Fig. 1. Orientation distribution functions (ϕ2 = 45° sections) revealing the slow texture evolution with increasing strain for Ta-4% W: (a) 0% c.r., (b) 70 % c.r. and (c) 90 % c.r. and (d) orientation intensity along the α-fiber and γ-fiber at different rolling reductions.

Fig. 2. Deformation microstructures after 10 % c.r. illustrating different morphologies: (a) two sets of GNBs, (b) one set of GNBs, (c) a diffuse cell structure, (d) a diffuse cell structure delineated by GNBs marked by arrows. Dashed lines mark the traces of the indicated crystallographic planes in the TEM images, while in the tracings solid black lines indicate GNBs and dashed gray lines indicate IDBs. Orientations: (a) ND/RD = (-0.66 -0.51 0.55)/[0.75 -0.43 0.50] 6.4° to γ-fiber and 27.6° to α-fiber (b) ND/RD = (-0.96 0.23 0.15)/[-0.25 -0.96 -0.14] 39.3° to γ-fiber and 31.4° to α-fiber, (c) ND/RD = (0.36 0.70 -0.62)/[-0.64 -0.30 -0.71] 14.7° to γ-fiber and 17.8° to α-fiber, (d) ND/RD = (-0.97 0.15 -0.20)/[-0.11 -0.970-0.22] 40.3° to γ-fiber and 32.6° to α-fiber.

Fig. 3. Comparison of (a) diffuse cells showing a magnified view of a region in Fig. 2(c) to a Taylor lattice (b) with dislocations on slip planes as well as nascent cells forming at dislocation tangles after 10 % c.r. For the Taylor lattice the foil plane is (011); primary [11-1] and conjugate [1-11] dislocations are parallel to the foil plane and along gray stripes in the insert schematic. Dashed lines mark the traces of crystallographic planes. Thick banded lines in the insert schematic represent nascent cell walls.

Fig. 4. Deformation microstructure after 30 % c.r. showing more developed cell structures between GNBs: (a) one set of GNBs, (b) two sets of GNBs, (c) diffuse cell structure with some suggestion that GNBs may be forming as shown by the white arrows. Dashed lines mark the traces of crystallographic planes in the TEM images. Orientations: (a) ND/RD = (0.16 -0.49 0.86)/[0.95 0.31 0.01] 29.8° to γ-fiber and 26.9° to α-fiber, (b) ND/RD = (-0.51 0.13 -0.85)/[-0.76 -0.53 0.38] 30.8° to γ-fiber and 24.3° to α-fiber, (c) ND/RD = (-0.96 0.06 -0.29)/[0.05 -0.94 -0.34] 41.1° to γ-fiber and 25.2° to α-fiber.

Fig. 5. Deformation microstructure after 50 % c.r. showing also the emergence of S-bands: (a) one set of GNBs, (b) two sets of GNBs and very short S-bands, (c) two sets of GNBs. Dashed lines mark the traces of crystallographic planes. Orientations: (a) ND/RD = (0.18 -0.47 0.87)/[0.96 0.29 -0.04] 29.4° to γ-fiber and 28.5° to α-fiber, (b) ND/RD = (-0.52 0.65 -0.55)/[-0.85 -0.31 0.44] 5.6° to γ-fiber and 25.1° to α-fiber, (c) ND/RD = (-0.15 -0.91 0.39)/[0.62 0.22 0.75] 33.5° to γ-fiber and 13.6° to α-fiber.

Fig. 6. Deformation microstructure after 70 % c.r. with S-bands occurring more frequently but still widely spaced (dashed arrows indicate the shearing associated with the S-bands).

Fig. 7. TEM images and illustrations of how deformation structure is realigned to the RD by intersecting slip in S-bands after 90 % c.r.: (a) TEM image (corresponding sketch (c)) GNBs in the form of MBs and LBs coexist with S-bands; (b) TEM image (corresponding sketch (d)) GNBs form LBs near the RD. Solid lines indicate GNBs, dashed lines IDBs.

Fig. 8. Decrease in average boundary spacing and increase in misorientation angle across (a) GNBs and (b) IDBs as a function of increasing strain.

Fig. 9. Cumulative distributions for (a) the spacing between and (b) the misorientation angles across the IDBs. The curves are shifted from right to left with increasing strain for the spacing while they are shifted from left to right with increasing strain for the misorientation angles.

Fig. 10. Cumulative distribution for (a) GNBs spacing and (b) GNBs misorientations. Histograms show the development of high angle GNBs with a second peak in the distribution developing at the largest strain: (c) 70 % c.r. and (d) 90 % c.r.

Fig. 11. Alternating misorientation angles across GNBs with increasing strain indicate the influence of stress screening on dislocation patterning. (a, b) 10 % c.r., (c, d) 30 % c.r. and (e, f) 50 % c.r.

Fig. 12. The width of GNBs decreases linearly with spacing but the width is much thicker in Ta-4% W than in Ni (data from Ref. [16]).

Fig. 13. The mixed character of GNBs at different reductions: (a) 10 % c.r., (b) 30 % c.r. and (c) 50 % c.r.

Fig. 14. The probability densities of (a) GNB spacings, (b) GNB misorientation angles, (c) IDB spacings, and (d) IDB misorientation angle at different strain levels collapse into a single function for each parameter when scaled by their individual averages.

Fig. 15. Increasing tungsten content linearly increases the initial lattice friction stress: σ0, which provides the constant value of σ0 = 240 MPa at 4% W used in the flow stress equation.

Fig. 16. Flow stress calculations based on the measured microstructural parameters and Eq. (7) agree very well with the experimentally measured values (blue squares), taken as average values from the two tensile tests at each condition.