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Updated: Aug 15, 2026

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Determining the Mechanical Strength of Ultra-Fine-Grained Metals
Published on: November 22, 2021
Grain-Size-Dependent Hall-Petch Relationship in CoCrFeTiNi2.1 High-Entropy Alloys
Maoli Yang1,2, Kangchun Li1, Wenping Zhou2
1School of Mechanical Engineering, Guangxi University, Nanning 530004, China.
ACS Omega
|August 14, 2026
Summary
The study reveals a critical 12 nm grain size for maximum strength in CoCrFeTiNi2.1 high-entropy alloys. Temperature and strain rate significantly alter mechanical properties by affecting microstructure and deformation mechanisms.
Area of Science:
- Materials Science
- Computational Materials Science
- Alloy Design
Background:
- High-entropy alloys (HEAs) exhibit unique mechanical properties due to their complex solid-solution structures.
- Understanding the interplay between microstructure, temperature, and strain rate is crucial for designing advanced HEAs.
- Nanocrystalline materials often display size-dependent mechanical behaviors, including inverse Hall-Petch effects.
Purpose of the Study:
- To investigate the size-dependent mechanical behavior of CoCrFeTiNi2.1 high-entropy alloys using molecular dynamics simulations.
- To explore the influence of temperature and strain rate on the alloy's mechanical response.
- To elucidate the atomistic mechanisms governing the structure-property relationships in nanocrystalline HEAs.
Main Methods:
- Atomistic simulations using molecular dynamics (MD).
- Systematic variation of grain size (6-18 nm), temperature (300-1200 K), and strain rate (4 × 10^10–10 × 10^10 s^-1).
- Analysis of tensile strength, flow stress, phase transformations, and dislocation dynamics.
Main Results:
- A transition from inverse Hall-Petch (IHP) to classical Hall-Petch (HP) behavior was observed at a critical grain size of 12 nm.
- Maximum tensile strength and flow stress were achieved at the critical grain size of 12 nm.
- Elevated temperatures reduced strength by 15.67% due to phase depletion and reduced dislocation density.
- Increased strain rate enhanced strength by 18.12% via BCC/HCP transformations and dislocation proliferation.
Conclusions:
- The study establishes a clear "structure-temperature/strain rate-property" linkage in the CoCrFeTiNi2.1 HEA.
- An atomistic understanding of grain size effects under thermal and kinetic loading is provided.
- Findings offer mechanistic insights for designing nanocrystalline HEAs with tailored mechanical performance.

