Unified Analysis Method for High/Low Cycle Fatigue Behavior of Welded Structures Based on Structural Strain Parameters

doi:10.3901/JME.2025.16.102

Abstract

Abstract: Welded structures are experiencing increasingly stringent service conditions, enduring a mix of high- and low-cycle fatigue loads throughout their service life. A holistic approach to assess fatigue damage stemming from both load types is presented, expanding structural stress parameters to include the formulation of the structural strain parameter. A numerical technique is introduced, employing through-thickness resultant force and moment and accommodating three common structural lateral constraints： plane stress, plane strain, and predefined stress triaxiality factors. Simultaneously, three types of elastic-plastic hardening model are considered： linear hardening modulus, Ramberg-Osgood equation, and a customized stress-strain curve. Analysis of 872 sets of highand low-cycle fatigue data from welded structures with diverse base materials, utilizing the structural strain method alongside the master E-N curve, reveals the ability of equivalent structural strain parameters to correlate fatigue data across various materials. The equivalent structural strain parameter emerges as a universal fatigue metric, offering an effective foundation for comprehensive analyses on welded joint fatigue performance compared to the equivalent structural stress method.

Key words: low-cycle fatigue, high-cycle fatigue, welded structure, structural strain, fatigue parameter, master E-N curve

CLC Number:

TG406

LEI Linsen, LI Xiangwei, XING Shizhu, LIU Xiaochao, LI Yongzhe, PEI Xianjun. Unified Analysis Method for High/Low Cycle Fatigue Behavior of Welded Structures Based on Structural Strain Parameters[J]. Journal of Mechanical Engineering, 2025, 61(16): 102-115.

References

[1] 张勇,陈子壮,袁少波,等. 焊接接头疲劳评价进展[J]. 兵器材料科学与工程, 2023, 46: 134-141. ZHANG Yong, CHEN Zizhuang, YUAN Shaobo, et al. Progress in fatigue evaluation of welded joints[J]. Ordnance Material Science and Engineering, 2023, 46: 134-141.
[2] 杨建国,郝建松,李曰兵,等. 含表面裂纹焊接结构疲劳评定的质量等级方法[J]. 机械工程学报, 2018, 54(14): 82-89. YANG Jianguo, HAO Jiansong, LI Yuebing, et al. Quality grade method for fatigue evaluation of welded structures with surface cracks[J]. Journal of Mechanical Engineering, 2018, 54(14): 82-89.
[3] LIU X, LEI L, XING S, et al. A post-processing procedure for predicting high-and low-cycle fatigue life of welded structures based on the master E-N curve[J]. Fatigue Fract. Eng. Mater. Struct., 2023, 46(9): 3387-3403.
[4] 周海波,蒋翔,葛珅玮. 船舶焊接结构件的疲劳特性分析与结构设计[J]. 舰船科学技术 , 2023, 45: 186-189. ZHOU Haibo, JIANG Xiang, GE Shenwei. Fatigue characteristics analysis and structural design of welded structural parts of ships[J]. Ship Science and Technology, 2023, 45: 186-189.
[5] 汤之南,蔡志鹏,吴健栋. 热影响区元素晶界偏聚对焊接构件低周疲劳性能的影响[J]. 机械工程学报, 2015, 51(14): 78-85. TANG Zhinan, CAI Zhipeng, WU Jiandong. Effect of grain boundary segregation of heat affected zone elements on low cycle fatigue properties of welded components[J]. Journal of Mechanical Engineering, 2015, 51(14): 78-85.
[6] ZHU S, YUE P, YU Z, et al. A combined high and low cycle fatigue model for life prediction of turbine blades[J]. Materials, 2017, 10(7): 698.
[7] 王苹,裴宪军,钱宏亮,等. 焊接结构抗疲劳设计新方法与应用[J]. 机械工程学报, 2021, 57(16): 349-360. WANG Ping, PEI Xianjun, QIAN Hongliang, et al. New methods and applications for fatigue resistance design of welded structures[J]. Journal of Mechanical Engineering, 2021, 57(16): 349-360.
[8] MENEGHETTI G, LAZZARIN P. The peak stress method for fatigue strength assessment of welded joints with weld toe or weld root failures[J]. Welding in the World, 2011, 55: 22-29.
[9] HAIBACH E. Fatigue strength of welded joints from viewpoint of local strain measurement[J]. Report FB-77, Fraunhofer-Institut für Betriebsfestigkeit (LBF) , Darmstadt, 1968: 1-63.
[10] 周强,张群,姬存民,等. 基于热点应力法和结构应力法的保温支撑圈焊接接头疲劳评估及对比[J]. 化工设备与管道, 2023, 60: 6-13. ZHOU Qiang, ZHANG Qun, JI Cunmin, et al. Fatigue evaluation and comparison of welded joints of thermal insulation support rings based on hot spot stress method and structural stress method[J]. Chemical Equipment and Pipelines, 2023, 60: 6-13.
[11] 彭凡,姚云建,顾勇军. 考虑热点应力梯度的焊接接头疲劳评定[J]. 机械工程学报, 2010, 46(22): 65-69. PENG Fan , YAO Yunjian , GU Yongjun. Fatigue evaluation of welded joints considering hot spot Stress gradient[J]. Journal of Mechanical Engineering, 2010, 46(22): 65-69.
[12] FRICKE W. ⅡW recommendations for the fatigue assessment of welded structures by notch stress analysis: ⅡW-2006-09[M]. Cambridge: Woodhead Publishing, 2012.
[13] MADDOX S. Hot-spot stress design curves for fatigue assessment of welded structures[J]. International Journal of Offshore and Polar Engineering, 2002, 12(2): 134-141.
[14] VIANA C O, CARVALHO H, CORREIA J, et al. Fatigue assessment based on hot-spot stresses obtained from the global dynamic analysis and local static sub-model[J]. International Journal of Structural Integrity, 2021, 12(1): 31-47.
[15] RADAJ D , SONSINO C M , FRICKE W. Fatigue assessment of welded joints by local approaches[M]. Cambridge: Woodhead Publishing, 2006.
[16] RADAJ D , SONSINO C , FRICKE W. Recent developments in local concepts of fatigue assessment of welded joints[J]. International Journal of Fatigue, 2009, 31(1): 2-11.
[17] KARAKAS Ö. Consideration of mean-stress effects on fatigue life of welded magnesium joints by the application of the Smith-Watson-Topper and reference radius concepts[J]. International Journal of Fatigue, 2013, 49: 1-17.
[18] KARAKAŞ Ö, BAUMGARTNER J, SUSMEL L. On the use of a fictitious notch radius equal to 0.3 mm to design against fatigue welded joints made of wrought magnesium alloy AZ31[J]. International Journal of Fatigue, 2020, 139: 105747.
[19] ZHOU W, DONG P, PEI X, et al. Evaluation of magnesium weldment fatigue data using traction and notch stress methods[J]. International Journal of Fatigue, 2020, 138: 105695.
[20] XIAO Z G, YAMADA K. A method of determining geometric stress for fatigue strength evaluation of steel welded joints[J]. International Journal of Fatigue, 2004, 26(12): 1277-1293.
[21] WEI Z, PEI X, JIN H. Evaluation of welded cast steel joint fatigue data using structural stress methods[J]. Journal of Constructional Steel Research, 2021, 186: 106895.
[22] DONG P. A structural stress definition and numerical implementation for fatigue analysis of welded joints[J]. International Journal of Fatigue, 2001, 23(10): 865-876.
[23] DONG P, HONG J. The master SN curve approach to fatigue of piping and vessel welds[J]. Welding in the World, 2004, 48: 28-36.
[24] 樊俊铃. 基于能量耗散的 Q235 钢高周疲劳性能评估[J]. 机械工程学报, 2018, 54(6): 1-9. FAN Junling. High cycle fatigue performance evaluation of Q235 steel based on energy dissipation[J]. Journal of Mechanical Engineering, 2018, 54(6): 1-9.
[25] LAZZARIN P , TOVO R. A notch intensity factor approach to the stress analysis of welds[J]. Fatigue Fract. Eng. Mater. Struct., 1998, 21(9): 1089-1103.
[26] LAZZARIN P, LIVIERI P. Notch stress intensity factors and fatigue strength of aluminium and steel welded joints[J]. International Journal of Fatigue, 2001, 23(3): 225-232.
[27] 陈超核,杨跃富,李平,等. 海洋结构物腐蚀损伤及腐蚀疲劳评估方法研究综述[J]. 船舶力学, 2023, 27: 1413-1429. CHEN Chaohe, YANG Yuefu, LI Ping, et al. Review of corrosion damage and corrosion fatigue evaluation methods for marine structures[J]. Ship Mechanics, 2023, 27: 1413-1429.
[28] SONG W, LIU X, ZHOU G, et al. Notch energy-based low and high cycle fatigue assessment of load-carrying cruciform welded joints considering the strength mismatch[J]. International Journal of Fatigue, 2021, 151: 106410.
[29] FENG L, QIAN X. A hot-spot energy indicator for welded plate connections under cyclic axial loading and bending[J]. Engineering Structures, 2017, 147: 598-612.
[30] RADAJ D, SONSINO C, FLADE D. Prediction of service fatigue strength of a welded tubular joint on the basis of the notch strain approach[J]. International Journal of Fatigue, 1998, 20(6): 471-480.
[31] 钱令希. 余能理论[J]. 中国科学, 1950, 1: 449-456. QIAN Lingxi. The theory of residual energy[J]. Science in China, 1950, 1: 449-456.
[32] GERE J M, GOODNO B J. Mechanics of materials[M]. Stamford: Cengage Learning, 2012.
[33] ANDERSON T L. Fracture mechanics: Fundamentals and applications[M]. Boca Raton: CRC Press, 1991.
[34] KOROBEYNIKOV S, LARICHKIN A Y, ROTANOVA T. Hyperelasticity models extending Hooke’s law from small to moderate strains and experimental verification of their scope of application[J]. International Journal of Solids and Structures, 2022, 252: 111815.
[35] DUNNE F, PETRINIC N. Introduction to computational plasticity[M]. Oxford: OUP Oxford, 2005.
[36] BAHMANI A, FARAHMAND F, JANBAZ M, et al. On the comparison of two mixed-mode I+ Ⅲ fracture test specimens[J]. Engineering Fracture Mechanics, 2021, 241: 107434.
[37] BRESLOW N E. Generalized linear models: Checking assumptions and strengthening conclusions[J]. Statistica Applicata, 1996, 8(1): 23-41.
[38] RAMBERG W , OSGOOD W R. Description of stress-strain curves by three parameters[R]. National Advisory Committee for Aeronautics, 1943.
[39] BAI L, WADEE M A, KÖLLNER A, et al. Variational modelling of local-global mode interaction in long rectangular hollow section struts with Ramberg-Osgood type material nonlinearity[J]. International Journal of Mechanical Sciences, 2021, 209: 106691.
[40] PEI X, DONG P. An analytically formulated structural strain method for fatigue evaluation of welded components incorporating nonlinear hardening effects[J]. Fatigue Fract. Eng. Mater. Struct., 2019, 42(1): 239-255.
[41] 杜志钢,魏昕,杨宇辉,等. 42CrMo 钢超声滚压残余应力及等效塑性应变研究[J]. 塑性工程学报, 2023, 30: 141-149. DU Zhigang, WEI Xin, YANG Yuhui, et al. Study on residual stress and equivalent plastic strain in ultrasonic rolling of 42CrMo steel[J]. Journal of Plasticity Engineering, 2023, 30: 141-149.
[42] MADENCI E , OTERKUS S. Ordinary state-based peridynamics for plastic deformation according to von-Mises yield criteria with isotropic hardening[J]. Journal of the Mechanics and Physics of Solids, 2016, 86: 192-219.
[43] SIMO J C, HUGHES T J. Computational inelasticity[M]. New York: Springer Science & Business Media, 2006.
[44] PEI X, RAVI S K, DONG P, et al. A multi-axial vibration fatigue evaluation procedure for welded structures in frequency domain[J]. Mechanical Systems and Signal Processing, 2022, 167: 108516.
[45] KIM M. A structural strain method for low-cycle fatigue evaluation of welded components[J]. International Journal of Pressure Vessels and Piping, 2014, 119: 39-51.
[46] MOSER S, VORMWALD M. Structural strain approach to assess thermo-mechanical fatigue of thin-walled welded joints[J]. International Journal of Fatigue, 2020, 139: 105722.
[47] DONG Y, GARBATOV Y, SOARES C G. Improved effective notch strain approach for fatigue reliability assessment of load-carrying fillet welded cruciform joints in low and high cycle fatigue[J]. Marine Structures, 2021, 75: 102849.
[48] GUO W , WANG C , ROSE L. The influence of cross-sectional thickness on fatigue crack growth[J]. Fatigue Fract. Eng. Mater. Struct., 1999, 22(5): 437-444.
[49] LÜ S, XIA C, LIU C, et al. Fatigue equation for asphalt mixture under low temperature and low loading frequency conditions[J]. Construction and Building Materials, 2019, 211: 1085-1093.
[50] KYUBA H, DONG P. Equilibrium-equivalent structural stress approach to fatigue analysis of a rectangular hollow section joint[J]. International Journal of Fatigue, 2005, 27(1): 85-94.
[51] DONG P, HONG J K, DE JESUS A M. Analysis of recent fatigue data using the structural stress procedure in ASME Div 2 rewrite[J]. Journal of Pressure Vessel Technology, 2007, 129: 355-362.
[52] DONG P, HONG J. A robust structural stress parameter for evaluation of multiaxial fatigue of weldments[J]. Journal of ASTM International, 2006, 3(7): 1-17.
[53] DONG P, HONG J, CAO Z. Stresses and stress intensities at notches: “anomalous crack growth” revisited[J]. International Journal of Fatigue, 2003, 25(9-11): 811-825.
[54] MURAKAMI Y, TAKAGI T, WADA K, et al. Essential structure of SN curve: Prediction of fatigue life and fatigue limit of defective materials and nature of scatter[J]. International Journal of Fatigue, 2021, 146: 106138.
[55] INSTITUTE W. Fatigue performance of welded high strength steels: a compendium of reports from a sponsored research programme[M]. Cambridge: Welding Institute, 1974.
[56] PEI X, LI X, ZHAO S, et al. Low cycle fatigue evaluation of welded structures with arbitrary stress-strain curve considering stress triaxiality effect[J]. International Journal of Fatigue, 2022, 162: 106969.
[57] XING S, DONG P, THRESTHA A. Analysis of fatigue failure mode transition in load-carrying fillet-welded connections[J]. Marine Structures, 2016, 46: 102-126.
[58] XING S, PEI X, MEI J, et al. Weld toe versus root fatigue failure mode and governing parameters : A study of aluminum alloy load-carrying fillet joints[J]. Marine Structures, 2023, 88: 103344.
[59] XING S, DONG P. Fatigue of titanium weldments: SN testing and analysis for data transferability among different joint types[J]. Marine Structures, 2017, 53: 1-19.
[60] KARAKAŞ Ö. Application of Neuber’s effective stress method for the evaluation of the fatigue behaviour of magnesium welds[J]. International Journal of Fatigue, 2017, 101: 115-126.
[61] CORIGLIANO P, CRUPI V, PEI X, et al. DIC-based structural strain approach for low-cycle fatigue assessment of AA 5083 welded joints[J]. Theoretical and Applied Fracture Mechanics, 2021, 116: 103090.
[62] HINNANT C, PAULIN T. Experimental evaluation of the markl fatigue methods and ASME piping stress intensification factors[C]//ASME Pressure Vessels and Piping Conference, 2008, 48241: 97-113
[63] WANG P, PEI X, DONG P, et al. Analysis of weld root fatigue cracking in load-carrying high-strength aluminum alloy cruciform joints[J]. International Journal of Fatigue, 2020, 139: 105735.
[64] CORIGLIANO P , CRUPI V , FRICKE W , et al. Experimental and numerical analysis of fillet-welded joints under low-cycle fatigue loading by means of full-field techniques[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2015, 229(7): 1327-1338.
[65] SCAVUZZO R, SRIVATSAN T, LAM P. Report 1: Fatigue of butt-welded pipe[J]. WRC Bulletin, 1998: 1-56.
[66] ASME Boiler and Pressure Vessel Code , Rules for construction of pressure vessels[S]. New York: ASME, 2019.
[67] British Standard, Guide to fatigue design and assessment of steel products[S]. London: BSI Standards Publication, 2014.
[68] HOBBACHER A. Recommendations for fatigue design of welded joints and components[M]. Cham: Springer, 2016.
[69] PEI X, DONG P, KIM M H. A simplified structural strain method for low-cycle fatigue evaluation of girth-welded pipe components[J]. International Journal of Fatigue, 2020, 139: 105732.