On the evaluation of uniaxial tensile and fracture properties of Ti-6Al-4V by spherical indentation tests with different calculation models
Jianxun Li
Engineering and Technology Research Center for Special Equipment Safety of Shandong Province, Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan, China
Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow, UK
Search for more papers by this authorMinghang Wang
Engineering and Technology Research Center for Special Equipment Safety of Shandong Province, Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan, China
Search for more papers by this authorYing Li
Commercial Aircraft Engine Company Limited, AECC Commercial Aircraft Engine Co, Ltd, Shanghai, China
Search for more papers by this authorHaofeng Chen
Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow, UK
Key Laboratory of Pressure Systems and Safety, School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, China
Search for more papers by this authorCorresponding Author
Tairui Zhang
School of Mechanical Engineering, Southeast University, Nanjing, China
Correspondence
Tairui Zhang, School of Mechanical Engineering, Southeast University, Nanjing, China.
Email: [email protected]
Weiqiang Wang, Engineering and Technology Research Center for Special Equipment Safety of Shandong Province, Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan, China.
Email: [email protected]
Search for more papers by this authorCorresponding Author
Weiqiang Wang
Engineering and Technology Research Center for Special Equipment Safety of Shandong Province, Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan, China
College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao, China
Correspondence
Tairui Zhang, School of Mechanical Engineering, Southeast University, Nanjing, China.
Email: [email protected]
Weiqiang Wang, Engineering and Technology Research Center for Special Equipment Safety of Shandong Province, Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan, China.
Email: [email protected]
Search for more papers by this authorJianxun Li
Engineering and Technology Research Center for Special Equipment Safety of Shandong Province, Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan, China
Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow, UK
Search for more papers by this authorMinghang Wang
Engineering and Technology Research Center for Special Equipment Safety of Shandong Province, Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan, China
Search for more papers by this authorYing Li
Commercial Aircraft Engine Company Limited, AECC Commercial Aircraft Engine Co, Ltd, Shanghai, China
Search for more papers by this authorHaofeng Chen
Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow, UK
Key Laboratory of Pressure Systems and Safety, School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, China
Search for more papers by this authorCorresponding Author
Tairui Zhang
School of Mechanical Engineering, Southeast University, Nanjing, China
Correspondence
Tairui Zhang, School of Mechanical Engineering, Southeast University, Nanjing, China.
Email: [email protected]
Weiqiang Wang, Engineering and Technology Research Center for Special Equipment Safety of Shandong Province, Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan, China.
Email: [email protected]
Search for more papers by this authorCorresponding Author
Weiqiang Wang
Engineering and Technology Research Center for Special Equipment Safety of Shandong Province, Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan, China
College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao, China
Correspondence
Tairui Zhang, School of Mechanical Engineering, Southeast University, Nanjing, China.
Email: [email protected]
Weiqiang Wang, Engineering and Technology Research Center for Special Equipment Safety of Shandong Province, Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan, China.
Email: [email protected]
Search for more papers by this authorAbstract
This study assessed the efficacy of models in predicting uniaxial tensile and fracture properties of Ti-6Al-4V (TC4) alloys via spherical indentation tests (SITs). Four models, including one empirical, one numerical, and two analytical, were selected as representatives to evaluate uniaxial tensile properties. A series of experiments were conducted on TC4 alloys obtained from three manufacturing processes: selective laser melting (SLM), forging, and welding. The empirical model underestimated the material's strength, while the other models were mostly conservative, with errors within 10%, acceptable for engineering applications. However, although the incremental model is able to provide a desirable result, it may be inaccurate for calculating the yield strength. Thus, the source of errors in each model was thoroughly investigated through theoretical analysis and finite element calculations. Additionally, based on the results of optimal strength assessment, this study validated the effectiveness of the critical stress model to evaluate the fracture toughness of TC4 alloys.
Highlights
- This study evaluated the mechanical properties of TC4 alloys with different indentation models.
- This study used the indentation response analysis of TC4 alloys from the SLM, forging, and welding.
- Sources of errors in each representative model were discussed in detail.
- Selection of the optimal stain threshold in the incremental model was examined.
CONFLICT OF INTEREST STATEMENT
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Open Research
DATA AVAILABILITY STATEMENT
Data will be made available on request.
REFERENCES
- 1Banerjee D, Williams JC. Perspectives on titanium science and technology. Acta Mater. 2013; 61(3): 844-879.
- 2Lutjering G. Influence of processing on microstructure and mechanical properties of (alpha+beta) titanium alloys. Mater Sci Eng A-Struct. 1998; 243(1-2): 32-45.
- 3Williams JC, Starke EA. Progress in structural materials for aerospace systems. Acta Mater. 2003; 51(19): 5775-5799.
- 4Jin N, Yan ZY, Wang YW, Cheng HW, Zhang HM. Effects of heat treatment on microstructure and mechanical properties of selective laser melted Ti-6Al-4V lattice materials. Int J Mech Sci. 2021; 190: 106042.
- 5Emmens WC. Formability: A Review of Parameters and Processes that Control, Limit or Enhance the Formability of Sheet Metal. Springer; 2011.
- 6Wang L, Chen W, Tan X, Yang J. The impact of various crack geometrical parameters on stress field over tip under different mixed loading conditions and inclination angles. Theor Appl Fract Mec. 2019; 102: 239-254.
- 7Li K, Peng J, Zhou C. Construction of whole stress-strain curve by small punch test and inverse finite element. Results Phys. 2018; 11: 440-448.
- 8Bolzon G, Buljak V. An indentation-based technique to determine in-depth residual stress profiles induced by surface treatment of metal components. Fatigue Fract Eng M. 2011; 34(2): 97-107.
- 9Ragavendran M, Kumar JG, Vasudevan M. Evaluation of tensile properties using uni-axial and ball indentation testing and correlation with microstructure variations across the 316LN stainless steel weld joints. Mater Sci Eng A-Struct. 2022; 832: 832, 142445.
- 10Zhang T, Wang S, Wang W. A unified energy release rate based model to determine the fracture toughness of ductile metals from unnotched specimens. Int J Mech Sci. 2019; 150: 35-50.
- 11Ohta H, Miura H, Kitano M. A ball-indentation method to evaluate the critical stress for dislocation generation in a silicon substrate. Fatigue Fract Eng M. 2001; 24(12): 877-884.
- 12Zhang T, Wang S, Wang W. A constitutive model independent analytical method in determining the tensile properties from incremental spherical indentation tests (ISITs). Int J Mech Sci. 2018; 148: 9-19.
- 13Byun TS, Hong JH, Haggag FM, Farrell K, Lee EH. Measurement of through-the-thickness variations of mechanical properties in SA508 gr.3 pressure vessel steels using ball indentation test technique. Int J Pres Ves pip. 1997; 74(3): 231-238.
- 14Kim JY, Lee KW, Lee JS, Kwon D. Determination of tensile properties by instrumented indentation technique: representative stress and strain approach. Surf Coat Technol. 2006; 201(7): 4278-4283.
- 15Zhang T, Wang S, Wang W. Method to determine the optimal constitutive model from spherical indentation tests. Results Phys. 2018; 8: 716-727.
- 16Zhang T, Wang S, Wang W. An energy-based method for flow property determination from a single-cycle spherical indentation test (SIT). Int J Mech Sci. 2020; 171: 105369.
- 17Jiang P, Zhang T, Feng Y, Yang R, Liang N. Determination of plastic properties by instrumented spherical indentation: expanding cavity model and similarity solution approach. J Mater Res. 2009; 24(3): 1045-1053.
- 18Kang SK, Kim YC, Kim KH, Kim JY, Kwon D. Extended expanding cavity model for measurement of flow properties using instrumented spherical indentation. Int J Plasticity. 2013; 49: 1-15.
- 19Chen H, Cai LX. Theoretical model for predicting uniaxial stress-strain relation by dual conical indentation based on equivalent energy principle. Acta Mater. 2016; 121: 181-189.
- 20Balasubramanian TS, Balakrishnan M, Balasubramanian V, Manickam MAM. Influence of welding processes on microstructure, tensile and impact properties of Ti-6Al-4V alloy joints. T Nonferr Metal Soc. 2011; 21(6): 1253-1262.
- 21Guo P, Zhao YQ, Zeng WD, Hong Q. The effect of microstructure on the mechanical properties of TC4-DT titanium alloys. Mater Sci Eng A-Struct. 2013; 563: 106-111.
- 22Zhao ZY, Li L, Bai PK, et al. The heat treatment influence on the microstructure and hardness of TC4 titanium alloy manufactured via selective laser melting. Materials. 2018; 11(8): 11.
- 23Koike M, Greer P, Owen K, et al. Evaluation of titanium alloys fabricated using rapid prototyping technologies—electron beam melting and laser beam melting. Materials. 2011; 4(10): 1776-1792.
- 24Li YZ, Omacht D, Yu F, Sun MC. A new spherical indentation approach to determine fracture toughness of high strength steels. Eng Fract Mech. 2022; 272: 108695.
- 25Haggag FM, Byun TS, Hong JH, Miraglia PQ, Murty KL. Indentation-energy-to-fracture (IEF) parameter for characterization of DBTT in carbon steels using nondestructive automated ball indentation (ABI) technique. Scr Mater. 1998; 38(4): 645-651.
- 26Jeon SW, Lee KW, Kim JY, Kim WJ, Park CP, Kwon D. Estimation of fracture toughness of metallic materials using instrumented indentation: critical indentation stress and strain model. Exp Mech. 2017; 57(7): 1013-1025.
- 27Lee JS, Jang J, Lee BW, Choi Y, Lee SG, Kwon D. An instrumented indentation technique for estimating fracture toughness of ductile materials: a critical indentation energy model based on continuum damage mechanics. Acta Mater. 2006; 54(4): 1101-1109.
- 28Zhang T, Wang S, Wang W. A comparative study on fracture toughness calculation models in spherical indentation tests (SITs) for ductile metals. Int J Mech Sci. 2019; 160: 114-128.
- 29Okocha SI, Yu F, Jar PYB, Hendry MT. Indentation testing method for determining mechanical properties and tensile flow curve of high-strength rail steels. Exp Mech. 2023; 63(5): 839-852.
- 30Yu F, Fang J, Omacht D, Sun MC, Li YZ. A new instrumented spherical indentation test methodology to determine fracture toughness of high strength steels. Theor Appl Fract Mec. 2023; 124: 124, 103744.
- 31Tabor D. The Hardness of Metals. Oxford University Press; 2000.
10.1093/oso/9780198507765.001.0001 Google Scholar
- 32Johnson KL. Contact Mechanics. Cambridge University Press; 1985.
10.1017/CBO9781139171731 Google Scholar
- 33Haggag FM, Wang JA, Theiss TJ. Using portable/in-situ stress-strain microprobe system to measure mechanical properties of steel bridges during service. In: Conference on Nondestructive Evaluation of Bridges and Highways; Dec 04-05, 1996; Scottsdale, Az.
- 34Haggag FM. Phenomenological analysis of plastic spherical indentation. J Eng Mater Technol. 1976; 98(3): 272-281.
- 35Hartmann S, Gibmeier J, Scholtes B. Experiments and material parameter identification using finite elements. Uniaxial tests and validation using instrumented indentation tests. Exp Mech. 2006; 46(1): 5-18.
- 36de Santana EC, Misiolek WZ, Costa ALM. Numerical study on the surface morphology evolution and hardness during the spherical indentation of copper with plastic behavior described by different stress-strain relationships. Int J Solids Struct. 2022; 252: 252, 111817.
- 37Liu ZS, Harsono E, Swaddiwudhipong S. Material characterization based on instrumented and simulated indentation tests. Int J App Mech. 2009; 1(01): 61-84.
10.1142/S175882510900006X Google Scholar
- 38Lee H, Haeng Lee J, Pharr GM. A numerical approach to spherical indentation techniques for material property evaluation. J Mech Phys Solids. 2005; 53(9): 2037-2069.
- 39Lee JH, Lee H, Kim DH. A numerical approach to evaluation of elastic modulus using conical indenter with finite tip radius. J Mater Res. 2008; 23(9): 2528-2537.
- 40Gao XL. An expanding cavity model incorporating strain-hardening and indentation size effects. Int J Solids Struct. 2006; 43(21): 6615-6629.
- 41Lee JH, Kim T, Lee H. A study on robust indentation techniques to evaluate elastic-plastic properties of metals. Int J Solids Struct. 2010; 47(5): 647-664.
- 42Ogasawara N, Chiba N, Chen X. A simple framework of spherical indentation for measuring elastoplastic properties. Mech Mater. 2009; 41(9): 1025-1033.
- 43Beghini M, Bertini L, Fontanari V. Evaluation of the stress-strain curve of metallic materials by spherical indentation. Int J Solids Struct. 2006; 43(7-8): 2441-2459.
- 44Minh-Quy L. Material characterization by instrumented spherical indentation. Mech Mater. 2012; 46: 42-56.
- 45Noii N, Aghayan I. Characterization of elastic-plastic coated material properties by indentation techniques using optimisation algorithms and finite element analysis. Int J Mech Sci. 2019; 152: 465-480.
- 46Xu B, Chen X. Determining engineering stress-strain curve directly from the load-depth curve of spherical indentation test. J Mater Res. 2010; 25(12): 2297-2307.
- 47Zhang T, Wang S, Wang W. Improved methods to determine the elastic modulus and area reduction rate in spherical indentation tests. Mater Test. 2018; 60(4): 355-362.
- 48Ma D, Wo OC. Further analysis of energy-based indentation relationship among Young's modulus, nominal hardness, and indentation work. J Mater Res. 2010; 25(6): 1131-1136.
- 49Yang R, Zhang T, Feng Y. Theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation for work-hardening materials. J Mater Res. 2010; 25(11): 2072-2077.
- 50Yu C, Feng Y, Yang R, Peng G, Lu Z, Zhang T. An integrated method to determine elastic-plastic parameters by instrumented spherical indentation. J Mater Res. 2014; 29(9): 1095-1103.
- 51Zhang TR, Li JX, Sun X, Shang XD, Wang WQ. Improving the tensile property calculations with plastic zone radius measurements in depth-sensing spherical indentation tests. J Strain Anal Eng. 2022; 57(7): 513-529.
- 52Campbell JE, Thompson RP, Dean J, Clyne TW. Comparison between stress-strain plots obtained from indentation plastometry, based on residual indent profiles, and from uniaxial testing. Acta Mater. 2019; 168: 87-99.
- 53Chen H, Cai LX. Unified elastoplastic model based on a strain energy equivalence principle. App Math Model. 2017; 52: 664-671.
- 54Chen H, Cai LX, Bao C. Equivalent-energy indentation method to predict the tensile properties of light alloys. Mater des. 2019; 162: 322-330.
- 55Pan B, Qian KM, Xie HM, Asundi A. Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol. 2009; 20(6): 062001.
- 56Dong YL, Pan B. A review of speckle pattern fabrication and assessment for digital image correlation. Exp Mech. 2017; 57(8): 1161-1181.
- 57Johnson GR. A constitutive model and data for materials subjected to large strains, high strain rates, and high temperatures. In: Proc 7th Inf Sympo Ballistics. Vol. 1983: 541-547.
- 58Murty KL, Mathew MD, Wang Y, Shah VN, Haggag FM. Nondestructive determination of tensile properties and fracture toughness of cold worked A36 steel. Int J Pres Ves pip. 1998; 75(11): 831-840.
- 59Kumar P, Prakash O, Ramamurty U. Micro-and meso-structures and their influence on mechanical properties of selectively laser melted Ti-6Al-4V. Acta Mater. 2018; 154: 246-260.
- 60Thijs L, Verhaeghe F, Craeghs T, Humbeeck JV, Kruth J-P. A study of the microstructural evolution during selective laser melting of Ti–6Al–4V. Acta Mater. 2010; 58(9): 3303-3312.
- 61 ASTM B381–13, Standard Specification for Titanium and Titanium Alloys Forging, 2013.
- 62 ASTM E8/E8M-16a, Standard Test Methods for Tension Testing of Metallic Materials, 2016.
- 63 GB/T 21143–2014. Metallic Materials-Unifified Method of Test for Determination of Quasistatic Fracture Toughness. Standardization Administration of the PRC.
- 64Zhang T, Wang S, Wang W. A comparative study on uniaxial tensile property calculation models in spherical indentation tests (SITs). Int J Mech Sci. 2019; 155: 159-169.
- 65Wang L, Vuik C, Hajibeygi H. A stabilized mixed-FE scheme for frictional contact and shear failure analyses in deformable fractured media. Eng Fract Mech. 2022; 267:108427.
- 66Liu X, Li Z, Zhong K, Chao Y, Miraldo P, Shi Y. Generic distortion model for metrology under optical microscopes. Opt Lasers Eng. 2018; 103: 119-126.