Stress-strain behavior describes how a metal changes shape when a load is applied. Engineers use this relationship to predict whether a part will spring back, permanently deform, or break. The stress-strain curve is one of the most important tools for choosing materials for bridges, machines, aircraft, and tools.
It connects measurable forces and shape changes to material properties such as stiffness, strength, and toughness.
For a ductile metal, the curve begins with a nearly straight elastic region where stress is proportional to strain. After yielding, the metal enters plastic deformation, so removing the load no longer returns it to its original length. The curve usually rises to an ultimate tensile strength as strain hardening occurs, then drops during necking until fracture.
The area under the curve represents toughness, which measures how much energy per unit volume the metal can absorb before breaking.
Key Facts
- Engineering stress is σ = F/A0, where F is the applied force and A0 is the original cross-sectional area.
- Engineering strain is ε = ΔL/L0, where ΔL is change in length and L0 is original length.
- In the elastic region, Hooke's law applies: σ = Eε, where E is Young's modulus.
- Yield strength is the stress where noticeable plastic deformation begins, often found using the 0.2% offset method.
- Ultimate tensile strength is the maximum engineering stress reached on the stress-strain curve.
- Toughness is energy absorbed per unit volume and equals the area under the stress-strain curve up to fracture.
Vocabulary
- Stress
- Stress is the internal force per unit area in a material caused by an external load.
- Strain
- Strain is the fractional change in length or shape of a material compared with its original size.
- Elastic deformation
- Elastic deformation is temporary deformation that disappears when the load is removed.
- Plastic deformation
- Plastic deformation is permanent deformation that remains after the load is removed.
- Toughness
- Toughness is the ability of a material to absorb energy before fracturing.
Common Mistakes to Avoid
- Confusing stress with force is wrong because stress also depends on the cross-sectional area carrying the load.
- Treating strain as a length is wrong because strain is a ratio, such as ΔL/L0, and has no units.
- Assuming the material returns to its original shape after yielding is wrong because yielding marks the start of permanent plastic deformation.
- Calling the ultimate tensile strength the fracture strength is wrong because the maximum engineering stress usually occurs before the specimen actually breaks.
Practice Questions
- 1 A metal rod has an original cross-sectional area of 50 mm^2 and carries a tensile force of 10,000 N. Calculate the engineering stress in MPa.
- 2 A 200 mm long metal specimen stretches by 0.40 mm in the elastic region under load. Calculate the engineering strain, and if the stress is 140 MPa, find Young's modulus.
- 3 Two metals have the same yield strength, but one has a much larger area under its stress-strain curve before fracture. Explain which metal is tougher and why that matters in impact loading.