Correction Method for Calculating Critical Plane Position of Geometric Discontinuity Steel Structure Under Multiaxial Loading

doi:10.1007/s12204-019-2128-9

Abstract

Abstract: Critical plane method is one of the most promising approaches to predict the fatigue life when the structure is subjected to the multiaxial loading. The stress-strain status and the critical plane position for smooth specimens are calculated using theoretical approaches when the loading mode is a continuous function. However, because of the existence of stress concentration and the characteristic of multiaxial non-proportion, it is difficult to calculate the stress-strain status and the critical plane position of geometric discontinuity structure by theory method. In this paper, a new numerical simulation method is proposed to determine the critical plane of geometric discontinuity structure under multiaxial loading. Firstly, the strain status of dangerous point is analyzed by finite element method. Secondly, the maximum shear strain amplitude of arbitrary plane is calculated using coordinate transformation principle. Finally, the plane which has the maximum shear strain amplitude is defined as the critical plane. The critical plane positions are analyzed when loading mode and notch parameters are different. Meanwhile, the relationship between notch depth and associated parameters on critical plane as well as that between loading amplitude and associated parameters on critical plane are given quantitatively.

Key words: critical plane position| geometric discontinuity structure| stress-strain status| maximum shear strain| multiaxial loading

摘要： Critical plane method is one of the most promising approaches to predict the fatigue life when the structure is subjected to the multiaxial loading. The stress-strain status and the critical plane position for smooth specimens are calculated using theoretical approaches when the loading mode is a continuous function. However, because of the existence of stress concentration and the characteristic of multiaxial non-proportion, it is difficult to calculate the stress-strain status and the critical plane position of geometric discontinuity structure by theory method. In this paper, a new numerical simulation method is proposed to determine the critical plane of geometric discontinuity structure under multiaxial loading. Firstly, the strain status of dangerous point is analyzed by finite element method. Secondly, the maximum shear strain amplitude of arbitrary plane is calculated using coordinate transformation principle. Finally, the plane which has the maximum shear strain amplitude is defined as the critical plane. The critical plane positions are analyzed when loading mode and notch parameters are different. Meanwhile, the relationship between notch depth and associated parameters on critical plane as well as that between loading amplitude and associated parameters on critical plane are given quantitatively.

关键词: critical plane position| geometric discontinuity structure| stress-strain status| maximum shear strain| multiaxial loading

CLC Number:

LI Bin (李斌), WANG Xiuli (王秀丽), LIU Jianhui (刘俭辉), LANG Shanshan (郎珊珊). Correction Method for Calculating Critical Plane Position of Geometric Discontinuity Steel Structure Under Multiaxial Loading[J]. Journal of Shanghai Jiao Tong University (Science), 2019, 24(6): 799-804.

References 22

[12]	FATEMI A, SOCIE D F. A critical plane approach tomultiaxial fatigue damage including out-of-phase loading[J]. Fatigue & Fracture of Engineering Materials &Structures, 1988, 11(3): 149-165.
[1]	LIU J H, WANG S N, JIN W Y, et al. A modifiedmethod for calculating notch-root stresses and strainsunder multiaxial loading [J]. Advances in Mechanical Engineering, 2014, 2014: 513804.
[13]	GATES N, FATEMI A. Notch deformation and stressgradient effects in multiaxial fatigue [J]. Theoreticaland Applied Fracture Mechanics, 2016, 84: 3-25.
[2]	KAUSHIK V, NARASIMHAN R, MISHRA R K. Finiteelement simulations of notch tip fields in magnesiumsingle crystals [J]. International Journal of Fracture,2014, 189(2): 195-216.
[14]	SUSMEL L, TAYLOR D. A critical distance/planemethod to estimate finite life of notched componentsunder variable amplitude uniaxial/multiaxial fatigueloading [J]. International Journal of Fatigue, 2012, 38:7-24.
[3]	CARPINTERI A, SPAGNOLI A, VANTADORI S, etal. A multiaxial criterion for notch high-cycle fatigueusing a critical-point method [J]. Engineering FractureMechanics, 2008, 75(7): 1864-1874.
[15]	MARCINIAK Z, ROZUMEK D, MACHA E. Verificationof fatigue critical plane position according to varianceand damage accumulation methods under multiaxialloading [J]. International Journal of Fatigue,2014, 58: 84-93.
[4]	KAMAL M, RAHMAN M M. Multiaxial fatigue lifemodelling using hybrid approach of critical plane andgenetic algorithm [J]. Fatigue & Fracture of EngineeringMaterials & Structures, 2016, 39(4): 479-490.
[16]	NAIK R A, LANNING D B, NICHOLAS T, et al. Acritical plane gradient approach for the prediction ofnotched HCF life [J]. International Journal of Fatigue,2005, 27(5): 481-492.
[5]	ZHENG M L, LI P, YANG J G, et al. Fatigue life predictionof high modulus asphalt concrete based on thelocal stress-strain method [J]. Applied Sciences, 2017,7(3): 305.
[17]	BERGARA A, DORADO J I, MARTIN-MEIZOSOA, et al. Fatigue crack propagation in complex stressfields: Experiments and numerical simulations usingthe Extended Finite Element Method(XFEM) [J]. InternationalJournal of Fatigue, 2017, 103: 112-121.
[6]	RAO D, HEERENS J, PINHEIRO G A, et al. On characterisationof local stress-strain properties in frictionstir welded aluminium AA 5083 sheets using microtensilespecimen testing and instrumented indentationtechnique [J]. Materials Science and Engineering: A,2010, 527(18/19): 5018-5025.
[18]	CITARELLA R, GIANNELLA V, LEPORE M, etal. Dual boundary element method and finite elementmethod for mixed-mode crack propagation simulationsin a cracked hollow shaft [J]. Fatigue & Fracture of EngineeringMaterials & Structures, 2018, 41(1): 84-98.
[7]	CARPINTERI A, RONCHEI C, SPAGNOLI A, et al.On the use of the Prismatic Hull method in a criticalplane-based multiaxial fatigue criterion [J]. InternationalJournal of Fatigue, 2014, 68: 159-167.
[19]	LIU J H, ZHANG R L, WEI Y B, et al. A new methodfor estimating fatigue life of notched specimen [J].Theoretical and Applied Fracture Mechanics, 2018, 93:137-143.
[8]	JIANG C, LIU Z C, WANG X G, et al. A structuralstress-based critical plane method for multiaxial fatiguelife estimation in welded joints [J]. Fatigue &Fracture of Engineering Materials & Structures, 2016,39(3): 372-383.
[20]	QVALE P, H¨ARKEG?ARD G. A simplified method forweakest-link fatigue assessment based on finite elementanalysis [J]. International Journal of Fatigue, 2017,100: 78-83.
[9]	LANGLAIS T E, VOGEL J H, CHASE T R. Multiaxialcycle counting for critical plane methods [J]. InternationalJournal of Fatigue, 2003, 25(7): 641-647.
[21]	SPEAR A D, HOCHHALTER J D, CERRONE A R,et al. A method to generate conformal finite-elementmeshes from 3D measurements of microstructurallysmall fatigue-crack propagation [J]. Fatigue & Fractureof Engineering Materials & Structures, 2016, 39(6):737-751.
[10]	MIKHAILOV S E. A functional approach to non-localstrength conditions and fracture criteria—II. Discretefracture [J]. Engineering Fracture Mechanics, 1995,52(4): 745-754.
[22]	XU Y J, YUAN H. Computational modeling of mixedmodefatigue crack growth using extended finite elementmethods [J]. International Journal of Fracture,2009, 159(2): 151-165.
[11]	ˇSRAML M, FLAˇSKER J, POTRˇC I. Critical planemodelling of fatigue initiation under rolling and slidingcontact [J]. Journal of Strain Analysis for EngineeringDesign, 2004, 39(2): 225-236.
[12]	FATEMI A, SOCIE D F. A critical plane approach tomultiaxial fatigue damage including out-of-phase loading[J]. Fatigue & Fracture of Engineering Materials &Structures, 1988, 11(3): 149-165.
[13]	GATES N, FATEMI A. Notch deformation and stressgradient effects in multiaxial fatigue [J]. Theoreticaland Applied Fracture Mechanics, 2016, 84: 3-25.
[14]	SUSMEL L, TAYLOR D. A critical distance/planemethod to estimate finite life of notched componentsunder variable amplitude uniaxial/multiaxial fatigueloading [J]. International Journal of Fatigue, 2012, 38:7-24.
[15]	MARCINIAK Z, ROZUMEK D, MACHA E. Verificationof fatigue critical plane position according to varianceand damage accumulation methods under multiaxialloading [J]. International Journal of Fatigue,2014, 58: 84-93.
[16]	NAIK R A, LANNING D B, NICHOLAS T, et al. Acritical plane gradient approach for the prediction ofnotched HCF life [J]. International Journal of Fatigue,2005, 27(5): 481-492.
[17]	BERGARA A, DORADO J I, MARTIN-MEIZOSOA, et al. Fatigue crack propagation in complex stressfields: Experiments and numerical simulations usingthe Extended Finite Element Method(XFEM) [J]. InternationalJournal of Fatigue, 2017, 103: 112-121.
[18]	CITARELLA R, GIANNELLA V, LEPORE M, etal. Dual boundary element method and finite elementmethod for mixed-mode crack propagation simulationsin a cracked hollow shaft [J]. Fatigue & Fracture of EngineeringMaterials & Structures, 2018, 41(1): 84-98.
[19]	LIU J H, ZHANG R L, WEI Y B, et al. A new methodfor estimating fatigue life of notched specimen [J].Theoretical and Applied Fracture Mechanics, 2018, 93:137-143.
[20]	QVALE P, H¨ARKEG?ARD G. A simplified method forweakest-link fatigue assessment based on finite elementanalysis [J]. International Journal of Fatigue, 2017,100: 78-83.
[21]	SPEAR A D, HOCHHALTER J D, CERRONE A R,et al. A method to generate conformal finite-elementmeshes from 3D measurements of microstructurallysmall fatigue-crack propagation [J]. Fatigue & Fractureof Engineering Materials & Structures, 2016, 39(6):737-751.
[22]	XU Y J, YUAN H. Computational modeling of mixedmodefatigue crack growth using extended finite elementmethods [J]. International Journal of Fracture,2009, 159(2): 151-165.