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How is hardness related to strength and toughness?

Hardness, strength, and toughness are very similar concepts, but come with important distinctions. Hardness is simply the degree of resistance to deformation. Alternatively, strength refers to the amount of elasticity and plasticity of a material. In other words, how much can a material temporarily change shape (elasticity) and how much can a material permanently change shape without any damage (plasticity). These qualities in combination make strength. Toughness, then, is the greatest amount of energy that a material is able to absorb before breaking. This is distinct from hardness because hardness references the amount of force that can be applied before a change in structure. Toughness has to do with how much energy can be taken in by the material before a fracture occurs, and is sort of the opposing feature to hardness.
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