Size-dependent Elastic Behavior of Micro Scale Copper Beams
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To investigate single crystal copper elastic behavior in micro-scale, microcantilevers with the beam axis having a [11 ̅0] orientation and thicknesses ranging from 5.41μm to 0.74μm were fabricated by focus ion beam (FIB) milling. Then, several series of indentation tests were performed by atomic force microscopy (AFM). According to the experimentally measured spring constants, significant size-dependent elastic behavior was observed, when the cantilever thickness is approximately 1μm or less for single crystal copper. An Euler-Bernoulli beam model based on consistent couple stress theory (C-CST) was applied to interpret this observed size effect. Instead of interpreting size-dependent behavior as a varying elastic modulus, an estimation of the length scale introduced in C-CST was made, resulting in a value in the range of 0.2μm-0.4μm. The corresponding couple stress coefficient η is determined qualitatively, which is estimated to be of order 10^3 μN in the current work.