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

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.

Size effect in micro-scale cantilever beam bending

“…From Eq. (39), the beam bending rigidity for the couple-stress theory can be expressed as (72) and that for the C-W gradient theory can be found from Eq. (66),…”

“…The micro-beam bending problem has already been analyzed in several works using different strain gradient theories, such as Wang et al [66], Lam et al [21], McFarland and Colton [67], Park and Gao [68], Ma et al [69], Challamel and Wang [70], Giannakopoulos and Stamoulis [71], Ji et al [72], and Shi et al [73]. Whether the simple C-W strain gradient theory [2] could predict the size effect in a micro-cantilever beam is another motivation that we present in this paper.…”

Nonlinear dynamic response of beam and its application in nanomechanical resonator

“…For a nanometer scale beam, the effects such as surface layer, surface tension [33], the strain gradient [34] can stand out, which effectively changes E and I. Furthermore, the effect of surface layer can also have impact on the the damping coefficient of C [35], which indicates the energy dissipation of the system.…”