Investigating Strain Rate Effects on Indentation Size Effect in Nickel-Based Single Crystal Superalloy DD6


The accurate measurement of mechanical properties at small scales is becoming increasingly essential because of the push for miniaturization and densification of advanced structures which should operate under extreme conditions and the mechanical behavior at micro- and nano-scales significantly can influence the overall performance and reliability. Previous traditional mechanical testing methods can operate well at larger scale, however, they are inadequate for these small-scale measurements, which calls for the urgent need to develop new and more sophisticated techniques. Nanoindentation technology, initially presented by Oliver et al., has emerged as an important tool to evaluate the mechanical properties of materials at micro- and nano-scales because it can do high-resolution measurements of both load and penetration depth. However, despite its widespread use, several challenges remain, particularly related to the indentation size effect (ISE). The ISE describes the phenomenon where the measured hardness of a material decreases with increasing load on the indenter, especially at shallow penetration depths. This effect is significant because it can skew the interpretation of a material’s mechanical properties, leading to inaccurate assessments. It is essential to understand and characterize the ISE for accurate mechanical property measurements at small scales. However, the ISE is influenced by several external factors, including surface roughness, indentation tip curvature, and strain rate. Most existing studies have focused on high strain rates, leaving a gap in the understanding of the ISE at low strain rates. The primary challenges addressed in this study are the accurate characterization of the ISE and the quantification of its dependence on strain rate and indenter tip curvature. Nickel-based single crystal superalloys, such as DD6, are widely used in high-temperature applications due to their excellent mechanical properties. However, their behavior under nanoindentation, particularly concerning the ISE, has not been fully investigated. To this end, new study published in Journal of Materials Research and Technology and led by Professor Xu Long from the School of Mechanics, Civil Engineering and Architecture at Northwestern Polytechnical University and conducted by Ziyi Shen, Jiao Li, Ruipeng Dong, and Yutai Su and along side Professor Ming Liu from the Fuzhou University and Dr. Chuantong Chen from Osaka University investigated the ISE of the nickel-based single crystal superalloy DD6 using nanoindentation experiments and finite element (FE) simulations. They developed a comprehensive understanding of how these factors influence the ISE by emphasizing the strain rate effect. This understanding is critical for applications requiring precise mechanical property measurements at small scales, such as in the aerospace and power generation industries where these materials are widely used.

The researchers conducted nanoindentation tests on the nickel-based single crystal superalloy DD6 using a Berkovich indenter. They designed an experimental setup which involves a nanoindentation tester, NHT2 from Anton Paar, operating under ambient conditions. The team chose three different loading rates: 100 mN/min, 500 mN/min, and 1000 mN/min, with the maximum penetration depth set at 600 nm. These loading rates were selected to examine the strain rate effect on the ISE. The authors found that the overall load-penetration depth (P–h) curves were slightly influenced by the loading rate. However, a notable trend emerged when analyzing the localized region underneath the indenter: the higher the loading rate, the greater the reaction force at the same penetration depth. This observation highlighted the significance of strain rate effects in nanoindentation responses.  To complement their experimental work, they developed a two-dimensional axisymmetric FE model using ABAQUS software. The model represented the substrate as a cylinder and approximated the Berkovich indenter with a conical indenter with a half-angle of 70.3°. The contact between the indenter and the specimen was defined as frictionless. The model utilized a combination of fine and coarse meshes to ensure accurate results without excessive computational costs. Moreover, the FE simulations incorporated the Johnson-Cook constitutive model to account for strain rate sensitivity. The model parameters, previously calibrated for the DD6 superalloy, included a yield stress of 1486 MPa, a hardening constant of 1678 MPa, a strain rate constant of 0.024, and a hardening index of 0.3215. The authors’ simulation results showed excellent agreement with the experimental data across all loading rates which validated the FE model’s accuracy. One of the significant findings from the FE simulations was the effect of strain rate on the kinetic energy per volume of the deformed region underneath the indenter. The results indicated that higher strain rates led to more pronounced acceleration effects, even at low strain rates. This finding highlights the importance of considering strain rate effects in nanoindentation studies. Additionally, to provide a comprehensive understanding of the ISE, the researchers developed a dimensionless hardness model. The new model decoupled the effects of indentation strain rate and indenter tip curvature radius from the hardness measurements and the resulting dimensionless model accurately predicted the hardness responses for various loading conditions and indenter tip curvature radii. Furthermore, the proposed dimensionless hardness model was validated by comparing the predicted P–h and H–h curves with experimental and FE simulation results. The good agreement between the model and actual data confirmed the model’s reliability in predicting the ISE independent of external factors.

In conclusion, the study led by Professor Xu Long and his team is significant particularly in the characterization of mechanical properties at small scales. The key significance of the authors’ work lies in its comprehensive approach to understanding and characterizing the ISE in nickel-based single crystal superalloys, specifically DD6.  Moreover, the author’ new dimensionless hardness model that decouples the effects of indentation strain rate and indenter tip curvature radius is a significant contribution. The model can enhance the theoretical understanding of the ISE and also provide a practical tool for accurately predicting hardness measurements independent of external factors. There are several practical implications of the study, for instance in aerospace industry where nickel-based single crystal superalloys like DD6 are extensively used in high-temperature applications, such as turbine blades in jet engines. Accurate characterization of their mechanical properties at small scales ensures reliable performance under extreme conditions and the study’s findings can help improve these materials to be more efficient and durable aerospace components. Furthermore, in power generation, especially in gas turbines, where the mechanical stability of materials under high temperatures and stress is vital. Once again, the enhanced understanding of the ISE and the developed hardness model can guide the development of more robust materials, leading to longer-lasting and more efficient turbine components.

Additionally, another advantage of nanoindentation tests lies in microelectronics and microelectromechanical systems. With devices continue to shrink in size, the mechanical properties of materials at micro- and nano-scales become increasingly important. As the very first pioneer of indentation theory and testing instrument in the electronic packaging industry, the research group led by Professor Xu Long has been working on this since 2017. The methods and models developed by Professor Xu Long and his colleagues can be applied to characterize and optimize these materials used in miniaturized devices. So far, we have published more than 20 papers in top journals on indentation and this applications to various materials.

Investigating Strain Rate Effects on Indentation Size Effect in Nickel-Based Single Crystal Superalloy DD6 - Advances in Engineering

About the author


School of Mechanics, Civil Engineering and Architecture
Northwestern Polytechnical University, China.

My research interests are related to the mechanics of electronic packaging, including multi-field multi-scale material constitutive and damage model, life prediction and reliability analysis. In recent years, my research group has published more than 100 peer-reviewed journal papers in mechanics, mechanical and materials areas, including more than 80 SCI-indexed articles as first author and corresponding author. As the first or only author, I have published 3 books. My paper was selected as the Featured article in Journal of Micromechanics and Molecular Physics (JMMP). According to Google Scholar, the citations of my publications are 1878 with the h-index of 26 and i10-index of 61.

Now, I serve as the Associate Editor of Computer Modeling in Engineering & Sciences. I was also invited to be the Guest Editor-in-Chief of Journals, including Frontiers in Physics (JCR Q2, IF= 3.718), Frontiers in Materials (JCR Q2, IF= 3.985) and Coatings (JCR Q2, IF= 3.236), etc. I was selected as IAAM fellow in 2023, and IEEE Senior Member in 2022.


Xu Long, Ziyi Shen, Jiao Li, Ruipeng Dong, Ming Liu, Yutai Su, Chuantong Chen, Size effect of nickel-based single crystal superalloy revealed by nanoindentation with low strain rates, Journal of Materials Research and Technology, Volume 29, 2024, Pages 2437-2447,

Go to Journal of Materials Research and Technology

Recommended Readings

  1. ZY Shen, RP Dong, J Li, YT Su*, X Long* (2024). Determination of gradient residual stress for elastoplastic materials by nanoindentation. Journal of Manufacturing Processes. V. 109, pp 359–366. (Q1, TOP, IF=6.2)
  2. X Long*, ZY Shen, QP Jia, J Li, RP Dong, YT Su, X Yang, K Zhou* (2022), Determine the unique constitutive properties of elastoplastic materials from their plastic zone evolution under nanoindentation. Mechanics of Materials. V. 175, 104485. (Q2, IF=4.137)
  3. X Long*, QP Jia, ZY Shen, M Liu*, C Guan (2021). Strain rate shift for constitutive behaviour of sintered silver nanoparticles under nanoindentation. Mechanics of Materials, V. 158, 103881. (ESI highly cited paper, Q2, IF=3.266)
  4. X Long*, QP Jia, Z Li, ZX Wen (2020). Reverse analysis of constitutive properties of sintered silver particles from nanoindentations. International Journal of Solids and Structures, V. 191–192, pp 351–362. (Q2, IF=3.900)
  5. X Long*, B Hu, YH Feng, C Chang, MY Li* (2019). Correlation of microstructure and constitutive behaviour of sintered silver particles via nanoindentation. International Journal of Mechanical Sciences, V.161–162, 105020. (Q1, TOP, IF=5.329)
  6. X Long*, WB Tang, YH Feng, Y Yao, LM. Keer (2018). Strain rate sensitivity of sintered silver nanoparticles using rate-jump indentation. International Journal of Mechanical Sciences. V. 140, pp 60–67. (Q1, TOP, IF=5.329)
  7. X Long*, SB Wang, YH Feng, Y Yao, LM Keer (2017). Annealing effect on residual stress of Sn-3.0Ag-0.5Cu solder measured by nanoindentation and constitutive experiments. Materials Science & Engineering: AV. 696, No.1, pp. 90–95. (Q1, IF=3.414)
  8. X Long*, WB Tang, J Liu, XZ Lu, C Zhou, WJ Xia, YP Wu (2018). Estimating the constitutive behaviour of sintered silver nanoparticles by nanoindentation. 19th International Conference on Electronic Packaging Technology (ICEPT 2018), IEEE, Shanghai, August 8–11, 2018. (Outstanding Paper Award)

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