Stress-strain Curve

When a metal wire is stretched by applying a load, it undergoes deformation. The relationship between the applied stress and the resulting strain can be studied by plotting a stress-strain curve. This curve helps us understand how materials behave under different loading conditions and determine their elastic and plastic properties.

A graph drawn by taking tensile strain along the x-axis and tensile stress along the y-axis, obtained by gradually increasing the load on a metal wire suspended vertically from a rigid support until the wire breaks, and measuring the elongation produced during each step.

• Region OA: Straight line portion where Hooke's law is obeyed, and stress is directly proportional to strain
• Point A (Proportional Limit): The stress at which the straight line portion ends
• Region OB: Elastic region where deformation is reversible
• Point B (Yield Point/Elastic Limit): The point beyond which the material loses elastic behavior
• Beyond Point B: Plastic deformation region where deformation is irreversible
• Point D: Fracture point where the material breaks
• Permanent Set: The increased length retained by the wire when stress is removed beyond the elastic limit

Initial Region (OA - Elastic Region within Hooke's Law):

• The graph starts as a straight line from O to A
• Stress is directly proportional to strain
• Hooke's law is valid in this region
• If the load is removed, the wire returns to its original length

Extended Elastic Region (AB):

• Stress and strain are no longer proportional
• Hooke's law is not valid
• Deformation is still reversible
• If the load is removed anywhere between O and B, the wire regains its original length

Plastic Deformation Region (Beyond B):

• When stress increases beyond point B, strain continues to increase
• Deformation becomes irreversible
• If the load is removed (e.g., at point C), the wire follows line CE
• The wire has a greater length than the original, even with no stress
• The material acquires a permanent set

Fracture Region (D):

• Large increase in strain occurs for small increases in stress
• Point D is where the fracture (breaking) takes place
• Material shows plastic flow from B to D

Brittle Materials:

• Materials: Glass, ceramics
• Break within the elastic limit
• No significant plastic deformation before breaking

Ductile Materials:

• Materials: Copper, aluminum, wrought iron
• Have a large plastic range of extension
• Lengthen considerably before breaking
• Undergo significant plastic deformation

Malleable Materials:

• Materials: Gold, silver
• Can be hammered into thin sheets
• Undergo plastic deformation under compressive stress

Elastomers:

• Material: Rubber
• Have a large elastic region
• It can be stretched many times its original length
• Return to the original state after stress removal
• Stress-strain curve is not a straight line

Phenomenon:

• Occurs in materials like vulcanized rubber
• When stress decreases to zero, strain does not return to zero immediately
• Strain lags behind the stress

Stress-Strain Curve for Loading and Unloading:

• The loading and unloading curves do not coincide
• They form a closed loop
• The area of the loop represents energy dissipated during deformation

When a rubber band is repeatedly stretched and released, it undergoes elastic hysteresis. During each cycle of loading and unloading, some energy is dissipated (shown by the area of the hysteresis loop). This repeated deformation causes the rubber band to lose some of its elastic properties gradually, resulting in a permanent set. The material does not return completely to its original length after each use, making the rubber band progressively looser.