Physics only work in one way. There's always this 'best possible build with the given material and technology' of a weapon, and all civilizations with the same amount of technology and materials will eventually build weapons that look more or less the same, with some space for traditional and artistic influences.
Take for example, native Southern America. As they didn't had the ability (technology or materials, don't know that much about their metallurgy skills) to use metals in their weapons, they resorted to pieces of obsidian stuck between two pieces of wood bound together. It was functually very similar to a sword (or a sharp club, depending on the quality), as that is a design that works.
It's not hard to develop spears, nor is it that hard to develop axes; and it only takes hald a brain to combine them and make a halberd.