Tensile strain is the amount a material stretches when pulled, expressed as a fraction of its original length. If you pull a rubber band and it goes from 10 cm to 12 cm, the tensile strain is 2/10, or 0.2 (20%). It’s one of the most fundamental measurements in physics and engineering because it tells you exactly how much a material deforms under a pulling force.
The Formula
Tensile strain (ε) equals the change in length divided by the original length:
ε = ΔL / L₀
ΔL is how much the object got longer, and L₀ is its length before any force was applied. Because you’re dividing a length by a length, strain is dimensionless: it has no units. You’ll see it written as a plain decimal (0.05), a percentage (5%), or in microstrain for very small deformations. One microstrain equals one millionth of the original length, which is useful when measuring things like steel beams that deform only slightly under normal loads.
Tensile strain is considered positive. Its opposite, compressive strain (when a material gets squeezed shorter), is written as negative.
How Strain Relates to Stress
Strain doesn’t happen on its own. It’s the result of stress, which is the force applied per unit of cross-sectional area. The relationship between the two is described by Hooke’s Law: within a material’s elastic range, strain is directly proportional to stress. Double the pulling force, and the material stretches exactly twice as much.
The constant that links them is called Young’s modulus (Y). The equation is:
Y = stress / strain = (F/A) / (ΔL/L₀)
Young’s modulus is a property of the material itself. Steel has a very high Young’s modulus, meaning it resists stretching strongly. Rubber has a low one, meaning it stretches easily under the same force. If you know a material’s Young’s modulus and the stress being applied, you can predict the exact strain it will experience.
Elastic vs. Plastic Strain
When you stretch a material gently and release it, it snaps back to its original shape. This is elastic deformation, and the strain is fully reversible. At the atomic level, the atoms are being pulled slightly apart from their equilibrium positions but never permanently displaced.
Push past a threshold called the elastic limit, and the material enters plastic deformation. The atoms shift permanently through a process called dislocation motion, and part of the strain remains even after the force is removed. If you bend a paperclip and it stays bent, that’s plastic strain.
For structural steels like A36, the plastic range begins at relatively small strains (around 1.8%), but the material can stretch much further before breaking. A36 steel reaches about 40% elongation at fracture. Rubber behaves entirely differently: natural rubber compounds can stretch to 250% to 370% of their original length before failing, depending on their chemical makeup.
How Different Materials Compare
The maximum tensile strain a material can withstand before breaking varies enormously:
- Structural steel: Roughly 32% to 41% elongation at fracture, depending on the grade. Higher-strength steels tend to stretch less before breaking.
- Natural rubber: Can sustain strains of 230% to 370%, making it one of the most stretchable common materials.
- Human tendons: Fail at about 10% strain. The collagen fibrils that give tendons their strength begin breaking apart at 8% to 10% strain, with complete rupture typically occurring in the 10% to 15% range.
These numbers reveal something practical: a material’s strength (how much force it can bear) and its stretchability (how much strain it tolerates) are two separate properties. Steel is far stronger than rubber, but rubber can deform far more before it breaks.
Engineering Strain vs. True Strain
The basic formula (ΔL / L₀) gives you what’s called engineering strain. It’s simple and works well for small deformations, but it has a built-in assumption: it always divides by the original length, even as the material is actively getting longer.
True strain accounts for this by measuring each tiny increment of stretch relative to the material’s current length at that moment, not its original length. For small deformations, the two values are nearly identical. As deformation increases, they diverge. At 30% engineering strain (0.30), the true strain is only 0.26, a difference of more than 10%.
In everyday applications, engineering strain is the standard. True strain becomes important in manufacturing processes like metal forming, where materials undergo large deformations and precision matters.
How Tensile Strain Is Measured
In a laboratory, tensile strain is measured during a tensile test: a sample of material is clamped at both ends and pulled until it deforms or breaks. Two instruments do most of the measuring.
An extensometer is a device that clips directly onto the sample and tracks how much it elongates between two fixed points. Some extensometers use mechanical arms that physically ride along the surface, while more advanced versions use laser or video tracking. For tests that involve both pulling and twisting, specialized extensometers can measure both types of strain simultaneously.
A strain gauge is a thin sensor bonded to the surface of a material. As the material stretches, the gauge stretches with it, changing its electrical resistance. That resistance change is converted into a strain reading, typically through a circuit called a Wheatstone bridge. Strain gauges are especially useful outside the lab because they can be permanently attached to structures like bridges, aircraft wings, or pipelines to monitor strain in real time.