# Stress-Strain Curve

The stress-strain curve is a graph of stress as a function of strain. It can be constructed from data obtained in any mechanical test where load is applied to a material, and continuous measurements of stress and strain are made simultaneously. It is constructed for compression, tension and torsion tests.

The graph shows a typical Stress-Strain curve for a material such as mild steel.

The total area under the curve indicates how tough the material is – how much energy it can absorb while deforming plastically and not breaking.

The stress-strain curve for each material is different and unique. From these curves it is possible to extract a number of the materials properties.

The stress-strain curve is a key materials engineering metric and gives an insight into the mechanical properties of a set of materials.

The stress-strain curve for concrete is nearly straight and then stops. This shows a brittle material. Cast iron is also a brittle material. The mild steel curve extends further and the material continues to strain (stretch if under tension) with the stress remaining relatively constant. This shows a high ductility.

#### Hooke’s Law

Hooke’s Law states that, in a linear system, the restoring force is proportional to the displacement of the body, acting in a direction as to restore equilibrium.

#### Stress

Defined as the force per unit area of cross-section.

σ = F / A

where: σ = stress [Nm-2], F = force [N], A = cross-sectional area [m2]

#### Strain

When a structure or component is subjected to stress individual fibres or elements in the material either lengthen or shorten. Strain is a measure of how much these elements extend or contract, and is defined as the change in length divided by the original length of the element. Strains can be defined at a point if the strained element is considered to be of infinitesimal size.

ε = e / l

where ε = strain, e = extension [m], l = original length [m]

#### Stress-Strain Ratio

Stress divided by strain at any load or deflection, below the elastic limit of a material it is equal to tangent modulus of elasticity.

#### Tangent Modulus of Elasticity

Instantaneous rate of change of stress as a function of strain. It is the slope at any point on a stress-strain diagram.

#### Young’s Modulus

Modulus of elasticity is the slope of the initial, linear-elastic part of the stress-strain diagram.