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Sample size effect on creep in bending: An interplay between strain gradient and surface proximity effects

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Abstract

Miniature cantilevers are associated with amplification in strain gradient and dislocation recovery. These contrasting phenomena interplay to impart strengthening via the injection of geometrically necessary dislocations because of strain gradients and softening due to the surface proximity effect. In this work, creep studies on Al cantilevers of thicknesses ranging from 0.070 to 7 mm demonstrate this interplay. The 2D strain field and dislocation substructure were examined to understand the steady-state creep response in miniaturized cantilevers. The average creep response of the cantilever strengthens with decreasing cantilever thickness; however, regimes of hardening, softening, and bulk-like behavior were observed while traveling along the length of the cantilever. Consistently, refinement in the steady-state dislocation substructure was observed in the regions of large strain gradients. The locations in a miniaturized cantilever with insignificant strain gradients registered surface proximity effect-induced enhanced creep rates. An analytical model has been developed to describe the strain gradient-surface proximity interplay.

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Data availability

The datasets generated during and/or analyzed during the current study are not publicly available but are available from the corresponding author on reasonable request.

Notes

  1. For Al, a uniaxial sample with the thickness ≥ 2 mm can be considered as bulk-sized sample [9, 29].

  2. If a bending creep experiment is performed at \(\sigma_{max} < \sigma_{YS}\), where \(\sigma_{max}\) and \(\sigma_{YS}\) are the maximum stress in the cantilever at any time and the yield strength of the material, respectively, then the stress-state, σ, at the stress-invariant points can be given by \(\sigma = My/I\), where M and I are the moment and area inertia, respectively [6].

  3. GND density was calculated by EDAX OIM EBSD software using the default G.N.D. dislocation density tensor (Nye tensor).

  4. This estimate is based on the highest value of the strain gradient prevalent in the bulk-sized cantilevers (i.e., h ≥ 2.5 mm) at a strain of 5% (which is well inside the steady-state creep regime at the stress and temperature range used in this study).

  5. Euler- Bernoulli cantilevers have a length to thickness ratio, i.e., h/L, of ≥ 6, which allows neglecting the shear stresses in comparison to normal or bending stress along the length of the cantilever [3, 4]. The cantilevers in this work are designed to have chamfers on all four sides, which precludes stress concentration at the fixed-end [6, 7], and ensures applicability of the standard beam equations to obtain stress–strain relationships.

  6. Rust-Oleum is a commercial high temperature spray paint manufactured by Rust-Oleum Global, U.S.A.

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Acknowledgments

The authors would like to thank Aeronautical Research and Development Board, India (ARDB 0242), and the Ministries of Human Resource Development and of Power, Government of India (IMPRINT 0009) for financially supporting this work. The authors also thank Anton-Paar and Bruker for extending the courtesy to use their facilities to conduct a part of this work. The use of scanning electron microscopy facilities from the Advanced Facility for Microscopy and Microanalysis (AFMM) at the Indian Institute of Science, Bangalore, is gratefully acknowledged.

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  1. Department of Materials Engineering, Indian Institute of Science, Bangalore, 560012, India

    Syed Idrees Afzal Jalali, Vikram Jayaram & Praveen Kumar

  2. Bruker, Minneapolis, MN, USA

    Sanjit Bhowmick

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Jalali, S.I.A., Bhowmick, S., Jayaram, V. et al. Sample size effect on creep in bending: An interplay between strain gradient and surface proximity effects. Journal of Materials Research 38, 3059–3077 (2023). https://doi.org/10.1557/s43578-023-01026-5

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