压痕蠕变实验的力学模型与蠕变力学性能表征
摘要
压痕实验是一种可以检测和评定材料多种力学性能的实验方法。通过压痕实验可以连续测定材料的载荷-位移曲线,进而评定其硬度,弹性模量,屈服强度,塑性等性能。由于它简单易行,成本低廉,可信度高,在同一试件上可以多次实验,能弥补传统实验方法的不足又不具破坏性等种种优点,压痕实验在各行各业都有着广泛的应用,业已成为工业界和科研领域对材料性能表征的标准方法和研究手段。
本文采用压痕实验来研究材料的蠕变性能。目前获得材料蠕变参数的标准实验是单轴拉伸蠕变测试,需要大量的试样和测试时间,而采用压痕蠕变测试技术仅需要很小体积的材料,试样的制备也非常简单。另外对于薄膜这类本身体积很小的材料,或者难于加工的陶瓷等高硬度或者脆性材料以及类似于铅之类的非常软的材料,如果仅需要考察材料的局部的蠕变性能,也只能通过压痕蠕变来获得其蠕变性能参数。因此采用压痕实验来研究材料蠕变是非常有意义的。
应用Zwick ZHU 2.5压痕仪器对一种力学性能未知的有机玻璃分别进行了压痕实验和压痕蠕变实验,得到其载荷—位移曲线和压痕深度—时间曲线,从曲线中取得数据进行处理,得到了该有机玻璃的弹性模量和蠕变指数。对实验过程进行了有限元仿真,对比弹性模量和蠕变指数的仿真值,仿真结果与实验结果相比非常接近,证明了用有限元的方法来仿真压痕实验是非常可靠的。最后提出了一种通过压痕蠕变实验和有限元仿真相结合来计算材料的蠕变常数的方法。
通过有限元仿真曲线与实验曲线的对比表明:本文提出的采用压痕实验来计算材料蠕变参数的方法是准确可行的,其计算结果可以满足工程的需要。这说明用压痕实验来测量材料蠕变性能是准确可行的,由于压痕实验适用于难以加工成标准试件的材料,可以表征材料表面微区力学性能,具有经济方便、可信度高、不具破坏性等种种优点,假以时日必将发展成为测量材料蠕变性能的标准实验。
Indentation test has seen a broader application in physics, materials science, mechanics and other areas. With it, the structure, mechanics and dynamics response of materials to external loading can be determined. Thus it can be employed to obtain many mechanical properties, such as the hardness, elastic modulus, yield strength, plastic properties etc. In addition, due to its simple implementation, low cost, high validity and the possibility of many tests on one specimen, indentation experiment is regarded as a standard technique in industry and scientific research field.
In this paper, we take indentation test to study the creep properties of materials. Early method, which depends on uniaxial tensile to obtain the creep parameters, usually requires a large mount of samples and time. However, those drawbacks prevent its applications on many specimens, such as film with small volume, ceramic, stiff or brittle materials and some soft materials like plumbum, etc. Therefore indentation test, which needs only a small specimen, can be employed to evaluate the creep properties. The preparation of samples is also very simple. In addition, if we want to consider the local creep properties, indentation test is the only way to achieve that. From the description above, indentation test is a very significant experimental technique to study the creep of materials.
Zwick ZHU 2.5 indentation apparatus is employed to do some indentation experiments and indentation creep experiments for organic glass with the unknown mechanical properties, its load-displacement curve and the indentation depth-time curve are obtained, the data of the curve are processed, and then the elastic modulus and creep exponential of the organic glass are obtained. Then the experimental process of finite element simulation is made, contrast elastic modulus and creep exponential value of the simulation, Simulation results compared with the experimental results are very close, the finite element method is proved that simulation indentation experiment is very reliable. Finally a method is presented to calculate the creep constant with the creep experiment and FEM combined.
Compared with finite element simulations and experimental data, the validity of our technique has been proved, i.e., the calculation method proposed to calculate creep parameter by indentation experiment is feasible and the calculated results can satisfy the need of the engineering. That indicates that measuring materials creep properties by the indentation test is feasible, and indentation experiment is apply to process the materials which can not be made into standard samples, it can characterize the surface micro-mechanical properties, and it has a lot of advantages, such as economically convenient, high credibility, not destructive and so on, it will become the standard experiment to test the material’s creep properties in the future.
本文采用压痕实验来研究材料的蠕变性能。目前获得材料蠕变参数的标准实验是单轴拉伸蠕变测试,需要大量的试样和测试时间,而采用压痕蠕变测试技术仅需要很小体积的材料,试样的制备也非常简单。另外对于薄膜这类本身体积很小的材料,或者难于加工的陶瓷等高硬度或者脆性材料以及类似于铅之类的非常软的材料,如果仅需要考察材料的局部的蠕变性能,也只能通过压痕蠕变来获得其蠕变性能参数。因此采用压痕实验来研究材料蠕变是非常有意义的。
应用Zwick ZHU 2.5压痕仪器对一种力学性能未知的有机玻璃分别进行了压痕实验和压痕蠕变实验,得到其载荷—位移曲线和压痕深度—时间曲线,从曲线中取得数据进行处理,得到了该有机玻璃的弹性模量和蠕变指数。对实验过程进行了有限元仿真,对比弹性模量和蠕变指数的仿真值,仿真结果与实验结果相比非常接近,证明了用有限元的方法来仿真压痕实验是非常可靠的。最后提出了一种通过压痕蠕变实验和有限元仿真相结合来计算材料的蠕变常数的方法。
通过有限元仿真曲线与实验曲线的对比表明:本文提出的采用压痕实验来计算材料蠕变参数的方法是准确可行的,其计算结果可以满足工程的需要。这说明用压痕实验来测量材料蠕变性能是准确可行的,由于压痕实验适用于难以加工成标准试件的材料,可以表征材料表面微区力学性能,具有经济方便、可信度高、不具破坏性等种种优点,假以时日必将发展成为测量材料蠕变性能的标准实验。
Indentation test has seen a broader application in physics, materials science, mechanics and other areas. With it, the structure, mechanics and dynamics response of materials to external loading can be determined. Thus it can be employed to obtain many mechanical properties, such as the hardness, elastic modulus, yield strength, plastic properties etc. In addition, due to its simple implementation, low cost, high validity and the possibility of many tests on one specimen, indentation experiment is regarded as a standard technique in industry and scientific research field.
In this paper, we take indentation test to study the creep properties of materials. Early method, which depends on uniaxial tensile to obtain the creep parameters, usually requires a large mount of samples and time. However, those drawbacks prevent its applications on many specimens, such as film with small volume, ceramic, stiff or brittle materials and some soft materials like plumbum, etc. Therefore indentation test, which needs only a small specimen, can be employed to evaluate the creep properties. The preparation of samples is also very simple. In addition, if we want to consider the local creep properties, indentation test is the only way to achieve that. From the description above, indentation test is a very significant experimental technique to study the creep of materials.
Zwick ZHU 2.5 indentation apparatus is employed to do some indentation experiments and indentation creep experiments for organic glass with the unknown mechanical properties, its load-displacement curve and the indentation depth-time curve are obtained, the data of the curve are processed, and then the elastic modulus and creep exponential of the organic glass are obtained. Then the experimental process of finite element simulation is made, contrast elastic modulus and creep exponential value of the simulation, Simulation results compared with the experimental results are very close, the finite element method is proved that simulation indentation experiment is very reliable. Finally a method is presented to calculate the creep constant with the creep experiment and FEM combined.
Compared with finite element simulations and experimental data, the validity of our technique has been proved, i.e., the calculation method proposed to calculate creep parameter by indentation experiment is feasible and the calculated results can satisfy the need of the engineering. That indicates that measuring materials creep properties by the indentation test is feasible, and indentation experiment is apply to process the materials which can not be made into standard samples, it can characterize the surface micro-mechanical properties, and it has a lot of advantages, such as economically convenient, high credibility, not destructive and so on, it will become the standard experiment to test the material’s creep properties in the future.
引文
1林志,王艳丽,林均品.纳米力学探针的基本原理及其应用实例.航空材料学报. 2001: 56-61
2 D. Tabor. Indentation Hardness: Fifty Years on a Personal View. Philosophical Magazine A: Physics of Condensed Matter Structure Defects and Mechanical Properties. 1996, 74(5): 1207-1212
3张泰华.微/纳米力学测试技术及其应用.机械工业出版社. 2004: 21-24
4 Li. X. D. A review of nanoindentation continuous stiffness measurement technique and its applications. Materials Characterization. 2002: 11-36
5 Brotzen. F. R. Mechanical testing of thin films. Int. Materials Reviews. 1994, 39 :24-45
6谢存毅.纳米压痕技术在材料科学中的应用实验技术. 2001: 432-435
7万建松,岳珠峰.采用压痕实验获得材料性能的研究现状.实验力学. 2002: 131-137
8陈隆庆,赵明皋,张统一.薄膜的力学测试技术.机械强度. 2001, 23(4): 413-429
9 W.C. Oliver, GM. Pharr. 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
10 J. Malzbender. Comment on Hardness Definitions. Journal of the European Ceramic Society. 2003, 23(9): 1355-1359
11 J. S. Field, M. V Swain. Determining the Mechanical Properties of Small Volumes of Material from Sub-micrometer Spherical Indentations. Journal of Materials Research. 1995, 10(1): 101-112
12 M. X. Swain. Mechanical Property Characterization of Small Volumes of Brittle Materials with Spherical Tipped Indenters. Materials Science& Engineering A. 1998, 253: 160-166
13 S. Umemura, Y. Andoh, S. Hirono, T. Miyamoto, R. Kaneko. Nanoindentation and Nanowear Tests on Amorphous Carbon Films. Philosophical Magazine A. 1996, 74(1): 1143-1157
14 B. Bhushan, V. N. Koinkar. Tribological Studies of Silicon for Magnetic Recording Applications. Journal of Applied Physics. 1994, 75(10): 5741-5746
15 M. J. Mayo, W. D. Nix. A Micro-Indentation Study of Super-plasticity in Pb,Sn, and Sn-38 wt% Pb. Acta Metallurgica. 1988, 36(8): 2183-2192
16 B. N. Lucas, W. C. Oliver. Indentation Power-Law Creep of High-Purity Indium. Metallurgical &Materials Transaction A. 1999, 30: 601-610
17 G. M. Pharr. Measurement of Mechanical Properties by Ultra-low Load Indentation. Materials Science & Engineering A. 1998, 253: 151-159
18 D. S. Harding, W. C. Oliver, G. M. Pharr. Cracking during Nanoindentation and its Use in the Measurement of Fracture Toughness. Materials Research Society. 1995: 663-668
19 S. Suresh, A. E. Giannakopoulos. A New Method for Estimating Residual Stresses by Instrumented Sharp Indentation. Acta Materialia. 1998, 46(16): 5755-5767
20 S. Carlson, P. L. Larsson. On the Determination of Residual Stress and Strain Fields by Sharp Indentation Testing Part II: Experimental Investigation. Acta Materialia. 2001,49(12): 2193-2203
21 T. Y. Tsui, C. A. Ross. A Method for Making Substrate Independent Hardness Measurements of Soft Metallic Films on Hard Substrates by Nanoindentation. Journal of Materials Research. 2003, 18(6): 1383-1391
22 D. E. Kramer, A. A. Volins, N.R. Moody, W. W. Gerbberish. Substrate Effects on Indentation Plastic Zone Development in Thin Soft Films. Journal of Materials Research. 2001, 16(11): 3150-3157
23郑哲敏. 20 -21世纪的力学. 21世纪中国力学. 1994
24黄克智,余寿文.固体力学研究的某些新趋势.人、环境与力学.科学出版社. 1991
25杨挺青.粘弹塑性本构理论及其应用.力学进展. 1992, 22(1): 10-19
26袁龙蔚.缺陷体流变学.国防工业出版社. 1994
27余寿文.固体力学与材料科学交缘的几个新课题.力学进展. 1994. 24(1): 24-36
28杨挺青.带缺陷物体流变学.力学与实践, 1996. 18(3): 13-17
29穆霞英.蠕变力学.西安交通大学出版社. 1990
30杨挺青.粘弹性力学.华中理工大学出版社. 1990
31张淳源.粘弹性断裂力学.华中理工大学出版社. 1994
32魏文光.金属力学性能测试.科学出版社. 1980
33平修二(日).金属材料的高温强度理论、设计.科学出版社. 1983
34艾芒,杨镇,王志文.小冲孔实验法的起源、发展和应用[J].机械强度. 2000, 22 (4): 279-282.
35 MAHMUD I R, ROUM INA R, RAEISIN IA B. Investigation of stress exponent in the power-law creep of Pb-Sb alloys [J]. Materials Science and Engineering A. 2004, 382: 15-22
36 NGAN A H W,WANG H T, TANG B, et al. Correcting power-law viscoelastic effects in elastic modulus measurement using depth-sensing indentation [J]. International Journal of Solids and Structures. 2005, 42: 1831-1846.
37 MA X, YOSH IDA F. Rate-dependent indentation hardness of a power-law creep solder alloy [J]. Appl Phys Lett. 2003, 82: 188-190.
38 MA YO M J, SIEGEL W, NARA YANA SAMY A, et al. Mechanical properties of nanophase TiO2 as determined by nanoindentation[J]. J Mater Res. 1990, 5: 1073-1082.
39 HANNULA S P, STONE D S, L I C Y. Determination of time-dependent plastic properties of metals by indentation load relaxation techniques [J]. Mater Res Soc Sump Proc. 1985, 40: 217-224.
40陈维峰. KDP晶体压痕试验及有限元仿真.哈尔滨工业大学硕士论文. 2006
41 W. C. Oliver, Hutchings R, J. B. Pethica. Measurement of Hardness at Indentation Depths as Low as 20 Nanometres. ASTM Special Technical Publication. 1985, (5): 90-108
42李渊.镁合金循环蠕变-松驰的实验研究与本构描述.重庆大学硕士论文. 2004
43 S. H. Goods and L. M. Brown. The Nucleation of Cavities by Plastic Deformation. Acta Metall. 1979, 27: 1-15
44 S. H. Goods. Mechanisms of Intergranular Cavity Nucleation and Growth during Creep. Scripta Metall. 1983, 17: 23-30
45王军.损伤力学的理论与应用.科学出版社. 1997
46 D. R. Hayhurst. The Use of Continuum Damage Mechanics in Creep Analysis for Design. J. Strain Analysis. 1994, 29(3): 233-241
47 Z. L. Kowalewski, et al. Mechanisms-based Creep Constitutive Equations for an Aluminum Alloy. J. Strain Analysis. 1994, 29(4): 309-316
48余寿文,冯西桥.损伤力学.清华大学出版社. 1997
49 H. Kraus. Creep Analysis. A wileg-Interscience. Pub. John Wiley Andson.1980
50岳珠峰,万建松,吕震宙.由压痕蠕变试验确定材料的蠕变性能参数.应用数学和力学. 2003, 24(3): 275-281
51张泰华,杨业敏.纳米硬度技术的发展和应用.力学进展. 2002: 349-364
52庄茁,张帆,岑松. ABAQUS非线性有限元分析与实例.科学出版社. 2005
53许宝星,岳珠峰.平头压痕试验确定材料蠕变参数的一种新方法.科学技术与工程. 2005,5(7): 441-443
2 D. Tabor. Indentation Hardness: Fifty Years on a Personal View. Philosophical Magazine A: Physics of Condensed Matter Structure Defects and Mechanical Properties. 1996, 74(5): 1207-1212
3张泰华.微/纳米力学测试技术及其应用.机械工业出版社. 2004: 21-24
4 Li. X. D. A review of nanoindentation continuous stiffness measurement technique and its applications. Materials Characterization. 2002: 11-36
5 Brotzen. F. R. Mechanical testing of thin films. Int. Materials Reviews. 1994, 39 :24-45
6谢存毅.纳米压痕技术在材料科学中的应用实验技术. 2001: 432-435
7万建松,岳珠峰.采用压痕实验获得材料性能的研究现状.实验力学. 2002: 131-137
8陈隆庆,赵明皋,张统一.薄膜的力学测试技术.机械强度. 2001, 23(4): 413-429
9 W.C. Oliver, GM. Pharr. 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
10 J. Malzbender. Comment on Hardness Definitions. Journal of the European Ceramic Society. 2003, 23(9): 1355-1359
11 J. S. Field, M. V Swain. Determining the Mechanical Properties of Small Volumes of Material from Sub-micrometer Spherical Indentations. Journal of Materials Research. 1995, 10(1): 101-112
12 M. X. Swain. Mechanical Property Characterization of Small Volumes of Brittle Materials with Spherical Tipped Indenters. Materials Science& Engineering A. 1998, 253: 160-166
13 S. Umemura, Y. Andoh, S. Hirono, T. Miyamoto, R. Kaneko. Nanoindentation and Nanowear Tests on Amorphous Carbon Films. Philosophical Magazine A. 1996, 74(1): 1143-1157
14 B. Bhushan, V. N. Koinkar. Tribological Studies of Silicon for Magnetic Recording Applications. Journal of Applied Physics. 1994, 75(10): 5741-5746
15 M. J. Mayo, W. D. Nix. A Micro-Indentation Study of Super-plasticity in Pb,Sn, and Sn-38 wt% Pb. Acta Metallurgica. 1988, 36(8): 2183-2192
16 B. N. Lucas, W. C. Oliver. Indentation Power-Law Creep of High-Purity Indium. Metallurgical &Materials Transaction A. 1999, 30: 601-610
17 G. M. Pharr. Measurement of Mechanical Properties by Ultra-low Load Indentation. Materials Science & Engineering A. 1998, 253: 151-159
18 D. S. Harding, W. C. Oliver, G. M. Pharr. Cracking during Nanoindentation and its Use in the Measurement of Fracture Toughness. Materials Research Society. 1995: 663-668
19 S. Suresh, A. E. Giannakopoulos. A New Method for Estimating Residual Stresses by Instrumented Sharp Indentation. Acta Materialia. 1998, 46(16): 5755-5767
20 S. Carlson, P. L. Larsson. On the Determination of Residual Stress and Strain Fields by Sharp Indentation Testing Part II: Experimental Investigation. Acta Materialia. 2001,49(12): 2193-2203
21 T. Y. Tsui, C. A. Ross. A Method for Making Substrate Independent Hardness Measurements of Soft Metallic Films on Hard Substrates by Nanoindentation. Journal of Materials Research. 2003, 18(6): 1383-1391
22 D. E. Kramer, A. A. Volins, N.R. Moody, W. W. Gerbberish. Substrate Effects on Indentation Plastic Zone Development in Thin Soft Films. Journal of Materials Research. 2001, 16(11): 3150-3157
23郑哲敏. 20 -21世纪的力学. 21世纪中国力学. 1994
24黄克智,余寿文.固体力学研究的某些新趋势.人、环境与力学.科学出版社. 1991
25杨挺青.粘弹塑性本构理论及其应用.力学进展. 1992, 22(1): 10-19
26袁龙蔚.缺陷体流变学.国防工业出版社. 1994
27余寿文.固体力学与材料科学交缘的几个新课题.力学进展. 1994. 24(1): 24-36
28杨挺青.带缺陷物体流变学.力学与实践, 1996. 18(3): 13-17
29穆霞英.蠕变力学.西安交通大学出版社. 1990
30杨挺青.粘弹性力学.华中理工大学出版社. 1990
31张淳源.粘弹性断裂力学.华中理工大学出版社. 1994
32魏文光.金属力学性能测试.科学出版社. 1980
33平修二(日).金属材料的高温强度理论、设计.科学出版社. 1983
34艾芒,杨镇,王志文.小冲孔实验法的起源、发展和应用[J].机械强度. 2000, 22 (4): 279-282.
35 MAHMUD I R, ROUM INA R, RAEISIN IA B. Investigation of stress exponent in the power-law creep of Pb-Sb alloys [J]. Materials Science and Engineering A. 2004, 382: 15-22
36 NGAN A H W,WANG H T, TANG B, et al. Correcting power-law viscoelastic effects in elastic modulus measurement using depth-sensing indentation [J]. International Journal of Solids and Structures. 2005, 42: 1831-1846.
37 MA X, YOSH IDA F. Rate-dependent indentation hardness of a power-law creep solder alloy [J]. Appl Phys Lett. 2003, 82: 188-190.
38 MA YO M J, SIEGEL W, NARA YANA SAMY A, et al. Mechanical properties of nanophase TiO2 as determined by nanoindentation[J]. J Mater Res. 1990, 5: 1073-1082.
39 HANNULA S P, STONE D S, L I C Y. Determination of time-dependent plastic properties of metals by indentation load relaxation techniques [J]. Mater Res Soc Sump Proc. 1985, 40: 217-224.
40陈维峰. KDP晶体压痕试验及有限元仿真.哈尔滨工业大学硕士论文. 2006
41 W. C. Oliver, Hutchings R, J. B. Pethica. Measurement of Hardness at Indentation Depths as Low as 20 Nanometres. ASTM Special Technical Publication. 1985, (5): 90-108
42李渊.镁合金循环蠕变-松驰的实验研究与本构描述.重庆大学硕士论文. 2004
43 S. H. Goods and L. M. Brown. The Nucleation of Cavities by Plastic Deformation. Acta Metall. 1979, 27: 1-15
44 S. H. Goods. Mechanisms of Intergranular Cavity Nucleation and Growth during Creep. Scripta Metall. 1983, 17: 23-30
45王军.损伤力学的理论与应用.科学出版社. 1997
46 D. R. Hayhurst. The Use of Continuum Damage Mechanics in Creep Analysis for Design. J. Strain Analysis. 1994, 29(3): 233-241
47 Z. L. Kowalewski, et al. Mechanisms-based Creep Constitutive Equations for an Aluminum Alloy. J. Strain Analysis. 1994, 29(4): 309-316
48余寿文,冯西桥.损伤力学.清华大学出版社. 1997
49 H. Kraus. Creep Analysis. A wileg-Interscience. Pub. John Wiley Andson.1980
50岳珠峰,万建松,吕震宙.由压痕蠕变试验确定材料的蠕变性能参数.应用数学和力学. 2003, 24(3): 275-281
51张泰华,杨业敏.纳米硬度技术的发展和应用.力学进展. 2002: 349-364
52庄茁,张帆,岑松. ABAQUS非线性有限元分析与实例.科学出版社. 2005
53许宝星,岳珠峰.平头压痕试验确定材料蠕变参数的一种新方法.科学技术与工程. 2005,5(7): 441-443