Materials In Today's World

Elastic Region


What is the elastic region? It is the region where the material can be deformed and when released will return back to its original configuration. Many metals in the elastic region have a resulting strain that is proportional to the tensile load when the applied tensile load is small. Mathematically, this can be written as σ=Eε , and more generally is known as a form of Hooke's law. E is the proportionality constant and is called the modulus of elasticity or Young's modulus. Physically, the larger the value of the modulus of elasticity the stiffer the material is, i.e., the more resistant to bending the material is. If we look at a stress-strain diagram for a metal in the elastic region such as that shown in the figure below, the slope of the curve is the modulus of elasticity.

Stress-strain diagram. Epsilon on the x axis and sigma on the y axis. Line through the origin labeled linear-elastic
Stress-Strain Diagram
Credit: Callister

If we look at the figure below it is not surprising that the material listed with the highest E is diamond. Diamond has strong carbon bonds and is incredibly stiff. Larger E indicates a stronger bond. Later when we study composites in more detail, we will see that fibers are added to polymers to increase the stiffness of the material. Increased stiffness implies increased E, which you can see in the figure for the composite/fiber materials.

E value: Metal Alloys (40-400), Graphite, Cermaics & Semiconductors (10-1200), polymers (0.2-4), Composites/fibers (.6-400)
Room-temperature elastic moduli for various materials
Credit: Callister

To Read

Now that you have been introduced to elasticity, please go to your e-textbook and read section 7.3 (pages 71 to 74 in Chapter 4 of Materials for Today's World, Custom Edition for Penn State University) of this lesson's reading. When finished with the reading proceed to the next web page.