Stress-Strain Curve
How materials deform, yield, and fail under tensile loading
Difficulty
Intermediate
Read time
9 min
Review status
Needs review
Concept sketch
Tensile response by material type
Illustrative, not to scale
Overview
A stress-strain curve shows how a material responds as tensile load increases. It helps students compare stiffness, yield behavior, ductility, strain hardening, necking, and fracture across metals, ceramics, polymers, and rubber-like materials.
How to read it
- Use the initial slope to compare stiffness, not strength.
- Find yield to estimate where permanent deformation begins.
- Use the peak engineering stress as the ultimate tensile strength.
- Use strain at fracture and area under the curve to reason about ductility and toughness.
When to use it
- Comparing material behavior from tensile test data.
- Distinguishing stiffness, strength, ductility, and toughness.
- Understanding why a brittle material can be stiff but not ductile.
- Choosing a material model or checking whether elastic assumptions are reasonable.
What the graph shows
The horizontal axis is strain, which measures deformation relative to the original length. The vertical axis is engineering stress, which represents the applied tensile force divided by the original cross-sectional area. The curve is useful because it shows both how stiff a material is and how it behaves after elastic deformation ends.
Elastic region
At the beginning of many curves, stress and strain are approximately proportional. This is the elastic region: if the load is removed, the material returns close to its original shape. The slope in this region is Young's modulus, so a steeper line means the material is stiffer, not necessarily stronger.
Yield and plastic deformation
Yield marks the point where permanent deformation becomes important. Ductile metals can continue deforming after yield, while brittle materials often fracture with little plastic deformation. Some materials do not have a sharp yield point, so engineers may use an offset method such as the 0.2% proof stress.
Ultimate strength, necking, and fracture
The highest engineering stress on the curve is the ultimate tensile strength. After this point, ductile specimens often neck locally, meaning deformation concentrates in a smaller region. The engineering stress may drop before fracture even though the local true stress can continue increasing.
How to compare materials
Compare stiffness from the initial slope, yield resistance from the yield point, strength from the maximum stress, and ductility from the strain at fracture. Toughness is related to the area under the curve, so a material can be very strong but not very tough if it fractures at low strain.