# Stress Strain Curve : Strength of Materials

Stress Strain curve represents the behavior of material when an external force is applied to it. This diagram is used by product design engineers during material selection and structure design calculations. In this article we will discuss “Engineering and True Stress-Strain-Diagram” for ductile and brittle materials.

To understand stress-strain Curve we suggest you to first read this article on What is Stress and What is Strain?

#### How to Plot Stress Strain Curve ?

Stress-strain curve for a material is plotted by applying tensile /Elongation in the standard test sample. Variation in stress acting on test sample is recorded with respect to strain value until the test sample fractures.

After recording all values, stress-strain diagram is plotted by putting stress in Vertical Axis and strain in Horizontal Axis.

#### Understanding Stress-Strain Curve for Ductile Materials Proportional Limit (From “O” to “A”)

According to Hook’s Law stress is directly proportional to strain and this limit is known as Proportional Limit. Stress-strain curve is a straight line (from “O” to “A”) within proportional limit.

Ratio of stress and strain for a material is a constant, known as young modulus of elasticity.

Elastic Limit (From “O” to “B”)

It is the limit beyond which the material will no longer go back to its original shape when the external force is removed. In stress strain diagram upto point B (Yield Point) material has elastic properties.

If we increase the external load (stress) beyond elastic limit, the material will not come back to its original shape.

Upper Yield Point (Point B)

Beyond elastic limit a ductile material has plastic properties. Upper yield point is the point at which maximum external load or stress is required to initiate plastic deformation inside the material. Strength of material corresponding to point B is known as yield strength.

Lower Yield Point (Point C)

After point C, material length will increase with a very small increase in external load (stress). In other words it is the point at which minimum load is required to maintain the plastic behavior of the material.

Ultimate Tensile Strength (Point D)

Material Strength corresponding to  on stress strain diagram indicates ultimate tensile strength of the material. A material has the maximum stress at Point D, that it can bear before breaking. After this point necking starts inside the material.

Rapture / Fracture / Breaking Strength (Point E)

Point E is the point at which material fracture/breaks. Stress associates with this point is known as breaking strength.

##### Stress Strain Diagram Comparison ( Ductile Brittle and Plastic Materials)

Most of products we see in our daily life are made of either brittle, ductile, Plastic or rubber material. All of these materials behaves differently when external force is applied to them. Ductile Materials

Ductile materials are the materials that exhibit elastic as well as plastic deformation. As shown above in ductile materials ultimate stress point and fracture point is not same. Copper, aluminum, steel etc are ductile materials.

Example

When a metal wire is bent. Up to a limit wire will regain its initial position. But after this limit, it starts showing plastic behavior and maintains its position. If we continue applying the force it breaks at  fracture point. Brittle Materials

When stress is applied to brittle materials, they breaks with very small elastic deformation and without plastic deformation. For brittle materials elastic limit, yield strength, ultimate tensile strength and breaking strength is same. Brittle materials absorb relatively little energy prior to fracture. Brittle materials include ceramic, wood, glass, PMMA, Graphite, cast iron etc,

Example

When we try to bend a pencil or glass. After a little deformation, it will break suddenly with a snapping sound.

Plastic Materials

As shown in stress-strain curve for plastic materials, Similar to ductile materials some of plastic materials exhibit elastic properties upto proportional limit. But plastic materials requires very less stress compared to ductile materials to produce deformation. Plastic materials do not show any work hardening during plastic deformation.

Example

When we try to bend a plastic spoon, after a certain limit it will not retain its position,

##### Engineering Stress-Strain Curve vs True Stress Strain Curve

True Stress and True Strain are different from Engineering Stress and Engineering Strain respectively. When tensile force is applied, after necking area of the test specimen starts reducing. Engineering stress-strain diagram do not consider reduction in this area. Therefore we gets different stress values. To draw true stress-strain diagram true stress and strain values are considered. Whereas in engineering stress strain diagram initial values are considered.

• Engineering Stress is always less than corresponding True Stress during tensile loading. Because Specimen initial cross-section area is used to calculate engineering stress. Initial cross section area is less than actual cross section area.
• During tensile loading Engineering Strain is always higher than corresponding true strain.

#### Conclusion

To sum up, Stress strain curve / diagram for a material is required for material selection during product design. It helps designers in selection of best material for their application.

Got Questions?  We will be happy to help.

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