The scaling exponent in the size effect of small scale plastic deformation

Compression testing of micropillars (yield stress as a function of pillar diameter) has been interpreted in terms of very different scaling exponents for the size effect (smaller is stronger) in fcc and bcc metals and for ceramics, strongly correlated with the yield strengths of the materials. We show that the data is compatible with a single scaling exponent x = 1, and that the reported exponents in the range 0–1 express no more than the micropillar diameters and bulk strengths. The single scaling exponent implies a minimum strength which scales with size in the same way for all materials. This size effect is not fundamentally different in the presence of and in the absence of a strain gradient. It is interpreted in terms of the space available for dislocation source operation. The absence of any experimental data below this minimum strength is strong confirmation of this interpretation.

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► Analytic fits to micromechanical testing data can be ambiguous or misleading.
► Similar problems have been resolved in semiconductor strained-layer work.
► The scaling exponent comes directly from the structure size and the bulk strength.
► The mechanical strength is the sum of the bulk strength and the size effect.
► The size-dependent component of strength has a scaling exponent of –1.