金属材料多轴疲劳累积损伤理论研究进展
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摘要
考虑到多轴载荷下累积损伤规律与单轴情况的不同,将现有的金属材料多轴疲劳累积损伤理论分为以下四类:(a)不分方向的线性累积模型;(b)不分方向的非线性累积模型;(c)分方向的线性累积模型;(d)分方向的非线性累积模型。首先对以上4类多轴疲劳累积损伤理论分别进行了回顾,并着重介绍了近年来的最新进展。接着,收集整理了目前使用这些模型处理过的金属材料多轴变幅载荷试验,给出了这些试验的载荷谱型和数据点数,并统计了各模型对各试验的预测准确率。最后,根据各类模型的准确率对它们的适用范围、计算效果进行了对比分析与讨论。
Taking the differences between the accumulative damage rules under multiaxial and uniaxial variable fatigue loadings into account,the multiaxial fatigue accumulative damage theories for metal materials were divided into the following four categories:(a) the directional linear models;(b) the directional nonlinear models;(c) the non-directional linear models;(d)the non-directional nonlinear models.In this paper,the above four categories were reviewed respectively,and the latest advances were emphatically introduced.Besides,the multiaxial variable loading tests which are processed by the above models were collected.The types of variable loadings and the amount of data samples were listed,and the accuracy rate of each model was calculated.Finally,the applicable scopes and application effects of the above four kinds of multiaxial accumulative damage rules were compared and discussed according to the accuracy rate.
Taking the differences between the accumulative damage rules under multiaxial and uniaxial variable fatigue loadings into account,the multiaxial fatigue accumulative damage theories for metal materials were divided into the following four categories:(a) the directional linear models;(b) the directional nonlinear models;(c) the non-directional linear models;(d)the non-directional nonlinear models.In this paper,the above four categories were reviewed respectively,and the latest advances were emphatically introduced.Besides,the multiaxial variable loading tests which are processed by the above models were collected.The types of variable loadings and the amount of data samples were listed,and the accuracy rate of each model was calculated.Finally,the applicable scopes and application effects of the above four kinds of multiaxial accumulative damage rules were compared and discussed according to the accuracy rate.
引文
[1]姚卫星.结构疲劳寿命分析[M].北京:国防工业出版社,2002:35-36.YAO WeiXing.Fatigue life prediction of structures[M].Beijing:National Defence Industry Press,2002:35-36(In Chinese).
[2]Papuga J.A survey on evaluating the fatigue limit under multiaxial loading[J].International Journal of Fatigue.2011,33(2):153-165.
[3]王英玉,姚卫星.材料多轴疲劳破坏准则回顾[J].机械强度.2003,25(3):246-250.WANG YingYu,YAO weiXing.Revriew on the multiaxial fatigue criteria[J].Journal of Mechanical Strength.2003,25(3):246-250(In Chinese).
[4]孙国芹,尚德广,李承山.高温时间相关单多轴疲劳损伤模型[J].机械强度.2009,31(6):1004-1006.SUN GuoQin,SHANG DeGuang,LI ChengShan.Uniaxial and multiaxial fatigue damage models corresponding to time and high temperature[J].Journal of Mechanical Strength.2009,31(6):1004-1006(In Chinese).
[5]张巧丽,陈旭.多轴非比例载荷下低周疲劳寿命估算方法[J].机械强度.2004(01):76-79.ZHANG QiaoLi,CHEN Xu.Low circle fatigue life prediction methods under multiaxial non-proportional loading[J].Journal of Mechanical Strength.2004,26(01):76-79(In Chinese).
[6]Kim K S,Park J C.Shear strain based multiaxial fatigue parameters applied to variable amplitude loading[J].International Journal of Fatigue.1999,21(5):475-483.
[7]Wang C H,Brown M W.Life prediction techniques for variable amplitude multiaxial fatigue——Part 1:Theories[J].Journal of Engineering Materials and Technology.1996,118(3):367-370.
[8]Wang C H,Brown M W.Life prediction techniques for variable amplitude multiaxial fatigue——Part 2:Comparison With Experimental Results[J].Journal of Engineering Materials and Technology.1996,118(3):371-374.
[9]Bannantine J A,Socie D F.Fatigue under biaxial and multiaxial loading[M]//Kussmaul K,Mcdiarmid D,Socie DF.A variable amplitude multiaxial fatigue life prediction method.London:1991,35-51.
[10]Susmel L.Estimating fatigue lifetime of steel weldments locally damaged by variable amplitude multiaxial stress fields[J].International Journal of Fatigue.2010,32(7):1057-1080.
[11]Chen Hong,Shang Deguang.An on-line algorithm of fatigue damage evaluation under multiaxial random loading[J].International Journal of Fatigue.2011,33(2):250-254.
[12]Marciniak Z,Rozumek D,Macha E.Fatigue lives of 18G2A and10HNAP steels under variable amplitude and random nonproportional bending with torsion loading[J].International Journal of Fatigue.2008,30(5):800-813.
[13]Bonacuse P,Kalluri S.Sequenced axial and torsional cumulative fatigue:Low amplitude followed by high amplitude loading[M].//Carpinteri A,De Freitas M,Spagnoli A.Biaxial/Multiaxial Fatigue and Fracture.Amsterdam:Oxford,2003:31,165-182.
[14]金丹.多轴非规则载荷下低周疲劳寿命预测[D].天津:天津大学,2004:39-41.JIN Dan.Prediction of low circle fatigue life under multiaxial irregular loading[D].Tianjin:Tianjin University,2004:39-41.(In Chinese).
[15]Aid A,Bendouba M,Aminallah L,et al.An equivalent stress process for fatigue life estimation under multiaxial loadings based on a new nonlinear damage model[J].Materials Science and Engineering:A.2012,538:20-27.
[16]金丹,陈旭.多轴随机载荷下的疲劳寿命估算方法[J].力学进展.2006(1):65-74.JIN Dan,CHEN Xu.Fatigue life estimation method under multiaxial random loading[J].Journal of Advances in Mechanics.2006(1):65-74(In Chinese).
[17]朱正宇,何国球,张卫华,等.非比例载荷下多轴疲劳微观机理的研究进展[J].同济大学学报:自然科学版.2006,34(11):1510-1514.ZHU ZhenYu,HE GuoQiu,ZHANG WeiHua,et al.The research development of multiaxial fatigue micromechanism under nonproportional loading[J].Journal of Tongji University:Natural Science Edition.2006,34(11):1510-1514(In Chinese).
[18]尚德广.比例与非比例加载下多轴疲劳断口分析[J].机械强度.2006,28(03):392-396.SHANG DeGuang.Multiaxial fatigue fracture analysis under proportional and non-proportional loading[J].Journal of Mechanical Strength.2006,28(03):392-396(In Chinese).
[19]Sonsino C M,Kueppers M.Multiaxial fatigue of welded joints under constant and variable amplitude loadings[J].Fatigue&Fracture of Engineering Materials&Structures.2001,24(5):309-327.
[20]Susmel L,Tovo R.Estimating fatigue damage under variable amplitude multiaxial fatigue loading[J].Fatigue&Fracture of Engineering Materials&Structures.2011,34(12):1053-1077.
[21]Carpinteri A,Spagnoli A,Vantadori S.A multiaxial fatigue criterion for random loading[J].Fatigue&Fracture of Engineering Materials&Structures.2003,26(6):515-522.
[22]Carpinteri A,Spagnoli A,Vantadori S.Structural integrity assessment of metallic components under multiaxial fatigue:the C–S criterion and its evolution[J].Fatigue&Fracture of Engineering Materials&Structures.2013,36(9):870-883.
[23]Xia Tianxiang,Yao Weixing.Comparative research on the accumulative damage rules under multiaxial block loading spectrum for 2024-T4 aluminum alloy[J].International Journal of Fatigue.2013,48:257-265.
[24]Morrow D J.The effect of selected sub-cycle sequences in fatigue loading histories[M].Random fatigue life predictions.1986,43-60.
[25]金丹,陈旭,Kwang Sookim.304不锈钢两阶段载荷模式下的疲劳寿命[J].机械强度.2004(S1):146-149.JIN Dan,CHEN Xu,Kwang Sookim.Fatigue life under two-stage load pattern in 304 stainless steel[J].Journal of Mechanical Strength.2004(S1):146-149(In Chinese).
[26]王英玉.金属材料的多轴疲劳行为与寿命估算[D].南京:南京航空航天大学,2005:68-74.WANG YinYu.Multiaxial fatigue behavior and life estimation in metal materials[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2005:68-74(in Chinese).
[27]Chen X,Jin D,Kim K S.Fatigue damage of medium carbon steel under sequential application of axial and torsional loading[J].Fatigue&Fracture of Engineering Materials&Structures.2006,29(3):243-253.
[28]金丹,陈旭,金光洙.S45C钢轴向-扭转两阶段载荷下的疲劳寿命预测[J].天津大学学报.2005,38(7):569-572.JIN Dan,CHEN Xu,JIN GuangZu.Fatigue life prediction under axial-torsional two-stage loading in S45C[J].Journal of Tianjin University.2005,38(7):569-572(In Chinese).
[29]Hua C T,Socie D F.Fatigue damage in 1045 steel under variable amplitude biaxial loading[J].Fatigue&Fracture of Engineering Materials&Structures.1985,8(2):101-114.
[30]尚德广,王德俊,姚卫星.多轴非线性连续疲劳损伤累积模型的研究[J].固体力学学报.1999,20(4):325-330.SHANG DeGuang,WANG DeJun,YAO WeiXing.Research of multiaxial nonlinear continuum fatigue damage cumulative models[J].Journal of Solid Mechanics.1999,20(4):325-330(In Chinese).
[31]Lin H,Nayeb-Hashemi H,Berg C A.Cumulative damage behavior of anisotropic Al-6061-T6 as a function of axial-torsional loading mode sequence[J].Journal of Engineering Materials and Technology.1994,116(1):27-34.
[32]徐姣,尚德广,孙国芹,等.多轴变幅加载下GH4169合金疲劳寿命预测[J].北京工业大学学报.2012,38(10):1462-1466.XU Jiao,SHANG DeGuang,SUN GuoQin,et al.Fatigue life prediction in GH4169 alloy under multiaxial variable-amplitude loading[J].Journal of Beijing University of Technology.2012,38(10):1462-1466(In Chinese).
[33]徐姣,尚德广,陈宏.多轴块载加载下疲劳损伤累积方法研究[J].机械强度.2012(6):875-880.XU Jiao,SHANG DeGuang,CHEN Hong.Research of fatigue damage accumulation methods under multiaxial block-spectrum loading[J].Journal of Mechanical Strength.2012(6):875-880(In Chinese).
[34]Chen X,Jin D,Kim K S.A weight function-critical plane approach for low-cycle fatigue under variable amplitude multiaxial loading[J].Fatigue&Fracture of Engineering Materials&Structures.2006,29(4):331-339.
[35]孙国芹,尚德广,王冬.高温多轴变幅疲劳损伤累积[J].北京工业大学学报.2012,38(11):1629-1632.SUN GuoQin,SHANG DeGuang,WANG Dong.High-temperature multiaxial variable amplitude fatigue damage accumulation[J].Journal of Beijing University of Technology.2012,38(11):1629-1632(In Chinese).
[36]Mesmacque G,Garcia S,Amrouche A,et al.Sequential law in multiaxial fatigue,a new damage indicator[J].International Journal of Fatigue.2005,27(4):461-467.
[37]Aid A,Amrouche A,Bouiadjra B B,et al.Fatigue life prediction under variable loading based on a new damage model[J].Materials&Design;Design.2011,32(1):183-191.
[38]Garcia S,Amrouche A,Mesmacque G,et al.Fatigue damage accumulation of cold expanded hole in aluminum alloys subjected to block loading[J].International Journal of Fatigue.2005,27(10–12):1347-1353.
[39]Cristofori A,Susmel L,Tovo R.A stress invariant based criterion to estimate fatigue damage under multiaxial loading A stress invariant based criterion to estimate fatigue damage under multiaxial loading[J].International Journal of Fatigue.2008,30(9):1646-1658.
[40]Cristofori A,Benasciutti D,Tovo R.A stress invariant based spectral method to estimate fatigue life under multiaxial random loading[J].International Journal of Fatigue.2011,33(7):887-899.
[41]Lee B L,Kim K S,Nam K M.Fatigue analysis under variable amplitude loading using an energy parameter[J].International Journal of Fatigue.2003,25(7):621-631.
[42]Shamsaei N,Gladskyi M,Panasovskyi K,et al.Multiaxial fatigue of titanium including step loading and load path alteration and sequence effects[J].International Journal of Fatigue.2010,32(11):1862-1874.
[43]Zhang Chengcheng,Yao Weixing.An improved multiaxial highcycle fatigue criterion based on critical plane approach[J].Fatigue&Fracture of Engineering Materials&Structures.2011,34(5):337-344.
[44]Inoue T,Hoshide T,Yoshikawa Y,et al.A damage mechanics approach to crack initiation in polycrystalline copper under multiaxial low cycle fatigue[M].Mechanical Behaviour of Materials,Beijing:1988,651-658.
[2]Papuga J.A survey on evaluating the fatigue limit under multiaxial loading[J].International Journal of Fatigue.2011,33(2):153-165.
[3]王英玉,姚卫星.材料多轴疲劳破坏准则回顾[J].机械强度.2003,25(3):246-250.WANG YingYu,YAO weiXing.Revriew on the multiaxial fatigue criteria[J].Journal of Mechanical Strength.2003,25(3):246-250(In Chinese).
[4]孙国芹,尚德广,李承山.高温时间相关单多轴疲劳损伤模型[J].机械强度.2009,31(6):1004-1006.SUN GuoQin,SHANG DeGuang,LI ChengShan.Uniaxial and multiaxial fatigue damage models corresponding to time and high temperature[J].Journal of Mechanical Strength.2009,31(6):1004-1006(In Chinese).
[5]张巧丽,陈旭.多轴非比例载荷下低周疲劳寿命估算方法[J].机械强度.2004(01):76-79.ZHANG QiaoLi,CHEN Xu.Low circle fatigue life prediction methods under multiaxial non-proportional loading[J].Journal of Mechanical Strength.2004,26(01):76-79(In Chinese).
[6]Kim K S,Park J C.Shear strain based multiaxial fatigue parameters applied to variable amplitude loading[J].International Journal of Fatigue.1999,21(5):475-483.
[7]Wang C H,Brown M W.Life prediction techniques for variable amplitude multiaxial fatigue——Part 1:Theories[J].Journal of Engineering Materials and Technology.1996,118(3):367-370.
[8]Wang C H,Brown M W.Life prediction techniques for variable amplitude multiaxial fatigue——Part 2:Comparison With Experimental Results[J].Journal of Engineering Materials and Technology.1996,118(3):371-374.
[9]Bannantine J A,Socie D F.Fatigue under biaxial and multiaxial loading[M]//Kussmaul K,Mcdiarmid D,Socie DF.A variable amplitude multiaxial fatigue life prediction method.London:1991,35-51.
[10]Susmel L.Estimating fatigue lifetime of steel weldments locally damaged by variable amplitude multiaxial stress fields[J].International Journal of Fatigue.2010,32(7):1057-1080.
[11]Chen Hong,Shang Deguang.An on-line algorithm of fatigue damage evaluation under multiaxial random loading[J].International Journal of Fatigue.2011,33(2):250-254.
[12]Marciniak Z,Rozumek D,Macha E.Fatigue lives of 18G2A and10HNAP steels under variable amplitude and random nonproportional bending with torsion loading[J].International Journal of Fatigue.2008,30(5):800-813.
[13]Bonacuse P,Kalluri S.Sequenced axial and torsional cumulative fatigue:Low amplitude followed by high amplitude loading[M].//Carpinteri A,De Freitas M,Spagnoli A.Biaxial/Multiaxial Fatigue and Fracture.Amsterdam:Oxford,2003:31,165-182.
[14]金丹.多轴非规则载荷下低周疲劳寿命预测[D].天津:天津大学,2004:39-41.JIN Dan.Prediction of low circle fatigue life under multiaxial irregular loading[D].Tianjin:Tianjin University,2004:39-41.(In Chinese).
[15]Aid A,Bendouba M,Aminallah L,et al.An equivalent stress process for fatigue life estimation under multiaxial loadings based on a new nonlinear damage model[J].Materials Science and Engineering:A.2012,538:20-27.
[16]金丹,陈旭.多轴随机载荷下的疲劳寿命估算方法[J].力学进展.2006(1):65-74.JIN Dan,CHEN Xu.Fatigue life estimation method under multiaxial random loading[J].Journal of Advances in Mechanics.2006(1):65-74(In Chinese).
[17]朱正宇,何国球,张卫华,等.非比例载荷下多轴疲劳微观机理的研究进展[J].同济大学学报:自然科学版.2006,34(11):1510-1514.ZHU ZhenYu,HE GuoQiu,ZHANG WeiHua,et al.The research development of multiaxial fatigue micromechanism under nonproportional loading[J].Journal of Tongji University:Natural Science Edition.2006,34(11):1510-1514(In Chinese).
[18]尚德广.比例与非比例加载下多轴疲劳断口分析[J].机械强度.2006,28(03):392-396.SHANG DeGuang.Multiaxial fatigue fracture analysis under proportional and non-proportional loading[J].Journal of Mechanical Strength.2006,28(03):392-396(In Chinese).
[19]Sonsino C M,Kueppers M.Multiaxial fatigue of welded joints under constant and variable amplitude loadings[J].Fatigue&Fracture of Engineering Materials&Structures.2001,24(5):309-327.
[20]Susmel L,Tovo R.Estimating fatigue damage under variable amplitude multiaxial fatigue loading[J].Fatigue&Fracture of Engineering Materials&Structures.2011,34(12):1053-1077.
[21]Carpinteri A,Spagnoli A,Vantadori S.A multiaxial fatigue criterion for random loading[J].Fatigue&Fracture of Engineering Materials&Structures.2003,26(6):515-522.
[22]Carpinteri A,Spagnoli A,Vantadori S.Structural integrity assessment of metallic components under multiaxial fatigue:the C–S criterion and its evolution[J].Fatigue&Fracture of Engineering Materials&Structures.2013,36(9):870-883.
[23]Xia Tianxiang,Yao Weixing.Comparative research on the accumulative damage rules under multiaxial block loading spectrum for 2024-T4 aluminum alloy[J].International Journal of Fatigue.2013,48:257-265.
[24]Morrow D J.The effect of selected sub-cycle sequences in fatigue loading histories[M].Random fatigue life predictions.1986,43-60.
[25]金丹,陈旭,Kwang Sookim.304不锈钢两阶段载荷模式下的疲劳寿命[J].机械强度.2004(S1):146-149.JIN Dan,CHEN Xu,Kwang Sookim.Fatigue life under two-stage load pattern in 304 stainless steel[J].Journal of Mechanical Strength.2004(S1):146-149(In Chinese).
[26]王英玉.金属材料的多轴疲劳行为与寿命估算[D].南京:南京航空航天大学,2005:68-74.WANG YinYu.Multiaxial fatigue behavior and life estimation in metal materials[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2005:68-74(in Chinese).
[27]Chen X,Jin D,Kim K S.Fatigue damage of medium carbon steel under sequential application of axial and torsional loading[J].Fatigue&Fracture of Engineering Materials&Structures.2006,29(3):243-253.
[28]金丹,陈旭,金光洙.S45C钢轴向-扭转两阶段载荷下的疲劳寿命预测[J].天津大学学报.2005,38(7):569-572.JIN Dan,CHEN Xu,JIN GuangZu.Fatigue life prediction under axial-torsional two-stage loading in S45C[J].Journal of Tianjin University.2005,38(7):569-572(In Chinese).
[29]Hua C T,Socie D F.Fatigue damage in 1045 steel under variable amplitude biaxial loading[J].Fatigue&Fracture of Engineering Materials&Structures.1985,8(2):101-114.
[30]尚德广,王德俊,姚卫星.多轴非线性连续疲劳损伤累积模型的研究[J].固体力学学报.1999,20(4):325-330.SHANG DeGuang,WANG DeJun,YAO WeiXing.Research of multiaxial nonlinear continuum fatigue damage cumulative models[J].Journal of Solid Mechanics.1999,20(4):325-330(In Chinese).
[31]Lin H,Nayeb-Hashemi H,Berg C A.Cumulative damage behavior of anisotropic Al-6061-T6 as a function of axial-torsional loading mode sequence[J].Journal of Engineering Materials and Technology.1994,116(1):27-34.
[32]徐姣,尚德广,孙国芹,等.多轴变幅加载下GH4169合金疲劳寿命预测[J].北京工业大学学报.2012,38(10):1462-1466.XU Jiao,SHANG DeGuang,SUN GuoQin,et al.Fatigue life prediction in GH4169 alloy under multiaxial variable-amplitude loading[J].Journal of Beijing University of Technology.2012,38(10):1462-1466(In Chinese).
[33]徐姣,尚德广,陈宏.多轴块载加载下疲劳损伤累积方法研究[J].机械强度.2012(6):875-880.XU Jiao,SHANG DeGuang,CHEN Hong.Research of fatigue damage accumulation methods under multiaxial block-spectrum loading[J].Journal of Mechanical Strength.2012(6):875-880(In Chinese).
[34]Chen X,Jin D,Kim K S.A weight function-critical plane approach for low-cycle fatigue under variable amplitude multiaxial loading[J].Fatigue&Fracture of Engineering Materials&Structures.2006,29(4):331-339.
[35]孙国芹,尚德广,王冬.高温多轴变幅疲劳损伤累积[J].北京工业大学学报.2012,38(11):1629-1632.SUN GuoQin,SHANG DeGuang,WANG Dong.High-temperature multiaxial variable amplitude fatigue damage accumulation[J].Journal of Beijing University of Technology.2012,38(11):1629-1632(In Chinese).
[36]Mesmacque G,Garcia S,Amrouche A,et al.Sequential law in multiaxial fatigue,a new damage indicator[J].International Journal of Fatigue.2005,27(4):461-467.
[37]Aid A,Amrouche A,Bouiadjra B B,et al.Fatigue life prediction under variable loading based on a new damage model[J].Materials&Design;Design.2011,32(1):183-191.
[38]Garcia S,Amrouche A,Mesmacque G,et al.Fatigue damage accumulation of cold expanded hole in aluminum alloys subjected to block loading[J].International Journal of Fatigue.2005,27(10–12):1347-1353.
[39]Cristofori A,Susmel L,Tovo R.A stress invariant based criterion to estimate fatigue damage under multiaxial loading A stress invariant based criterion to estimate fatigue damage under multiaxial loading[J].International Journal of Fatigue.2008,30(9):1646-1658.
[40]Cristofori A,Benasciutti D,Tovo R.A stress invariant based spectral method to estimate fatigue life under multiaxial random loading[J].International Journal of Fatigue.2011,33(7):887-899.
[41]Lee B L,Kim K S,Nam K M.Fatigue analysis under variable amplitude loading using an energy parameter[J].International Journal of Fatigue.2003,25(7):621-631.
[42]Shamsaei N,Gladskyi M,Panasovskyi K,et al.Multiaxial fatigue of titanium including step loading and load path alteration and sequence effects[J].International Journal of Fatigue.2010,32(11):1862-1874.
[43]Zhang Chengcheng,Yao Weixing.An improved multiaxial highcycle fatigue criterion based on critical plane approach[J].Fatigue&Fracture of Engineering Materials&Structures.2011,34(5):337-344.
[44]Inoue T,Hoshide T,Yoshikawa Y,et al.A damage mechanics approach to crack initiation in polycrystalline copper under multiaxial low cycle fatigue[M].Mechanical Behaviour of Materials,Beijing:1988,651-658.