Materials In Today's World

Tensile, Compressive, Shear, and Torsional Stress

Mechanical property terms listed such as: ductile, shear, elastic, stress, strain, and plastic.
Mechanical Property Terms
Credit: Ron Redwing

As we can see in the above graphic, there are quite a few materials terms that are used when describing the properties of materials. In this lesson, we are going to define the above terms. It turns out that many of the above terms are related to the stress-strain curve of a material. What are stress and strain, and how are they related?

Let us take a cylinder and stress it. To stress it, I would fix one end of the cylinder and pull from the other end as shown in the figure below.

The cylinder gets longer and narrower as force pulls it from either end.
Tensile Stress
Credit: Callister

According to Newton's third law, the cylinder will experience a force downward on the lower surface of the cylinder and an equal and opposite force on the upper surface of the cylinder. My cylinder has an original length of Io and surface area of Ao. As I pull on my material with the force F the cylinder will lengthen and the resulting length will be l. Stress, σ, is defined as the force divided by the initial surface area, σ=F/Ao. This pulling stress is called tensile stress. Strain is what results from this stress. Strain, ε, is defined as the change in length divided by the original length, ε=ΔI/Io. Before we proceed further with stress and strain, let's define some other types of stress. 

If instead of pulling on our material, we push or compress our cylinder we are introducing compressive stress. This is illustrated in the following figure:

The cylinder gets shorter and wider as force pushes it from either end.
Compressive Stress
Credit: Callister

If instead of applying a force perpendicular to the surface, we apply parallel but opposite forces on the two surfaces we are applying a shear stress. This is illustrated in the following figure:

A cube undergoing sheer stress. The face of cube becomes more of a rhombus.
Shear Stress
Credit: Callister

Stress related to shear is torsional stress. If we hold one end of our cylinder fixed and twist the other end as shown in the figure below, we are applying a torsional (or twisting) stress.

A cylinder twisting under torsional stress
Torsional Stress
Credit: Callister