Engineering Strain
Engineering strain is the ratio of the change in length of a specimen to its original length when subjected to axial loading, expressed as a dimensionless number or percentage. It quantifies how much a material deforms relative to its initial size and is the conventional measure plotted alongside engineering stress to produce stress-strain curves. Engineering strain assumes uniform deformation and uses the original gauge length, making it straightforward to measure experimentally.
Key Formula
epsilon = (L - L0) / L0
LaTeX: \varepsilon = \frac{\Delta L}{L_0} = \frac{L - L_0}{L_0}
| Symbol | Meaning | Unit |
|---|---|---|
| ε | Engineering strain | dimensionless |
| ΔL | Change in length | m |
| L | Final length | m |
| L₀ | Original gauge length | m |
Worked Example
Problem
A tensile specimen has an original gauge length of 50 mm. After loading it measures 53.5 mm. Calculate the engineering strain.
Solution
Step 1: Calculate change in length. ΔL = L − L₀ = 53.5 mm − 50 mm = 3.5 mm Step 2: Apply the formula. ε = ΔL / L₀ = 3.5 mm / 50 mm = 0.070 Step 3: Convert to percentage. ε = 0.070 × 100% = 7.0%
Answer
Engineering strain ε = 0.070 (7.0%)
Typical Failure Strains for Common Engineering Materials
| Material | Yield Strain (%) | Fracture Strain (%) | Behaviour |
|---|---|---|---|
| Low-carbon steel | 0.12 | 20–30 | Highly ductile |
| Aluminium 6061-T6 | 0.28 | 12 | Moderately ductile |
| Cast iron | < 0.01 | 0.6 | Brittle |
| Rubber (natural) | — | 500–800 | Hyper-elastic |
| Glass | < 0.01 | < 0.1 | Very brittle |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Engineering Stress
Engineering stress is defined as the applied force divided by the original cross-sectional area of a specimen, regardless of any deformation that occurs during loading. It is the conventional measure used in materials testing and structural analysis because the original dimensions are easily measured before the test begins. Engineering stress is widely used in design calculations, material data sheets, and stress-strain curves to characterise material behaviour under uniaxial loading.
Young's Modulus
Young's modulus (also called the modulus of elasticity) is the ratio of engineering stress to engineering strain in the linear-elastic region of a material's stress-strain curve. It is a fundamental mechanical property that quantifies the stiffness of a solid material — a higher value means the material resists deformation more effectively. Young's modulus is essential in structural design for calculating deflections, natural frequencies, and load-bearing capacity of components.
Ductility
Ductility is a mechanical property that describes a material's ability to undergo significant plastic (permanent) deformation before fracture under tensile stress. It is quantified as the percentage elongation or percentage reduction in area measured in a tensile test. Ductile materials such as mild steel and copper provide engineers with warning before failure (through visible deformation and "necking"), making them safer choices for structures subjected to overload or impact loading.
From Latin "stringere" (to bind or stretch). The term "strain" entered mechanics through Robert Hooke's 17th-century work on elasticity. The qualifier "engineering" was added in the 20th century to distinguish it from logarithmic (true) strain used in large-deformation analysis.