Stress–strain curve
Ductile materials
The appearance of necking in ductile materials is associated with geometrical instability in the system. Due to the natural inhomogeneity of the material, it is common to find some regions with small inclusions or porosity, within the material or on its surface, where strain will concentrate, leading to a local reduction in cross-sectional area. For strain less than the ultimate tensile strain, the increase of work-hardening rate in this region will be greater than the area reduction rate, thereby make this region harder to deform than others, so that the instability will be removed, i.e. the material increases in homogeneity before reaching the ultimate strain. However, beyond this, the work hardening rate will decrease, such that a region with smaller area is weaker than nearby regions, therefore reduction in area will concentrate in this region and the neck will become more and more pronounced until fracture. After the neck has formed in the material, further plastic deformation is concentrated in the neck while the remainder of the material undergoes elastic contraction owing to the decrease in tensile force.
Stress–strain curve
!Stress–strain curve typical of a [low-carbon steel](//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Stressstrainductile.svg/250px-Stressstrainductile.svg.png)
Stress–strain curve
In engineering and materials science, a stress–strain curve for a material gives the relationship between the applied pressure, known as stress) and amount of deformation, known as strain). It is obtained by gradually applying load to a test coupon and measuring the deformation), from which the stress and strain can be determined (see tensile testing). These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength, and the ultimate tensile strength.
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