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Saying carbon fiber is stronger than steel is much too general of a thing to say. There are many properties of a material that define it's strength.
Tensile strength is the amount of resistance to pulling a material has. Carbon fiber has a higher tensile strength than most steel alloys.
Compression strength is the opposite of tensile strength and is generally the same as tensile strength.
Shear strength is the resistance to sideways force, like from a puncture or a sheet of metal being cut by scissors. Carbon fiber is not strong at all in this area. This is why it's not good for a body material, it can get punctured easily by a flying pebble or something.
Then there's a whole lot of other things, like how fast the materials strength breaks down after a certian number of cycles, hardness, toughness, and all kinds of other properties.
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