What's the difference between toughness and strength?

1. Mar 14, 2005

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whoever could give a detailed explanation?

2. Mar 15, 2005

Staff: Mentor

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 $\sigma$ = E $\epsilon$, where $\sigma$ is the stress, E is the Elastic modulus, and $\epsilon$ is the strain.

At a point called the yield point, the relationship between stress and strain depart from linear, and the material yields meaning that permanent or inelastic and plastic deformation occur.

Beyond the yield point or yield strength, less stress is required for a given amount of strain (deformation). This proceeds up to the ultimate tensile strength, which is where uniform elongation is measured. At this point, a tensile specimen begins to 'neck', i.e. the change in cross-section becomes non-uniform. Also, beyond the ultimate tensile strength, the strain increases without additional stress. If the load is not immediately removed, the material will strain to failure.

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.

Toughness relates to the amount of energy absorbed in order to propagate a crack. Materials with high toughness require greater energy (by virtue of force or stress) to maintain crack propagation. Toughness is described in terms of a stress intensity factor (K) or J-integral, or the strain energy release rate of nonlinear elastic materials, (J).

See - http://www.efunda.com/formulae/solid_mechanics/fracture_mechanics/fm_epfm_J.cfm - for more on J-integral.

3. Mar 15, 2005