Local strain variability and force fluctuations during the martensitic transition under different driving mechanisms

The stress-induced martensitic transition in a Cu-Zn-Al shape memory alloy has been studied under three different driving conditions by using (i) a hard driving device which imposes a displacement rate on the sample heads, (ii) a soft driving device which imposes a loading rate on the sample, and (iii) a mixed driving in which the sample is driven using a spring. We have measured the local strain of different segments in the sample as a function of the applied force. During the transition, we have identified two regimes: one associated with nucleation of martensitic needle domains and another mainly associated with front propagation. For the hard and mixed driving conditions, local strain exhibits great variability between segments that is not present under soft driving. In addition, we have analyzed the distribution of force fluctuations. Fluctuations are essentially Gaussian during front propagation regimes, whereas fluctuations display a clear non-Gaussian tail in the nucleation regime for nonsoft driving conditions. Harder driving results in a wider non-Gaussian tail.

Figure 1

(a) Picture of the sample with the position of the segments that are monitored by the Zwick laser speckle extensometer. On the back of the sample one can observe traces of the markings for the Fiedler extensometer. The studied segments are labeled from top (1) to bottom (9). (b) Schematic representation of the mixed device.

Figure 2

Local strain versus time for the three different driving conditions and for the different segments as indicated by the legend. Panel (a) corresponds to the soft device, (b) to the mixed device, and (c) to the hard device.

Figure 3

Force versus time for three different driving conditions: panel (a) corresponds to the soft device, (b) to the mixed device, and (c) to the hard device. Letters indicate the nucleation regime AB, the front propagation regime BC and the end of the transformations D, as obtained from analysis of Fig. 5. The inset indicates the positions of the A,B,C,D points for the soft driving case, which are very close in time.

Figure 4

Force versus local strain for each segment, from top (1) to bottom (9). Column (a) corresponds to the soft device, (b) to the mixed device, and (c) to the hard device. Note the existence of retransformation phenomena (segment 3 for the mixed case or segment 7 for the hard case) and the fact that some segments remain not fully transformed where the transition has ended for the soft-driving case (for instance segments 7 and 8 for the hard driving case).

Figure 5

Total deformation $\mathrm{\Delta }X$ as a function of time for the three different driving conditions. The letters A, B, C, and D indicate the different regimes as discussed in the text. The inset reveals a magnification of the 60 s period, where the transition occurs for the soft driving case

Figure 6

Force as a function of the total strain $\mathrm{\Delta }X\left(t\right)/X\left(0\right)$, indicating the nucleation regime AB and the advance of the martensitic fronts BC. (a) Soft driving, (b) mixed driving, and (c) hard driving.

Figure 7

Force histograms for the three different driving mechanisms. AB corresponds to the nucleation regime and BC to the front propagation regime. Data has been normalized so that it can be read as a probability density function $g\left(F\right)$ with area 1. The thin lines show the Gaussian curves (parabolas) fitted from the corresponding mean and standard deviation values.