I can't see in the picture where the crack is.
If it's through the barrel threads.................
As above a cracked frame, especially in that area is considered to be non-repairable.
Jerry Kuhnhausen does show a repair method in his S&W Shop manual, but that's only for a steel frame gun.
Repair requires some extensive equipment, starting with a special copper heat sink that screws into the threads to handle heat spread.
The crack has to be beveled out to give the weld bead room to penetrate deeply, or the frame will just crack again, usually when the barrel is reinstalled.
This type of welding on a gun is NOT for your local welder, it's something to be done by a master pistolsmith/welder with experience in how this is done, and how to prevent unseen problems with the heat treating of the frame. These experts don't work cheap.
Few local welders will have any useful knowledge with the problems with welding a firearms frame. Guns really are "different".
Due to the problems associated with this and the very high cost of having a real expert pistolsmith do it, welding of this type is reserved for historic or highly collectible guns where the cost can be justified.
Last, we're dealing with a FIREARM. Just deciding that you'll weld it and loose nothing if it fails is a bad choice. The problem is that it may seem to work, but in fact, you're holding a hand grenade in your hand while it goes off.
My advice, due to the cost, I wouldn't have it done, and if you do, get a genuine pistolsmith-expert to do it.
The cost will be so high, you could easily buy a new gun and have a good deal of money left over.
With that said, if you're just going to do it anyway, you're going to have to invest in some rather expensive gunsmithing tools to remove and re-install the barrel.
Note that Colt Firearms themselves will not do any barrel work on an aluminum frame revolver due to the cracking problem.
What you'll need to remove and re-install the barrel is a set of barrel blocks to hold the barrel. You can make these from hardwood blocks and epoxy. Cut a groove in one block and use epoxy to mold it to the side of the barrel, then do another block for the other side. When mounted on the barrel you want the blocks to not quite meet, leaving a gap between the blocks when locked in a vise.
Fortunately, the Colt heavy, shrouded barrel is easier to grip than a round barrel.
For the frame you need a professional action wrench with polymer inserts that EXACTLY fit the Colt "D" frame. This supports and protects the frame from being bent or....cracked, right where your frame is cracked. People often try to remove or replace barrels by sticking a hammer handle or 2x2 through the frame window and are shocked when the frame bends or the threaded area for the barrel cracks.
Trying to remove the barrel from a cracked frame with expedient tools will absolutely bend the aluminum frame.
I don't know of anyone making "D" frame inserts for the action wrenches, so you'll probably have to cast your own using epoxy. You do this much the same way as making the barrel blocks only you cast them around the very front of the frame.
Here's what the action wrenches and inserts look like. The inserts fit inside and surround the front of the frame:
revolver action wrench at Brownells
Assuming you're successful in welding the frame, you'll have to have a tap that fits the Colt "D" frame threads to re-cut and clean up the welded threads.
Once welded, the threads and frame will have slightly changed size. Either the barrel will not screw back in far enough to get the front sight aligned and properly torqued, or it will screw in too far and be off to the left.
In either case, you'll need a lathe to trim the barrel shoulder to allow it to screw back in with the front sight aligned, and have the correct torque to prevent the barrel from shooting loose.
If the barrel screwed in too far, you'd have to cut the barrel shoulder enough to set the barrel back one full thread. That will require an expensive tool set that works down the barrel to cut the barrel-cylinder gap, and to re-cut and lap the forcing cone in the rear of the barrel.
This MUST be done and it MUST be done to a tight spec using a special drop-in precision plug gage.
So, if you expected this would be a simple job that could easily be done, and the barrel just removed and installed like a piece of threaded pipe, you're going to be very disappointed.
My best advice is, either convert the gun to a wall hanger, or break it down into parts and sell them. Use the proceeds to buy a new gun.