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Toughness as defined by the area under the stress–strain curve for one unit volume of the material. In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing. [1] Toughness is the strength with which the material opposes rupture.
Toughness is a material property defined as the area under the stress-strain curve. Toughness can be determined by integrating the stress-strain curve. [ 3 ] It is the energy of mechanical deformation per unit volume prior to fracture.
Fracture toughness varies by approximately 4 orders of magnitude across materials. Metals hold the highest values of fracture toughness. Cracks cannot easily propagate in tough materials, making metals highly resistant to cracking under stress and gives their stress–strain curve a large zone of plastic flow.
where Ur is the modulus of resilience, σy is the yield strength, εy is the yield strain, and E is the Young's modulus. [1] This analysis is not valid for non-linear elastic materials like rubber, for which the approach of area under the curve until elastic limit must be used.
The strain can be decomposed into a recoverable elastic strain (ε e) and an inelastic strain (ε p). The stress at initial yield is σ 0 . Work hardening , also known as strain hardening , is the process by which a material's load-bearing capacity (strength) increases during plastic (permanent) deformation.
The Ramberg–Osgood equation was created to describe the nonlinear relationship between stress and strain—that is, the stress–strain curve—in materials near their yield points. It is especially applicable to metals that harden with plastic deformation (see work hardening), showing a smooth elastic-plastic transition.
English: This plot shows one measure of toughness which is defined as the area under the stress strain curve. It is a measure of energy per unit volume. It is a measure of energy per unit volume. Date
The figure on the right shows the plot of an external force vs. the load-point displacement , in which the area under the curve is the strain energy. The white area between the curve and the P {\displaystyle P} -axis is referred to as the complementary energy.