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April 8, 2025Stress-Strain Curve: When we stretch a spring by applying load to its ends, the length of the spring increases slightly. When you remove the load at the ends, it regains its original size and shape. Similarly, rubber can be pulled to several times its original length and still return to its original shape. But after crossing a certain limit of the load, we will observe that cracks are generated, and then the rubber breaks. The same thing will happen with spring or any other material. This phenomenon also occurs in compression. After a certain limit of compressive force, the material fails.
When a deforming force is applied to a material such that the material is in static equilibrium, a resistive force is developed inside the material to oppose the external force. The resistive force per unit area is called stress
The relation between the stress and the strain for a given material under tensile stress can be found experimentally using a universal testing machine (UTM). In this standard test, a test cylindrical rod or a wire is stretched on the application of force (tensile). The strain and the stress due to the applied force needed to cause the strain are recorded. The applied force is gradually increased in steps, and the change in length is noted. Then a graph is plotted between the stress and the strain produced. A typical graph for metal is shown in the figure below.
The stress-strain curve has different regions and points.
From the graph, we can see that in the region between
In the region from
The portion of the curve between
When the load is removed, say at some point
Beyond point
As we have discussed the nature of stress-strain cure varies from material to material. For example, rubber can be pulled several times its original length but still return to its original shape. This does not happen with metals, the limit of elastic deformation of metals is very small.
A distinctly different stress-strain relation exists for vulcanized rubber. The behaviour is qualitatively shown in the figure.
Rubber remains elastic even when it is stretched to over several times its original length. In the case shown in the figure, the length is increased to
However, the magnitude of stress for a given strain is much more in steel than in rubber. This means large internal forces appear if the steel wire is deformed. In this sense, steel is more elastic than rubber. There are two important phenomena to note from the figure. There is almost no region of proportionality. Secondly, when the applied load is removed, the original curve is not retraced. Although the material finally acquires its original length.
The work done (area under the curve) by the material in returning to its original shape is less than the work done by the deforming force when it was deformed. A particular amount of energy is absorbed by the material in the cycle. This absorbed energy appears as heat. This phenomenon is called elastic hysteresis. Substances like tissue of aorta, rubber, etc., that can be stretched to cause large deformation are called elastomers.
Q.1. The figure shows the strain-stress curve for a given material. What are,
(a) Young’s modulus and
(b) approximate yield strength for this material?
Ans: (a) We have to find the slope of the curve to find out Young’s modulus. For finding slope, take two points lying on the line. For example, take origin
Since it is passing through the origin
Young’s modulus,
(b) Yield strength of a material is defined as the maximum stress it can withstand before failure. Here there is no plastic region, the yield strength and Ultimate tensile strength are almost the same. From the graph, the approximate yield strength of the given material,
The stress-strain curve is the relationship between stress and corresponding strain. Up to a certain limit only, the stress is directly proportional to strain. Hooke’s law is valid only in this linear part of the stress-strain curve. The slope of the linear curve gives Young’s modulus of the material. A material with a large value of Young’s modulus requires a large force to produce small changes in its length.
In daily life, we feel that a material that stretches more is more elastic, but it is a misnomer. In fact, material that stretches to a lesser extent even after the application of a large load is considered to be more elastic. Steel is more elastic than rubber.
Q.1. Why are steel and brass are preferred over copper and aluminum in heavy machines?
Ans: Steel and brass are preferred over copper and aluminum in heavy machines because steel and brass have high Young’s modulus and required a large force to deform.
Q.2. What are elastomers?
Ans: Many materials like rubber, tissue of aorta, etc., can have large elastic deformation. They can be stretched much larger than metals without plastic deformation.
Q.3. What is the relationship between stress and strain?
Ans: Under elastic limit, stress is directly proportional to strain. According to Hook’s law,
Young’s modulus,
Q.4. What is the use of a stress-strain diagram?
Ans: The stress-strain diagram provides an estimate of the strength and elasticity of the material. It also tells about the behaviour of the materials with the application of load.
Q.5. What is the elastic limit?
Ans: It is the point on the stress-strain curve after which material deforms plastically. Up to this point, the material returns to its original size after the load is released.
We hope this detailed article on Stress-Strain Curve helps you in your preparation. If you get stuck do let us know in the comments section below and we will get back to you at the earliest.
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