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Volume 55 Issue 1
Jan.  2023
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Wang Zhiqiang, Cai Lixun, Huang Maobo. Full solution for characterizing stress fields near the tip of mode-I crack under plane and power-law plastic conditions. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 95-112. DOI: 10.6052/0459-1879-22-360
Citation: Wang Zhiqiang, Cai Lixun, Huang Maobo. Full solution for characterizing stress fields near the tip of mode-I crack under plane and power-law plastic conditions. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 95-112. DOI: 10.6052/0459-1879-22-360
shu

FULL SOLUTION FOR CHARACTERIZING STRESS FIELDS NEAR THE TIP OF MODE-I CRACK UNDER PLANE AND POWER-LAW PLASTIC CONDITIONS

  • Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, China

  • Received Date: August 05, 2022
  • Accepted Date: November 13, 2022
  • Available Online: November 16, 2022
    Graphical Abstract
    • Abstract
  • In the fields of aerospace, ships, oil pipelines and nuclear power, there will be cracks inevitably in structure or component part when running for a long time under extreme conditions. Therefore, it is necessary to explore the features of the stress-strain fields near the crack tip, to study the quasi-static fracture behavior of cracked structures. In this paper, the stress distributions near the tip of mode-I cracked specimens under plane strain and plane stress conditions are studied for power-law hardening material. Based on the energy density equivalence and dimensional analysis, the analytical equation of equivalent stress of representative volume element (RVE) with the median energy density of a finite-dimensions specimen is proposed, and it is defined as the stress factor. Furthermore, for compact tension (CT) and single edge bend (SEB) finite size specimens under plane strain and plane stress conditions, the stress factor is used as a characteristic variable, and a special trigonometric function is assumed to characterize butterfly-wings type or scallop type contour lines of the equivalent stress near the mode-I crack tip, and then a semi-analytical model for compact tension specimens and single edge bend specimens under plane strain and plane stress and fully plastic conditions is proposed to describe the stress fields near the crack tip. As shown in comparing results given by finite element analysis to those predicted by the model for stress fields near the crack tip of the two cracked specimens, all agree well with each other. The semi-analytical model of stress field near the crack tip proposed in this paper is simple in form and accurate in result. It can be directly used to predict the stress distribution near the tip of mode-I crack, which is convenient for fracture safety evaluation and theoretical development.
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  • [1]
    Cherepanov GP. The propagation of cracks in a continuous medium. J Appl Math Mech, 1967, 31(3): 503-512 doi: 10.1016/0021-8928(67)90034-2
    [2]
    Rice JR. A path independent integral and the approximate analysis of concentration by notches and cracks. Int J Appl Mech, 1968, 35: 379-386 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: 13-31 doi: 10.1016/0022-5096(68)90014-8
    [4]
    Rice JR, Rosengren GF. Plane strain deformation near a crack tip in a power-law hardening material. J Mech Phys Solids, 1968, 16: 1-12 doi: 10.1016/0022-5096(68)90013-6
    [5]
    Shih CF. Tables of Hutchinson-Rice-Rosengren singular field quantities. Brown University Materials Research Laboratory Rep. MRL E-147, 1983
    [6]
    Betegon C, Hancock J. Two-parameter characterization of elastic-plastic crack-tip fields. Int J Appl Mech, 1991, 58: 104-113 doi: 10.1115/1.2897135
    [7]
    Sharma SM, Aravas N. Determination of higher-order terms in asymptotic elastoplastic crack tip solutions. J Mech Phys Solids, 1991, 39: 1043-1072 doi: 10.1016/0022-5096(91)90051-O
    [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): 629-647 doi: 10.1016/0022-5096(94)90055-8
    [9]
    Nikishkov GP, Bruckner-Foit A, Munz D. Calculation of the second fracture parameter for finite cracked bodies using a three-term elastic-plastic asymptotic expansion. Engng Fract Mech, 1995, 52(4): 685-701 doi: 10.1016/0013-7944(95)00024-P
    [10]
    O'Dowd NP, Shih CF. Family of crack-tip fields characterized by a triaxiality parameter-I. Structure of fields. J Mech Phys Solids, 1991, 39(8): 989-1015 doi: 10.1016/0022-5096(91)90049-T
    [11]
    O'Dowd NP, Shih CF. Family of crack-tip fields characterized by a triaxiality parameter-II. Fracture applications. J Mech Phys Solids, 1992, 40(5): 939-963 doi: 10.1016/0022-5096(92)90057-9
    [12]
    Li YC, Wang ZQ. High-order asymptotic field of tensile plane-strain nonlinear crack problems. Sci Sin (Ser A) , 1986, 29(9): 941-955
    [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: 79-98 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): 1-20 doi: 10.1016/0013-7944(93)90002-A
    [15]
    Nikishkov GP. An algorithm and a computer program for the three-term asymptotic expansion of elastic–plastic crack tip stress and displacement fields. Engng Fract Mech, 1995, 50(1): 65-83 doi: 10.1016/0013-7944(94)00139-9
    [16]
    Nikishkov GP, Matvienko YG. Elastic–plastic constraint parameter A for test specimens with thickness variation. Fatigue Fract Eng Mater Struct, 2016, 39(8): 939-949 doi: 10.1111/ffe.12390
    [17]
    Matvienko YG, Nikishkov GP. Two-parameter J-A concept in connection with crack-tip constraint. Theor Appl Fract Mech, 2017, 92: 306-317 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: 3462-3480 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: 295-311 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 LE-LHP material under tension. Acta Mech Sinica, 2019, 35(4): 828-838 doi: 10.1007/s10409-019-00846-1
    [21]
    Ji X, Zhu F. Elastic-plastic multi-Scale 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): 123-134 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 out-of-plane constraint in ductile fracture of aluminium alloy specimens. Fatigue & Fracture of Engineering Materials & Structures, 2010, 33: 724-739
    [25]
    Mostafavi M, Smith DJ, Pavier MJ. Fracture of aluminium alloy 2024 under biaxial and triaxial loading. Engineering Fracture Mechanics, 2011, 78(8): 1705-1716 doi: 10.1016/j.engfracmech.2010.11.006
    [26]
    Mostafavi M, Smith DJ, Pavier MJ. A micromechanical fracture criterion accounting for in-plane and out-of-plane constraint. Computational Materials Science, 2011, 50(10): 2759-2770 doi: 10.1016/j.commatsci.2011.04.023
    [27]
    Chen H, Cai LX. Theoretical model for predicting uniaxial stress-strain relation by dual conical indentation based on equivalent energy principle. Acta Materialia, 2016, 121: 181-189 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: 664-671 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: 405-421 doi: 10.1016/j.apm.2018.11.024
    [30]
    Peng YQ, Cai LX, Chen H, et al. A novel semi-analytical method based on equivalent energy principle to obtain J resistance curves of ductile materials. Int J Mech Sci, 2018, 148: 31-38 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): 361-364 doi: 10.1115/1.4011547
    [32]
    Anderson TL. Fracture Mechanics: Fundamentals and Applications, CRC Press: Boca Raton, 2005
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