for this question: "What is the difference between strength, hardness and toughness in materials?" i have searched and have found these following definitions
Strength refers to resistance to deformation, and also to a large elastic range. In the Elastic region of the stress-strain relationship, the relationship is described by a linear function, such that σ = E ϵ, where σ is the stress, E is the Elastic modulus, and ϵ is the strain.
Toughness is the resistance to failure or crack propagation. It is somewhat related to strength. Very strong materials will have low toughness, i.e. low tolerance for flaws or defects, i.e. incipient cracks.
i don't understand those definitions. Aren't deformation and failure one? Are toughness, strength and hardness both the ability to resist external forces?