Size Effect in Continuum Modeling

Abstract

The mechanical properties of some materials (Cu, Ni, Ag, etc.) have been shown to develop strong dependence on the geometric dimensions, resulting in a size effect. Several theories have been proposed to model size effects, but have been based on very few experiments conducted at appropriate scales. Some experimental results implied that size effects are caused by increasing strain gradients and have been used to confirm many strain gradient theories. On the other hand, some recent experiments show that a size effect exists in the absence of strain gradients. This report describes a brief analytical and experimental study trying to clarify the material and experimental issues surrounding the most influential size-effect experiments by Fleck et al (1994). This effort is to understand size effects intended to further develop predictive models.

Quasi-Static Torsion Characterization of Micro-diameter Copper Wires

“…The work hardening behavior of the copper wires will make significant difference in their yield strength. In this study we ensured all wire specimens in elasticity before torsional loading according to previous study in tensile response of the copper wires [3].…”

“…The EBSD results in Ref. [3] showed that the microstructures of these copper wires are quite similar: many annealing twins but no significant texture present. The larger-size wire has a larger average grain size but still at the same order of magnitude for all copper wires.…”

“…Figure 1 presents a typical optical image of the cross section of the 180-μm-diameter copper wire. Electron Backscatter Diffraction (EBSD) technique was also used to examine these samples in the scanning electron microscope (SEM) [3]. The EBSD results in Ref.…”

“…The larger-size wire has a larger average grain size but still at the same order of magnitude for all copper wires. Although there are many grains identified for a cross section (even the smallest size wire has at least 30 grains), the variation in grain size is quite large [3]. For example, the 180-μm-diameter wire has an average grain size of 7.3 μm whereas the largest grain size is 40 μm.…”

“…In this study, the value of the constant c 1 was individually calibrated for each specified configuration of the foam cylinder and the reflection tapes. For rotation measurements, the accuracy of θ S is better than 0.05 degrees certified by the manufacturer and the maximum error of the laser rotation sensor (or the specimen) θ S was 0.1 degrees determined from calibration [3].…”