I’ll try to show you my process of making ice axes from aluminum tubes and hardox steel. I'm amateur in mountaineering and I don't have a lot of experiences, but with some google images and looking at some well known manufacturers of equipment I think I managed to create some good and cheap picks.
First of all, it’s not fully homemade because I work in company which owns lasers for cutting steel and line for plastic coating, welding, etc. ... so I used some equipment for this small project of mine.
Ice axe handle is 28 mm diameter aluminum tube with 2.5 mm wall thickness and some none slip shrink tube for fishing rods as hand-grip (bought at aliexpress). Ice pick is above mentioned 5 mm hardox steel which have high strength, and good characteristics at low and high temperatures.
I managed to bend tubes using my own hands power, but it’s necessary to fill them with fine sea sand. That way, they are not going to deform much and I can get almost identical pieces. Those small scrapes which you can see at some early pictures are filled with plastic coating and shrink tube later in process, so they are nearly invisible on finished product.
Picks excised on laser are sharp enough that they doesn't need further sharpening. They only need some drilling and welding so they can fit nicely inside tube.
Here are some process photos (the quality of pictures is not great, cheap xiaomi phone):
