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a b s t r a c tAn analytical solution in couple stress elasto-plastic theory is presented for the pure bending beam under small deformation. This solution considers the effects of both elastic deformation and plastic deformation, and gives the relationship between the moment M and the curvature j implicitly. This solution can eliminate the shortcomings in the rigid-plastic solutions by Stolken and Evans (1998), Wang (2000, 2001) et al., and is proved to be more effective in materials with high plastic hardening or small plastic deformation. Moreover, numerical results show that the solution can be used to predict the size effects in the microbend tests and to measure their material length parameter.

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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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