Stress-Strain Curve for a Ductile Material

Overview

A tensile test stretches a specimen at a controlled rate and records the corresponding stress and strain. Plotting stress vertically against strain horizontally reveals elastic behavior, yielding, strain hardening, necking and fracture.

Learning Outcomes

• Identify the axes and regions of a stress-strain graph.
• Explain proportional and elastic limits.
• Describe upper and lower yield behavior.
• Define ultimate tensile strength and fracture stress.
• Distinguish elastic and plastic deformation.
• Compare ductile and brittle behavior.

Intermediate Level

How the Curve Is Obtained

A tensile testing machine gradually stretches a specimen while measuring force and extension. These are converted to stress and strain. Stress is plotted on the vertical axis and strain on the horizontal axis.

Region OA: Linear Elastic Behavior

From O to A, stress increases linearly with strain. The material obeys Hooke’s law, and removing the load returns it to its original shape.

The slope of the straight OA portion is Young’s modulus. Point A is the proportional limit: the greatest stress for which stress remains directly proportional to strain.

Region AB: Nonlinear Elastic Behavior

Beyond A, straight-line proportionality ends, but the material can still regain its original shape if unloaded. Point B is the elastic limit or upper yield point in the textbook graph.

Yielding and Point C

Some materials show a lower yield point C. Near yielding, a large increase in strain occurs with little change in stress. Beyond the elastic limit, unloading leaves a permanent set.

Plastic Region

After B, the specimen does not fully return to its original shape. This permanent deformation is plasticity. The textbook graph shows permanent set as a residual strain after unloading.

Point D: Ultimate Tensile Strength

As deformation continues, the required engineering stress rises to a maximum at D. This maximum stress is the ultimate tensile strength or breaking-strength maximum of the specimen.

From D to E: Necking and Fracture

After D, localized narrowing called necking reduces the specimen’s cross-section. The engineering stress falls until the specimen breaks at E, the fracture point. The stress at E is fracture stress.

Ductile and Brittle Materials

Ductile materials undergo noticeable plastic deformation before fracture; examples in the textbook include lead, copper and wrought iron. Brittle materials break soon after the elastic limit with little plastic deformation; glass and high-carbon steel are examples.

Reading the Graph

Common Mistakes

• Interchanging the stress and strain axes.
• Calling A the fracture point.
• Assuming proportional limit and elastic limit are always the same point.
• Saying plastic deformation disappears after unloading.
• Confusing ultimate tensile strength at D with fracture at E.
• Assuming brittle materials have a long plastic region.

Short-Question Preparation

Long-Question Preparation

Sticky Notes

• OA: Hooke’s law.
• A: proportional limit.
• B: elastic limit / upper yield.
• C: lower yield.
• D: ultimate tensile strength.
• E: fracture.
• Beyond B: permanent set.

60-Second Revision

Summary

The tensile stress-strain curve maps a material’s path from reversible linear elasticity through yielding and plastic deformation to ultimate tensile strength, necking and fracture.

Ask-the-Tutor Modes

• Explain every graph point.
• Compare proportional and elastic limits.
• Explain yielding and permanent set.
• Compare ductile and brittle materials.
• Test me with an MCQ.