikishkov GP, BrucknerFoit A, Munz D. Calculation of the second fracture parameter for finite cracked bodies using a threeterm elasticplastic asymptotic expansion. Engng Fract Mech, 1995, 52(4): 685701 doi: 10.1016/00137944(95)00024P

[10] 
O'Dowd NP, Shih CF. Family of cracktip fields characterized by a triaxiality parameterI. Structure of fields. J Mech Phys Solids, 1991, 39(8): 9891015 doi: 10.1016/00225096(91)90049T

[11] 
O'Dowd NP, Shih CF. Family of cracktip fields characterized by a triaxiality parameterII. Fracture applications. J Mech Phys Solids, 1992, 40(5): 939963 doi: 10.1016/00225096(92)900579

[12] 
Li YC, Wang ZQ. Highorder asymptotic field of tensile planestrain nonlinear crack problems. Sci Sin (Ser A)

[13] 
Yang S, Chao YJ, Sutton MA. Complete theoretical analysis for higher order asymptotic terms and the HRR zone at a crack tip for mode I and mode II loading of a hardening material. Acta Mech, 1993, 98: 7998 doi: 10.1007/BF01174295

[14] 
Yang S, Chao YJ, Sutton M. Higher order asymptotic crack tip fields in a power law hardening material. Engng Fract Mech, 1993, 45(1): 120 doi: 10.1016/00137944(93)90002A

[15] 
Nikishkov GP. An algorithm and a computer program for the threeterm asymptotic expansion of elastic–plastic crack tip stress and displacement fields. Engng Fract Mech, 1995, 50(1): 6583 doi: 10.1016/00137944(94)001399

[16] 
Nikishkov GP, Matvienko YG. Elastic–plastic constraint parameter A for test specimens with thickness variation. Fatigue Fract Eng Mater Struct, 2016, 39(8): 939949 doi: 10.1111/ffe.12390

[17] 
Matvienko YG, Nikishkov GP. Twoparameter JA concept in connection with cracktip constraint. Theor Appl Fract Mech, 2017, 92: 306317 doi: 10.1016/j.tafmec.2017.04.007

[18] 
Ding P, Wang X. Solutions of the second elastic–plastic fracture mechanics parameter in test specimens. Engng Fract Mech, 2010, 77: 34623480 doi: 10.1016/j.engfracmech.2010.09.007

[19] 
Ding P, Wang X. An estimation method for the determination of the second elastic–plastic fracture mechanics parameters. Engng Fract Mech, 2012, 79: 295311 doi: 10.1016/j.engfracmech.2011.11.010

[20] 
Ji X, Zhu F. Finite element simulation of elastoplastic field near crack tips and results for a central cracked plate of LELHP material under tension. Acta Mech Sinica, 2019, 35(4): 828838 doi: 10.1007/s10409019008461

[21] 
Ji X, Zhu F. Elasticplastic multiScale finite element analysis of fracture test on 304 stainless steel compact tension specimen. Nov Res Sci, 2021, 7(3): 000663

[22] 
Anderson TL, Dodds RH. Specimen size requirements for fracture toughness testing in the transition region. Journal of Testing and Evaluation, 1991, 19(2): 123134 doi: 10.1520/JTE12544J

[23] 
Mostafavi M, Pavier MJ, Smith DJ. Unified measure of constraint//International Conference on Engineering Structural Integrity Assessment, Manchester, 2009

[24] 
Mostafavi M, Smith DJ, Pavier MJ. Reduction of measured toughness due to outofplane constraint in ductile fracture of aluminium alloy specimens. Fatigue & Fracture of Engineering Materials & Structures, 2010, 33: 724739

[25] 
Mostafavi M, Smith DJ, Pavier MJ. Fracture of aluminium alloy 2024 under biaxial and triaxial loading. Engineering Fracture Mechanics, 2011, 78(8): 17051716 doi: 10.1016/j.engfracmech.2010.11.006

[26] 
Mostafavi M, Smith DJ, Pavier MJ. A micromechanical fracture criterion accounting for inplane and outofplane constraint. Computational Materials Science, 2011, 50(10): 27592770 doi: 10.1016/j.commatsci.2011.04.023

[27] 
Chen H, Cai LX. Theoretical model for predicting uniaxial stressstrain relation by dual conical indentation based on equivalent energy principle. Acta Materialia, 2016, 121: 181189 doi: 10.1016/j.actamat.2016.09.008

[28] 
Chen H, Cai LX. Unified elastoplastic model based on strain energy equivalence principle. Appl Math Model, 2017, 52: 664671 doi: 10.1016/j.apm.2017.07.042

[29] 
Chen H, Cai LX. An elastoplastic energy model for predicting the deformation behaviors of various structural components. Appl Math Model, 2019, 68: 405421 doi: 10.1016/j.apm.2018.11.024

[30] 
Peng YQ, Cai LX, Chen H, et al. A novel semianalytical method based on equivalent energy principle to obtain J resistance curves of ductile materials. Int J Mech Sci, 2018, 148: 3138 doi: 10.1016/j.ijmecsci.2018.08.016

[31] 
Irwin GR. Analysis of stress and strains near the end of a crack traversing a plate. Int J Appl Mech, 1957, 24(3): 361364 doi: 10.1115/1.4011547

[32] 
Anderson TL. Fracture Mechanics: Fundamentals and Applications, CRC Press: Boca Raton, 2005
