These terms have very strict definitions in material science. You’re quite wrong about carbon fibre, it doesn’t break easily.
What you’re talking about is the fact that it splinters when it does break. This seems to have given you the incorrect impression that a material that splinters does so easily. The way a material fails does not necessarily dictate it’s strength.
When steel fails, is plastically deforms (bends, dents etc) in most cases. Steel with high-carbon content or that has been heat treated can fracture instead of deform.
The method of failure is dictated by the molecular structure of the material. A strong material will withstand greater force before permanently changing shape. Once the forces exceed the yield strength, it will fail. How the failure happens doesn’t change the amount of force needed to deform it.
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