Bright x-rays reveal shifting deformation states and effects of the microstructure on the plastic deformation of crystalline materials

The plastic deformation of crystalline materials is usually modeled as smoothly progressing in space and time, yet modern studies show intermittency in the deformation dynamics of single-crystals arising from avalanche behavior of dislocation ensembles under uniform applied loads. However, once the prism of the microstructure in polycrystalline materials disperses and redistributes the load on a grain-by-grain basis, additional length and time scales are involved. Thus, the question is open as to how deformation intermittency manifests for the nonuniform grain-scale internal driving forces interacting with the finer-scale dislocation ensemble behavior. In this work we track the evolution of elastic strain within individual grains of a creep-loaded titanium alloy, revealing widely varying internal strains that fluctuate over time. The findings provide direct evidence of how flow intermittency proceeds for an aggregate of $\sim 700$ grains while showing the influences of multiscale ensemble interactions and opening new avenues for advancing plasticity modeling.

Figure 1

CT reconstruction showing Au fiducial markers on the bottom ($+x$) face. The markers, proceeding from left to right, are located at $y$ positions of 0.435, 0.0675, and $-0.0547$ mm. These positions were established by averaging the position of indexed Au grains contained in the markers. The tensile direction is along the horizontal.

Figure 2

Experimental configuration showing laboratory (APS) and sample coordinate systems.

Figure 3

Grains in the $1{\mathrm{mm}}^3$ region illuminated by high-energy x rays. Grains tracked during creep at $0.85{\sigma }_y$ are shown as spherical symbols. The symbol color corresponds to the maximum resolved shear stress for basal slip, and the size corresponds to the relaxation (decrease) of the effective stress over the duration of the scan ($\sim 15$ min). The origin is located at the center of the cube outline. The scan was taken at 3.3 h into the creep loading.

Figure 4

Grains at $y=0.3$ in a cluster (relaxing grains of Fig. 3) that shows a large transient (grain a), several transients of varying magnitude (grain b), and loading of a grain (grain c) adjacent to the cluster containing grains a and b. By comparison, grain d, located at approximately the same cross-sectional region but at a different vertical location along the tensile axis, $y=-0.3$, exhibits relatively quiescent behavior. The inset relates the position of the grains with respect to the center of the cube outline of Fig. 3.

Figure 5

Stress decrease at the outset of creep loading at 85% of the yield stress, with corresponding slip band developed at the location of the grain (illustrated using DIC images).

Figure 6

Scaling developed through unloading events for effective elastic strain (horizontal axis, in units of $\mu \varepsilon$), combining events from the $0.8{\sigma }_y$ and $0.85{\sigma }_y$ loading cases. Solid and dashed lines show fits to Eqs. (3) and (5), respectively. The event populations consist of relaxation events occurring within individual grains, even though some of the events occurred in the same time window.

Figure 7

Relaxation events as measured by change (magnitude of decrease) in effective strain, plotted against maximum resolved basal and prism slips.

Figure 8

Bending moment developed at $y=0.35$ mm along the tensile axis.