Stress–strain curve

A stress–strain curve is a graph derived from measuring load (stress – σ) versus extension (strain – ε) for a sample of a material. The nature of the curve varies from material to material. The following diagrams illustrate the stress–strain behaviour of typical materials in terms of the engineering stress and engineering strain where the stress and strain are calculated based on the original dimensions of the sample and not the instantaneous values. In each case the samples are loaded in tension although in many cases similar behaviour is observed in compression.

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Ductile materials

Steel generally exhibits a very linear stress–strain relationship up to a well defined yield point (figure 1). The linear portion of the curve is the elastic region and the slope is the modulus of elasticity or Young's Modulus. After the yield point the curve typically decreases slightly due to dislocations escaping from Cottrell atmospheres. As deformation continues the stress increases due to strain hardening until it reaches the ultimate strength. Until this point the cross-sectional area decreases uniformly due to Poisson contractions. However, beyond this point a neck forms where the local cross-sectional area decreases more quickly than the rest of the sample resulting in an increase in the true stress. On an engineering stress–strain curve this is seen as a decrease in the stress. Conversely, if the curve is plotted in terms of true stress and true strain the stress will continue to rise until failure. Eventually the neck becomes unstable and the specimen ruptures (fractures).

Most ductile metals other than steel do not have a well-defined yield point (figure 2). For these materials the yield strength is typically determined by the "offset yield method", by which a line is drawn parallel to the linear elastic portion of the curve and intersecting the abscissa at some arbitrary value (most commonly .2%). The intersection of this line and the stress–strain curve is reported as the yield point.

Brittle materials

Brittle materials such as ceramics do not have a yield point. For these materials the rupture strength and the ultimate strength are the same, therefore the stress-strain curve would consist of only the elastic region, followed by a failure of the material.

Properties

The area underneath the stress–strain curve is the toughness of the material—the energy the material can absorb prior to rupture.

The resilience of the material is the triangular area underneath the elastic region of the curve.