Stress-Strain Curve
A graph showing the relationship between stress and strain for a material, illustrating its elastic and plastic behavior.
What is Stress-Strain Curve?
Internal restoring force per unit area within a deformed body.
Key formula / rule: Stress
Key points
- To interpret the stress-strain curve for various materials.
- To identify and define key points on the curve.
- To calculate Young's modulus from the elastic region.
- To differentiate between ductile and brittle materials based on their curves.
Common exam trap
Confusing elastic limit with yield point.
Definitions
- Term
Stress
- Meaning
Internal restoring force per unit area within a deformed body.
- Term
Strain
- Meaning
The ratio of change in dimension to the original dimension; a measure of deformation.
- Term
Elastic Limit
- Meaning
The maximum stress that a material can withstand without undergoing permanent deformation.
- Term
Yield Point
- Meaning
The point on the stress-strain curve beyond the elastic limit where the material begins to deform plastically at a nearly constant stress.
- Term
Ultimate Tensile Strength (UTS)
- Meaning
The maximum stress that a material can withstand before it begins to neck and eventually fracture.
- Term
Young's Modulus
- Meaning
A measure of the stiffness of an elastic material; the ratio of tensile stress to tensile strain in the elastic region.
Learning objectives
To interpret the stress-strain curve for various materials.
To identify and define key points on the curve.
To calculate Young's modulus from the elastic region.
To differentiate between ductile and brittle materials based on their curves.
Formulae
- Name
Stress
- Note
F = Applied Force, A = Cross-sectional Area
- Expression
\σ = F/A
- Name
Strain
- Note
\Δ L = Change in Length, L0 = Original Length
- Expression
\ε = \Δ L / L0
- Name
Young's Modulus
- Note
Valid only in the linear elastic region of the stress-strain curve.
- Expression
E = \σ / \ε
Prerequisites
Understanding of Force and Pressure.
Concept of Deformation and Strain.
Basic understanding of Elasticity and Plasticity.
Common mistakes
Confusing elastic limit with yield point.
Incorrectly calculating Young's modulus from non-linear regions.
Assuming all materials have a distinct yield point.
Misinterpreting the meaning of ultimate tensile strength.
Keywords
Stress
Strain
Stress-Strain Curve
Elastic Limit
Yield Point
Ultimate Tensile Strength
Fracture Point
Young's Modulus
Ductility
Brittleness
Hooke's Law
Practice preview
Which of the following statements is INCORRECT regarding the stress-strain curve of a ductile material?…
medium
Which region of the stress-strain curve represents the elastic limit?…
easy
In a typical stress-strain curve for a ductile material, the region between the elastic limit and the fracture point is known as:…
easy