Deformation of Materials

Types of Deformation

Deformation can be classified based on whether the material returns to its original shape after the load is removed, and on the time dependence of the deformation.

1. Elastic Deformation

• Definition: Temporary change in shape or size that disappears upon unloading.
• Cause: Stretching of atomic bonds without breaking them.
• Characteristics: Proportional relationship between stress and strain (Hooke’s law) within the elastic limit.
• Example: Slight stretching of a steel spring under small load.

2. Plastic Deformation

• Definition: Permanent change in shape that remains after the load is removed.
• Cause: Movement of dislocations or slip of atomic planes.
• Characteristics: Occurs after the yield point; involves irreversible atomic rearrangements.
• Example: Bending a paper clip beyond its elastic limit.

3. Viscoelastic Deformation

• Definition: Time-dependent deformation showing both elastic and viscous behavior.
• Example: Polymers and biological tissues under sustained load.

4. Creep

• Definition: Time-dependent plastic deformation under constant load, significant at high temperatures (≥ 0.4 T_m).
• Stages: Primary (decelerating), secondary (steady-state), tertiary (accelerating to failure).

Stress–Strain Relationship

The stress–strain curve describes how a material responds to applied stress, revealing key mechanical properties.

Key Regions

1. Elastic Region: Linear relationship between stress (σ) and strain (ε); slope is the modulus of elasticity (E).
2. Yield Point: Stress at which plastic deformation begins; may be upper and lower yield points in some steels.
3. Plastic Region: Strain increases at a lower rate of stress increase; includes strain hardening.
4. Ultimate Tensile Strength (UTS): Maximum stress the material can withstand before necking.
5. Fracture Point: Material breaks; stress drops to zero.

Mathematical Form

• Hooke’s Law (Elastic region): σ = E × ε
• True stress–strain: Accounts for instantaneous cross-sectional area during plastic deformation.

Material Behavior

• Ductile materials: Large plastic region before fracture (e.g., mild steel, aluminum).
• Brittle materials: Little or no plastic deformation before fracture (e.g., glass, ceramics).

Strain Hardening (Work Hardening)

Strain hardening is the increase in a material’s strength and hardness due to plastic deformation.

Mechanism

• Plastic deformation increases dislocation density.
• Dislocations interact and impede each other’s motion, requiring higher stress for further deformation.

Stages in Metals

1. Stage I (Easy glide): Dislocations move on primary slip systems.
2. Stage II: Multiple slip systems activate; dislocation interactions increase.
3. Stage III: Dynamic recovery reduces hardening rate.

Effects

• Increased yield strength and hardness.
• Reduced ductility.

Applications

Cold working processes (rolling, drawing, forging) exploit strain hardening to strengthen metals without heat treatment.

Deformation Mechanisms

Deformation occurs through different atomic-scale mechanisms depending on material type, temperature, and stress state.

1. Slip

• Definition: Movement of dislocations along specific crystallographic planes and directions (slip systems).
• Example: FCC metals have 12 slip systems, making them highly ductile.

2. Twinning

• Definition: A portion of the crystal forms a mirror image of the lattice across a twin plane.
• Role: Contributes to plastic deformation, especially in HCP metals with limited slip systems.

3. Diffusional Flow

• Definition: Atom migration under stress gradients; important in creep at high temperatures.
• Types: Nabarro–Herring (lattice diffusion), Coble (grain boundary diffusion).

4. Grain Boundary Sliding

• Definition: Relative movement of grains along boundaries; significant in superplastic deformation.

5. Shear Transformation

• In amorphous materials: Localized shear bands form instead of dislocation slip.