Definition:Stress-Strain Diagram

Definition

Let $\BB$ be a body subjected to a stress.

Let the stress on $\BB$ be plotted on the $x$-axis of a graph with the strain caused by the stress plotted against the $y$-axis.

The resulting graph is called a stress-strain diagram.

The above diagram shows a typical graph of stress against strain.

The segment $OA$ represents the region in which Hooke's Law actually applies.

The slope of $OA$ is the modulus of elasticity of the material of which the body is composed.

The points and regions of the graph can be categorised as follows:

Elastic Region

The elastic region is the line $OB$, in which when the stress is removed, $\BB$ returns to its original shape.

Plastic Region

The plastic region is the line $BD$, in which when the stress is removed, $\BB$ no longer returns to its original shape, but takes on a deformation, known as a permanent set.

That is, the plastic region is where $\BB$ is plastic.

Permanent Set

Let $\BB$ be subjected to stress which takes the stress-strain diagram out of the elastic region and into the plastic region.

When the stress is removed, and $\BB$ no longer returns to its original shape, its deformed shape is known as a permanent set.

$OF$ represents the permanent set of $\BB$ after it has been subjected to the stress which has been removed at point $C$.

Breaking Stress

The breaking stress is the stress at which $\BB$ eventually fractures.

This breaking stress is indicated on the stress-strain diagram as point $E$.

Note that the breaking stress in this case is actually less than the stress needed to take $\BB$ to the end of the plastic region.

At this point $\BB$ has already started to break down internally, and it is no longer able to sustain that level of stress placed upon it.

Also see

• Hooke's Law

• Results about stress-strain diagrams can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Hooke's law
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hooke's law