Stiffness and hardness , strength and toughness

Cosmossos

Hello
can someone please tell me the difference between stiffness and hardness and between strength and toughness?

thanks

tiny-tim

Hello Cosmossos!
Sorry, don't know.
Breaking strength (of a material) is force per area (stress) just before failure (in N/m²)

Toughness (of a material) is energy per volume just before failure (in J/m³).

But isn't energy = force times displacement, so energy per volume = force times displacement per volume = force times area? 1 J/m³ = 1 N/m² ?

Yeees, but energy is the integral of force times displacement, so the total energy (per volume) absorbed by the material before failure depends on the shape of the force-displacement (per volume) curve (more usually called the strain-stress curve)

(strain = ∫ displacement per thickness = ∫ displacement times area per volume,
and stress = force per area,
so strain-stress = ∫ force times displacement per volume = energy per volume)

For good examples of stress-strain curves, see this diagram
on the page http://www.etomica.org/app/modules/s...ckground1.html …

the linear part is the elastic region, where energy per volume is proportional to force per area, the non-linear (curved) part is the plastic region (the ductile region, if we're talking about tension), and it ends at failure …

the total energy absorbed by the material (the area under the graph) depends on the shape of that non-linear part.

(it curves down at the end because of the difference between apparent stress and actual stress … the actual stress-strain curve keeps going up … see this diagram at http://en.wikipedia.org/wiki/Stress–strain_curve)

Brittle materials are strong but not tough … they fail almost immediately after the end of the linear part.

Yield strength (of a material) is force per area at the top of the linear part.

If we bothered to define yield toughness (of a material), it would be energy per volume at the top of the linear part, but that would simply be proportional to yield strength, so we don't bother.

Mapes

Stiffness and hardness are resistance to elastic (temporary) and plastic (permanent) deformation, respectively.

Cosmossos

thank you very much !!!