Ok, now lets see if I can address chipping/fracturing. This one is more complicated, at least to me. All steel have a range of load and deflection where they will deflect and recover after the load is removed. This is called the elastic region. In this region the steel acts just like a VERY stiff spring. This is what I was talking about with high strength (hardness). Once you exceed this elastic region, the steel (and any other metal for that matter) will either bend or break. Bending is permanent and does not recover when the load is removed, ALTHOUGH any elastic deflection will still recover. Picture a steel rod in a vice. Deflect it 20 degrees and let go and it will return to straight. Deflect it 21 degrees and it will start to bend, but when released, it will still recover the original 20 degrees of elastic deflection, and you will be left with a 1 degree bend. These numbers are just examples. In reality, even the hardest steels will still bend just a little before they break, but you aren't likely to notice unless you are measuring very carefully.
To elaborate on this a little further, higher strength (hardness) will allow more deflection and still recover, and the effort to get the extra deflection will be greater. Again, take a bar of soft steel and bar of hardened, high strength steel and put them in a vice. You push on the annealed (soft) bar with 50 lbs, and get that 20 degree deflection. Pushing on the hardened bar with 50 lbs will get that same 20 degrees of deflection. They will both return to straight when released. Now, push with 60 lbs. The annealed bar will flex to 20 degrees, then start to bend, and you can push it to 30 degrees without a great deal of extra effort. When released it will return to 10 degrees of straight (30 degrees - 20 degrees = 10 degrees).
Here's where the difference comes between the 2. To get the hardened bar to 30 degrees will take 75 lbs. And lo and behold, when released it will completely return to straight. 40 degrees will take 100 lbs, 60 degrees will take 150 pounds and we might be able to go further, but at some point the effort will level out,it will start to bend, then break. For the sake of arguement, lets say it makes it to 80 degrees, then bends a little and breaks, and it took 200 lbs of effort to get there. We'll get a new annealed rod and lean on it with 65-70 pounds and it will make it to 80 degrees, but it won't break. It will still recover the same 20 degrees of deflection from before, but it's bent to 60 degrees permanently, and only took about 70 pounds to get there. Again, these numbers are just examples, but you get the idea. For my own sake, I'll say it to remind myself later. Stronger (harder) steel will take more effort to flex than softer steel, but once it's limit is exceeded, it will break, not bend. People have to decide what they want their knife to do.
So, dulling by fracturing/chipping. Here we go. If the load is fast, like chopping, the edge can chip from impact. This is where high impact toughness is a direct benefit. If the load is slow, you run into a property called ductility. This is a measure of how much bending can happen before fracture. Once that is exceeded, fracture happens, in all metals. So lets take an edge at high hardness and cut with it, say some wood, and we encounter a knot. We just keep on pushing until the edge goes through. Now the edge is very thin, so any force will produce quite high stress and deflection. If we push too hard and the edge deflects too much, it will bend, even if it's just a tiny amount, then break. Thus we have a chip, and the edge is dull. Steels with bad heat treatments can have very low ductility, and will bend and chip with very low deflections, even if they are relatively soft. Some will have such low ductility that they can't even form a burr during sharpening, it just breaks off, leaving a dull edge behind. These steels will have chipping issues cutting even things like wood and cardboard, and will dull from fracture/chipping, even on relatively soft material.
I'm still thinking, so I'll get to wear tomorrow.
Edited to add: I keep putting hardness in parethesis when I say strength. That's because hardness testing was developed to allow a minimally destructive test to estimate strength. Higher hardness means higher strength. In individual heat treatement or metal manufacturing plants, some in house testing will get an accurate chart that can convert hardness to strength. Generic estimates are also possible from hardness charts on the web, but the in-house ones will be surprisingly accurate. Both in-house and generic hardness/strength charts are alloy specific.