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Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity

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Abstract

Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ 0 ≪ H ≪ E, where σ 0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.

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Authors and Affiliations

  1. State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, 116023, Dalian, China

    Bin Ji, Wanji Chen & Jie Zhao

  2. Department of Aeronautics and Space Navigation, Shenyang Institute of Aeronautical Engineering, Daoyi South Street 37, 110136, Shenyang, Liaoning, China

    Wanji Chen

Authors
  1. Bin Ji
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  2. Wanji Chen
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  3. Jie Zhao
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Correspondence to Bin Ji.

Additional information

The project supported by the National Natural Science Foundation of China (50479058, 10672032).

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Ji, B., Chen, W. & Zhao, J. Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity. Acta Mech Sin 25, 381–387 (2009). https://doi.org/10.1007/s10409-009-0226-x

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  • DOI: https://doi.org/10.1007/s10409-009-0226-x

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