SPHERICAL INDENTATION METHOD TO DETERMINE STRESS-STRAIN RELATIONS AND TENSILE STRENGTH OF METALLIC MATERIALS

Zhang Zhijie; Cai Lixun; Chen Hui; Bao Chen; Liu Xiaokun

doi:10.6052/0459-1879-18-200

Volume 51 Issue 1

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Theoretical and Applied Mechanics > 2019 > 51(1): 159-169

Zhang Zhijie, Cai Lixun, Chen Hui, Bao Chen, Liu Xiaokun. SPHERICAL INDENTATION METHOD TO DETERMINE STRESS-STRAIN RELATIONS AND TENSILE STRENGTH OF METALLIC MATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 159-169. doi: 10.6052/0459-1879-18-200

Citation:

Zhang Zhijie, Cai Lixun, Chen Hui, Bao Chen, Liu Xiaokun. SPHERICAL INDENTATION METHOD TO DETERMINE STRESS-STRAIN RELATIONS AND TENSILE STRENGTH OF METALLIC MATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 159-169. doi: 10.6052/0459-1879-18-200

Citation:

PDF( 5173 KB)

SPHERICAL INDENTATION METHOD TO DETERMINE STRESS-STRAIN RELATIONS AND TENSILE STRENGTH OF METALLIC MATERIALS

doi: 10.6052/0459-1879-18-200

Zhang Zhijie^{2)
,},
Cai Lixun^{3)
,},
Chen Hui^{4)
,},
Bao Chen,
Liu Xiaokun

Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University,Chengdu 610031, China

Publish Date: 2019-01-18

Abstract

Abstract

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 indentation tests 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.
- stress-strain relations,
- tensile strength,
- energy equivalence,
- RVE,
- Hollomon law,
- spherical indentation,
- SSI

FullText(HTML)

References(1)

References

[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
[5]	(Zhang Taihua, Xun Yong, Wang Xiulan.Nanoindentation and nanoscratch measurements on sub-micron 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
[10]	(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 through-the-thickness variations of mechanical properties in SA508 Gr. 3 pressure 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
[14]	(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
[15]	(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
[16]	(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
[20]	(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 stress-strain 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
[28]	(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
[29]	(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
[30]	(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
[31]	(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 through-the-thickness variations of mechanical properties in SA508 Gr. 3 pressure vessel steels using ball indentation test technique. International Journal of Pressure Vessels and Piping, 1997, 74(3): 231-238