Mechanical resonance of the austenite/martensite interface and the pinning of the martensitic microstructures by dislocations in ${\text{Cu}}_{74.08}{\text{Al}}_{23.13}{\text{Be}}_{2.79}$

A single crystal of ${\text{Cu}}_{74.08}{\text{Al}}_{23.13}{\text{Be}}_{2.79}$ undergoes a martensitic phase transition at 246 and 232 K under heating and cooling, respectively. The phase fronts between the austenite and martensite regions of the sample are weakly mobile with a power-law resonance under external stress fields. Surprisingly, the martensite phase is elastically much harder than the austenite phase showing that interfaces between various crystallographic variants are strongly pinned and cannot be moved by external stress while the phase boundary between the austenite and martensite regions in the sample remains mobile. This unusual behavior was studied by dynamical mechanical analysis (DMA) and resonant ultrasound spectroscopy. The remnant strain, storage modulus, and internal friction were recorded simultaneously for different applied forces in DMA. With increasing forces, the remnant strain increases monotonously while the internal friction peak height shows a minimum at 300 mN. Transmission electron microscopy shows that the pinning is generated by dislocations which are inherited from the austenite phase.

Figure 1

(Color online) DSC curves under cooling and heating.

Figure 2

(Color online) Temperature dependence of the probe position, storage modulus, and internal friction in the heating process with ramp rate of $\dot{T}=5\text{K}/\text{min}$, frequency $f=4\text{Hz}$ for various forces. The force dependence of the jump was inserted in (a); the force dependence of the peak height of the internal friction is inserted in (c), all forces are measured in mN.

Figure 3

(Color online) Temperature dependence of the probe position, storage modulus, and internal friction at ramp rate of 5 K/min (a) 200 mN under cooling and 500 mN under heating and (b) 500 mN under cooling and 200 mN under heating.

Figure 4

(Color online) Temperature dependence of storage modulus and internal friction with various frequencies in the heating process with $F_D/F_S=200/220\text{mN}$ and $\dot{T}=5\text{K}/\text{min}$.

Figure 5

(Color online) Double—logarithmic plot of the frequency dependence of the height of the loss peak in Fig. 4. The decay is consistent with $\text{tan}\left(\delta \right)=A{f}^{-0.2}$.

Figure 6

A section of RUS spectra collected during heating. The left-hand axis is really amplitude but the spectra have been shifted in proportion to the temperature at which they were collected and the temperature scale is shown instead. The two pairs of arrows (two low and two high-temperature peaks) indicate the two resonances which were analyzed in detail.

Figure 7

Variations in elastic constants obtained from fitting to resonance peaks with frequencies of (a) $\sim 284$ and (b) $\sim 65\text{kHz}$ at room temperature. Broken lines represent transition temperatures taken from the DSC analysis. The hardening in the martensitic phase is clearly visible.

Figure 8

Two-beam BF micrograph using $g=1\overline{2}\overline{8}$ showing a martensite plate inside the austenite matrix revealing an abundance of dislocations. The latter can roughly be divided into two groups, those with dislocation lines close to perpendicular to and those with dislocation lines close to parallel with the trace of the austenite-martensite interface. The inset shows a SADP of the 18R martensite along $\left[\overline{2}\overline{1}0\right]$ originating from the encircled region in the martensitic plate.

Figure 9

(a) WBDF micrograph obtained with $g=0018$ showing both types of martensite dislocations inherited from the austenite. Type A dislocations are seen as sharp white lines close to perpendicular to the trace of the austenite-martensite interface while type B dislocations are sharp white lines close to parallel with that interface trace (not to be mistaken with the fringes on the edge of the plate and due to the overlapping of the matrix and the plate). The black arrow points at an intersection of types A and B dislocation while the white arrows indicate intersection points of the type A dislocations with the austenite-martensite interface. (b) Stacking defects of the 18R stacking are seen to stop at a dislocation inside a martensite plate (white arrow).

Figure 10

Two-beam BF micrograph obtained with $g=0018$ revealing the dissociation of the type A dislocations as well as an increase in dissociation distance at the end of the dislocation line.

Figure 11

(a) Martensite plate showing a twin midrib with the corresponding SADP as inset revealing the respective spot splitting. (b) Dislocation lines arriving at the twin midrib of the martensite plate.

Figure 12

Two-beam DF micrograph obtained at $-20°\text{C}$ with $g=1\overline{2}10$ showing an enhanced strain contrast where transformation dislocations tangle with type A dislocations.

Figure 13

(Color online) Scheme of the pinning of the PD by a type A dislocation during cooling.