Fig. 1. (a) Schematic representation of the fracture analysis diagram reflecting the temperature dependence of the local effective yield and fracture stresses of the material. The intermediate temperature region represents the BDT region, where the fracture behavior of the material changes from brittle to ductile. (b) Schematic representation of a high-temperature nano-indentation system for evaluating local effective yield stress in the diagram. (c) Schematic illustration of a bcc bi-crystal cell with symmetric tilt GBs prepared for the present MD simulations. The color of atoms in the atomic snapshots is scaled according to the CNA pattern [61], where blue atoms correspond to a bcc structure and gray atoms indicate an unspecified structure.

Fig. 2. (a) EBSD orientation maps of 80rolled, 50rolled, as-received, and annealed specimens. To clarify the grain shape of each specimen, their crystallographic orientations of each specimen are presented using colored cuboidal surface maps along the ND, RD, and TD. (b) FWHM values obtained at major diffraction peaks of bcc W using CuKa1 radiation. (c) Experimental q values and the fraction of edge component calculated using the MWH method. Red dotted lines correspond to the theoretical q values for the pure screw (2.034) and pure edge (-0.841) components [42].

Fig. 3. Results of high-temperature nano-indentation tests to obtain the critical shear stress value for the onset of plastic yielding. (a) P-h curves of the as-received specimen at RT and elevated temperatures. Insets are SPM images that show a part of the indented area after the unloading. (b) Cumulative probability of the τmax experimentally obtained for the as-received specimen at different temperatures. Solid lines correspond to the best fit obtained between the experimental data and cumulative distribution function of the lognormal distribution. (c) Typical P-h curves of all the W specimens at RT and elevated temperatures. Among the various results obtained under certain conditions, the results with a cumulative probability of approximately 50% are shown as examples. Magnified images exhibiting the pop-in event are presented separately below each figure.

Fig. 4. Temperature dependence of the τmax obtained for the (a) 80rolled, (b) 50rolled, (c) as-received, and (d) annealed specimens. Experimental data at selected cumulative probabilities (F(τ) = 0.1, 0.3, 0.5, 0.7, and 0.9) are presented along with the corresponding linear regression of data points [Eq. (7)].

Fig. 5. Ideal (theoretical) mechanical responses in tensile simulation of bcc W single crystals for usual cleavage planes. (a) The resultant ideal stress-distance responses of predefined fracture surfaces of (100), (110), and (111) calculated using the molecular statics simulations based on present and previously published [46] 2NN MEAM potentials compared to the present DFT calculation. (b) Fracture stresses of bcc single crystal cells for the loading directions of [100], [110], and [111], which were obtained using MD simulations according to the present 2NN MEAM potential.

Fig. 6. Fracture behavior of tilt GBs with diverse misorientation angles in pure W. (a) GB energies of [100], [110], and [111] symmetrical tilt GBs in bcc W calculated using molecular statics simulations based on the present and previously published [46] 2NN MEAM potentials compared to the present DFT data [72] (b) Tensile stress-strain responses of bcc bi-crystal cells with special ([100] tilt 36.9°, Σ5), low-angle ([110] tilt 10.1°), and high-angle ([111] tilt 32.2°) GBs calculated via the MD simulations based on the 2NN MEAM potential developed in this study. Results of tensile loadings at selected temperatures (50, 300, 600, and 850 K) are presented as examples. Snapshots of bi-crystals at selected temperatures and different levels of strains are also presented. The color of atoms in the atomic snapshots is scaled according to the CNA [61] pattern. (c) Fracture stresses of symmetric tilt GBs with various misorientation angles. Results of tensile loadings at selected temperatures (50, 300, 600, and 850 K) are presented as examples.

Fig. 7. (a) Fractographs observed by the SEM after the tensile tests at different temperatures. The upper parts show the fracture morphologies of tests performed at lower temperatures and the lower parts at relatively higher temperatures. The corresponding values of energy plastically absorbed during the tensile loading are notated in the figures with yellow color. (b) Typical flexural stress-strain curves of three-point bending tests for selected as-received specimens as an example. (c) Fractured specimens corresponding to each curve in (b), showing BDT.

Fig. 8. Present fracture analysis diagram of (a) 80rolled, (b) 50rolled, (c) as-received, and (d) annealed W specimens established by combining the τmax measured using nano-indentation and fracture shear stress obtained using MD simulation. The red solid line indicates the temperature dependence of the τmax at [F(τ) = 97.7%] corresponding to (μ+2σ). Blue-colored solid and dotted lines correspond to the (μ-2σ) and (μ-3σ) of data points for the GB fracture stress, respectively. Here, μ is the mean of the distribution and σ is its standard deviation determined by the lognormal distribution fitting (Fig. S5 and S6). The BDT region corresponds to the range between two intersects of red solid and blue solid/dotted lines (gray-hatched areas).

Fig. 9. (a) Temperature dependence of absorbed energy during tensile and bending tests for 80rolled (purple), 50rolled (blue), as-received (green), and annealed (red) specimens. Data points with the circle and diamond-shape on the solid line represent the experimental values of the tensile test and three-point bending test, respectively, corresponding to the results shown in Fig. S7. (b) Temperature dependence of absorbed energy of the as-received specimens having different orientation. The inset is the schematic representation of the specimens extracted from the as-received rolled plate in different direction. Data points with the circle, diamond, triangle, and square-shape represent the experimental values, corresponding to the results shown in Fig. S8. The shaded areas in both (a) and (b) represent the BDT regions estimated using the present fracture analysis diagram in this study.

Fig. 10. Correlation between the dislocation density obtained by the XRD measurement, BDT region determined using the present fracture analysis diagram, activation enthalpy of pop-in determined by Eq. (7) and the shear strain rate calculated using Eq. (8) for eachWspecimen.