Metallurgical Engineering

                           

                                     Engineering Stress-Strain Curve

The engineering stress-strain curve gives the relationship between stress and strain for a ductile material. It is generally obtained by applying load to a tensile specimen. The curve reveal many properties of a material such as Young's Modulus(E), Yield point, UTS  etc.

Stress :

The stress in the engineering stress-strain diagram is given by load divided by the original area.

Strain :

The strain in the engineering stress-strain curve is giver by ratio of change in length / elongation to its initial length.

Strain has no unit since it’s a ratio of two quantities.

Proportionality limit :

In the curve, OA is linear. This is due to the fact that the stress is directly proportional to the strain i.e. it follows Hooke’s law. Hooke’s law states that within the elastic limit the stress is directly proportional to the strain. The point A represents the proportionality limit. Up to A if the load is removed the material regains its original shape along AO.

The constant of proportionality k is known Modulus of elasticity or Young’s Modulus. Thus, this is equal to the slope of the curve from OA.

Elastic limit :

The elastic limit is the point beyond which the material will no longer go back to its original shape when the load is removed. Here OC is the elastic limit.

Permanent set :

Beyond A the curve is not linear and in the region AC the material is partially plastic and partially elastic. The if we apply load and remove it deforms along C to the strain axis. Thus it doesn’t retain its original shape. Thus this permanent strain caused in the material offsets the OA by 0.2% and is considered as the permanent set.

Elastic and plastic regions :

The region from O to A is the elastic region and the region from A to B is partially plastic and partially elastic. And the region from B to E is plastic region.

Yield point :

Beyond B even a small amount of stress will lead to enormous strain. Thus, the point B is known as the yield point. Beyond this point the material starts to undergo plastic deformation. Now it is permanently deformed when the load is removed. The stress to produce continued plastic deformation increases with strain i.e. the material strain-hardens. The volume of specimen remains constant until point D. Thus from law of constancy of volume,

AL = AoLo 

Ultimate Tensile Strength(UTS) :

The maximum load that the material will withstand is denoted by the point D known as UTS. It is given by :

This is useful for purpose of specifications and quality control of a product. Beyond this point necking occurs.

Rupture strength :

The point D represents the UTS and further increase in load will lead to decrease in cross-sectional area a phenomenon known as necking. Now, because the cross-sectional area is decreasing the actual load required to deform a material decreases. Further increase in load will finally lead to fracture represented by point E. The strength of the material at this point is known as the fracture strength or rupture strength.

Resilience :

The ability of a material to absorb energy without creating any permanent distortion is known as resilience.

Modulus of resilience :

The work done on unit volume of a material as the force increases from O to A is known as the modulus of resilience. This can be calculated from the area under the curve from O to the elastic limit.

Here, s2 is the yield strength of the material and E is the Young’s modulus of the material. Its unit is .

Toughness :

The ability of a material to absorb energy without breaking is known as toughness.

Modulus of toughness :

The work done on unit volume of a material as the force increases from O to E is known as the modulus of toughness. This can be calculated from the area under the curve from O to E i.e. the entire stress strain curve.

Measure of ductility :

The measures of ductility in a material is the reduction in area of the material at the fracture and its elongation.

Both elongations and  reduction in area is represented in percentage.

Allowable stress :

The maximum safe stress that a material can withstand is knows as allowable stress. This must me usually within the proportionality limit.

Working stress :

The stress of a material under a given load is known as working stress.

Factor of safety :

The factor of safety is defined as the ratio of UTS to the working stress.