Short Answer:

Breaking stress is the maximum stress a material can withstand just before it breaks or fractures. It is calculated by dividing the breaking load (the load at which the material fails) by the original cross-sectional area of the specimen.

In simple words, breaking stress represents the stress at the point of failure of a material under tension. It helps engineers determine how much load a material can safely carry before it breaks and is one of the most important parameters in material strength testing.

Detailed Explanation:

Breaking Stress

Definition and Meaning:
When a material is subjected to an external load, it deforms gradually. If the load continues to increase, the material first behaves elastically, then plastically, and finally reaches the point where it can no longer bear the stress. At this stage, the material breaks or fractures.

The stress corresponding to this point is known as the breaking stress or fracture stress. It is defined as the ratio of the breaking load to the original cross-sectional area of the specimen.

Mathematically,

\text{Breaking Stress} (\sigma_b) = \frac{\text{Breaking Load (P_b)}}{\text{Original Cross-sectional Area (A_0)}}

Where,

• σb = Breaking stress (N/m² or Pa)
• Pb = Load at which the specimen breaks (N)
• A₀ = Original cross-sectional area of the specimen (m²)

The breaking stress represents the ultimate strength limit of a material and determines the point beyond which the material cannot sustain any load without complete failure.

Explanation of Breaking Stress

During a tensile test, a material is subjected to gradually increasing load until it fractures. As the load increases, the material passes through different stages of deformation — elastic, plastic, and fracture. The breaking stress is the stress corresponding to the point of final rupture on the stress-strain diagram.

Initially, as the load increases, the material elongates proportionally, following Hooke’s Law. After reaching the elastic limit, the material undergoes plastic deformation. Then, it reaches the ultimate tensile strength (UTS) — the highest stress it can endure. Beyond this point, the material starts to neck, meaning its cross-sectional area begins to reduce locally.

As the necking continues, the load-carrying capacity decreases until the material breaks. The stress at this final breaking point is called breaking stress. It is always less than the ultimate tensile strength, since the specimen fails after necking and area reduction.

Behavior of Material Before Breaking Stress

To understand breaking stress clearly, let us briefly go through the sequence of deformation a material undergoes during a tensile test:

1. Elastic Region:
   The material behaves elastically, and the deformation is reversible. Stress is directly proportional to strain.
2. Plastic Region:
   The material deforms permanently but continues to sustain the load.
3. Ultimate Stress Point:
   The material reaches its maximum strength (ultimate tensile strength). Any further load application causes necking.
4. Necking Region:
   The cross-sectional area decreases significantly at a localized point due to excessive plastic deformation.
5. Breaking Point:
   Finally, the material fractures completely. The stress corresponding to this point is the breaking stress.

Thus, breaking stress marks the end of the stress-strain curve, representing complete failure of the material.

Mathematical Representation

If the original cross-sectional area of the specimen is  and the breaking load is , then

However, due to necking, the actual area at the point of fracture (Aₙ) is smaller than the original area. If we use this actual area instead of the original one, we obtain the true breaking stress, which is greater than the calculated one based on the original area.

Therefore,

where .

In engineering practice, breaking stress is usually calculated based on the original area for consistency and comparison.

Significance of Breaking Stress

1. Indicator of Failure Strength:
   Breaking stress shows the maximum stress a material can handle before it completely fails.
2. Material Selection:
   Helps engineers select materials that can safely bear specific loads without breaking.
3. Safety and Reliability:
   Structures and machines are designed to operate well below the breaking stress to avoid sudden failures.
4. Comparison of Material Properties:
   Breaking stress helps compare the strength of different materials under similar testing conditions.
5. Design of Components:
   The factor of safety (FOS) is determined based on the breaking stress or ultimate stress to ensure that the working stress remains within safe limits.

Typical Values of Breaking Stress

Different materials have different breaking stresses depending on their nature and composition:

• Mild Steel: 400 – 550 MPa
• Cast Iron: 100 – 200 MPa
• Copper: 200 – 250 MPa
• Aluminum: 150 – 250 MPa
• Rubber: 10 – 25 MPa

From these values, it can be observed that ductile materials like steel have high breaking stress, while brittle materials like cast iron have lower breaking stress.

Factors Affecting Breaking Stress

1. Material Type:
   Ductile materials have higher breaking stress than brittle materials.
2. Temperature:
   As temperature increases, breaking stress generally decreases because materials become softer.
3. Rate of Loading:
   Fast application of load may increase breaking stress since the material has less time to deform.
4. Cross-sectional Area:
   The distribution of stress depends on the geometry and uniformity of the area.
5. Heat Treatment and Impurities:
   Heat treatment and impurities can strengthen or weaken materials, changing their breaking stress.

Practical Example

Consider a mild steel rod with an original cross-sectional area of 200 mm². The rod fractures under a load of 90,000 N.

Hence, the breaking stress of the rod is 450 MPa. This means that the steel rod can sustain a stress of up to 450 MPa before breaking.

Importance in Engineering Design

Breaking stress is a critical property considered in the design and analysis of all mechanical and structural components. Engineers must ensure that materials are never subjected to stresses near the breaking stress to prevent catastrophic failure. Instead, materials are used within a safe working stress range, determined by dividing the breaking stress by a suitable factor of safety.

For example, in bridges, pressure vessels, or machinery parts, the design must ensure that the induced stresses under working loads remain well below the breaking stress value.

Conclusion:

The breaking stress is the maximum stress a material can sustain just before it fractures. It is obtained by dividing the breaking load by the original cross-sectional area of the specimen. It represents the final point of failure on the stress-strain curve and indicates the absolute strength of the material under tension. Breaking stress is vital in determining a material’s suitability for engineering applications and ensures that all structural and mechanical designs operate safely within their limits, preventing failure and ensuring long-term reliability.