Acta Mechanica

, Volume 230, Issue 12, pp 4259–4271 | Cite as

Size-dependent yield function for single crystals with a consideration of defect effects

  • Bo PanEmail author
  • Hiro Tanaka
  • Chao Ling
  • Yoji Shibutani
  • Shufeng Li
Original Paper


In this work, a size-dependent yield function for a single crystal is developed by considering defect effects, including dislocation pile-up, dislocation starvation, and source exhaustion, especially for micro-pillars. It is found that the proposed yield function compares well with the experimental data, and the proposed model is the extension of a single-arm source model to describe the yielding behavior under a more complicated loading case, not only the uniaxial compression test. Our quantitative conclusions suggest that the stacking-fault energy (SFE), the crystallographic orientation, and the slip system are significant factors for the shape of the yield surface: the slip system determines the number of the edges of the yield surface; the crystallographic orientation controls the angles between the adjacent edges but does not change the number of the edges; the low SFE can make sharp corners rounded and contract the shape of the yield surface, or even curve the edge of the yield surface. Moreover, we investigate the explicit relationship among the stacking-fault energy, the dislocation pile-up effect inside the sample, and the shape of the yield surface: materials with a low stacking-fault energy exhibit pronounced dislocation pile-up effects, and their yield surfaces tend to display rounded vertices, corresponding to the v. Mises yield criterion for the single-crystal sample with a {1 1 1} slip system for example; those with a high stacking-fault energy show typical Tresca criterion-type yield surfaces displaying sharp vertices for the single-crystal sample with a {1 1 1} slip system for example. We also show that this yield function can describe the size-dependent yield surface by considering the stochastic length of the dislocation source and the dislocation pile-up length in single-crystalline micro-pillars.



Y. Shibutani gratefully acknowledges the financial support from Grants-in-Aid for Scientific Research (A) (26249002), and H. Tanaka thanks Young Scientists (A) (25709001) for financial support. S. Li thanks the National Natural Science Foundation of China (Grant numbers 51571160 and 51871180) and Natural Science Basic Research Plan in Shaanxi Province of China (Grant number 2015JM5233) for the financial support of this study. The authors thank Mr. Kenta Yukihiro (a former graduate student in Osaka University) who performed the experiments.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Xi’an Thermal Power Research Institute Co. Ltd.Xi’anChina
  2. 2.Department of Mechanical EngineeringOsaka UniversitySuitaJapan
  3. 3.Southern University of Science and TechnologyShenzhenChina
  4. 4.School of Materials Science and EngineeringXi’an University of TechnologyXi’anChina
  5. 5.Joining and Wedding Research InstituteOsaka UniversityIbarakiJapan

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