A numerical analysis of cracks emanating from a surface elliptical hole in infinite body in tension

This paper deals with such a kind of surface crack problem with an approximately same depth, which is called a liked-plane crack problem. Based on the previous investigations on internal rectangular crack and surface rectangular crack in infinite solid in tension and a hybrid displacement discontinu...

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Vydané v:	Meccanica (Milan) Ročník 46; číslo 2; s. 263 - 278
Hlavní autori:	Yan, Xiangqiao, Liu, Baoliang
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Dordrecht Springer Netherlands 01.04.2011
Predmet:	Automotive Engineering Boundary element method Civil Engineering Classical Mechanics Cracks Discontinuity Displacement Emission Mathematical analysis Mechanical Engineering Numerical analysis Physics Physics and Astronomy Surface cracks Stress intensity factors Boundary element Surface crack Displacement discontinuity
ISSN:	0025-6455, 1572-9648
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Abstract	This paper deals with such a kind of surface crack problem with an approximately same depth, which is called a liked-plane crack problem. Based on the previous investigations on internal rectangular crack and surface rectangular crack in infinite solid in tension and a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, a numerical approach for the liked-plane crack problem in hand is presented. Numerical examples are given to illustrate the numerical approach is simple, yet accurate for calculating the SIFs of a liked-plane crack. Specifically, a pair of cracks emanating from a surface elliptical hole in infinite body in tension are investigated in detail.
AbstractList	This paper deals with such a kind of surface crack problem with an approximately same depth, which is called a liked-plane crack problem. Based on the previous investigations on internal rectangular crack and surface rectangular crack in infinite solid in tension and a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, a numerical approach for the liked-plane crack problem in hand is presented. Numerical examples are given to illustrate the numerical approach is simple, yet accurate for calculating the SIFs of a liked-plane crack. Specifically, a pair of cracks emanating from a surface elliptical hole in infinite body in tension are investigated in detail.
Author	Yan, Xiangqiao Liu, Baoliang
Author_xml	– sequence: 1 givenname: Xiangqiao surname: Yan fullname: Yan, Xiangqiao email: yanxiangqiao@hotmail.com organization: Research Laboratory on Composite Materials, Harbin Institute of Technology – sequence: 2 givenname: Baoliang surname: Liu fullname: Liu, Baoliang organization: Research Laboratory on Composite Materials, Harbin Institute of Technology
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Cites_doi	10.1002/sapm195635160 10.1016/j.cma.2003.07.002 10.1243/030932405X16089 10.1016/j.engfailanal.2004.12.043 10.1016/0013-7944(83)90027-9 10.1016/0013-7944(91)90096-J 10.1299/kikai1938.44.423 10.1115/1.2127955 10.1243/030932405X16133 10.1115/1.3157614 10.1243/030932404323042669 10.1016/j.engfracmech.2003.08.005 10.1046/j.1460-2695.1998.00015.x 10.1016/0013-7944(94)00231-2 10.1299/kikaia.49.1572 10.1115/1.1796449 10.1016/j.euromechsol.2005.06.005 10.1016/j.engfracmech.2006.02.003 10.1016/j.euromechsol.2010.01.001 10.1299/kikaia.51.1050 10.1016/j.ijsolstr.2008.04.001 10.1007/BF01140626 10.1016/j.ijsolstr.2009.07.002 10.1115/1.2127957 10.1016/j.mechrescom.2003.07.003 10.1016/j.apm.2003.12.005 10.1016/j.ijsolstr.2009.09.023 10.1046/j.1460-2695.2003.00706.x 10.1016/j.compstruct.2006.11.010 10.1016/0013-7944(81)90116-8 10.1016/0013-7944(93)90299-8 10.1007/BF02465433 10.1016/0167-6636(87)90023-8 10.1016/j.mechrescom.2004.10.005
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References	NewmanJCJrRajuISEmpirical stress-intensity factor equation for surface crackEng Fract Mech1981151–218519210.1016/0013-7944(81)90116-8 YanXAn efficient and accurate numerical method of SIFs calculation of a branched crackASME J Appl Mech20057233303401111.7471710.1115/1.1796449 NewmanJCJrBigelowCAShivakumarKNThree-dimensional elastic-plastic finite element analyses of constraint variations in cracked bodiesEng Fract Mech199346111310.1016/0013-7944(93)90299-8 BabuPRPradhanBThermoelastic effects on mixed-mode delamination growth emanating from circular holes in laminated FRP compositesCompos Struct200882506010.1016/j.compstruct.2006.11.010 YanXAn effective numerical approach for multiple void-crack interactionASME J Appl Mech20067345255351111.7471810.1115/1.2127955 Yoshida T (1984) Effect of boundaries on stress intensity factors. PhD thesis, Kyushu University, Fukuoka, Japan Newman JC Jr (1971) An improved method of collocation for the stress analysis of cracked plates with various shaped boundaries. NASA TN, D-6376, pp 1–45 MurakamiYA method of stress intensity factor calculation for the crack emanating from an arbitrarily shaped hole or the crack in the vicinity of an arbitrarily shape holeTrans Jpn Soc Mech Eng19784437842343210.1299/kikai1938.44.423 ShivakumarKNNewmanJCJrStress intensity factors for large aspect ratio surface and corner cracks at a semi-circular notch in a tension specimenEng Fract Mech199138646747310.1016/0013-7944(91)90096-J TanPWNewmanJCJrBigelowCAThree-dimensional finite-element analyses of corner cracks at stress concentrationsEng Fract Mech199655350551210.1016/0013-7944(94)00231-2 YanXAnalysis of the interaction of arbitrary multiple cracks in an infinite plate interference effect of arbitrary multiple parabolic cracks in plane elasticity by using a new boundary element methodComput Methods Appl Mech Eng200319247–48509951212003CMAME.192.5099Y1075.7469210.1016/j.cma.2003.07.002 ZhaoWNewmanJCJrSuttonMAStress intensity factors for surface cracks at a hole by a three-dimensional weight function method with stresses from the finite element methodFatigue Fract Eng Mater Struct199821222923910.1046/j.1460-2695.1998.00015.x IsidaMNoguchiHYoshidaTTension and bending of finite thickness plates with a semi-elliptical surface cracksInt J Fract19842615718810.1007/BF01140626 Murakami Y, Endo M (1985) Effects of hardness and crack geometry on ΔKth of small cracks emanating from small defects. Presented at int symposium on the behavior of short fatigue cracks, University of Sheffield, pp 25–28 CharambidesPGMcMeekingRMFinite element method simulation of a crack propagation in a brittle microcracked solidMech Mater19876718710.1016/0167-6636(87)90023-8 YanXA numerical analysis of cracks emanating from a square hole in a rectangular plate under biaxial loadsEng Fract Mech200471111615162310.1016/j.engfracmech.2003.08.005 YanXStress intensity factors for asymmetric branched cracks in plane extension by using crack tip displacement discontinuity elementsMech Res Commun20053243753841192.7414310.1016/j.mechrescom.2004.10.005 HasebeNBucherCHeuerRHeat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crackInt J Solids Struct2010471381471193.7402910.1016/j.ijsolstr.2009.09.023 YanXAn effective boundary element method for analysis of crack problems in a plane elastic plateAppl Math Mech20052668148221144.7438210.1007/BF02465433 RajuISNewmanJCJrStress-intensity factors for two symmetric corner cracksASTM STP1979677411430 WangYJGaoCFThe mode III cracks originating from the edge of a circular hole in a piezoelectric solidInt J Solids Struct200845459045991169.7455610.1016/j.ijsolstr.2008.04.001 KassirKKStress intensity factors for a three-dimensional rectangular crackASME J Appl Mech19814823093120471.7308710.1115/1.3157614 IsidaMYoshidaTNoguchiHTension of a plate with a pair of semi-elliptical surface cracksTrans Jpn Soc Mech Eng1983494481572158010.1299/kikaia.49.1572 YanXA numerical analysis of perpendicular cracks under general in-plane loading with a hybrid displacement discontinuity methodMech Res Commun20043121751832004OptCo.231..175Y1045.7458710.1016/j.mechrescom.2003.07.003 HuangXKarihalooBLInteraction of penny shaped cracks with a half plane crackInt J Solids Struct199325591607 Nisitani H, Isida M (1982) Simple procedure for calculating KI of a notch with a crack of arbitrary size and its application to non-propagating fatigue crack. In: Proc ioint JSME-SESA conf on experimental mechanics, Part I, pp 150–155 YanXMicrodefect interacting with a finite main crackJ Strain Anal Eng Des200540542143010.1243/030932405X16089 CrouchSLStarfiedAMBoundary element method in solid mechanics, with application in rock mechanics and geological mechanics1983LondonGeore Allon & Unwin MurakamiYIsidaMAnalysis of an arbitrarily shaped surface crack and stress field at crack front near surfaceTrans Jpn Soc Mech Eng1985514641050105610.1299/kikaia.51.1050 MurakamiYStress intensity factors handbook1987ElmsfordPergamon NewmanJCJrReuterWGAvelineCRJrStress and fracture analyses of semi-elliptical surface cracksASTM STP19991360403423 YanXAn effective method of stress intensity factor calculation for cracks emanating form a triangular or square hole under biaxial loadsFatigue Fract Eng Mater Struct200326121127113310.1046/j.1460-2695.2003.00706.x GuoJHLuZ-XThe behavior of two non-symmetrical permeable cracks emanating from an elliptical hole in a piezoelectric solidEur J Mech, A Solids201029465466310.1016/j.euromechsol.2010.01.001 YanXA numerical analysis of cracks emanating from an elliptical hole in a 2-D elasticity plateEur J Mech A20062511421531084.7404610.1016/j.euromechsol.2005.06.005 GuoJHLuZ-XExact solutions for anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric materialInt J Solids Struct200946379938091176.7415810.1016/j.ijsolstr.2009.07.002 YanXInteraction of arbitrary multiple cracks in an infinite plateJ Strain Anal Eng Des200439323724410.1243/030932404323042669 YanXAnalysis for a crack emanating form a corner of a square hole in an infinite plate using the hybrid displacement discontinuity methodAppl Math Model20042898358471147.7440610.1016/j.apm.2003.12.005 BowieOLAnalysis of an infinite plate containing radial cracks originating at the boundary of an internal circular holeJ Math Phys1956356071781550072.18904 YanXCracks emanating from circular hole or square hole in rectangular plate in tensionEng Fract Mech200673121743175410.1016/j.engfracmech.2006.02.003 MurakamiYNemat-NasserSGrowth and stability of interacting surface flaws of arbitrary shapeEng Fract Mech198317319321010.1016/0013-7944(83)90027-9 YanXNumerical analysis of stress intensity factor for two kinds of mixed-mode crack specimensJ Strain Anal Eng Des200641191810.1243/030932405X16133 YanXA brief evaluation of approximation methods for microcrack shielding problemsASME J Appl Mech20067346946961111.7471910.1115/1.2127957 YanXA numerical analysis of stress intensity factors at bifurcated cracksEng Fail Anal200613462963710.1016/j.engfailanal.2004.12.043 M Isida (9302_CR19) 1984; 26 PG Charambides (9302_CR21) 1987; 6 X Yan (9302_CR10) 2005; 72 X Yan (9302_CR26) 2005; 40 M Isida (9302_CR20) 1983; 49 X Yan (9302_CR23) 2006; 73 KK Kassir (9302_CR9) 1981; 48 YJ Wang (9302_CR41) 2008; 45 KN Shivakumar (9302_CR14) 1991; 38 X Yan (9302_CR30) 2005; 26 X Yan (9302_CR33) 2004; 31 N Hasebe (9302_CR39) 2010; 47 OL Bowie (9302_CR2) 1956; 35 Y Murakami (9302_CR7) 1983; 17 9302_CR8 IS Raju (9302_CR16) 1979; 677 9302_CR4 W Zhao (9302_CR11) 1998; 21 X Yan (9302_CR36) 2003; 26 Y Murakami (9302_CR5) 1978; 44 X Yan (9302_CR32) 2006; 25 9302_CR3 X Yan (9302_CR34) 2004; 28 JC Newman Jr (9302_CR12) 1999; 1360 X Yan (9302_CR24) 2003; 192 X Yan (9302_CR37) 2004; 71 X Yan (9302_CR35) 2006; 73 JH Guo (9302_CR40) 2010; 29 X Yan (9302_CR28) 2005; 32 9302_CR18 PW Tan (9302_CR15) 1996; 55 X Huang (9302_CR22) 1993; 25 X Yan (9302_CR27) 2006; 73 PR Babu (9302_CR42) 2008; 82 X Yan (9302_CR25) 2004; 39 X Yan (9302_CR31) 2006; 41 JH Guo (9302_CR38) 2009; 46 Y Murakami (9302_CR1) 1987 JC Newman Jr (9302_CR13) 1993; 46 JC Newman Jr (9302_CR17) 1981; 15 SL Crouch (9302_CR43) 1983 Y Murakami (9302_CR6) 1985; 51 X Yan (9302_CR29) 2006; 13
References_xml	– reference: YanXNumerical analysis of stress intensity factor for two kinds of mixed-mode crack specimensJ Strain Anal Eng Des200641191810.1243/030932405X16133 – reference: BabuPRPradhanBThermoelastic effects on mixed-mode delamination growth emanating from circular holes in laminated FRP compositesCompos Struct200882506010.1016/j.compstruct.2006.11.010 – reference: RajuISNewmanJCJrStress-intensity factors for two symmetric corner cracksASTM STP1979677411430 – reference: YanXA numerical analysis of cracks emanating from a square hole in a rectangular plate under biaxial loadsEng Fract Mech200471111615162310.1016/j.engfracmech.2003.08.005 – reference: NewmanJCJrReuterWGAvelineCRJrStress and fracture analyses of semi-elliptical surface cracksASTM STP19991360403423 – reference: MurakamiYNemat-NasserSGrowth and stability of interacting surface flaws of arbitrary shapeEng Fract Mech198317319321010.1016/0013-7944(83)90027-9 – reference: TanPWNewmanJCJrBigelowCAThree-dimensional finite-element analyses of corner cracks at stress concentrationsEng Fract Mech199655350551210.1016/0013-7944(94)00231-2 – reference: YanXAn efficient and accurate numerical method of SIFs calculation of a branched crackASME J Appl Mech20057233303401111.7471710.1115/1.1796449 – reference: CrouchSLStarfiedAMBoundary element method in solid mechanics, with application in rock mechanics and geological mechanics1983LondonGeore Allon & Unwin – reference: YanXStress intensity factors for asymmetric branched cracks in plane extension by using crack tip displacement discontinuity elementsMech Res Commun20053243753841192.7414310.1016/j.mechrescom.2004.10.005 – reference: Yoshida T (1984) Effect of boundaries on stress intensity factors. PhD thesis, Kyushu University, Fukuoka, Japan – reference: IsidaMNoguchiHYoshidaTTension and bending of finite thickness plates with a semi-elliptical surface cracksInt J Fract19842615718810.1007/BF01140626 – reference: ShivakumarKNNewmanJCJrStress intensity factors for large aspect ratio surface and corner cracks at a semi-circular notch in a tension specimenEng Fract Mech199138646747310.1016/0013-7944(91)90096-J – reference: KassirKKStress intensity factors for a three-dimensional rectangular crackASME J Appl Mech19814823093120471.7308710.1115/1.3157614 – reference: MurakamiYIsidaMAnalysis of an arbitrarily shaped surface crack and stress field at crack front near surfaceTrans Jpn Soc Mech Eng1985514641050105610.1299/kikaia.51.1050 – reference: YanXCracks emanating from circular hole or square hole in rectangular plate in tensionEng Fract Mech200673121743175410.1016/j.engfracmech.2006.02.003 – reference: YanXMicrodefect interacting with a finite main crackJ Strain Anal Eng Des200540542143010.1243/030932405X16089 – reference: ZhaoWNewmanJCJrSuttonMAStress intensity factors for surface cracks at a hole by a three-dimensional weight function method with stresses from the finite element methodFatigue Fract Eng Mater Struct199821222923910.1046/j.1460-2695.1998.00015.x – reference: YanXA numerical analysis of stress intensity factors at bifurcated cracksEng Fail Anal200613462963710.1016/j.engfailanal.2004.12.043 – reference: Newman JC Jr (1971) An improved method of collocation for the stress analysis of cracked plates with various shaped boundaries. NASA TN, D-6376, pp 1–45 – reference: CharambidesPGMcMeekingRMFinite element method simulation of a crack propagation in a brittle microcracked solidMech Mater19876718710.1016/0167-6636(87)90023-8 – reference: YanXA numerical analysis of cracks emanating from an elliptical hole in a 2-D elasticity plateEur J Mech A20062511421531084.7404610.1016/j.euromechsol.2005.06.005 – reference: NewmanJCJrBigelowCAShivakumarKNThree-dimensional elastic-plastic finite element analyses of constraint variations in cracked bodiesEng Fract Mech199346111310.1016/0013-7944(93)90299-8 – reference: Murakami Y, Endo M (1985) Effects of hardness and crack geometry on ΔKth of small cracks emanating from small defects. Presented at int symposium on the behavior of short fatigue cracks, University of Sheffield, pp 25–28 – reference: YanXAnalysis for a crack emanating form a corner of a square hole in an infinite plate using the hybrid displacement discontinuity methodAppl Math Model20042898358471147.7440610.1016/j.apm.2003.12.005 – reference: MurakamiYA method of stress intensity factor calculation for the crack emanating from an arbitrarily shaped hole or the crack in the vicinity of an arbitrarily shape holeTrans Jpn Soc Mech Eng19784437842343210.1299/kikai1938.44.423 – reference: YanXAn effective numerical approach for multiple void-crack interactionASME J Appl Mech20067345255351111.7471810.1115/1.2127955 – reference: GuoJHLuZ-XThe behavior of two non-symmetrical permeable cracks emanating from an elliptical hole in a piezoelectric solidEur J Mech, A Solids201029465466310.1016/j.euromechsol.2010.01.001 – reference: MurakamiYStress intensity factors handbook1987ElmsfordPergamon – reference: Nisitani H, Isida M (1982) Simple procedure for calculating KI of a notch with a crack of arbitrary size and its application to non-propagating fatigue crack. 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NewmanJCJrRajuISEmpirical stress-intensity factor equation for surface crackEng Fract Mech1981151–218519210.1016/0013-7944(81)90116-8 – reference: YanXAnalysis of the interaction of arbitrary multiple cracks in an infinite plate interference effect of arbitrary multiple parabolic cracks in plane elasticity by using a new boundary element methodComput Methods Appl Mech Eng200319247–48509951212003CMAME.192.5099Y1075.7469210.1016/j.cma.2003.07.002 – reference: GuoJHLuZ-XExact solutions for anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric materialInt J Solids Struct200946379938091176.7415810.1016/j.ijsolstr.2009.07.002 – reference: YanXA brief evaluation of approximation methods for microcrack shielding problemsASME J Appl Mech20067346946961111.7471910.1115/1.2127957 – reference: YanXA numerical analysis of perpendicular cracks under general in-plane loading with a hybrid displacement discontinuity methodMech Res 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Snippet	This paper deals with such a kind of surface crack problem with an approximately same depth, which is called a liked-plane crack problem. Based on the previous...
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SubjectTerms	Automotive Engineering Boundary element method Civil Engineering Classical Mechanics Cracks Discontinuity Displacement Emission Mathematical analysis Mechanical Engineering Numerical analysis Physics Physics and Astronomy Surface cracks
Title	A numerical analysis of cracks emanating from a surface elliptical hole in infinite body in tension
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