Multi-aspect size effect transition from micro to macroscale: Modelling and experiment

Z. Y. Feng, H. Li, D. Zhang, X. X. Guo, Y. Q. Chen, M. W. Fu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

18 Citations (Scopus)


Size effects (SEs) impede the mass production of high-performance miniaturised components via micro-forming. Although many studies have examined SEs from multiple aspects, such as flow stress, deformation, and ductile fracture, the SE transitions characterised by the significant changes of these phenomena across the micro- and macroscale remain ambiguous. These SE transitions must be fully and deeply explored to enable the transformation of microscale deformations to macroscale ones by the design of products with appropriate dimensions, grain sizes and loading boundaries. This study involved experimental and numerical studies of multi-aspect SE transitions in flow stress, heterogeneous deformation (surface roughening and strain localisation) and ductile fracture at the micro- and macroscale in copper (Cu) sheets, which are widely used in electronic industries. The Cu sheets for tensile tests were designed and fabricated to be with a thickness (t) of 0.05-1.50 mm, a grain size (d) of 3-260 μm and t/d of 0.63-65.30. The crystal plasticity finite element model (CPFEM) and the Voronoi-based polycrystalline geometric model (VPGM) with t/d of 1-30 were established. Compared with the phenomenological work hardening model (PM), the dislocation density-based model (DDBM) can better predict the multi-aspect behaviours within the scope of above-mentioned scales. An obvious SE transition point (λ) was observed: when t/d < λ, there is a sharp decrease in materials strength and necking strain, an increase in surface roughness and a transformation of fracture mode, as well as a remarkable scattering of the aforementioned responses. The SE transition points vary from t/d = 3 to 11 for different responses, and generally the stress-related λ is smaller than the strain-related one. The larger the t/d, the closer the stress and strain distributions are to the normal distribution. The distribution irregularity of grain-scale stress to the change of t/d is more sensitive than that of strain. Different distributions in grain orientations are the primary inducers of this scattering of responses when t/d < λ. Grain-scale deformation heterogeneity and scattering could be decreased through controlling scale factor t/d > λ, thereby entering the macroscale deformation domain. Case studies of micro-pin extrusion and thin-walled tube-drawing confirmed that setting t/d > λ or using a boundary constraint could alleviate the negative influences of SEs, thus enabling a more uniform deformation.

Original languageEnglish
Article number103364
JournalInternational Journal of Plasticity
Publication statusPublished - Sept 2022


  • Crystal plasticity
  • Deformation behaviour
  • Ductile fracture
  • Micro-forming
  • Size effect
  • Size effect transition

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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