Abstract
Structures with notches have a tendency to develop critical crack growth because of the stress concentration. The strength of the structures with stress gradient usually shows strong three-dimensional (3D) effects even under in-plane loading. The commonly two-dimensional (2D) models for fracture assessments of bodies with notches and cracks may lead to inaccurate predictions when in-plane loading is applied to certain 3D geometries. In the paper, the recent researches on the 3D effects of stress concentrations at notches and 3D stress fields of cracks are summarized. A new concept of equivalent thickness of the point on the crack front line is proposed based on the detailed analyses of the 3D out-of-plane stress fields of cracks, and then new empirical formulae of the 3D out-of-plane stress constraint factor T z of I–II mixed-mode cracks are obtained by use of the equivalent thickness. Combining the T z with the in-plane constraint parameters T or Q, the 3D multi-parameter descriptions of the stress field in front of various types of cracks using K–T z, J–T z, K–T–T z and J–Q–T z combination can be formulated.
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References
Bellett D, Taylor D (2006) The effect of crack shape on the fatigue limit of three-dimensional stress concentrations. Int J Fatigue 28: 114–123 doi:10.1016/j.ijfatigue.2005.04.010
Bellett D, Taylor D, Marco S, Mazzeo E, Guillois J, Pircher T (2005) The fatigue behaviour of three-dimensional stress concentrations. Int J Fatigue 27: 207–221 doi:10.1016/j.ijfatigue.2004.07.006
Betegon C, Hancock JW (1991) Two-parameter characterization of elastic-plastic crack tip fields. J Appl Mech 58: 104–113 doi:10.1115/1.2897135
Chao YJ, Yang S, Sutton MA (1994) On the fracture of solids characterized by one or two parameters: theory and practice. J Mech Phys Solids 42: 629–647 doi:10.1016/0022-5096(94)90055-8
Clatterbuck DM, Chrzan DC, Morris JW Jr (2003) The influence of triaxial stress on the ideal tensile strength of iron. Scr Mater 49: 1007–1011 doi:10.1016/S1359-6462(03)00490-1
Guo W (1993a) Elastoplastic three-dimensional crack border field-I. Singular structure of the field. Eng Fract Mech 46: 93–104 doi:10.1016/0013-7944(93)90306-D
Guo W (1993b) Elastoplastic three-dimensional crack border field-II. Asymptotic solution for the field. Eng Fract Mech 46: 105–113 doi:10.1016/0013-7944(93)90307-E
Guo W (1995) Elastoplastic three-dimensional crack border field-III. Fracture parameters. Eng Fract Mech 51: 51–71 doi:10.1016/0013-7944(94)00215-4
Guo W (2000) Recent advances in three-dimensional fracture mechanics. Key Eng Mater 183: 193–198
Hutchinson JW (1968) Singular behavior at the end of a tensile crack in a hardening material. J Mech Phys Solids 16: 13–31 doi:10.1016/0022-5096(68)90014-8
Irwin GR (1948) Fracture dynamics. In: Fracturing of metals. American Society for Metals, pp 147–166
Irwin GR (1958) Fracture. Handbuch der Physik, 6. Springer-Verlag, Heidelberg, pp 551–590
Kane TR, Mindlin RD (1956) High frequency extensional vibrations of plates. J Appl Mech Trans ASME 23: 277–283
Kosmodamianskiy AS (1970) Three dimensional stress state of the plate with holes. Educational Book, Donetsk
Kotousov A, Wang CH (2002) Three-dimensional stress constraint in an elastic plate with a notch. Int J Solids Struct 39: 4311–4326 doi:10.1016/S0020-7683(02)00340-2
Li ZH, Guo W (2001) Three-dimensional elastic stress fields ahead of blunt V-notches in finite thickness plates. Int J Fract 107: 53–71 doi:10.1023/A:1026586819885
Li YC, Wang ZQ (1986) High-order asymptotic field of tensile plane-strain nonlinear crack problems. Scientia Sin A 29: 941–955
Li ZH, Guo W, Kuang ZB (2000) Three-dimensional elastic stress fields near notches in finite thickness plates. Int J Solids Struct 37: 7617–7631 doi:10.1016/S0020-7683(99)00311-X
Moftahar A, Buczynski A, Glinka G (1995) Calculation of elastoplastic strain and stress in notches under multiaxial loading. Int J Fract 70: 357–373 doi:10.1007/BF00032453
Muskhelishvili NI (1963) Some basic problems of the mathematical theory of elasticity. Noordhoff, Groningen
O’Dowd NP, Shih CF (1991) Family of crack-tip fields characterized by a triaxiality parameter—I. Structure of fields. J Mech Phys Solids 39: 989–1015 doi:10.1016/0022-5096(91)90049-T
O’Dowd NP, Shih CF (1992) Family of crack-tip fields characterized by a triaxiality parameter—II. Fracture applications. J Mech Phys Solids 40: 939–963 doi:10.1016/0022-5096(92)90057-9
Rice JR, Rosengren GF (1968) Plane strain deformation near a crack tip in a power-law hardening material. J Mech Phys Solids 16: 1–12 doi:10.1016/0022-5096(68)90013-6
Sadowsky MA, Sternberg E (1947) Stress concentration around an ellipsoidal cavity in an infinite body under arbitrary plane stress perpendicular to the axis of revolution of the cavity. J Appl Mech Trans ASME 14: A191–A210
Savin GN (1961) Stress concentration around holes. Pergamon Press, New York
Sharma SM, Aravas N (1991) Determination of high-order terms in asymptotic elastoplastic crack tip solutions. J Mech Phys Solids 39: 1043–1072
She C, Guo W (2006) Numerical investigations of maximum stress concentration at elliptic holes in finite thickness piezoelectric plates. Int J Fatigue 28: 438–445 doi:10.1016/j.ijfatigue.2005.06.046
She C, Guo W (2007a) Three-dimensional stress concentrations at elliptic holes in elastic isotropic plates subjected to tensile stress. Int J Fatigue 29(2): 330–335 doi:10.1016/j.ijfatigue.2006.03.012
She C, Guo W (2007b) The out-of-plane constraint of mixed-mode cracks in thin elastic plates. Int J Solids Struct 44(9): 3021–3034 doi:10.1016/j.ijsolstr.2006.09.002
Shin CS, Man KC, Wang CM (1994) A practical method to estimate the stress concentration of notches. Int J Fatigue 16: 242–256 doi:10.1016/0142-1123(94)90338-7
Singh MNK, Glinka G, Dubey RN (1996) Elastic-plastic stress-strain calculation in notch bodies subjected to non-proportional loading. Int J Fract 76: 36–60
Sternberg E, Sadowsky MA, Chicago ILL (1949) Three-dimensional solution for the stress concentration around a circular hole in a plat of arbitrary thickness. J Appl Mech 16: 27–36
Vorovich II, Malkina OS (1967) The state of stress in a thick plate. J Appl Math Mech 31: 252–264 doi:10.1016/0021-8928(67)90150-5
Wang CH, Guo W, Rose LRF (1999) Elastoplastic analysis of notch-tip fields in strain hardening materials. J Eng Mater Tech ASME 121: 313–320 doi:10.1115/1.2812380
Williams ML (1957) On the stress distribution at the base of a stationary crack. J Appl Mech 24: 109–114
Yang Z, Guo W, Xu X (2003) Three-dimensional elastic stress fields near notches in finite thickness bimaterial plates. J Mech Strength 25: 90–94
Yu P, Guo W, She C, Zhao J (2008) The influence of Poisson’s ratio on thickness-dependent stress concentration at elliptic holes in elastic plates. Int J Fatigue 30: 165–171 doi:10.1016/j.ijfatigue.2007.02.007
Zhang B, Guo W (2005) Tz constraints of semi-elliptical surface cracks in elastic plates subjected to uniform tension loading. Int J Fract 131: 173–187 doi:10.1007/s10704-004-5105-7
Zhang B, Guo W (2007) Three-dimensional stress state around quarter-elliptical corner cracks in elastic plates subjected to uniform tension loading. Eng Fract Mech 74: 386–398 doi:10.1016/j.engfracmech.2006.05.011
Zhao J, Guo W, She C (2006) Three dimensional K-Tz stress fields around the embedded center elliptical crack front in elastic plates. Acta Mech Sin 22: 148–155 doi:10.1007/s10409-006-0095-5
Zhao J, Guo W, She C (2007a) The in-plane and out-of-plane stress constraint factors and K-T-Tz description of stress field near the border of a semi-elliptical surface crack. Int J Fatigue 29(3): 435–443 doi:10.1016/j.ijfatigue.2006.05.005
Zhao J, Guo W, She C (2007b) The in-plane and out-of-plane stress constraint factors and K-T-Tz description of stress field near the border of a quarter-elliptical corner crack. Fatigue Fract Eng Mater Struct 30(8): 673–681
Zhao J, Guo W, She C (2007c) The three-parameter description of stress field near the border of an embedded elliptical crack. Acta Mech 190: 29–44 doi:10.1007/s00707-006-0409-5
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She, C., Zhao, J. & Guo, W. Three-dimensional stress fields near notches and cracks. Int J Fract 151, 151–160 (2008). https://doi.org/10.1007/s10704-008-9247-x
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DOI: https://doi.org/10.1007/s10704-008-9247-x