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Acta Metall Sin  2026, Vol. 62 Issue (6): 1117-1127    DOI: 10.11900/0412.1961.2025.00204
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Exploring the Influence of Experimental Conditions on Indentation Relaxation Behavior of a Heat-Resistant Steel Based on the Finite Element Method
WU Xiaodan, ZHAO Jie, CAO Tieshan(), CHEN Jiawan, LIN Tong, ZHANG Haojie
School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China
Cite this article: 

WU Xiaodan, ZHAO Jie, CAO Tieshan, CHEN Jiawan, LIN Tong, ZHANG Haojie. Exploring the Influence of Experimental Conditions on Indentation Relaxation Behavior of a Heat-Resistant Steel Based on the Finite Element Method. Acta Metall Sin, 2026, 62(6): 1117-1127.

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Abstract  

The indentation technique imposes high requirements on the accuracy of testing equipment in practical applications and is susceptible to disturbances from the testing environment and factors such as sample preparation quality. To optimize the key parameters of indentation experiments and enhance the reliability and scientific validity of this method, this study investigates the influence of experimental conditions on the indentation relaxation behavior of Sanicro25 austenitic heat-resistant steel using the finite element method. The simulation results indicate that the friction coefficient has an obvious impact on the test results. When the friction coefficient increases from 0 to 0.30, the corresponding maximum force increases by 18.41%. At the same time, the surface morphology of the indentation changes significantly. As the friction coefficient increases, the material stacking height decreases. However, when the friction coefficient exceeds 0.15, the change in stacking height becomes less pronounced, and the results under different friction coefficients tend to be consistent; the indentation response is also affected by the ratio of sample thickness to indentation depth (thickness-to-depth ratio). The results show that when the ratio is ≥ 20, the relaxation curves are essentially consistent. Further increasing the thickness-to-depth ratio does not lead to significant changes in the relaxation curve. Under the same indentation depth conditions, a quadrangular pyramid indenter produces a larger equivalent creep strain and a faster initial relaxation rate than a conical indenter.

Key words:  indentation simulation      influencing factor      measurement error      indenter shape     
Received:  12 July 2025     
ZTFLH:  TB302  
Fund: National Science and Technology Major Project(MGT2023001)
Corresponding Authors:  CAO Tieshan, associate professor, Tel: 13354054601, E-mail: tieshan@dlut.edu.cn

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2025.00204     OR     https://www.ams.org.cn/EN/Y2026/V62/I6/1117

Fig.1  Schematics of conical (a) and quadrangular pyramid (b) indenters
Fig.2  Finite element calculation mesh for the three-dimensional cross-section (a) and surface (b) of the specimen (Insets are corresponding partially enlarged views)
Fig.3  Comparison of simulation and experimental results for Sanicro25 steel under conical (a) and quadrangular pyramid (b) indenters with a depth of 0.1 mm (F—maximum force, t—compression head pressing time)
Indenter
shape
Force at 1500 s / NError
%
Curvature
difference
(STDEV)
ExperimentSimulation
Conical276.36270.282.204.55
Quadrangular pyramid335.21329.571.686.90
Table 1  Comparison of experimental and simulation results of Sanicro25 steel under different indenters (The maximum penetration depth is 0.1 mm)
Fig.4  Effect of mesh density of sample model on relaxation curve
Fig.5  Effects of thickness-to-depth ratio on relaxation curve (a) and maximum force (b)
Fig.6  Effect of friction coefficient (f) on relaxation curve
Fig.7  From the red path (a) on the specimen surface, the indentation surface profile diagrams (b) extracted under different friction coefficients (Inset in Fig.7b is the locally enlarged diagram)
Fig.8  Mises stress (S) distributions of indentation on specimen surface under maximum indentation (0.1 mm) depth with conical (a) and quadrangular pyramid (b) indenters
Fig.9  Mises stress distributions of indentation on specimen surface after conical (a) and quadrangular pyramid (b) indenters are completely unloaded (SR—stress ring)
Fig.10  Profile Mises stress distribution nephograms and partially enlarged views (insets) of Sanicro25 steel at maximum inden-tation depth (a, c) and after unloading (b, d) under two shapes of indenters (The maximum penetration depth is 0.1 mm)
(a, b) conical indenter (c, d) quadrangular pyramid indenter
Fig.11  After complete unloading of the conical indenter (a, b) and quadrangular pyramidal indenter (c, d), residual stress distribution curves (b, d) of Sanicro25 steel along different paths (a, c) on the specimen are shown (Insets in Figs.11b and d are the locally enlarged diagrams)
Fig.12  Equivalent plastic strain (PEEQ) (a, b, e, f) and equivalent creep strain (CEEQ) (c, d, g, h) nephograms of Sanicro25 steel under two shapes of indenters at the maximum indentation depth (0.1 mm) (a-d) and after complete unloading (e-h) on the surface
Fig.13  Along different paths (a, d) on the specimen of Sanicro25 steel after unloading by two shapes of indenters, PEEQ (b, e) and CEEQ (c, f) distribution curves are shown (Insets in Figs.13c, e, and f are the locally enlarged diagrams)
(a-c) conical indenter (d-f) quadrangular pyramid indenter
Fig.14  Relaxation curves of two indenters at 0.1 mm maximum pressure depth
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