Nucleation Theory for Yielding of Nearly Defect-Free Crystals: Understanding Rate Dependent Yield Points

Experiments and simulations show that when an initially defect-free rigid crystal is subjected to deformation at a constant rate, irreversible plastic flow commences at the so-called yield point. The yield point is a weak function of the deformation rate, which is usually expressed as a power law with an extremely small nonuniversal exponent. We reanalyze a representative set of published data on nanometer sized, mostly defect-free Cu, Ni, and Au crystals in light of a recently proposed theory of yielding based on nucleation of stable stress-free regions inside the metastable rigid solid. The single relation derived here, which is not a power law, explains data covering 15 orders of magnitude in timescales.

Figure 1

Schematic phase diagram and $\mathcal{N}$, $\mathcal{M}$ phases [18] corresponding to the $d=2$ square lattice, in the $h_X-ϵ$ plane (see text). The blue line is the first-order phase boundary. The dotted lines show slip planes in the $\mathcal{M}$ phase.

Figure 2

(a),(b) Nonlinear least-square fits (solid lines) of Eq. (1) to experimental results (symbols) on Cu and Ni samples, both single crystal (SC) and ultrafine grained polycrystalline (PC); see text and Table 1 for details. (c),(d) Same as (a) and (b) but for MD simulations of Au, Cu, and Ni. (e) Plot of the data in (a)–(d) using scaled variables [with the same symbols as in (a)–(d)] showing collapse onto the single master curve (1) (solid black line). (Dashed) Approximate asymptotic form (2). Three experimental datasets with excessive ($>50\%$) scatter have been omitted. (f) A log-linear plot of Eq. (1) shows that the parameters ${\gamma }_s$ and ${\tau }_0$, obtained from MD of Cu [43], are able to predict the results of experiments [33] performed ${10}^{-12}$ times more slowly. The light blue band on the solid line shows the uncertainty of our prediction at 95% confidence [from fit (2), see Table 1].