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Volume 15
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10.3390/cryst15060561
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Article

Crystal Plasticity Finite Element Analysis of Spherical Nanoindentation Stress–Strain Curve of Single-Crystal Copper

by
Haoming Xia
1,
Zhanfeng Wang
1,2,3,*,
Shichao Qu
2,
Weijie Shan
1 and
Rongkai Tan
1,3
1
School of Mechanical and Electrical Engineering, Suqian University, Suqian 223800, China
2
NO. 1 Drilling Engineering Company, CNPC Bohai Drilling Engineering Company Limited, Tianjin 300280, China
3
Jiangsu Engineering Research Center of Key Technology for Intelligent Manufacturing Equipment, Suqian 223800, China
*
Author to whom correspondence should be addressed.
Crystals 2025, 15(6), 561; https://doi.org/10.3390/cryst15060561
Submission received: 7 May 2025 / Revised: 10 June 2025 / Accepted: 12 June 2025 / Published: 13 June 2025
(This article belongs to the Special Issue Performance and Processing of Metal Materials)
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Abstract

In this paper, we perform crystal plasticity finite element (CPFE) simulations of spherical nanoindentation to extract the indentation stress–strain (ISS) curve for a single-crystalline copper. The load–displacement curves on the Cu (010) surface at incremental indentation depths are obtained. Surface pile-up topography is explored and characterized by the activated slip systems on the indented surface and stress distribution on the cross-section to reveal the crystal anisotropy. And the effect of indentation depth on the stiffness and surface pile-up height is further analyzed. Finally, the zero point is defined, and the indentation stress–strain (ISS) curve is extracted from load–displacement curves. The validity of the ISS curve is demonstrated for crystalline copper materials by comparing measured results published in the literature.
Keywords: nanoindentation; single-crystal copper; stress–strain curve; crystal plasticity finite element; dislocation nanoindentation; single-crystal copper; stress–strain curve; crystal plasticity finite element; dislocation

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MDPI and ACS Style

Xia, H.; Wang, Z.; Qu, S.; Shan, W.; Tan, R. Crystal Plasticity Finite Element Analysis of Spherical Nanoindentation Stress–Strain Curve of Single-Crystal Copper. Crystals 2025, 15, 561. https://doi.org/10.3390/cryst15060561

AMA Style

Xia H, Wang Z, Qu S, Shan W, Tan R. Crystal Plasticity Finite Element Analysis of Spherical Nanoindentation Stress–Strain Curve of Single-Crystal Copper. Crystals. 2025; 15(6):561. https://doi.org/10.3390/cryst15060561

Chicago/Turabian Style

Xia, Haoming, Zhanfeng Wang, Shichao Qu, Weijie Shan, and Rongkai Tan. 2025. "Crystal Plasticity Finite Element Analysis of Spherical Nanoindentation Stress–Strain Curve of Single-Crystal Copper" Crystals 15, no. 6: 561. https://doi.org/10.3390/cryst15060561

APA Style

Xia, H., Wang, Z., Qu, S., Shan, W., & Tan, R. (2025). Crystal Plasticity Finite Element Analysis of Spherical Nanoindentation Stress–Strain Curve of Single-Crystal Copper. Crystals, 15(6), 561. https://doi.org/10.3390/cryst15060561

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