Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Stiffness and hardness , strength and toughness

  1. Jul 15, 2011 #1
    can someone please tell me the difference between stiffness and hardness and between strength and toughness?

  2. jcsd
  3. Jul 15, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hello Cosmossos! :smile:
    Sorry, don't know. :redface:
    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 ? :confused:

    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 http://www.etomica.org/app/modules/sites/MaterialFracture/Images/SSPicture2.jpg" [Broken]
    on the page http://www.etomica.org/app/modules/sites/MaterialFracture/Background1.html" [Broken] …

    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 :rolleyes: … see http://upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Stress_v_strain_A36_2.svg/300px-Stress_v_strain_A36_2.svg.png" [Broken])

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

    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. :wink:
    Last edited by a moderator: May 5, 2017
  4. Jul 16, 2011 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Stiffness and hardness are resistance to elastic (temporary) and plastic (permanent) deformation, respectively.
  5. Jul 17, 2011 #4
    thank you very much !!!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook