This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Al Laham S, Branch SI. Stress intensity factor and limit load handbook. Gloucester, Volume 3. UK: British Energy Generation Limited; 1998.Al LahamSBranchSIStress intensity factor and limit load handbook3Gloucester, UKBritish Energy Generation Limited1998Search in Google Scholar
Tada H, Paris PC, Irwin GR, Tada H. The stress analysis of cracks handbook, Volume 130. New YorkTadaHParisPCIrwinGRTadaHThe stress analysis of cracks handbook130New YorkSearch in Google Scholar
Sih, G.; Liebowitz, H. Mathematical Fundamentals. In Fracture, Academic Press New York: 1968; Vol. 2, pp. 67–190.SihG.LiebowitzHMathematical FundamentalsInFractureAcademic PressNew York1968267190Search in Google Scholar
Hellan K. Introduction to fracture mechanics. McGraw-Hill; New York, 1985.HellanKIntroduction to fracture mechanicsMcGraw-HillNew York1985Search in Google Scholar
Barsom J, Rolfe S. Fracture and fatigue in structure: Application of fracture mechanics. Philadelphia, PA: American Society for Testing and Materials; 1999.BarsomJRolfeSFracture and fatigue in structure: Application of fracture mechanicsPhiladelphia, PAAmerican Society for Testing and Materials199910.1520/MNL41-3RD-EBSearch in Google Scholar
Hasan, S.; Akhtar, N. Dugdale model for three equal collinear straight cracks: An analytical approach. Theoretical and Applied Fracture Mechanics2015, 78, 40–50.HasanS.AkhtarNDugdale model for three equal collinear straight cracks: An analytical approachTheoretical and Applied Fracture Mechanics201578405010.1016/j.tafmec.2015.04.002Search in Google Scholar
Hasan, S.; Akhtar, N. Mathematical model for three equal collinear straight cracks: A modified Dugdale approach. Strength, Fracture and Complexity2015, 9, 211–232.HasanS.AkhtarN.Mathematical model for three equal collinear straight cracks: A modified Dugdale approachStrength, Fracture and Complexity2015921123210.3233/SFC-160189Search in Google Scholar
Kumar S, Singh I, Mishra B, Singh A. New enrichments in XFEM to model dynamic crack response of 2-D elastic solids. Int J Impact Eng. 2016;87:198–211.KumarSSinghIMishraBSinghANew enrichments in XFEM to model dynamic crack response of 2-D elastic solidsInt J Impact Eng20168719821110.1016/j.ijimpeng.2015.03.005Search in Google Scholar
Pandey V, Singh I, Mishra B, Ahmad S, Rao AV, Kumar V. A new framework based on continuum damage mechanics and XFEM for high cycle fatigue crack growth: ASME Press; 2000.PandeyVSinghIMishraBAhmadSRaoAVKumarVA new framework based on continuum damage mechanics and XFEM for high cycle fatigue crack growthASME Press2000Search in Google Scholar
Alshoaibi AM, Fageehi YA. 2D finite element simulation of mixed mode fatigue crack propagation for CTS specimen. J Mater Res Technol. 2020;9:7850–61.AlshoaibiAMFageehiYA2D finite element simulation of mixed mode fatigue crack propagation for CTS specimenJ Mater Res Technol2020978506110.1016/j.jmrt.2020.04.083Search in Google Scholar
Li X, Li H, Liu L, Liu Y, Ju M, Zhao J. Investigating the crack initiation and propagation mechanism in brittle rocks using grain-based finite-discrete element method. Int J Rock Mech Min Sci. 2020;127:104219.LiXLiHLiuLLiuYJuMZhaoJInvestigating the crack initiation and propagation mechanism in brittle rocks using grain-based finite-discrete element methodInt J Rock Mech Min Sci202012710421910.1016/j.ijrmms.2020.104219Search in Google Scholar
Leclerc W, Haddad H, Guessasma M. On the suitability of a discrete element method to simulate cracks initiation and propagation in heterogeneous media. Int J Solids Struct. 2017;108:98–114.LeclercWHaddadHGuessasmaMOn the suitability of a discrete element method to simulate cracks initiation and propagation in heterogeneous mediaInt J Solids Struct20171089811410.1016/j.ijsolstr.2016.11.015Search in Google Scholar
Shao Y, Duan Q, Qiu S. Adaptive consistent element-free Galerkin method for phase-field model of brittle fracture. Comput Mech. 2019;64:741–67.ShaoYDuanQQiuSAdaptive consistent element-free Galerkin method for phase-field model of brittle fractureComput Mech2019647416710.1007/s00466-019-01679-2Search in Google Scholar
Kanth SA, Harmain G, Jameel A. Modeling of nonlinear crack growth in steel and aluminum alloys by the element free galerkin method. Mater Today Proc. 2018;5:18805–14.KanthSAHarmainGJameelAModeling of nonlinear crack growth in steel and aluminum alloys by the element free galerkin methodMater Today Proc20185188051410.1016/j.matpr.2018.06.227Search in Google Scholar
Huynh HD, Nguyen MN, Cusatis G, Tanaka S, Bui TQ. A polygonal XFEM with new numerical integration for linear elastic fracture mechanics. Eng Fract Mech. 2019;213:241–63.HuynhHDNguyenMNCusatisGTanakaSBuiTQA polygonal XFEM with new numerical integration for linear elastic fracture mechanicsEng Fract Mech20192132416310.1016/j.engfracmech.2019.04.002Search in Google Scholar
Surendran M, Natarajan S, Palani G, Bordas SP. Linear smoothed extended finite element method for fatigue crack growth simulations. Eng Fract Mech. 2019;206:551–64.SurendranMNatarajanSPalaniGBordasSPLinear smoothed extended finite element method for fatigue crack growth simulationsEng Fract Mech20192065516410.1016/j.engfracmech.2018.11.011Search in Google Scholar
Rozumek D, Marciniak Z, Lesiuk G, Correia J. Mixed mode I/II/III fatigue crack growth in S355 steel. Procedia Struct Integr. 2017;5:896–903.RozumekDMarciniakZLesiukGCorreiaJMixed mode I/II/III fatigue crack growth in S355 steelProcedia Struct Integr2017589690310.1016/j.prostr.2017.07.125Search in Google Scholar
Dekker R, van der Meer F, Maljaars J, Sluys L. A cohesive XFEM model for simulating fatigue crack growth under mixed-mode loading and overloading. Int J Numer Methods Eng. 2019;118:561–77.DekkerRvan der MeerFMaljaarsJSluysLA cohesive XFEM model for simulating fatigue crack growth under mixed-mode loading and overloadingInt J Numer Methods Eng20191185617710.1002/nme.6026Search in Google Scholar
Rezaei S, Wulfinghoff S, Reese S. Prediction of fracture and damage in micro/nano coating systems using cohesive zone elements. Int J Solids Struct. 2017;121:62–74.RezaeiSWulfinghoffSReeseSPrediction of fracture and damage in micro/nano coating systems using cohesive zone elementsInt J Solids Struct2017121627410.1016/j.ijsolstr.2017.05.016Search in Google Scholar
Xu W, Wu X. Weight functions and strip-yield model analysis for three collinear cracks. Eng Fract Mech. 2012;85: 73–87.XuWWuXWeight functions and strip-yield model analysis for three collinear cracksEng Fract Mech201285738710.1016/j.engfracmech.2012.02.009Search in Google Scholar
Zhang W, Tabiei A. An efficient implementation of phase field method with explicit time integration. J Appl Comput Mech. 2020;6:373–82.ZhangWTabieiAAn efficient implementation of phase field method with explicit time integrationJ Appl Comput Mech2020637382Search in Google Scholar
Dirik H, Yalçinkaya T. Crack path and life prediction under mixed mode cyclic variable amplitude loading through XFEM. Int J Fatigue. 2018;114:34–50.DirikHYalçinkayaTCrack path and life prediction under mixed mode cyclic variable amplitude loading through XFEMInt J Fatigue2018114345010.1016/j.ijfatigue.2018.04.026Search in Google Scholar
Demir O, Ayhan AO, İriç S. A new specimen for mixed mode-I/II fracture tests: Modeling, experiments and criteria development. Eng Fract Mech. 2017;178:457–76.DemirOAyhanAOİriçSA new specimen for mixed mode-I/II fracture tests: Modeling, experiments and criteria developmentEng Fract Mech20171784577610.1016/j.engfracmech.2017.02.019Search in Google Scholar
Zhang R, Guo R. Determination of crack tip stress intensity factors by singular Voronoi cell finite element model. Eng Fract Mech. 2018;197:206–16.ZhangRGuoRDetermination of crack tip stress intensity factors by singular Voronoi cell finite element modelEng Fract Mech20181972061610.1016/j.engfracmech.2018.04.042Search in Google Scholar
Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng. 1999;45:601–20.BelytschkoTBlackTElastic crack growth in finite elements with minimal remeshingInt J Numer Methods Eng1999456012010.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-SSearch in Google Scholar
Bergara A, Dorado J, Martin-Meizoso A, Martínez-Esnaola J. Fatigue crack propagation in complex stress fields: Experiments and numerical simulations using the Extended Finite Element Method (XFEM). Int J Fatigue. 2017;103:112–21.BergaraADoradoJMartin-MeizosoAMartínez-EsnaolaJFatigue crack propagation in complex stress fields: Experiments and numerical simulations using the Extended Finite Element Method (XFEM)Int J Fatigue20171031122110.1016/j.ijfatigue.2017.05.026Search in Google Scholar
Demir O, Ayhan AO, Sedat I, Lekesiz H. Evaluation of mixed mode-I/II criteria for fatigue crack propagation using experiments and modeling. Chinese J Aeronaut 2018;31:1525–34.DemirOAyhanAOSedatILekesizHEvaluation of mixed mode-I/II criteria for fatigue crack propagation using experiments and modelingChinese J Aeronaut20183115253410.1016/j.cja.2018.05.009Search in Google Scholar
Sajith S, Murthy K, Robi P. Experimental and numerical investigation of mixed mode fatigue crack growth models in aluminum 6061-T6. Int J Fatigue. 2020;130:105285.SajithSMurthyKRobiPExperimental and numerical investigation of mixed mode fatigue crack growth models in aluminum 6061-T6Int J Fatigue202013010528510.1016/j.ijfatigue.2019.105285Search in Google Scholar
Alshoaibi AM. Finite element procedures for the numerical simulation of fatigue crack propagation under mixed mode loading. Struct Eng Mech. 2010;35:283–99.AlshoaibiAMFinite element procedures for the numerical simulation of fatigue crack propagation under mixed mode loadingStruct Eng Mech2010352839910.12989/sem.2010.35.3.283Search in Google Scholar
Alshoaibi AM. Comprehensive comparisons of two and three dimensional numerical estimation of stress intensity factors and crack propagation in linear elastic analysis. Int J Integr Eng. 2019;11:45–52.AlshoaibiAMComprehensive comparisons of two and three dimensional numerical estimation of stress intensity factors and crack propagation in linear elastic analysisInt J Integr Eng201911455210.30880/ijie.2019.11.06.006Search in Google Scholar
Fageehi YA, Alshoaibi AM. Numerical simulation of mixed-mode fatigue crack growth for compact tension shear specimen. Adv Mater Sci Eng. 2020;1–14. https://doi.org/10.1155/2020/5426831FageehiYAAlshoaibiAMNumerical simulation of mixed-mode fatigue crack growth for compact tension shear specimenAdv Mater Sci Eng2020114https://doi.org/10.1155/2020/542683110.1155/2020/5426831Search in Google Scholar
Chen H, Wang Q, Zeng W, Liu G, Sun J, He L, et al. Dynamic brittle crack propagation modeling using singular edge-based smoothed finite element method with local mesh rezoning. Eur J Mech A Solids 2019;76:208–23.ChenHWangQZengWLiuGSunJHeLDynamic brittle crack propagation modeling using singular edge-based smoothed finite element method with local mesh rezoningEur J Mech A Solids2019762082310.1016/j.euromechsol.2019.04.010Search in Google Scholar
Gomes G, Miranda AC. Analysis of crack growth problems using the object-oriented program bemcracker2D. Frattura ed Integrità Strutturale 2018;12:67–85.GomesGMirandaACAnalysis of crack growth problems using the object-oriented program bemcracker2DFrattura ed Integrità Strutturale201812678510.3221/IGF-ESIS.45.06Search in Google Scholar
Fageehi YA, Alshoaibi AM. Nonplanar crack growth simulation of multiple cracks using finite element method. Adv Mater Sci Eng. 2020; 1–12.FageehiYAAlshoaibiAMNonplanar crack growth simulation of multiple cracks using finite element methodAdv Mater Sci Eng202011210.1155/2020/8379695Search in Google Scholar
Alshoaibi AM. Numerical modeling of crack growth under mixed-mode loading. Appl Sci. 2021;11:2975.AlshoaibiAMNumerical modeling of crack growth under mixed-mode loadingAppl Sci202111297510.3390/app11072975Search in Google Scholar
Paris P, Erdogan F. A critical analysis of crack propagation laws; J. Basic Eng. Dec 1963, 85(4): 528–53337.ParisPErdoganFA critical analysis of crack propagation lawsJ. Basic Eng.Dec19638545285333710.1115/1.3656900Search in Google Scholar
Coffin L. Cyclic deformation and fatigue of metals. Fatigue and Endurance of Metals [Russian translation], Moscow; 1963. 257–72.CoffinLCyclic deformation and fatigue of metalsFatigue and Endurance of Metals [Russian translation]Moscow196325772Search in Google Scholar
Wöhler A. Versuche zur Ermittlung der auf die Eisenbahnwagenachsen einwirkenden Kräfte und die Widerstandsfähigkeit der Wagen-Achsen. Zeitschrift für Bauwesen. 1860;10:583–614.WöhlerAVersuche zur Ermittlung der auf die Eisenbahnwagenachsen einwirkenden Kräfte und die Widerstandsfähigkeit der Wagen-AchsenZeitschrift für Bauwesen186010583614Search in Google Scholar
Bjørheim F. Practical comparison of crack meshing in ANSYS mechanical APDL 19.2. Norway: University of Stavanger; 2019.BjørheimFPractical comparison of crack meshing in ANSYS mechanical APDL 19.2NorwayUniversity of Stavanger2019Search in Google Scholar
Erdogan F, Sih G. On the crack extension in plates under plane loading and transverse shear. J Basic Eng. 1963;85:519–525.ErdoganFSihGOn the crack extension in plates under plane loading and transverse shearJ Basic Eng19638551952510.1115/1.3656897Search in Google Scholar
Hussain M, Pu S, Underwood J. Strain energy release rate for a crack under combined mode I and mode II. In Proceedings of the Fracture analysis: Proceedings of the 1973 national symposium on fracture mechanics, Part II; West Conshohocken, PA, 1974.HussainMPuSUnderwoodJStrain energy release rate for a crack under combined mode I and mode IIInProceedings of the Fracture analysis: Proceedings of the 1973 national symposium on fracture mechanics, Part IIWest Conshohocken, PA1974Search in Google Scholar
Nuismer R. An energy release rate criterion for mixed mode fracture. Int J Fract. 1975;11:245–50.NuismerRAn energy release rate criterion for mixed mode fractureInt J Fract1975112455010.1007/BF00038891Search in Google Scholar
Lee Y-L, Pan J, Hathaway R, Barkey M. Fatigue testing and analysis: Theory and practice, Volume 13. Burlington, Mass.: Butterworth-Heinemann, 2005.LeeY-LPanJHathawayRBarkeyMFatigue testing and analysis: Theory and practice13Burlington, Mass.Butterworth-Heinemann2005Search in Google Scholar
Irwin GR. Analysis of stresses and strains near the end of a crack transversing a plate. Trans ASME Ser E J Appl Mech. 1957;24:361–4.IrwinGRAnalysis of stresses and strains near the end of a crack transversing a plateTrans ASME Ser E J Appl Mech195724361410.1115/1.4011547Search in Google Scholar
Bashiri AH, Alshoaibi AM. Adaptive finite element prediction of fatigue life and crack path in 2D structural components. Metals. 2020;10:1316.BashiriAHAlshoaibiAMAdaptive finite element prediction of fatigue life and crack path in 2D structural componentsMetals202010131610.3390/met10101316Search in Google Scholar
Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech. 1968;35:379–86.RiceJRA path independent integral and the approximate analysis of strain concentration by notches and cracksJ Appl Mech1968353798610.21236/AD0653716Search in Google Scholar
Alshoaibi AM. Finite element simulation of fatigue life estimation and crack path prediction of two dimensional structures components. HKIE Trans. 2013;15:1–6.AlshoaibiAMFinite element simulation of fatigue life estimation and crack path prediction of two dimensional structures componentsHKIE Trans2013151610.1080/1023697X.2008.10668103Search in Google Scholar
Alshoaibi AM. An adaptive finite element framework for fatigue crack propagation under constant amplitude loading. Int J Appl Sci Eng. 2015;13:261–70.AlshoaibiAMAn adaptive finite element framework for fatigue crack propagation under constant amplitude loadingInt J Appl Sci Eng20151326170Search in Google Scholar
Alshoaibi AM. A two dimensional simulation of crack propagation using adaptive finite element analysis. J Comput Appl Mech. 2018;49:335.AlshoaibiAMA two dimensional simulation of crack propagation using adaptive finite element analysisJ Comput Appl Mech201849335Search in Google Scholar
Alshoaibi AM, Hadi M, Ariffin A. Two-dimensional numerical estimation of stress intensity factors and crack propagation in linear elastic analysis. Struct Durability Health Monit. 2007;3:15.AlshoaibiAMHadiMAriffinATwo-dimensional numerical estimation of stress intensity factors and crack propagation in linear elastic analysisStruct Durability Health Monit2007315Search in Google Scholar
Knowles JK, Sternberg E. On a class of conservation laws in linearized and finite elastostatics. California Institute of Technology, Pasadena Division of Engineering and Applied Science; 1971.KnowlesJKSternbergEOn a class of conservation laws in linearized and finite elastostaticsCalifornia Institute of Technology, Pasadena Division of Engineering and Applied Science197110.1007/BF00250778Search in Google Scholar
Liu Y, Li Y, Xie WJ. Modeling of multiple crack propagation in 2-D elastic solids by the fast multipole boundary element method. Eng Fract Mech. 2017;172:1–16.LiuYLiYXieWJModeling of multiple crack propagation in 2-D elastic solids by the fast multipole boundary element methodEng Fract Mech201717211610.1016/j.engfracmech.2017.01.010Search in Google Scholar
Ingraffea AR, Grigoriu M. Probabilistic fracture mechanics: A validation of predictive capability. Cornell University Ithaca, NY, Department of Structural Engineering; 1990.IngraffeaARGrigoriuMProbabilistic fracture mechanics: A validation of predictive capabilityCornell University Ithaca, NY, Department of Structural Engineering1990Search in Google Scholar
Ma W, Liu G, Wang W. A coupled extended meshfree – Smoothed meshfree method for crack growth simulation. Theor Appl Fract Mech. 2020;107:102572.MaWLiuGWangWA coupled extended meshfree – Smoothed meshfree method for crack growth simulationTheor Appl Fract Mech202010710257210.1016/j.tafmec.2020.102572Search in Google Scholar
Bittencourt T, Wawrzynek P, Ingraffea A, Sousa J. Quasi-automatic simulation of crack propagation for 2D LEFM problems. Eng Fract Mech. 1996;55:321–34.BittencourtTWawrzynekPIngraffeaASousaJQuasi-automatic simulation of crack propagation for 2D LEFM problemsEng Fract Mech1996553213410.1016/0013-7944(95)00247-2Search in Google Scholar