The stress–strain curve is obtained from the tensile test and shows the relationship between applied stress and resulting strain in a material.

It helps engineers understand how a material behaves under loading and indicates elastic behavior, plastic deformation, yielding, and fracture.

This curve is one of the most frequently asked concepts in JE/AE mechanical engineering exams.

Definition

Stress

Internal resisting force per unit area developed inside a material when external load is applied.

\sigma = \frac{F}{A}

Strain

Deformation produced per unit original length due to applied stress.

\varepsilon = \frac{\Delta L}{L_0}

Core Concept Explanation

During a tensile test, when the load is gradually increased, the material experiences deformation. The stress and strain values are plotted on a graph, forming the stress–strain curve.

The curve for mild steel contains several important regions and points.

Important Regions of Stress–Strain Curve (Mild Steel)

1. Proportional Limit (Hooke’s Law Region)

In this region:

• Stress is directly proportional to strain.

• The material obeys Hooke's Law.

\sigma = E\varepsilon

Where E = Modulus of Elasticity.

If the load is removed in this region, the material returns to its original shape.

2. Elastic Limit

The maximum stress up to which the material returns to its original shape after removal of load.

Beyond this point, permanent deformation begins.

3. Yield Point

At this stage:

• The material starts plastic deformation.

• Large strain occurs with little or no increase in stress.

Two yield points exist in mild steel:

• Upper yield point

• Lower yield point

4. Strain Hardening Region

After yielding:

• Stress starts increasing again

• Material becomes stronger due to strain hardening

5. Ultimate Tensile Strength (UTS)

This is the maximum stress the material can withstand during the test.

After this point, the material begins necking.

6. Necking Region

Localized reduction in cross-sectional area occurs.

The specimen becomes thinner at one section.

7. Fracture Point

The final point where the material breaks into two pieces.

Important Points on Stress–Strain Curve

Properties Determined from Stress–Strain Curve

The stress–strain curve helps determine:

• Modulus of elasticity

• Yield strength

• Ultimate tensile strength

• Ductility

• Toughness

• Resilience

Applications in Engineering

Understanding stress–strain behavior helps in:

• Designing machine components

• Selecting suitable materials

• Preventing structural failure

• Determining safe working stress

It is widely used in:

• Structural engineering

• Automobile design

• Aerospace structures

• Machine element design

Exam-Focused Points

Important for TGPSC / TSPSC / SSC JE / RRB JE exams:

• Stress–strain curve is obtained from tensile testing.

• Mild steel has distinct upper and lower yield points.

• Proportional limit follows Hooke's Law.

• Ultimate tensile strength is the maximum stress on the curve.

• Necking begins after ultimate tensile strength.

• Fracture occurs after necking.

Common Exam Traps

Confusion 1

Students confuse proportional limit and elastic limit.

• Proportional limit → Hooke’s law valid

• Elastic limit → No permanent deformation

Confusion 2

Many assume necking occurs at yield point.

Correct concept:

• Necking occurs after ultimate tensile strength.

Confusion 3

Upper and lower yield points exist only in some materials like mild steel, not all materials.

Example Competitive Exam Questions

Question: Which law is followed in the proportional limit region of the stress–strain curve?
Answer: Hooke’s Law.

Question: What is the maximum stress a material experiences in a tensile test?
Answer: Ultimate tensile strength.

Question: At which stage does plastic deformation begin in mild steel?
Answer: Yield point.

Question: What phenomenon occurs after ultimate tensile strength in the stress–strain curve?
Answer: Necking.

Question: Which region represents permanent deformation?
Answer: Plastic region.

Quick Revision Summary

• Stress–strain curve shows relationship between stress and strain.

• Obtained from tensile test.

• Important points:

  • Proportional limit

  • Elastic limit

  • Yield point

  • Ultimate tensile strength

  • Fracture point

• Necking occurs after UTS.

• Hooke’s law is valid only in elastic region.