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I'm studying biomedical engineering and I'm about to take "Biomaterials" (basically materials science applied to medicine) final exam. In one recorded class, the professor mentions the elastic modulus depending only on cohesion energy between the structure species, which is consistent with "Materials Science and Engineering An Introduction - Callister 9th edition" page 204 statement that reads: "Yield and tensile strengths and ductility are sensitive to any prior deformation, the presence of impurities, and/or any heat treatment. Modulus of elasticity is relatively insensitive to these conditions". But every time I search for strengthening mechanisms on the internet, most places, even reputable ones mention the increase in hardness, but hardness is the qualitative way of interpreting the elastic modulus, so the presence of crystal defects are not factors for changing hardness. So just to confirm, are people confusing hardness with strength?

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hardness is the qualitative way of interpreting the elastic modulus

This is incorrect; stiffness is the qualitative way of interpreting the elastic modulus. The soft–hard dichotomy applies to plastic or permanent deformation; the compliant–stiff dichotomy applies to elastic or recoverable deformation, which is quantified by the elastic modulus.

Hardness and strength both refer to a material's robustness against permanent deformation; hardness typically refers to—and is tested at—the surface region, whereas strength typically refers to the bulk. One can apply various models relating hardness measurements (on the Rockwell, Vickers, Shore, or Brinell scales, for example) to strength measurements (in units of pressure).

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