Whenever I work with air-dry clays, the sculpture shrinks in size and there occurs lots of cracks. It is really time consuming, and hard to fix. So far, I tried filling in the cracks with glue and clay, then I sand the sculpture to get a smooth surface as much as I can. However, it is never very smooth, and like I said time consuming. Are there any other ways to fix it? (I let it dry covered with a plastic bag to increase the drying time.)
My experience so far is that cheaper air-drying clays tend to shrink more than quality clays while drying. Many types of clay list the expected shrinkage on the package. If there is no information about shrinkage, you should expect it to be non-negligible (sometimes as much as 10%). As far as I understand it, different fibres added to the clay are to blame. Cheap clays use fibres that soak up more water because you pay by weight. More water in the clay means less expensive ingredients by weight.
"Super soft" and "super light" clays are also full of fibres. I would always prefer a clay with the texture and consistency of natural clay.
Slowing the drying process down is a very good idea. If the outer layer of clay dries and shrinks faster than the inner layer, it cannot shrink uniformly and has to crack. If there are badly mended cracks in the soft clay, they tend to reopen while drying.
The thickness of the clay may have an effect as well. When you form very thick structures like a fist-sized ball, you should substitute part of the clay with another material like a ball of aluminium foil.
When your sculpture cracks, you should moisten the cracked area, fill it in with fresh clay and really rub it into the crack to attach it to the dried clay. If the fresh clay won't stick at all, it's a sign of bad quality clay.
I let it dry covered with a plastic bag to increase the drying time.
That is probably one of the best choices.
I will tell you a short story, even though it is from a totally different context.
A loooong time ago, they applied a thin layer of some kind of cement-based mix on my grandmother's house - mostly for decorative purposes. That was some tedious work, done manually, but the interesting part just follows. For the next XY days (I have no idea how many, maybe up to a week or more), they richly wetted the entire surface (the new layer of cement), on a daily basis.
The explanation I was given was that without the water, the new layer of cement would crack.
So you might want to try it on some test "shape". Make it as usual - the kind of way that would lead to cracking, and after it is finished, abundantly spray water on it "as often as needed" (you are the expert of your work, so you decide what that means). Depending on the details, soaking might be an alternative - you need to make the analysis yourself.
Try using Sakura air dry clay, from Japan. It's a paper clay, if that suits your purpose.
It is light weight and dries crispy, like very hard but light card. It is very strong.
What I like is that you can build directly on top when dry. It doesn't crack.
I build in smallish parts as, after 5 minutes of modelling, the clay enters a fragile breakable stage until it hardens in about 24 hours.
But you can build components and stick them together. I use Uhu glue to join pieces; it avoids them snapping apart later. For heavier needs, I add the weightier Das, in the base for example, to help it stand up.