考虑应力梯度影响的多轴缺口疲劳寿命预测
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摘要
给出了几种典型拉-扭加载路径在新定义主坐标系下的π平面投影路径,并基于π平面投影路径提出了一种新的多轴疲劳损伤参量;考虑材料多轴加载的非比例附加强化效应,提出了一种非比例附加强化系数的预测方法和非比例度的定义方法;进一步考虑缺口试样多轴加载下的拉-扭应力梯度分布,结合有限元弹性分析的结果,提出了一种考虑多轴效应的等效应力梯度因子,从而发展了一种新的考虑应力梯度影响的多轴缺口疲劳寿命预测模型,并选用GH4169合金650℃下的多轴缺口疲劳试验结果对所提出的寿命模型进行验证。结果表明:(1)所提出的多轴疲劳损伤参量有明确的物理意义,不仅适用于多轴疲劳,也适用于单轴疲劳;(2)所提出的等效应力梯度因子仅需通过弹性有限元分析确定,适合工程实际应用;(3)新的寿命预测模型对GH4169材料多轴缺口疲劳试验的寿命预测结果较好,基本位于2倍分散带以内。
The projection paths on theπ-plane under the newly defined principal coordinate system of several typical tension-torsion loading paths were given.A new multiaxial fatigue damage parameter was proposed based on the projection path on theπ-plane.With the non-proportional additional hardening effect being considered,aprediction method of the non-proportional cyclic hardening coefficient was proposed and a new non-proportionality description was defined.Furthermore,a multiaxial effective stress gradient factor was defined by combining the tension stress gradient and the torsion stress gradient of finite element elastic analysis,and a multiaxial notch fatigue life prediction model was developed based on the multiaxial stress gradient effect.The multiaxial notch fatigue test results of GH4165 alloy at650℃ were used to verify the proposed model.On the basis of analytical study,conclusions can be drawn as follow:(1)the proposed multiaxial fatigue damage parameter is suitable for multiaxial fatigue and uniaxial fatigue with a clearly physical meaning;(2)the equivalentstress gradient factor can be determined only by elastic finite element analysis,which is suitable for practical application;(3)the predicted multiaxial fatigue lives of GH4169 alloy using the proposed model agree better with the experimental results,which are almost within two-time scatter band of the test results.
The projection paths on theπ-plane under the newly defined principal coordinate system of several typical tension-torsion loading paths were given.A new multiaxial fatigue damage parameter was proposed based on the projection path on theπ-plane.With the non-proportional additional hardening effect being considered,aprediction method of the non-proportional cyclic hardening coefficient was proposed and a new non-proportionality description was defined.Furthermore,a multiaxial effective stress gradient factor was defined by combining the tension stress gradient and the torsion stress gradient of finite element elastic analysis,and a multiaxial notch fatigue life prediction model was developed based on the multiaxial stress gradient effect.The multiaxial notch fatigue test results of GH4165 alloy at650℃ were used to verify the proposed model.On the basis of analytical study,conclusions can be drawn as follow:(1)the proposed multiaxial fatigue damage parameter is suitable for multiaxial fatigue and uniaxial fatigue with a clearly physical meaning;(2)the equivalentstress gradient factor can be determined only by elastic finite element analysis,which is suitable for practical application;(3)the predicted multiaxial fatigue lives of GH4169 alloy using the proposed model agree better with the experimental results,which are almost within two-time scatter band of the test results.
引文
[1]钟波,王延荣,魏大盛,等.基于应变路径非比例度的多轴疲劳寿命预测[J].航空动力学报,2016,31(2):317-322.ZHONG Bo,WANG Yanrong,WEI Dasheng,et al.Multiaxial fatigue life prediction based on non-proportionality of strain path[J].Journal of Aerospace Power,2016,31(2):317-322.(in Chinese)
[2] SUSMEL L.Multiaxial notch fatigue[M].Cambridge,UK:Woodhead Publishing Limited,2009.
[3] SAKANE M,ZHANG S,KIM T.Notch effect on multiaxial low cycle fatigue[J].International Journal of Fatigue,2011,33(8):959-968.
[4] FATEMI A,SHAMSAEI N.Multiaxial fatigue:an overview and some approximation models for life estimation[J].International Journal of Fatigue,2011,33(8):948-958.
[5] GATES N,FATEMI A.Notched fatigue behavior and stress analysis under multiaxial states of stress[J].International Journal of Fatigue,2014,67:2-14.
[6] FATEMI A,SOCIE D F.A critical plane approach to multiaxial fatigue damage including out-of-phase loading[J].Fatigue&Fracture of Engineering Materials&Structures,1988,11(3):149-165.
[7] ITOH T,YANG T.Material dependence of multiaxial low cycle fatigue lives under non-proportional loading[J].International Journal of Fatigue,2011,33(8):1025-1031.
[8] WU Z R,HU X T,SONG Y D.Multiaxial fatigue life prediction for titanium alloy TC4under proportional and nonproportional loading[J].International Journal of Fatigue,2014,59:170-175.
[9] SHAMSAEI N,MCKELVEY S A.Multiaxial life predictions in absence of any fatigue properties[J].International Journal of Fatigue,2014,67:62-72.
[10] BROWN M W,MILLER K J.Biaxial cyclic deformation behaviour of steels[J].Fatigue&Fracture of Engineering Materials&Structures,1979,1(1):93-106.
[11] KANDIL F A,BROWN M W,MILLER K J.Biaxial lowcycle fatigue fracture of 316stainless steel at elevated temperatures[M].London:The Metals Society,1982.
[12] FATEMI A,SOCIE D F.A critical plane approach to multiaxial fatigue damage including out-of-phase loading[J].Fatigue&Fracture of Engineering Materials&Structures,1988,11(3):149-165.
[13] WANG C,BROWN M.A path-independent parameter for fatigue under proportional and non-proportional loading[J].Fatigue&Fracture of Engineering Materials&Structures,1993,16(12):1285-1297.
[14]尚德广,姚卫星.基于临界面法的多轴疲劳损伤参量的研究[J].航空学报,1999,20(4):295-298.SHANG Deguang,YAO Weixing.Study on multiaxial fatigue damage parameters based on the critical plane approach[J].Acta Aeronautica et Astronautica Sinica,1999,20(4):295-298.(in Chinese)
[15] SHANG D G,WANG D J,YAO W X.A simple approach to the description of multiaxial cyclic stress-strain relationship[J].International Journal of Fatigue,2000,22(3):251-256.
[16] JIANG Y,HERTEL O,VORMWALD M.An experimental evaluation of three critical plane multiaxial fatigue criteria[J].International Journal of Fatigue,2007,29(8):1490-1502.
[17] SHANG D G,SUN G Q,DENG J,et al.Multiaxial fatigue damage parameter and life prediction for medium-carbon steel based on the critical plane approach[J].International Journal of Fatigue,2007,29(12):2200-2207.
[18] LI J,ZHANG Z P,SUN Q,et al.A new multiaxial fatigue damage model for various metallic materials under the combination of tension and torsion loadings[J].International Journal of Fatigue,2009,31(4):776-781.
[19] SUN G Q,SHANG D G,BAO M.Multiaxial fatigue damage parameter and life prediction under low cycle loading for GH4169alloy and other structural materials[J].International Journal of Fatigue,2010,32(7):1108-1115.
[20] LI J,LI C W,QIAO Y J,et al.Fatigue life prediction for some metallic materials under constant amplitude multiaxial loading[J].International Journal of Fatigue,2014,68:10-23.
[21] CASTRO F,JIANG Y.Fatigue life and early cracking predictions of extruded AZ31Bmagnesium alloy using critical plane approaches[J].International Journal of Fatigue,2016,88:236-246.
[22] GATES N R,FATEMI A.On the consideration of normal and shear stress interaction in multiaxial fatigue damage analysis[J].International Journal of Fatigue,2017,100:322-336.
[23] FATEMI A,MOLAEI R,SHARIFIMEHR S,et al.Multiaxial fatigue behavior of wrought and additive manufactured Ti-6Al-4Vincluding surface finish effect[J].International Journal of Fatigue,2017,100:347-366.
[24] GARUD Y.A new approach to the evaluation of fatigue under multiaxial loadings[J].Journal of Engineering Materials and Technology,1981,103(2):118-125.
[25] ELLYIN F,KUJAWSKI D.Plastic strain energy in fatigue failure[J].Journal of Pressure Vessel Technology,1984,106(4):342-347.
[26] ELLYIN F,GOLOS K.Multiaxial fatigue damage criterion[J].Journal of Engineering Materials and Technology,1988,110(1):63-68.
[27] LIU K,WANG J.An energy method for predicting fatigue life,crack orientation,and crack growth under multiaxial loading conditions[J].International Journal of Fatigue,2001,23:129-134.
[28] KANAZAWA K,MILLER K,BROWN M.Cyclic deformation of 1%Cr-Mo-V steel under out-of-phase loads[J].Fatigue&Fracture of Engineering Materials&Structures,1979,2(2):217-228.
[29] ITOH T,SAKANE M,SOCIE D F,et al.Nonproportional low cycle fatigue criterion for type 304stainless steel[J].Journal of Engineering Materials and Technology,1995,117(3):285-292.
[30]肖林,白菊丽.Zr-4合金双轴疲劳行为及其微观变形机理Ⅰ:双轴疲劳变形行为[J].金属学报,2000,36(9):913-918.XIAO Lin,BAI Juli.Biaxial fatigue behavior and microscopic deformation mechanism of Zircaloy-4Ⅰ:biaxial fatigue deformation behavior of Zircaloy-4[J].Acta Metallurgica Sinica,2000,36(9):913-918.(in Chinese)
[31]于良,白菊丽,肖林.Zr-4合金双轴加载中的非比例附加软化与附加强化[J].西安交通大学学报,2004,38(3):299-302.YU Liang,BAI Juli,XIAO Lin.Additional softening and strengthening behavior of hydrided Zr-4under biaxial outof-phase loading[J].Journal of Xi'an Jiaotong University,2004,38(3):299-302.(in Chinese)
[32]何国求,陈成澍,高庆,等.基于微结构分析定义应变路径非比例度[J].金属学报,2003,39(7):715-720.HE Guoqiu,CHEN Chengshu,GAO Qing,et al.Definition of non-proportionality of strain path based on microstructures analysis[J].Acta Metallurgica Sinica,2003,39(7):715-720.(in Chinese)
[33] KANAZAWA K,MILLER K J,BROWN M W.Cyclic deformation of 1%Cr-Mo-V steel under out of phase loads[J].Fatigue&Fracture of Engineering Materials&Structures,1979,2(3):217-228.
[34] KIDA S,ITOH T,SAKANE M,et al.Dislocation structure and non-proportional hardening of type 304stainless steel[J].Fatigue&Fracture of Engineering Materials&Structures,1997,20(10):1375-1386.
[35] BORODII M V,STRIZHALO V A.Analysis of the experimental data on a low cycle fatigue under nonproportional straining[J].International Journal of Fatigue,2000,22(4):275-282.
[36] LIU Y,MAHADEVAN S.Strain-based multiaxial fatigue damage modelling[J].Fatigue&Fracture of Engineering Materials&Structures,2005,28(12):1177-1189.
[37] WU M,ITOH T,SHIMIZU Y,et al.Low cycle fatigue life of Ti-6Al-4Valloy under non-proportional loading[J].International Journal of Fatigue,2012,44:14-20.
[38] MEGGIOLARO M A,CASTRO J T P D.Prediction of non-proportionality factors of multiaxial histories using the moment of inertia method[J].International Journal of Fatigue,2014,61:151-159.
[39] BEES M R,PATTISON S J,FOX N,et al.The non-proportional behaviour of a nickel-based superalloy at room temperature,and characterisation of the additional hardening response by a modified cyclic hardening curve[J].International Journal of Fatigue,2015,67(10):134-141.
[40] BABAEI S,GHASEMI-GHALEBAHMAN A.Damagebased modification for fatigue life prediction under nonproportional loadings[J].International Journal of Fatigue,2015,77:86-94.
[41] LI B C,JIANG C,HAN X,et al.A new approach of fatigue life prediction for metallic materials under multiaxial loading[J].International Journal of Fatigue,2015,78:1-10.
[42] LUU D H,MAITOURNAM M H,NGUYEN Q S.Formulation of gradient multiaxial fatigue criteria[J].International Journal of Fatigue,2014,61:170-183.
[43] SHI L,WEI D S,WANG Y R,et al.An investigation of fretting fatigue in a circular arc dovetail assembly[J].International Journal of Fatigue,2016,82:226-237.
[44] GATES N,FATEMI A.Notch deformation and stress gradient effects in multiaxial fatigue[J].Theoretical&Applied Fracture Mechanics,2016,84:3-25.
[45] ZHONG B,WANG Y R,WEI D S,et al.A new life prediction model for multiaxial fatigue under proportional and non-proportional loading paths based on pi-plane projection[J].International Journal of Fatigue,2017,102:241-251.
[46] BORODII M V,SHUKAEV S M.Additional cyclic strain hardening and its relation to material structure,mechanical characteristics,and lifetime[J].International Journal of Fatigue,2007,29(6):1184-91.
[47]姜潮,邓群,李博川.考虑非比例附加损伤的多轴低周疲劳寿命模型[J].力学学报,2015,47(4):634-641.JIANG Chao,DENG Qun,LI Bochuan.A new multiaxial fatigue life prediction model based on the nonproportional additional damage)[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(4):634-641.(in Chinese)
[48] SHAMSAEI N,FATEMI A.Effect of microstructure and hardness on non-proportional cyclic hardening coefficient and predictions[J].Materials Science and Engineering:A,2010,527(12):3015-3024.
[49]孙国芹.高温多轴疲劳行为及寿命预测研究[D].北京:北京工业大学,2009.SUN Guoqin.Rearch on multiaxial fatigue behavior and life prediction at high temperature[D].Beijing:Beijing University of Technology.(in Chinese)
[50]王延荣,李宏新,袁善虎,等.考虑应力梯度的缺口疲劳寿命预测方法[J].航空动力学报,2013,28(6):1208-1214.WANG Yanrong,LI Hongxin,YUAN Shanhu,et al.Method for notched fatigue life prediction with stress gradient[J].Journal of Aerospace Power,2013,28(6):1208-1214.(in Chinese)
[2] SUSMEL L.Multiaxial notch fatigue[M].Cambridge,UK:Woodhead Publishing Limited,2009.
[3] SAKANE M,ZHANG S,KIM T.Notch effect on multiaxial low cycle fatigue[J].International Journal of Fatigue,2011,33(8):959-968.
[4] FATEMI A,SHAMSAEI N.Multiaxial fatigue:an overview and some approximation models for life estimation[J].International Journal of Fatigue,2011,33(8):948-958.
[5] GATES N,FATEMI A.Notched fatigue behavior and stress analysis under multiaxial states of stress[J].International Journal of Fatigue,2014,67:2-14.
[6] FATEMI A,SOCIE D F.A critical plane approach to multiaxial fatigue damage including out-of-phase loading[J].Fatigue&Fracture of Engineering Materials&Structures,1988,11(3):149-165.
[7] ITOH T,YANG T.Material dependence of multiaxial low cycle fatigue lives under non-proportional loading[J].International Journal of Fatigue,2011,33(8):1025-1031.
[8] WU Z R,HU X T,SONG Y D.Multiaxial fatigue life prediction for titanium alloy TC4under proportional and nonproportional loading[J].International Journal of Fatigue,2014,59:170-175.
[9] SHAMSAEI N,MCKELVEY S A.Multiaxial life predictions in absence of any fatigue properties[J].International Journal of Fatigue,2014,67:62-72.
[10] BROWN M W,MILLER K J.Biaxial cyclic deformation behaviour of steels[J].Fatigue&Fracture of Engineering Materials&Structures,1979,1(1):93-106.
[11] KANDIL F A,BROWN M W,MILLER K J.Biaxial lowcycle fatigue fracture of 316stainless steel at elevated temperatures[M].London:The Metals Society,1982.
[12] FATEMI A,SOCIE D F.A critical plane approach to multiaxial fatigue damage including out-of-phase loading[J].Fatigue&Fracture of Engineering Materials&Structures,1988,11(3):149-165.
[13] WANG C,BROWN M.A path-independent parameter for fatigue under proportional and non-proportional loading[J].Fatigue&Fracture of Engineering Materials&Structures,1993,16(12):1285-1297.
[14]尚德广,姚卫星.基于临界面法的多轴疲劳损伤参量的研究[J].航空学报,1999,20(4):295-298.SHANG Deguang,YAO Weixing.Study on multiaxial fatigue damage parameters based on the critical plane approach[J].Acta Aeronautica et Astronautica Sinica,1999,20(4):295-298.(in Chinese)
[15] SHANG D G,WANG D J,YAO W X.A simple approach to the description of multiaxial cyclic stress-strain relationship[J].International Journal of Fatigue,2000,22(3):251-256.
[16] JIANG Y,HERTEL O,VORMWALD M.An experimental evaluation of three critical plane multiaxial fatigue criteria[J].International Journal of Fatigue,2007,29(8):1490-1502.
[17] SHANG D G,SUN G Q,DENG J,et al.Multiaxial fatigue damage parameter and life prediction for medium-carbon steel based on the critical plane approach[J].International Journal of Fatigue,2007,29(12):2200-2207.
[18] LI J,ZHANG Z P,SUN Q,et al.A new multiaxial fatigue damage model for various metallic materials under the combination of tension and torsion loadings[J].International Journal of Fatigue,2009,31(4):776-781.
[19] SUN G Q,SHANG D G,BAO M.Multiaxial fatigue damage parameter and life prediction under low cycle loading for GH4169alloy and other structural materials[J].International Journal of Fatigue,2010,32(7):1108-1115.
[20] LI J,LI C W,QIAO Y J,et al.Fatigue life prediction for some metallic materials under constant amplitude multiaxial loading[J].International Journal of Fatigue,2014,68:10-23.
[21] CASTRO F,JIANG Y.Fatigue life and early cracking predictions of extruded AZ31Bmagnesium alloy using critical plane approaches[J].International Journal of Fatigue,2016,88:236-246.
[22] GATES N R,FATEMI A.On the consideration of normal and shear stress interaction in multiaxial fatigue damage analysis[J].International Journal of Fatigue,2017,100:322-336.
[23] FATEMI A,MOLAEI R,SHARIFIMEHR S,et al.Multiaxial fatigue behavior of wrought and additive manufactured Ti-6Al-4Vincluding surface finish effect[J].International Journal of Fatigue,2017,100:347-366.
[24] GARUD Y.A new approach to the evaluation of fatigue under multiaxial loadings[J].Journal of Engineering Materials and Technology,1981,103(2):118-125.
[25] ELLYIN F,KUJAWSKI D.Plastic strain energy in fatigue failure[J].Journal of Pressure Vessel Technology,1984,106(4):342-347.
[26] ELLYIN F,GOLOS K.Multiaxial fatigue damage criterion[J].Journal of Engineering Materials and Technology,1988,110(1):63-68.
[27] LIU K,WANG J.An energy method for predicting fatigue life,crack orientation,and crack growth under multiaxial loading conditions[J].International Journal of Fatigue,2001,23:129-134.
[28] KANAZAWA K,MILLER K,BROWN M.Cyclic deformation of 1%Cr-Mo-V steel under out-of-phase loads[J].Fatigue&Fracture of Engineering Materials&Structures,1979,2(2):217-228.
[29] ITOH T,SAKANE M,SOCIE D F,et al.Nonproportional low cycle fatigue criterion for type 304stainless steel[J].Journal of Engineering Materials and Technology,1995,117(3):285-292.
[30]肖林,白菊丽.Zr-4合金双轴疲劳行为及其微观变形机理Ⅰ:双轴疲劳变形行为[J].金属学报,2000,36(9):913-918.XIAO Lin,BAI Juli.Biaxial fatigue behavior and microscopic deformation mechanism of Zircaloy-4Ⅰ:biaxial fatigue deformation behavior of Zircaloy-4[J].Acta Metallurgica Sinica,2000,36(9):913-918.(in Chinese)
[31]于良,白菊丽,肖林.Zr-4合金双轴加载中的非比例附加软化与附加强化[J].西安交通大学学报,2004,38(3):299-302.YU Liang,BAI Juli,XIAO Lin.Additional softening and strengthening behavior of hydrided Zr-4under biaxial outof-phase loading[J].Journal of Xi'an Jiaotong University,2004,38(3):299-302.(in Chinese)
[32]何国求,陈成澍,高庆,等.基于微结构分析定义应变路径非比例度[J].金属学报,2003,39(7):715-720.HE Guoqiu,CHEN Chengshu,GAO Qing,et al.Definition of non-proportionality of strain path based on microstructures analysis[J].Acta Metallurgica Sinica,2003,39(7):715-720.(in Chinese)
[33] KANAZAWA K,MILLER K J,BROWN M W.Cyclic deformation of 1%Cr-Mo-V steel under out of phase loads[J].Fatigue&Fracture of Engineering Materials&Structures,1979,2(3):217-228.
[34] KIDA S,ITOH T,SAKANE M,et al.Dislocation structure and non-proportional hardening of type 304stainless steel[J].Fatigue&Fracture of Engineering Materials&Structures,1997,20(10):1375-1386.
[35] BORODII M V,STRIZHALO V A.Analysis of the experimental data on a low cycle fatigue under nonproportional straining[J].International Journal of Fatigue,2000,22(4):275-282.
[36] LIU Y,MAHADEVAN S.Strain-based multiaxial fatigue damage modelling[J].Fatigue&Fracture of Engineering Materials&Structures,2005,28(12):1177-1189.
[37] WU M,ITOH T,SHIMIZU Y,et al.Low cycle fatigue life of Ti-6Al-4Valloy under non-proportional loading[J].International Journal of Fatigue,2012,44:14-20.
[38] MEGGIOLARO M A,CASTRO J T P D.Prediction of non-proportionality factors of multiaxial histories using the moment of inertia method[J].International Journal of Fatigue,2014,61:151-159.
[39] BEES M R,PATTISON S J,FOX N,et al.The non-proportional behaviour of a nickel-based superalloy at room temperature,and characterisation of the additional hardening response by a modified cyclic hardening curve[J].International Journal of Fatigue,2015,67(10):134-141.
[40] BABAEI S,GHASEMI-GHALEBAHMAN A.Damagebased modification for fatigue life prediction under nonproportional loadings[J].International Journal of Fatigue,2015,77:86-94.
[41] LI B C,JIANG C,HAN X,et al.A new approach of fatigue life prediction for metallic materials under multiaxial loading[J].International Journal of Fatigue,2015,78:1-10.
[42] LUU D H,MAITOURNAM M H,NGUYEN Q S.Formulation of gradient multiaxial fatigue criteria[J].International Journal of Fatigue,2014,61:170-183.
[43] SHI L,WEI D S,WANG Y R,et al.An investigation of fretting fatigue in a circular arc dovetail assembly[J].International Journal of Fatigue,2016,82:226-237.
[44] GATES N,FATEMI A.Notch deformation and stress gradient effects in multiaxial fatigue[J].Theoretical&Applied Fracture Mechanics,2016,84:3-25.
[45] ZHONG B,WANG Y R,WEI D S,et al.A new life prediction model for multiaxial fatigue under proportional and non-proportional loading paths based on pi-plane projection[J].International Journal of Fatigue,2017,102:241-251.
[46] BORODII M V,SHUKAEV S M.Additional cyclic strain hardening and its relation to material structure,mechanical characteristics,and lifetime[J].International Journal of Fatigue,2007,29(6):1184-91.
[47]姜潮,邓群,李博川.考虑非比例附加损伤的多轴低周疲劳寿命模型[J].力学学报,2015,47(4):634-641.JIANG Chao,DENG Qun,LI Bochuan.A new multiaxial fatigue life prediction model based on the nonproportional additional damage)[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(4):634-641.(in Chinese)
[48] SHAMSAEI N,FATEMI A.Effect of microstructure and hardness on non-proportional cyclic hardening coefficient and predictions[J].Materials Science and Engineering:A,2010,527(12):3015-3024.
[49]孙国芹.高温多轴疲劳行为及寿命预测研究[D].北京:北京工业大学,2009.SUN Guoqin.Rearch on multiaxial fatigue behavior and life prediction at high temperature[D].Beijing:Beijing University of Technology.(in Chinese)
[50]王延荣,李宏新,袁善虎,等.考虑应力梯度的缺口疲劳寿命预测方法[J].航空动力学报,2013,28(6):1208-1214.WANG Yanrong,LI Hongxin,YUAN Shanhu,et al.Method for notched fatigue life prediction with stress gradient[J].Journal of Aerospace Power,2013,28(6):1208-1214.(in Chinese)