3.1. Processing
The slow cooling (1 K/min) after solution heat treatment at 1473 K leads to a low nucleation rate of the γ′-phase and therefore few but big precipitates. This overaged γ/γ′ microstructure results in a low hardness of the material so that it is easy to roll.
As the next step, the bicontinuous γ/γ′ microstructure is produced, using the heat treatment protocol mentioned in
Section 2. In the microstructural images,
Figure 5, the octodendritic morphology of the incoherent γ′ particles is clearly visible. As explained in [
16], during slow, continuous cooling the γ′ morphology changes to octodendrites and later dendrites. Since the former cube corners grow preferentially, at these dendritic arms the precipitates coalesce and thus build a continuous network. The cross-links between two separately grown octodendrites are marked with red arrows in
Figure 5a. They are relatively narrow. Consequently, the filter rating and permeability of the final membranes will be determined by the dimensions of these cross-links rather than the size of the relatively coarse octodendrites. Note that only a fraction of the cross-links present in three dimensions can be discerned in a 2D-section.
As shown in
Figure 5b, the γ′ precipitates are significantly coarser at the grain boundaries than in the grain interior. This is a result of preferred nucleation at grain boundaries during slow cooling. Depending on the misorientation of adjacent grains, grain boundary precipitates vary in their size, i.e., big precipitates are found on large misorientations, the smallest on low angle and none at twin boundaries [
14]. Around those precipitates in some cases bigger areas of γ are present. However, the arrows in
Figure 5b show that the precipitates in the grain are connected to the precipitates at the grain boundaries.
In
Figure 6a an optical microscope image of an etched membrane is shown. It is fully porous; no massive core remains. Since the whole cross-section is uniformly porous, the cross-links must occur not only occasional but at all precipitates, independent of their location in the grain or at the grain boundary, thus creating a bicontinuous structure. The permeability is also confirmed by an alcohol drop test.
As already illustrated in
Figure 3 and
Figure 4,
Figure 6b clearly shows the narrow γ-ligaments between the voids (i.e., former γ′-precipitates) at the grain boundary that ensure the grains holding together. Certainly, those locations will lead to weak links regarding mechanical properties in the membranes. As explained in
Section 2.1.2, the amount of precipitates at the grain boundaries was determined to estimate the amount of pores and ligaments at the grain boundary. As result an amount of about 15% ligaments was found, whereby the values vary between 5 and 22% (see
Table 1). In contrast, the overall γ-content is about 56%. The related pore content was estimated on the basis of microstructural images as explained in
Section 2.1.1. By means of three SEM images a pore volume of about 44% was determined, which corresponds to the phase content of γ′ calculated with the thermodynamic simulation software Thermo-Calc at 1273 K.
This membrane shows that the process route is generally possible. However, there are occasional damages on the surface of the specimens, which are depicted in
Figure 7. These damages are caused by a non-selective etching around the grain boundaries. In addition to the etching of γ′, a removal of the γ phase also took place, leading however only to quite shallow trenches. Still, it demonstrates a slight instability of the extraction process.
3.2. Mechanical Properties
In the tensile tests the mechanical behavior of the produced membranes was examined. For the results it is important to say that all values were related to the cross-section area of the whole porous structure and not the load-bearing cross section. Therefore, all parameters are marked with an asterisk (*).
The membranes have an average ultimate tensile strength of
= 121 MPa and an average fracture strain of
= 0.26%, whereby sample 5 differs most with
= 132 MPa and
= 0.31%. For determination of Young’s modulus, specimen 1 and 2 were unloaded again after reaching approx. 50 MPa, the elastic stiffness E* was then evaluated using the unloading curve. The value for both specimens is
= 48 GPa. The stress strain diagram in
Figure 8 shows macroscopically an essentially linear elastic behavior. This also can be seen when the elastic stiffness is estimated by E* =
/
leading to an average value of 46.3 GPa for the five specimens. All values are listed in
Table 2.
The strain distribution, depicted as exemplary for sample 5 in
Figure 9, clearly shows that all membranes are deformed over their entire length and not only locally. Significantly lower strains can be seen in the grip section where the material is solid. This area is not considered further and is not included in any analyses (see
Section 2). Note that the grip section refers to the former coated area and not the position where the clamps are attached. To illustrate this, grip section and end position of the clamps are marked in the right hand side of
Figure 9. Although the coating prevents the acid from penetrating the surface, it does not prevent it from reaching inner areas through the uncoated area. This results in a slightly gradual transition from solid to porous and therefore a gradual increase in strain from solid to porous regions can be expected. This internal condition can be seen as compensation for an external dog bone design, both lead to a continuous increase of the cross section.
Differences between the examined samples can be seen for the area of the fracture. There, in specimen 5, the strain is slightly higher at every stage of the deformation. For all four other specimens, the fracture area either does not differ from the whole specimen or even shows slightly lower strains up to the last frame before fracture. For example, even in the last frame it is not obvious where the specimen is failing. Furthermore, in the area of sample 5 where fracture occurs, the difference between porous structure and grip section is clearly visible and very abrupt compared to the other specimens.
For specimens 1 and 2, the values for the strain at unloading and the second loading are essentially the same as for the first loading (in
Figure 8 measuring points for loading and unloading are present). This is also shown by the strain distribution. The visualization at the three loading respectively unloading stages does not differ for the same strain.
All fractures occur in the uncoated area, i.e., in the reduced cross section when comparing to a dog bone shape. Nevertheless, it must be mentioned that with the exception of specimen 2, the failure occurs in the immediate vicinity of transition between former coated and uncoated area. However, only in specimen 5 the strain distribution is this abrupt as it can be seen in
Figure 9. There can be various reasons for this. One might be an unselective etching inside the specimen caused by the coating or a stronger attack of the surface and thus stronger notch effect. Another possibility are stress concentrations due to the rather abrupt transition from porous to solid and the close proximity between porous section and the end of the clamped section. Due to these possible effects, the intrinsic strength of the porous material might be somewhat underestimated. However, we do not expect this influence to be large as the strength of specimen 2 is similar to the other ones (see
Table 2).
Looking at the case where four out of five specimens fail in the transition area of the etched zone, strictly speaking these tests should be considered invalid in terms of determining the mechanical properties of the porous structure. It becomes clear that the internal increase of the cross-section does not seem to be sufficient and that the increase should be within the etched zone, such as in form of a dog bone specimen. However, as a lower estimation or the application case that membranes made in this way generally have a transition between porous and solid and thus this weak point, the results in our view provide relevant information about the mechanical properties.
The fracture surfaces in
Figure 10 show an intercrystalline fracture pattern over most parts of the specimens. Furthermore, specimens 1 to 4 have fracture paths over the whole cross section parallel to the surface shown in
Figure 9, i.e., perpendicular to the main fracture path, in the core of the specimen. Based on similar findings in [
12] and observations in other experiments, this can be attributed to a non-selective dissolution of both phases at this very locally limited depth. When the crack reaches this weakened zone, it follows this zone for a while before it kinks back in the direction of the main fracture path. How and especially when this dissolution occurs is under investigation.
Localized transcrystalline fracture patterns occur repeatedly on all fracture surfaces. These can be divided into three categories. The most frequent transcrystalline fractures occur in the area of the damage in the core of the specimen. In this area, as already mentioned, the fracture first follows the non-selectively dissolved zone parallel to the applied load. In order to get back to the main path, the fracture must pass through the core area. If there locally is no grain boundary or none with a suitable orientation, the fracture occurs transcrystalline. Further, it is still possible that a grain boundary is present and has a suitable orientation, but an adjacent area has higher stresses due to a smaller cross-section and therefore fails first.
A similar situation may occur with the second type, where fragments of grains remain at the intersection of several grains. Here, intercrystalline fracture requires a large change in direction of the fracture path. Apparently, it is then sometimes easier to avoid this and follow a transcrystalline path for a while.
Finally, grains are observed which fail completely transcrystalline. These are surrounded by several grains whose broken grain boundaries are all in a similar plane. During the evaluation of the γ-ligament portion along grain boundaries it became clear that there are also grain boundaries with high ligament content. If the change of the fracture direction is too large or adjacent grain boundaries have a high fraction of ligaments, the fracture resistance along the grain boundary is sufficient for the fracture path to pass through the grain.
With further magnification it becomes clear that the grain boundaries are weakened due to the low amount of γ, as already stated in
Section 3.1 on the basis of microsections. In
Figure 11a the surface of specimen 5 after the tensile test is depicted. Since the fracture path is intercrystalline, it shows the surface of a single grain being situated on one side of the grain boundary. Four different areas can be distinguished, which are highlighted in
Figure 11b. First, there are massive flat areas that are either smooth (yellow) or rough (green). After the heat treatment but before selective dissolution of the γ′-phase, coarse γ-precipitates were here. As already described in the course of determining the ligament fraction at grain boundaries, these precipitates have smooth interfaces on the grain boundary side and rough ones on the matrix side. These interfaces are revealed in
Figure 11a as the γ′-particles were selectively dissolved. On the left side of
Figure 11, the interfacial dislocation network of rough interfaces can be best seen. Here was a γ′-particle that belonged to the visible grain. The smooth surfaces are matrix of the shown grain to which precipitates of the neighboring grain were adjacent. Both cases result in the two grains not being connected to each other at those areas.
Between these large pores narrow ligaments connect the two grains. Those γ ligaments have tapered in the course of deformation and are finally broken in the form of narrow knife edges (red). Furthermore, in some cases plastic deformation continues even into the surrounding matrix of these ligaments and can be recognized as slip bands (white arrow in
Figure 12a). This shows that the material behaves ductile. However, since plastic deformation is concentrated along the weak grain boundary areas, it is not visible in the stress-strain diagram, from which a macroscopically linear elastic behavior is deduced.
Finally, open porosity (blue) is visible. The octodendritic pores connect the coarse pores at the grain boundary with those from inside the grain and thus ensure permeability (compare with
Figure 5b, blue arrows). This already was shown in
Section 3.1 on the basis of microstructural images. At this particular grain boundary in
Figure 11, only a few pores that reach into the grain are present. On other grain boundaries without the formation of massively covering γ′-precipitates, significantly more cross-links into the grain can be seen in
Figure 12b.
Figure 11 shows, however, that despite the large precipitates and thus large pores, the characteristic pore size can be significantly smaller. In the grain interior and at the grain boundaries, it is often only the arms of the octodendrites that touch each other, resulting in pore diameters of often less than 1 µm. What kind of filter fineness this results in has not yet been further investigated.
In [
17] the mechanical behavior of nanoporous superalloy membranes was analyzed. They were produced from single crystalline CMSX-4 by both creep deformation and load-free coarsening and electrochemical extraction. For the best microstructure obtained by creep deformation, an ultimate tensile strength of ~100 MPa was reached and an open porosity of 26% was reported. Considering the significantly higher porosity of 44% the strength levels observed here, even surpassing 100 MPa, are remarkable. In this context it has to be noted that single crystals and also the resulting single crystalline superalloy membranes are highly anisotropic in a number of respects. Firstly, the primary dendrites with [001]-orientation are essentially oriented in parallel to the growth direction of the single crystal. Between those dendrites small misorientations occur leading to small angle boundaries [
18]. This disturbs the arrangement of the γ′-precipitates in such a way that weak fracture paths result in parallel to the primary dendrites when the single crystalline superalloy membrane is loaded perpendicular to the growth direction of the crystal [
17]. In contrast, the length of dendrites is limited to the grain size in polycrystals and their orientation changes from grain to grain. Thus, such a weak fracture path extending throughout the sample cannot arise in a polycrystalline superalloy membrane. Secondly, tensile creep deformation of single crystalline superalloys such as CMSX-4 leads to pronounced directional γ′-growth perpendicular to the [001]-direction. When the resulting membrane is loaded in growth direction, the load is perpendicular to those ligaments, once again leading to a relatively weak fracture path [
17]. In contrast, such a preferred γ′-orientation throughout the material does not occur in the polycrystalline superalloy membranes investigated here because (i) the crystallographic orientation changes from grain to grain and (ii) growth of incoherent γ′-particles is less regular. Even though polycrystalline superalloy membranes have their own weak fracture path as discussed above, it turns out that they are not inferior to those occurring in single crystalline membranes. This opens up an avenue for inexpensive production of strong, polycrystalline superalloy membranes.
Another frequently studied method of producing porous metals is dealloying. Here, porous structures with even smaller ligament diameters than in the membranes shown in the present article, down to a few 10 nm, are formed from mostly single-phase starting materials (often gold-based). [
19,
20,
21,
22,
23,
24,
25] Due to significant volume shrinkage, large internal stresses and surface oxidation during the process, stress-corrosion cracking occurs, leading to the formation of extensive fabrication flaws [
20,
21,
22]. This usually leads to poor mechanical properties, especially under tension, when the specimen dimensions are large enough to include these flaws. As mechanically studied specimen sizes are on a much smaller scale overall than shown here for compression and especially for tensile tests [
23,
24,
25], these results are not comparable to those obtained here.
In [
20], for nanoporous nickel, these cracks could be partially healed by using an ultrafine grained precursor alloy and post-dealloying annealing. During the heat treatment at 1173 K the ligament diameters grow from 15 nm to 450 nm. The tensile strength is anisotropic due to the rolling direction of the precursor material and reaches 150 MPa parallel and 94 MPa perpendicular to it. The specimens with a porosity of 53% obtain a fracture strain of 2.5%. However, these are also tensile specimens with a gauge length of 6 mm, a width of 1.2 mm, and a thickness of 30 µm.