Some context, right off the bat: I am a mad scientist. This means that evolution has been defenestrated; as such, I am not interested in determining what evolutionary pressures might lead to the adoption of such a material as a supportive structure, and nor am I interested in where this thing might find aluminum to keep its bones intact; we're talking mad science and the limits of what's possible within the laws of physics and mortal biology here, not boring old evolution.
Now, before we get any further, the question: What are some structural or biological weaknesses of using aluminum oxide monocrystaline whiskers suspended in a collagen matrix as a material for bones - i.e., why shouldn't I?
Please note that the core of these bones is plain 'ol bone marrow. You gotta have that to live if you're Earthly life; I might be a mad scientist, but I'm not a mad scientist, y'know?
However, the other parts of these bones - i.e. where there would normally be carbonated hydroxyapatite - are made of aluminum oxide. Here's why that's great:
A modulus of rupture - that is, the maximum amount of stress each fiber of it can withstand right before it fails - of 152 to 800 megapascals. I cannot find a source for bone's modulus of rupture. However, it is likely to be within the range of 104 to 121 megapascals - around its tensile strength - since it is a relatively homogeneous material, and, according to Wikipedia, this means that its tensile strength is likely comparable to, if potentially less than, its flexural strength. I would handwave this, since I might be inaccurate here for lack of a source, but I actually have a solution to it below, and, at the very least, bone and aluminum oxide are likely comparable in terms of their modului of rupture; aluminum oxide is probably stronger.
A tensile strength (as mentioned above) of 69 to 665 megapascals, as opposed to bone's 101-124 megapascals. While this could potentially be less than that of bone, let's assume it isn't, since the higher end of aluminum oxide's tensile strength is significantly higher than the high end of bone's.
A Young's modulus - how stiff it is against lengthwise force - of 215 to 413 gigapascals, as opposed to bone's ~1 gigapascal; while I do not have a direct source for that figure, the ratio of Young's modulus to the shear modulus of bone is 20:1, and 20 * 51.6 = 1,032.
An elastic modulus - how much force it can take before it non-permanently deforms - of 275 gigapascals (even at a relatively low concentration of 90%, i.e. 10% of it isn't aluminum oxide) as opposed to bone's 34.11 gigapascals. Note that the elastic modulus is different from the elastic limit I mention below; the elastic modulus is related to non-permanent deformation, whereas the elastic limit is related to permanent deformation.
Now, as I mentioned further up this post, it might seem that aluminum oxide has a few glaring weaknesses in comparison to bone; it likely has a lesser ductility and elastic limit, and I had to handwave its fracture toughness and Poisson's ratio.
While I cannot find figures on the elastic limit - how much force per unit of area it can withstand without being permanently deformed - and ductility - how much it can be elastically deformed without fracturing - I'm willing to bet that bone's elastic limit is greater than aluminum oxide's elastic limit of 69 to 665 megapascals, and that bone's ductility is greater than aluminum oxide's ductility of of 0.00018.
The only relevant areas in which I know for a fact that it's possible for bone to beat aluminum oxide are fracture toughness - how hard it is for an already-established crack in the substance to grow further - and Poisson's ratio - how much a substance squishes out to the sides when compressed.
Cortical bone also has a Poisson's ratio of 0.12 to 0.63 (if you want to find that particular bit, use control-F to find it, since it's a long source), as opposed to aluminum oxide's 0.21 to 0.33, meaning that aluminum oxide might be squishier. Again, a handwave is completely possible here, but these things will become irrelevant once I implement my solution to aluminum oxide's flexibility and brittleness problems below.
I have a solution to these things, you see; you structure the aluminum oxide bones like limpet teeth. Limpet teeth contain monocrystalline whiskers of goethite - that is, crystals of goethite that are so small that they're flaw-insensitive, meaning that they do not have structural impurities that make larger crystals more susceptible to structural failures. Moreover - and this is the important point - these goethite crystals are embedded in a matrix of collagen, which allows the teeth of a limpet to be flexible, non-brittle, etc.
In addition to that, these goethite crystals have a low critical fiber length relative to their total, meaning that they're very good at transferring loads to the collagen matrix - in other words, they don't need to be very long to act as good shock absorbers.
My solution to this, therefore, is to suspend crystals/fibers of aluminum oxide within a collagen matrix - much like a limpet's teeth are crystals/fibers of iron(III) oxide-hydroxide (goethite) within a collagen matrix - to bring the flexibility of these bones up to a level more comparable to more conventional Earthly life.
All in all, I'd say that aluminum oxide monocrystalline whiskers suspended within a collagen matrix are - mechanically speaking, at least - a much better bone than the ones that actually exist in real life, but of course I'd say that, because I came up with 'em. It remains to be seen whether there are actually problems with them, which is where you come in:
What are some structural or biological weaknesses of using aluminum oxide monocrystaline whiskers suspended in a collagen matrix as a material for bones - i.e., why shouldn't I?
Assume that this creature with aluminum oxide bones is designed to operate under "normal" Earth-standard conditions, on land, at sea level, etc, and that, other than its unique supportive structures, it is essentially a tiger in all other aspects of its biology.
Good answers will point out a problem with these types of bones, and have a sense of biology, physics, and chemistry at least as strong as my rudimentary ones.
Here are three answers that I already have solutions for, and that I would not like people to answer with:
Weight. Aluminum oxide is 3.95 grams/cm^3, whereas bone is ~0.92-1.4 grams/cm^3. These bones will be ~2.75-4 times heavier per unit of mass. I know this, and have found a way around it.
Availability. Aluminum has to be extracted from substances like bauxite, and new metabolic pathways need to be developed to process and handle it. I know this, and have found a way around it.
Toxicity. Aluminum oxide fibers are apparently bad for you; I personally imagine that they're an inhalant risk, but have no hard sources on that. I don't consider this a problem, for various reasons outside of the scope of this question; i.e. toxic bones are awesome.