Interactive Stress–Strain Curve (Ductile)

Strain (ε) Stress (σ) A: Elastic limit B: Upper Yield Point C: Lower Yield Point D: UTS peak E: Fracture

Brittle Stress–Strain Curve

Strain (ε) Stress (σ) Elastic limit UTS (≈ fracture strength)

True Stress–Strain Curve

True Strain (εtrue) True Stress (σtrue)

Stress–Strain Curve Concepts

Resilience (Elastic Energy)

Definition: Energy stored in a material up to the elastic limit.

Key Idea: Fully recoverable when the load is removed.

Importance: High resilience means the material can absorb shocks without permanent deformation.

Examples: Spring steel, rubber bands.

Plastic Energy

Definition: Energy absorbed beyond the yield point until fracture.

Key Idea: Causes permanent deformation.

Importance: Indicates how much a material can plastically deform before breaking.

Examples: Copper, aluminum.

Toughness

Definition: Total energy absorbed until fracture (entire area under curve).

Key Idea: Measures ability to absorb energy before breaking.

Examples: Mild steel (high toughness), glass (low toughness).

Elastic Limit

Definition: Maximum stress a material can withstand without permanent deformation.

Key Idea: Beyond this, the material will not return to its original shape.

Examples: Low‑carbon steel has a clear elastic limit.

Yield Point

Definition: Stress at which noticeable plastic deformation begins.

Key Idea: Material starts to flow permanently without much increase in load.

Examples: Mild steel shows a distinct yield point.

Ultimate Tensile Strength (UTS)

Definition: Maximum stress the material can withstand.

Key Idea: Beyond this, necking begins and engineering stress decreases.

Examples: Structural steels, aluminum alloys.

Fracture Point

Definition: Final breaking point of the material.

Key Idea: Specimen fails and separates into pieces.

Examples: Brittle fracture in glass, ductile fracture in mild steel.

Ductile vs. Brittle Materials

Property Ductile Materials Brittle Materials
Definition Materials that undergo significant plastic deformation before fracture. Materials that fracture with little or no plastic deformation.
Stress–Strain Curve Long curve with clear yield point, large plastic region, high toughness. Short curve, almost linear until sudden fracture, low toughness.
Energy Absorption Absorb large amounts of energy before breaking. Absorb very little energy before breaking.
Fracture Behavior Necking and gradual failure. Sudden, catastrophic failure.
Examples Mild steel, copper, aluminum. Glass, cast iron, ceramics.