Determining the activation energy and volume for the onset of plasticity during nanoindentation

Nanoindentation experiments are performed on single crystals of platinum, and the elastic-plastic transition is studied statistically as a function of temperature and indentation rate. The experimental results are consistent with a thermally activated mechanism of incipient plasticity, where higher time-at-temperature under load promotes yield. Using a statistical thermal activation model with a stress-biasing term, the data are analyzed to extract the activation energy, activation volume, and attempt frequency for the rate-limiting event that controls yield. In addition to a full numerical model without significant limiting assumptions, a simple graphical approximation is also developed for quick and reasonable estimation of the activation parameters. Based on these analyses, the onset of plasticity is believed to be associated with a heterogeneous process of dislocation nucleation, with an atomic-scale, low-energy event as the rate limiter.

Figure 1

Examples of typical experimental loading functions (load, $P$, vs time, $t$) used in the present study. Most indentations were performed using a constant loading rate (solid line), while some also used a cubic loading function (dashed line).

Figure 2

Representative load-displacement $\left(P\text{−}h\right)$ curves for the loading portion of indentations, obtained at constant loading rate $\dot{P}=250\mu \mathrm{N}∕\mathrm{s}$ and various temperatures. Curves for 100 and $200°\mathrm{C}$ are offset along the $h$ axis for clarity, and the predictions of Eq. (1) for elastic contact are shown as a solid line for each case.

Figure 3

Procedure for identifying the first displacement burst during nanoindentation of (110)-oriented platinum at $25°\mathrm{C}$ with a constant loading rate of $250\mu \mathrm{N}{\mathrm{s}}^{-1}$. The first burst (denoted by a large black circle) is associated with the first departure from the Hertzian elastic contact theory [Eq. (1)] in the $P\text{−}h$ curve (a), as well as a measurable velocity spike (b).

Figure 4

Examples of the statistical data acquired for the first displacement burst during nanoindentation of (110)-oriented platinum. The cumulative fraction, $F$, of experimental loads, $P$, at the burst point are plotted for many indentations performed with the same experimental conditions. Part (a) shows the effect of test temperature for sets of indentations at a constant loading rate $\dot{P}=25\mu \mathrm{N}∕\mathrm{s}$, while part (b) shows the effect of rate at a constant temperature $T=100°\mathrm{C}$.

Figure 5

Example of the linear least-squares procedure used to extract the activation volume from experimental data by the first-order analysis, omitting less-reliable data near the tails of the curves. Experimental data like those from Fig. 4b (but at $T=25°\mathrm{C}$) are plotted according to the form of Eq. (20), and the solid lines are the best fits of that equation to the data.

Figure 6

Graphical construction of Eq. (23), used to extract the activation enthalpy for the first displacement burst. The points show experimental data obtained at $\dot{P}=25\mu \mathrm{N}∕\mathrm{s}$ for three different temperatures, and the solid lines are the best fits of Eq. (23). The three trendlines shown converge to a common $y$ intercept $(\sim 0.0276\pm 0.005{\mathrm{N}}^{1∕3})$ at $T=0$, which is proportional to the activation enthalpy via Eq. (23).

Figure 7

All of the experimental data collected in this study for constant loading rate indentations on (110) platinum are shown here as symbols, with the fit obtained using the second-order shear-biased model [Eq. (3), $(\sigma =\tau )$] shown as solid lines. The goodness of the fit with respect to loading rate variations can be seen in (a)–(c) at temperatures of 25, 100, and $200°\mathrm{C}$, respectively. In (d) all the data sets obtained at $25\mu \mathrm{N}∕\mathrm{s}$ are displayed to better illustrate the subtle temperature effects captured by the model.

Figure 8

Data from experiments performed using a cubic loading function [$P=A{t}^3$, Eq. (24)] are shown by the symbols. The experimental data are well predicted without adjustable parameters using the second-order shear-biased model, shown here as solid lines. Evaluation of the model takes as input the activation parameters extracted earlier from the constant loading rate data (Table , row 2).

Figure 9

Experimental data collected for constant loading rate indentations on (111)-oriented platinum, plotted as cumulative fractions of the load $P$ at the first displacement burst. Fitting this data with the second-order analysis with a shear bias according to Eq. (18) yields the solid lines, and the activation parameters resulting from this fit are similar to those obtained from analysis of the data for (110)-oriented platinum in Fig. 7 (cf. Table ).