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.
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
- 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