Influence of external and internal length scale on the flow stress of copper

Abstract

The flow stress of bulk specimens is known to depend on the microstructure. With a reduction of specimen dimensions into the micrometer and nanometer regime, specimen size-effects also influence the mechanical properties. We characterized the size-dependent flow stress of copper over more than three orders of magnitude, starting from several tens of micrometers down to a few tens of nanometers. For this purpose nanoindentation, micro-compression, and tensile testing experiments were performed. Additionally, different grain sizes were generated by severe plastic deformation. The observed increase in flow stress with reduced critical dimension is discussed with respect to the different stress states and microstructures present in the reported experiments. The mechanism controlling deformation changes from dislocation pile-up for critical dimensions > 1 lm via a transition regime (1 lm > critical dimensions > 100 nm) to dislocation nucleation for critical dimensions < 100 nm.

Micro-compression testing: A critical discussion of experimental constraints

“…A potential fit to the data leads to a power exponent of −0.4. For comparison, the shear stress at 10% tensile strain of high purity bulk Cu with an average grain size of 10 m, comparable to the largest inves- tigated specimen size, amounts to 72 MPa [38,39] (dashed line in Fig. 3).…”

Microstructure evolution during severe plastic deformation

“…There are several publications in which experimental evidence for dislocation pile-ups and forests in severely deformed FCC metals has been presented, e.g. [55][56][57]. With decreasing grain size, the density of dislocations increases strongly and their interactions prevent reliable observations in TEM experiments.…”

Yield and plastic flow of soft metals in small volumes loaded in tension and flexure

“…Some data for copper wires in tension using an in situ tensometer have been previously published in part [21,22]. New fits are made to the data and are reported here.…”

“…However, rather than try to fit each theory separately to the data (which can require iterative numerical calculations [21]), here we parameterise the data by using the approximation that " P (z) is given by substituting " ¼ L z into Equations (14) and (15), for the fits to the square-root and linear strain-hardening parts of the data sets, respectively. Then we define z 0 as the height above the neutral plane at which the strain reaches AE" Y , given by z…”

“…These formulae varied with the grain size d but had no dependence on the foil thickness h. We present here new tensile data on Ni foils, which are directly comparable with the flexure data. Also, much more accurate tensile data has become available for polycrystalline copper wire [21,22]. We have therefore carried out flexure experiments on copper foils for direct comparison with both the Ni foil tensile and flexure data and with the Cu tensile data.…”