Crack deflection at high-toughness GBs

We conducted our investigation on a 1 mm-diameter cylindrical sample of alloy 725 that had been electrochemically charged with H and loaded to failure in tension (Methods). The sample contains the tip of a large, intergranular secondary crack. Figure 1a shows the XRAT scan of our sample with the void volume within the secondary crack shown in black. All the fracture surfaces observed in the sample are interconnected: no independent cracks disconnected from the main crack were observed. We determine the average orientation of the fracture surface by manually fitting a plane to the crack within the core sample and find that this plane is not perpendicular to the sample axis. We attribute this deviation to the marked, non-uniform plastic distortion of the tensile specimen (Methods), which causes the tensile axis to drift away from the sample axis during the test. Similarly, we identify a nominal crack propagation direction as the direction within the nominal crack plane that lies perpendicular to the crack front. Figure 1b, c shows the crack along its nominal plane and parallel to its propagation direction. They show that the crack exhibits pronounced local deviations from its average orientation.

Fig. 1 3D sample reconstruction. a X-ray attenuation tomography (XRAT) data with metal shown in gray and void space inside the secondary crack shown in black. Scale bar: 200 μm. b Isolated section of the XRAT reconstruction with an edge-on view of the nominal crack plane (X–Y), indicated in blue. The nominal crack propagation direction (X) is into the page. c High-energy diffraction microscopy (HEDM) reconstruction of the microstructure viewed from the same direction as b. Each voxel is colored according to the crystallographic orientation of the crystal at that location relative to the laboratory reference frame. Scale bar for b and c: 100 μm. The black void space indicating the space inside the crack was obtained from the XRAT reconstruction and digitally fused with the HEDM data Full size image

By investigating the morphology of the fracture surface in detail, we identified a set of crack deflection events (CDEs): local surface morphologies where the crack deviates markedly from the nominal fracture plane, even though a less tortuous path is available for the crack to propagate. Figure 2a shows an example of such a CDE. Here, and in the remainder of this work, the grains are stylized as 3D surface meshes of the segmented HEDM data and colored according to their average orientation relative to the laboratory reference frame. Part of the crack surface—labeled n for nominal in Fig. 2a—is aligned with a GB oriented parallel to the nominal fracture plane. Another part of the crack surface—labeled d for deflected—is aligned with a GB inclined at a high angle with respect to the nominal fracture plane. There is a GB to the left of the location where the crack surface orientation changes. The adjacent grains that form this GB are labeled G1 and G2.

Fig. 2 Crack deflection event (CDE). a CDE at the boundary between grains 1 and 2 (labeled G1 and G2, respectively). Scale bar: 50 μm. b Schematic illustrating the dihedral angles, θ crack and θ resist , used to define our criterion for identifying CDEs. Traces of the incoming and deflected crack planes have been labeled in a with n and d, respectively Full size image

Our interpretation of the events responsible for the formation of the crack surface configuration in Fig. 2a is as follows. The crack initially propagates from right to left along a single GB—generating crack surface n—until it reaches a triple-line between three grains. The GB between grains 1 and 2 is well aligned with the nominal crack plane orientation and therefore appears to be a favorable path along which the crack may continue to propagate. Nevertheless, the crack does not propagate along the boundary between grains 1 and 2. Instead, it proceeds along another GB inclined at a high angle with respect to the nominal crack plane, generating surface d. Thus, the crack propagates along the GB that—based on geometry—appears to be the less favorable of the two available intergranular fracture paths.

We developed a quantitative criterion for identifying CDEs based on the dihedral angle θ crack between surfaces n and d and angle θ resist between surface n and the plane of the un-cracked GB between grains 1 and 2, as illustrated in Fig. 2b. We define a CDE as a surface morphology where θ crack > θ resist . The incoming crack plane, n, and propagation direction are always assumed to be parallel to the previously described nominal crack plane and direction, respectively. Plane d and the un-cracked GB plane are fitted such that all three planes intersect at a common point along the crack front, which may be considered the decision point for the crack as it proceeds along one of the two available GBs. Both of these planes are fitted manually to match as closely as possible with surface d and the un-cracked GB, neither of which is ever perfectly flat. In a comprehensive search through our HEDM/XRAT reconstruction, we identified ten CDEs. The dihedral angles, θ crack , and θ resist , are listed in Table 1. θ deflection , the difference between θ crack , and θ resist , indicates the magnitude of the deflection, and is also reported in the Table. The CDE illustrated in Fig. 2 is labeled as event #5 in Table 1.

Table 1 Dihedral angles θ crack , θ resist , and θ deflection for the ten CDEs identified in our HEDM/XRAT reconstruction Full size table

It is surprising that CDEs should occur in situations where more favorably oriented crack propagation paths appear to be available. Indeed, if the crack propagation resistance of all GBs in the sample had been the same, then crack deflection would increase the work required to propagate a crack53. One possible reason for the occurrence of CDEs is that the local orientation of the tensile axis deviates markedly from the direction normal to the crack plane, n, favoring a change in crack propagation direction. However, the purpose of defining our CDE identification criterion with respect to an average nominal crack plane orientation is to maximize the likelihood that the tensile axis is indeed perpendicular to the crack plane. Thus, while we cannot exclude a priori that mixed mode loading affects the crack path, we believe that the likelier explanation for crack deflection is that the boundary between grains 1 and 2 is more resistant to crack propagation than the GB aligned with surface d, along which the crack eventually propagates.

To substantiate this interpretation, we sought to determine whether the apparently crack-resistant GBs in our CDEs have any common characteristics. To this end, we used the HEDM reconstructions to determine their full crystallographic character. Table 2 reports the vector components of the misorientation axis (defined in the crystal coordinate system of grain 1) and the misorientation angle, θ, for the high-toughness GBs ahead of the propagating crack in all ten CDEs. Based on this data, we assign Σ values to each GB according to the Brandon criterion54,55. Following the common distinction between special and general boundaries14,56, only Σ values between 1 and 29 are reported. Four of the ten observed CDEs occur on Σ3 boundaries. Of the remaining six crack-resistant GBs, none were low-Σ boundaries (1 < Σ ≤ 29) and none were low-angle GBs (θ < 15°). Therefore, based on misorientation alone, all six would be classified as general GBs14,56. The character of the fractured GBs along the d surfaces could not be identified due to the separation of the crack faces and the plastic deformation of the grains adjoining the crack surfaces, which results in low-confidence HEDM voxels in those grains.

Table 2 Misorientation axes (defined in the crystal coordinate system of grain 1) and angles as well as the coincidence site lattice (CSL) designations for crack-resistant GBs in the ten CDEs found in our data Full size table

Table 3 provides the plane orientations of the two grain facets that meet at the crack-resistant GB in each CDE. The plane normal directions are given in the Nye frames of each of the two crystals that meet at the GB. The lowest-index Miller plane that best matches the GB plane is also reported for each plane normal along with the deviation of this lowest-index plane from the true GB plane determined from the HEDM reconstruction. Out of the ten GBs reported in Table 3, nine have at least one grain with a low Miller index facet along the GB plane. We define {001}, {011}, and {111} as low-index planes, and consider a GB plane to be low-index if it is within 10° of any member of these plane families.

Table 3 Plane normal directions for the crack-resistant GB in each CDE, provided in the Nye frames of both adjoining grains. Lowest-index Miller planes that best match each GB plane are given along with the angle describing the deviation between the two Full size table

For CDEs 1 through 4, both adjoining grain facets are {111} planes. Therefore, considering both Tables 2 and 3, we conclude that all four of the GBs in these CDEs are Σ3 CTBs. Consistent with previous studies on CTB traces along free surfaces57,58, these boundaries show a few degrees deviation from ideal {111} facets. For the GB in CDE 5—which is illustrated in Fig. 2—the GB plane is within 9° of {001} in grain 1 and within 6° of {111} in grain 2. Both are low-index planes, according to our definition. The GB in CDE 6 has one low-index plane ({111} in grain 2) and one {123} plane (in grain 1), which does not qualify as low-index. Indeed, the only CDE with a crack-resistant GB that has no low-index facets is CDE 10. These findings suggest that the common feature of GBs resistant to H-assisted intergranular fracture is that they are most often boundaries with low-index planes: GBs with at least one grain facet along a low-index plane. Figure 3 summarizes the GB plane orientations in the ten CDEs we observed.

Fig. 3 Crack resistant boundary facets. Orientation of plane normal directions for each pair of grains meeting at the un-cracked grain boundary in a crack deflection event (CDE). Plane orientations are expressed as Miller indices in one irreducible triangle of the stereographic projection. Lines connect corresponding planes at individual grain boundaries (GBs), with open circles representing plane normal orientations. Blue circles represent low-index planes, and red circles represent all other planes. Dotted lines indicate the 10° cutoff used to identify planes as low-index. Blue lines indicate boundaries with low-index planes (BLIPs), i.e., boundaries that contain at least one low-index plane, while the red line indicates the single CDE occurring at a GB without any low-index planes Full size image

Following Seita et al.21, we assess the statistical significance of our conclusion by computing its P value. This analysis assumes the null hypothesis that there is no correlation between a GB’s designation as a BLIP and its crack propagation resistance. It then computes the probability that nine out of ten CDEs nevertheless occur at BLIPs by dint of chance alone. To carry out this calculation, we first determine what fraction of all GBs in our sample are BLIPs. Using the data in ref. 59, which reports the GB character distribution in the sample investigated here, we find that 38% (by area) of all GBs in our sample are BLIPs. Using the binomial distribution, we find that the probability of nine or more out of ten CDEs occurring at BLIPs by chance alone—given that 38% of all GBs are BLIPs and assuming BLIPs are equally likely to deflect cracks as non-BLIPs—is 0.1% (P = 0.001). Consequently, we view the null hypothesis as having been falsified by our experiment and conclude that BLIPs are more resistant to crack propagation than non-BLIPs.

Twin intersection-induced GB toughening

Of the nine BLIPs listed in Table 3, four are CTBs. This finding is consistent with previous investigations14, which concluded that twin boundaries—specifically CTBs21—reduce susceptibility to H-assisted propagation of pre-existing cracks in Ni and Ni-base alloys. Here, we find that, in addition to generating CTBs, twins may also reduce a material’s susceptibility to H-assisted fracture in another way, namely by modifying the character of other GBs upon which they impinge.

We observed two instances (including CDE #6 in Tables 1–3) in which GBs were intersected by a twin lamella and the altered character of the GB at the twin intersection caused an intergranular crack to arrest or change course. Figure 4a shows a 3D reconstruction of one of these two cases (CDE #6). The crack initially propagates along the boundary between grains 3 and 4. However, at the boundary between grains 1 and 4 it becomes arrested and instead continues along a different, more tortuous path. To further illustrate this behavior, Fig. 4b provides a 2D section through Fig. 4a. This finding suggests that the boundary between grains 1 and 4 has elevated crack-propagation resistance compared to the boundary between grains 3 and 4, even though the alignment of both GBs with respect to the nominal crack plane is nearly identical.

Fig. 4 Twin intersection toughening. a Crack deflection event (CDE) #6 taking place at a boundary with low-index plane (BLIP) created by the impingement of a twin lamella on a grain boundary (GB). b A 2D section through the 3D reconstruction in a showing traces of the incoming, deflected, and grain boundary planes (see schematic Fig. 2b) as well as values of the dihedral angles, θ crack and θ resist , used to identify the CDE. Solid arrows indicate the path of the crack, the dashed line indicates the nominal crack direction, and the dotted arrow indicates the path along the crack-resistant boundary that deflected the crack. The angles indicated are the dihedral angles defined in Fig. 2b. Scale bar: 50 μm. c, d Schematic showing the role of twin lamellae in altering the crack-propagation resistance of GBs. c A crack reaching a triple junction propagates along a low-toughness GB that is aligned well with the crack plane. d A twin lamella intersecting the GB locally alters the GB character, creating a BLIP that arrests the propagating crack and deflects it onto a different, more tortuous path Full size image

The crack-resistant GB created by the twin lamella is not a low-Σ or low-angle boundary. However, by measuring its full five-parameter crystallographic character, we find that it is in fact a BLIP. Thus, BLIPs may be generated by intersections of twins with other GBs. In the case of Fig. 4, the twin locally alters the GB character to transform part of the original boundary into a more crack-resistant one, ultimately toughening the microstructure. Figure 4c and d illustrates this effect schematically. This result demonstrates that a GB is as tough as its toughest part. Therefore, by increasing the variety of crystal facets on GBs, twin lamellae toughen these boundaries, on average.

Frictional sliding and crack arrest in grain interiors

Figure 5 demonstrates the occurrence of frictional sliding53 in our sample: impingement of opposing crack surfaces upon each other followed by their sliding relative to each other along their area of contact. This instance of frictional sliding occurred in CDE #4 from Tables 1 to3. Here, the crack was deflected around grain 4 at a dihedral angle greater than 90°, leading to the impingement of grain 4 upon grain 5 during continued loading. The XRAT reconstruction in Fig. 5c shows contact between the two grains. The very-low-confidence index of the HEDM data in surrounding grains, shown in Fig. 5d, is consistent with extensive plastic deformation, as would be expected at surfaces that have undergone frictional sliding. Figure 5e and f shows a schematic illustration of the frictional sliding mechanism.

Fig. 5 Frictional sliding. a 3D reconstruction of crack deflection event (CDE) #4 and b a 2D cross section showing the grains that undergo frictional sliding. c A 2D section through the corresponding x-ray absorption tomography data showing opposing crack faces in contact in the region around grains 4 and 5. Scale bar: 100 μm. d Low confidence index voxels in the high-energy diffraction microscopy reconstruction in the vicinity of the sliding contact (highlighted by the white circle), indicating severe local plastic deformation. e, f Schematic of frictional sliding mechanism. e A crack is deflected past vertical due to a crack-resistant boundary, leading to f the re-impingement of grains from opposing crack faces upon each other followed by sliding along their area of contact Full size image

In addition to CDEs, we also observed two distinct cases (not shown) where the crack propagated into a grain interior and became arrested, and only a single case of transgranular fracture. These instances demonstrate that there are isolated regions within the microstructure where there are no low-toughness or favorably oriented GBs along which an intergranular crack may propagate. They also demonstrate that there is very little H-assisted transgranular fracture in these samples, as crack segments that are forced into grain interiors are likely to blunt and cease propagating. This observation reinforces the view that HE in alloy 725 is fundamentally connected to a change in fracture mode from transgranular to intergranular.