Materials: Stress and Strain

Fundamental Concepts of Stress and Strain

Stress is a measure of the internal forces in a material that resists deformation.
It is defined as the force applied per unit cross-sectional area and is measured in Pascals (Pa), the unit of pressure.
Strain is a measure of deformation representing the displacement between particles in the material body divided by the original length of the material.
Strain is dimensionless and has no units, as it is the ratio of two lengths. However, it is often reported as a percentage.

Stress (σ) can be calculated using the formula: Stress = Force / Area
Strain (ε) can be calculated using the formula: Strain = Change in length / Original length

The relationship between stress and strain for a specific material can be plotted on a stress-strain graph.
The gradient of the graph up to the limit of proportionality is known as the Young’s modulus (E) of the material, representing its stiffness.
This is calculated using the formula: Young’s modulus = Stress / Strain
Materials can be compared using this graph by evaluating their gradients, with steeper gradients indicating stiffer materials.

For materials that obey Hooke’s Law, stress is directly proportional to strain within the elastic limit.
Beyond the elastic limit and up to the yield point, the material will undergo plastic deformation and will not return to its initial shape after removal of the force.

If a material is stressed beyond the yield point, it will experience plastic deformation, i.e., it will permanently change shape.
The point where plastic deformation begins is called the yield point. Fairly large amounts of strain occur with little increase in stress.

The maximum stress a material can withstand before its break is known as its ultimate tensile strength.
After reaching the ultimate tensile strength, the graph starts to slope downwards, the material begins to neck and becomes more and more brittle until it eventually breaks.

Understanding of stress and strain is essential for designing and testing materials for various applications including construction, transportation, and manufacturing.
For example, engineers must consider the yield point of concrete and steel when designing buildings to prevent the materials from undergoing plastic deformation under load.