金属材料的强度与应力–应变关系的球压入测试方法
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摘要
压入法获取材料单轴应力–应变关系和抗拉强度对服役结构完整性评价有重要的基础意义.假定材料均匀连续、各向同性、应力应变关系符合Hollomon律,基于能量等效假定,即代表性体积单元(representative volume element, RVE)的von Mises等效和有效变形域内能量中值等效假定,本文提出了关联材料载荷、深度、球压头直径和Hollomon律的四参数半解析球压入(semi-analytical spherical indentation, SSI)模型.通过球压入载荷–深度试验关系获得材料的应力–应变关系和抗拉强度.考虑压入过程中的损伤效应,针对金属材料提出了用于球压入测试的材料弹性模量修正模型.对11种延性金属材料完成了球压入试验,采用本文提出的球压入试验方法测到的弹性模量、应力–应变关系和抗拉强度与单轴拉伸试验结果吻合良好.
It is significant to obtain the uniaxial stress-strain relations and tensile strength of materials by indentation method for evaluating the integrity of structures in service. Based on energy equivalent assumptions, i.e., the Von Mises equivalence about a RVE(representative volume element) and the median energy equivalence in the effective deformation region, a semi-analytical spherical indentation(SSI) model is proposed to describe the relation among indented load, depth, the diameter of spherical indenter and Hollomon-law parameters if indented materials are uniform, continuous, isotropic and power-law hardening. The stress-strain relations and tensile strengths of the materials were obtained by the tested load-depth curves under spherical indenter loading. Considering the damage effect in the indentation process, a correction model for determining elastic modulus of the metallic materials due to the spherical indentationtests is proposed. For eleven kinds of tested ductile metallic materials with spherical indentation, the Young's modulus, stress-strain relations and tensile strength predicted by SSI model are in good agreement with the uniaxial tensile results.
It is significant to obtain the uniaxial stress-strain relations and tensile strength of materials by indentation method for evaluating the integrity of structures in service. Based on energy equivalent assumptions, i.e., the Von Mises equivalence about a RVE(representative volume element) and the median energy equivalence in the effective deformation region, a semi-analytical spherical indentation(SSI) model is proposed to describe the relation among indented load, depth, the diameter of spherical indenter and Hollomon-law parameters if indented materials are uniform, continuous, isotropic and power-law hardening. The stress-strain relations and tensile strengths of the materials were obtained by the tested load-depth curves under spherical indenter loading. Considering the damage effect in the indentation process, a correction model for determining elastic modulus of the metallic materials due to the spherical indentationtests is proposed. For eleven kinds of tested ductile metallic materials with spherical indentation, the Young's modulus, stress-strain relations and tensile strength predicted by SSI model are in good agreement with the uniaxial tensile results.
引文
1 Brinell JA.Way of determining the hardness of bodies and some applications of the same.Teknisk Tidskrift,1900,5:69
2 Rockwell HM,Rockwell SP.Hardness-tester.U.S.Patent 1294171.1919-02-11
3 Doerner MF,Nix WD.A method for interpreting the data from depth-sensing indentation instruments.Journal of Materials Research,1986,1(4):601-609
4 Oliver WC,Pharr GM.An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments.Journal of Materials Research,1992,7(6):1564-1583
5张泰华,郇勇,王秀兰.亚微米氮化钛膜的纳米压痕和划痕测定.力学学报,2003,35(4):498-502(Zhang Taihua,Xun Yong,Wang Xiulan.Nanoindentation and nanoscratch measurements on submicron tin coatings.Chinese Journal of Theoretical and Applied Mechanics,2003,35(4):498-502(in Chinese))
6 Hill R,Storakers B,Zdunek AB.A theoretical study of the Brinell hardness test//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.The Royal Society,1989,423(1865):301-330
7 Biwa S,Storakers B.An analysis of fully plastic Brinell indentation.Journal of the Mechanics and Physics of Solids,1995,43(8):1303-1333
8 Mesarovic SD,Fleck NA.Spherical indentation of elastic-plastic solids//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.The Royal Society,1999,455(1987):2707-2728
9 Lee H,Lee JH,Pharr GM.A numerical approach to spherical indentation techniques for material property evaluation.Journal of the Mechanics and Physics of Solids,2005,53(9):2037-2069
10冯元桢.连续介质力学初级教程.北京:清华大学出版社,2011:20-25(Feng Yuanzheng.A First Course in Continuum Mechanics.Beijing:Tsinghua University Press,2011:20-25(in Chinese))
11 Cheng YT,Cheng CM.Scaling relationships in conical indentation of elastic-perfectly plastic solids.International Journal of Solids and Structures,1999,36(8):1231-1243
12 Byun TS,Hong JH,Haggag FM,et al.Measurement of throughthe-thickness variations of mechanical properties in SA508 Gr.3pressure vessel steels using ball indentation test technique.International Journal of Pressure Vessels and Piping,1997,74(3):231-238
13 Ahn JH,Kwon D.Derivation of plastic stress-strain relationship from ball indentations:Examination of strain definition and pileup effect.Journal of Materials Research,2001,16(11):3170-3178
14伍声宝,徐彤,喻灿等.采用球压痕法测16MnR钢的拉伸性能.机械工程材料,2015,39(1):82-85(Wu Shengbao,Xu Tong,Yu Can,et al.Measuring tensile properties of 16MnR steel by ball indentation technology.Matreials for Mechanical Engineering,2015,39(1):82-85(in Chinese))
15苏成功,王威强,商显栋等.连续球压痕测定常用叶轮材料力学性能的研究.流体机械,2015,43(2):7-12(Su Chenggong,Wang Weiqiang,Shang Xiandong,et al.Research on the measurement of mechanical properties of common impeller materials through continuous ball indentation test.Fluid Machinery,2015,43(2):7-12(in Chinese))
16金桩,赵建平.微载荷连续球压痕法评价金属材料的屈服强度和应变硬化指数.机械工程材料,2018,42(1):72-77(Jin Zhuang,Zhao Jianping.Yield strength and strain hardening exponent of metal material evaluated by micro-load continuous ball indentation method.Matreials for Mechanical Engineering,2018,42(1):72-77(in Chinese))
17 Dao M,Chollacoop N,Van Vliet KJ,et al.Computational modeling of the forward and reverse problems in instrumented sharp indentation.Acta Materialia,2001,49(19):3899-3918
18 Cao YP,Lu J.A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve.Acta Materialia,2004,52(13):4023-4032
19 Collin JM,Mauvoisin G,Bartier O,et al.Experimental evaluation of the stress-strain curve by continuous indentation using different indenter shapes.Materials Science and Engineering:A,2009,501(1-2):140-145
20姜鹏,张泰华,杨荣等.基于球形压入法提取材料的塑性力学参数.力学学报,2009,41(5):730-738(Jiang Peng,Zhang Taihua,Yang Rong,et al.A new spherical indentation-based method to extract plastic material parameters.Chinese Journal of Theoretical and Applied Mechanics,2009,41(5):730-738(in Chinese))
21 Huber N,Tsakmakis C.Determination of constitutive properties fromspherical indentation data using neural networks.Part i:The case of pure kinematic hardening in plasticity laws.Journal of the Mechanics and Physics of Solids,1999,47(7):1569-1588
22 Tyulyukovskiy E,Huber N.Identification of viscoplastic material parameters from spherical indentation data:Part I.Neural networks.Journal of Materials Research,2006,21(3):664-676
23 Lee H,Lee JH,Pharr GM.A numerical approach to spherical indentation techniques for material property evaluation.Journal of the Mechanics and Physics of Solids,2005,53(9):2037-2069
24 Xu B,Chen X.Determining engineering stress-strain curve directly from the load-depth curve of spherical indentation test.Journal of Materials Research,2010,25(12):2297-2307
25 Chen H,Cai L.Unified elastoplastic model based on a strain energy equivalence principle.Applied Mathematical Modelling,2017,52:664-671
26 Chen H,Cai L.Theoretical model for predicting uniaxial stressstrain relation by dual conical indentation based on equivalent energy principle.Acta Materialia,2016,121:181-189
27 Chen H,Cai L.Unified ring-compression model for determining tensile properties of tubular materials.Materials Today Communications,2017,13:210-220
28赵康,鄢化彪,冯萧.基于能量法的矿柱稳定性分析.力学学报,2016,48(4):976-983(Zhao Kang,Yan Huabiao,Feng Xiao.Stability analysis of pillar based on energy law.Chinese Journal of Theoretical and Applied Mechanics,2016,48(4):976-983(in Chinese))
29张泰华.微/纳米力学测试技术及其应用.北京:机械工业出版社,2004:20-23(Zhang Taihua.Micro/nano Mechanical Testing Technology and Application.Beijing:China Machine Press,2004:20-23(in Chinese))
30章鹏,杜成斌,江守燕.比例边界有限元法求解裂纹面接触问题.力学学报,2017,49(6):1335-1347(Zhang Peng,Du Chengbin,Jiang Shouyan.Crack face contact problem analysis using the scaled boundary finite element method.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1335-1347(in Chinese))
31卢梦凯,张洪武,郑勇刚.应变局部化分析的嵌入强间断多尺度有限元法.力学学报,2017,49(3):649-658(Lu Mengkai,Zhang Hongwu,Zheng Yonggang.Embedded strong discontinuity model based multiscale finite element method for strain localization analysis.Chinese Journal of Theoretical and Applied Mechanics,2017,49(3):649-658(in Chinese))
32 Ammara HR,Haggag FM,Abdulaziz S,et al.Nondestructive measurements of flow properties of nanocrystalline Al-Cu-Ti alloy using Automated Ball Indentation(ABI)technique.Materials Science&Engineering A,2018,731:477-486
33 Tabor D.The Hardness of Metals.Oxford:Clarendon Press,1951
34 Xu B,Chen X.Determining engineering stress-strain curve directly from the load-depth curve of spherical indentation test.Journal of Materials Research,2010,25(12):2297-2307
35 Byun TS,Hong JH,Haggag FM,et al.Measurement of throughthe-thickness variations of mechanical properties in SA508 Gr.3pressure vessel steels using ball indentation test technique.International Journal of Pressure Vessels and Piping,1997,74(3):231-238
2 Rockwell HM,Rockwell SP.Hardness-tester.U.S.Patent 1294171.1919-02-11
3 Doerner MF,Nix WD.A method for interpreting the data from depth-sensing indentation instruments.Journal of Materials Research,1986,1(4):601-609
4 Oliver WC,Pharr GM.An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments.Journal of Materials Research,1992,7(6):1564-1583
5张泰华,郇勇,王秀兰.亚微米氮化钛膜的纳米压痕和划痕测定.力学学报,2003,35(4):498-502(Zhang Taihua,Xun Yong,Wang Xiulan.Nanoindentation and nanoscratch measurements on submicron tin coatings.Chinese Journal of Theoretical and Applied Mechanics,2003,35(4):498-502(in Chinese))
6 Hill R,Storakers B,Zdunek AB.A theoretical study of the Brinell hardness test//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.The Royal Society,1989,423(1865):301-330
7 Biwa S,Storakers B.An analysis of fully plastic Brinell indentation.Journal of the Mechanics and Physics of Solids,1995,43(8):1303-1333
8 Mesarovic SD,Fleck NA.Spherical indentation of elastic-plastic solids//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.The Royal Society,1999,455(1987):2707-2728
9 Lee H,Lee JH,Pharr GM.A numerical approach to spherical indentation techniques for material property evaluation.Journal of the Mechanics and Physics of Solids,2005,53(9):2037-2069
10冯元桢.连续介质力学初级教程.北京:清华大学出版社,2011:20-25(Feng Yuanzheng.A First Course in Continuum Mechanics.Beijing:Tsinghua University Press,2011:20-25(in Chinese))
11 Cheng YT,Cheng CM.Scaling relationships in conical indentation of elastic-perfectly plastic solids.International Journal of Solids and Structures,1999,36(8):1231-1243
12 Byun TS,Hong JH,Haggag FM,et al.Measurement of throughthe-thickness variations of mechanical properties in SA508 Gr.3pressure vessel steels using ball indentation test technique.International Journal of Pressure Vessels and Piping,1997,74(3):231-238
13 Ahn JH,Kwon D.Derivation of plastic stress-strain relationship from ball indentations:Examination of strain definition and pileup effect.Journal of Materials Research,2001,16(11):3170-3178
14伍声宝,徐彤,喻灿等.采用球压痕法测16MnR钢的拉伸性能.机械工程材料,2015,39(1):82-85(Wu Shengbao,Xu Tong,Yu Can,et al.Measuring tensile properties of 16MnR steel by ball indentation technology.Matreials for Mechanical Engineering,2015,39(1):82-85(in Chinese))
15苏成功,王威强,商显栋等.连续球压痕测定常用叶轮材料力学性能的研究.流体机械,2015,43(2):7-12(Su Chenggong,Wang Weiqiang,Shang Xiandong,et al.Research on the measurement of mechanical properties of common impeller materials through continuous ball indentation test.Fluid Machinery,2015,43(2):7-12(in Chinese))
16金桩,赵建平.微载荷连续球压痕法评价金属材料的屈服强度和应变硬化指数.机械工程材料,2018,42(1):72-77(Jin Zhuang,Zhao Jianping.Yield strength and strain hardening exponent of metal material evaluated by micro-load continuous ball indentation method.Matreials for Mechanical Engineering,2018,42(1):72-77(in Chinese))
17 Dao M,Chollacoop N,Van Vliet KJ,et al.Computational modeling of the forward and reverse problems in instrumented sharp indentation.Acta Materialia,2001,49(19):3899-3918
18 Cao YP,Lu J.A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve.Acta Materialia,2004,52(13):4023-4032
19 Collin JM,Mauvoisin G,Bartier O,et al.Experimental evaluation of the stress-strain curve by continuous indentation using different indenter shapes.Materials Science and Engineering:A,2009,501(1-2):140-145
20姜鹏,张泰华,杨荣等.基于球形压入法提取材料的塑性力学参数.力学学报,2009,41(5):730-738(Jiang Peng,Zhang Taihua,Yang Rong,et al.A new spherical indentation-based method to extract plastic material parameters.Chinese Journal of Theoretical and Applied Mechanics,2009,41(5):730-738(in Chinese))
21 Huber N,Tsakmakis C.Determination of constitutive properties fromspherical indentation data using neural networks.Part i:The case of pure kinematic hardening in plasticity laws.Journal of the Mechanics and Physics of Solids,1999,47(7):1569-1588
22 Tyulyukovskiy E,Huber N.Identification of viscoplastic material parameters from spherical indentation data:Part I.Neural networks.Journal of Materials Research,2006,21(3):664-676
23 Lee H,Lee JH,Pharr GM.A numerical approach to spherical indentation techniques for material property evaluation.Journal of the Mechanics and Physics of Solids,2005,53(9):2037-2069
24 Xu B,Chen X.Determining engineering stress-strain curve directly from the load-depth curve of spherical indentation test.Journal of Materials Research,2010,25(12):2297-2307
25 Chen H,Cai L.Unified elastoplastic model based on a strain energy equivalence principle.Applied Mathematical Modelling,2017,52:664-671
26 Chen H,Cai L.Theoretical model for predicting uniaxial stressstrain relation by dual conical indentation based on equivalent energy principle.Acta Materialia,2016,121:181-189
27 Chen H,Cai L.Unified ring-compression model for determining tensile properties of tubular materials.Materials Today Communications,2017,13:210-220
28赵康,鄢化彪,冯萧.基于能量法的矿柱稳定性分析.力学学报,2016,48(4):976-983(Zhao Kang,Yan Huabiao,Feng Xiao.Stability analysis of pillar based on energy law.Chinese Journal of Theoretical and Applied Mechanics,2016,48(4):976-983(in Chinese))
29张泰华.微/纳米力学测试技术及其应用.北京:机械工业出版社,2004:20-23(Zhang Taihua.Micro/nano Mechanical Testing Technology and Application.Beijing:China Machine Press,2004:20-23(in Chinese))
30章鹏,杜成斌,江守燕.比例边界有限元法求解裂纹面接触问题.力学学报,2017,49(6):1335-1347(Zhang Peng,Du Chengbin,Jiang Shouyan.Crack face contact problem analysis using the scaled boundary finite element method.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1335-1347(in Chinese))
31卢梦凯,张洪武,郑勇刚.应变局部化分析的嵌入强间断多尺度有限元法.力学学报,2017,49(3):649-658(Lu Mengkai,Zhang Hongwu,Zheng Yonggang.Embedded strong discontinuity model based multiscale finite element method for strain localization analysis.Chinese Journal of Theoretical and Applied Mechanics,2017,49(3):649-658(in Chinese))
32 Ammara HR,Haggag FM,Abdulaziz S,et al.Nondestructive measurements of flow properties of nanocrystalline Al-Cu-Ti alloy using Automated Ball Indentation(ABI)technique.Materials Science&Engineering A,2018,731:477-486
33 Tabor D.The Hardness of Metals.Oxford:Clarendon Press,1951
34 Xu B,Chen X.Determining engineering stress-strain curve directly from the load-depth curve of spherical indentation test.Journal of Materials Research,2010,25(12):2297-2307
35 Byun TS,Hong JH,Haggag FM,et al.Measurement of throughthe-thickness variations of mechanical properties in SA508 Gr.3pressure vessel steels using ball indentation test technique.International Journal of Pressure Vessels and Piping,1997,74(3):231-238