Stiffness and hardness , strength and toughness

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Discussion Overview

The discussion centers on the distinctions between stiffness and hardness, as well as strength and toughness, within the context of material properties. Participants explore theoretical definitions and relationships between these concepts, touching on aspects of material behavior under stress and deformation.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that stiffness relates to resistance to elastic deformation, while hardness pertains to resistance to plastic deformation.
  • One participant defines breaking strength as force per area just before failure, while toughness is described as energy per volume just before failure.
  • A participant questions the relationship between energy per volume and force per area, suggesting a potential equivalence but acknowledges that energy is the integral of force times displacement.
  • Discussion includes the significance of the stress-strain curve, noting that the total energy absorbed by a material before failure depends on the shape of this curve.
  • It is mentioned that brittle materials are characterized as strong but not tough, failing shortly after the linear region of the stress-strain curve.
  • Yield strength is defined as the force per area at the top of the linear part of the stress-strain curve, with a suggestion that yield toughness could be defined but is typically not due to its proportionality to yield strength.

Areas of Agreement / Disagreement

Participants express varying definitions and interpretations of stiffness, hardness, strength, and toughness, indicating that multiple competing views remain without a clear consensus.

Contextual Notes

Some definitions and relationships discussed depend on specific contexts and assumptions about material behavior, such as the shape of the stress-strain curve and the distinction between elastic and plastic deformation.

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

thanks
 
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Hello Cosmossos! :smile:
Cosmossos said:
Hello
can someone please tell me the difference between stiffness and hardness

Sorry, don't know. :redface:
… and between strength and toughness?

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"
on the page http://www.etomica.org/app/modules/sites/MaterialFracture/Background1.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 :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" )

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:
Stiffness and hardness are resistance to elastic (temporary) and plastic (permanent) deformation, respectively.
 
thank you very much !
 

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