Short Answer:

The permanent set is the amount of permanent deformation that remains in a material after the removal of a load that has caused plastic deformation. It represents the residual strain that does not disappear once the applied stress is removed.

In simple words, when a material is stressed beyond its elastic limit, it does not return to its original shape or size even after unloading. The part of deformation that remains is called the permanent set, and it indicates that the material has entered the plastic region of deformation.

Detailed Explanation:

Permanent Set

Definition and Meaning:
When a material is subjected to a gradually increasing load, it first deforms elastically. In the elastic region, the material regains its original shape after the load is removed. However, if the stress applied exceeds the elastic limit, the material undergoes plastic deformation, meaning it changes shape permanently.

The amount of deformation that remains after removing the load is called the permanent set. It is the irreversible strain that stays in the material even when the stress is reduced to zero. This property helps in understanding the plastic behavior and ductility of materials.

Mathematically,

Where,

• Total Strain is the total deformation produced under load.
• Elastic Strain is the recoverable part that disappears after unloading.

Thus, the remaining strain after unloading is the permanent set.

Explanation of Permanent Set

When a material is loaded, the deformation increases gradually as the stress increases. The stress-strain behavior can be divided into two regions: elastic region and plastic region.

1. Elastic Region (Before Elastic Limit):
   • Stress is directly proportional to strain (Hooke’s Law).
   • When the load is removed, the strain completely disappears.
   • The material returns to its original dimensions.
2. Plastic Region (Beyond Elastic Limit):
   • When the applied stress exceeds the elastic limit, the material starts deforming permanently.
   • In this region, the strain increases rapidly even if the stress does not increase much.
   • After removing the load, the material cannot return to its original length; some deformation remains — this is the permanent set.

Hence, the permanent set occurs when the material is stressed beyond its elastic limit. It represents the irreversible change in the material’s shape or dimension caused by plastic flow.

Permanent Set on Stress-Strain Diagram

In a stress-strain diagram, the permanent set can be clearly observed:

• From the origin (O) to the elastic limit (A), the material behaves elastically.
• Beyond point A, the material enters the plastic region.
• When the material is loaded up to a point B in the plastic region and then unloaded, the unloading curve follows a parallel line to the original elastic line (since unloading is elastic).
• The point where the unloading curve intersects the strain axis represents the permanent set.

This horizontal distance between the origin (O) and the intersection point on the strain axis represents the permanent strain or permanent set.

Thus, the greater the stress beyond the elastic limit, the larger the permanent set that remains after unloading.

Physical Meaning of Permanent Set

The permanent set represents the permanent rearrangement of the internal structure of a material. When stress exceeds the elastic limit, atomic bonds inside the material start to break and reform in new positions.

• In the elastic region, atoms stretch but return to their original positions after the load is removed.
• Beyond the elastic limit, atoms slip over each other, and the material cannot recover its initial configuration completely.

This atomic slipping and plastic flow cause the residual deformation that remains even after unloading. This is the permanent set.

Factors Affecting Permanent Set

1. Material Type:
   • Ductile materials like steel, copper, and aluminum exhibit a large permanent set due to their high plastic deformation capacity.
   • Brittle materials like glass or cast iron show very little or no permanent set because they fracture before yielding.
2. Amount of Stress Applied:
   • If the applied stress is slightly above the elastic limit, the permanent set will be small.
   • If the stress is much higher, the permanent set increases significantly.
3. Temperature:
   • Higher temperatures increase the permanent set because materials become softer and more ductile.
   • At low temperatures, the permanent set decreases as materials become brittle.
4. Duration of Loading:
   • If the load is applied for a longer time, the permanent set increases due to creep, especially in metals at high temperatures.
5. Heat Treatment:
   • Processes like annealing can reduce permanent set by relieving internal stresses and restoring ductility.

Importance of Permanent Set

1. Indication of Plastic Deformation:
   The permanent set clearly shows that the material has undergone plastic deformation and cannot fully return to its original shape.
2. Material Testing:
   In tensile testing, measuring the permanent set helps in determining yield stress, elastic limit, and ductility of the material.
3. Design Consideration:
   In mechanical design, engineers ensure that the working stress is always kept below the elastic limit to avoid permanent set and plastic deformation.
4. Ductility Measurement:
   A large permanent set indicates that the material is ductile, while a small permanent set indicates brittleness.
5. Forming and Manufacturing Processes:
   The concept of permanent set is used in processes such as forging, rolling, bending, and extrusion, where permanent shape change is desired without fracture.

Example of Permanent Set

Suppose a steel wire of length 1 m is loaded with an increasing force. Up to a stress of 200 MPa, the deformation is elastic and fully recoverable. When the stress reaches 300 MPa, the wire elongates permanently. After the load is removed, the wire’s length becomes 1.002 m instead of the original 1.000 m.

Thus, the permanent set is:

This shows that the wire has undergone a permanent deformation of 0.2% due to plastic flow beyond the elastic limit.

Engineering Significance

The concept of permanent set is important in both design and manufacturing:

• In structural design, engineers ensure materials are not loaded beyond the elastic limit to prevent permanent deformation.
• In metal forming processes, the permanent set is deliberately used to achieve permanent shape changes in materials without causing cracks or fractures.

For instance, in bending a steel plate for construction, the material is loaded beyond the elastic limit to produce a permanent curvature — a controlled permanent set.

Conclusion:

The permanent set is the residual deformation that remains in a material after the removal of a load that has caused plastic deformation. It occurs when the material is stressed beyond its elastic limit, and the atoms inside the material rearrange permanently. The permanent set marks the boundary between temporary elastic behavior and irreversible plastic deformation. It is an important concept in mechanical engineering because it helps in design safety, material testing, and forming processes, ensuring that materials perform reliably under applied loads.