Stress-strain curve
The relationship between the stress and strain that a particular material displays is known as that particular material's stress–strain curve. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress). These curves reveal many of the properties of a material (including data to establish the Modulus of Elasticity, E).
Stress–strain curves of various materials vary widely, and different tensile tests conducted on the same material yield different results, depending upon the temperature of the specimen and the speed of the loading. It is possible, however, to distinguish some common characteristics among the stress–strain curves of various groups of materials and, on this basis, to divide materials into two broad categories; namely, the ductile materials and the brittle materials.
Consider a bar of cross sectional area A being subjected to equal and opposite forces F pulling at the ends so the bar is under tension. The material is experiencing a stress defined to be the ratio of the force to the cross sectional area of the bar:
This stress is called the tensile stress because every part of the object is subjected to tension. The SI unit of stress is the newton per square meter, which is called the pascal.
1 pascal = 1 Pa = 1 N/m2
Now consider a force that is applied tangentially to an object. The ratio of the shearing force to the area A is called the shear stress.
If the object is twisted through an angle q, then the shear strain is:
Finally, the shear modulus MS of a material is defined as the ratio of shear stress to shear strain at any point in an object made of that material. The shear modulus is also known as the torsion modulus.
Ductile materials, which includes structural steel and many alloys of other metals, are characterized by their ability to yield at normal temperatures.
Low carbon steel generally exhibits a very linear stress–strain relationship up to a well defined yield point (Fig.2). The linear portion of the curve is the elastic region and the slope is the modulus of elasticity or Young's Modulus ( Young's Modulus is the ratio of the compressive stress to the longitudinal strain). After the yield point, the curve typically decreases slightly because of dislocations escaping from Cottrell atmospheres. As deformation continues, the stress increases on account of strain hardening until it reaches the ultimate tensile stress. Until this point, the cross-sectional area decreases uniformly and randomly because of Poisson contractions. The actual fracture point is in the same vertical line as the visual fracture point.
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