What is stress relaxation?

Short Answer:

Stress relaxation is the gradual decrease in stress within a material that is kept under constant strain or deformation over time. It occurs mainly in materials exposed to high temperature or over long durations, where internal atomic movements allow the material to adjust and reduce the stored stress.

In simple words, stress relaxation means that when a material is stretched or compressed and held in that position for some time, the force or stress required to maintain that position slowly decreases. This phenomenon is common in metals at high temperatures, and in polymers and rubbers even at room temperature.

Detailed Explanation:

Stress Relaxation

Stress relaxation is a time-dependent mechanical behavior of materials where the internal stress decreases gradually while the strain remains constant. This happens because the atoms or molecules within the material rearrange themselves to reach a more stable energy state, reducing internal stress without a change in overall shape or dimension.

It is a viscoelastic phenomenon, meaning it occurs in materials that exhibit both elastic (instantaneous deformation) and viscous (time-dependent flow) properties. Stress relaxation is important in the design of components that are subjected to constant deformation, such as bolts, springs, seals, gaskets, and pressure vessels.

Definition

When a material is suddenly stretched or compressed and that deformation (strain) is kept constant with time, the internal stress developed initially starts to decrease gradually. This gradual reduction of stress is called stress relaxation.

Mathematically, stress relaxation can be represented as:

where,

  •  = stress at time
  •  = initial stress
  •  = time
  •  = relaxation time constant (depends on material and temperature)

The exponential decay shows that stress reduces over time and approaches a stable value.

Explanation of the Phenomenon

When a constant strain is applied to a material, internal stresses develop because atoms or molecules are displaced from their equilibrium positions. With time and temperature, these particles tend to move or rearrange themselves to relieve the stored stress energy.

  • At low temperatures, this movement is very slow because atomic mobility is limited.
  • At high temperatures, atomic diffusion becomes more active, and the stress relaxation occurs faster.

In materials like rubber and polymers, molecular chains slide over each other slowly even at room temperature, leading to noticeable stress relaxation.

Mechanism of Stress Relaxation

  1. Elastic Deformation:
    Initially, when strain is applied, the material behaves elastically, and stress increases linearly with strain following Hooke’s law.
  2. Viscous Flow:
    With time, the material undergoes viscous flow. The atoms or molecules start to rearrange themselves slowly to reduce internal energy.
  3. Stress Reduction:
    The stress required to maintain the same amount of strain gradually decreases, and the material reaches a lower stress equilibrium state.

Thus, stress relaxation is a result of both elastic deformation and viscous flow occurring simultaneously in the material.

Factors Affecting Stress Relaxation

  1. Temperature:
    • The most important factor influencing stress relaxation.
    • Higher temperature accelerates atomic or molecular movement, leading to faster relaxation.
    • For metals, stress relaxation is noticeable at high temperatures; for polymers, it can occur even at room temperature.
  2. Material Type:
    • Metals, polymers, and ceramics behave differently under constant strain.
    • Polymers show strong stress relaxation due to their viscoelastic nature.
    • Metals show relaxation primarily at elevated temperatures.
    • Ceramics show very little relaxation due to their rigid atomic structure.
  3. Initial Stress Level:
    • Higher initial stress can accelerate stress relaxation because more internal energy is available for atomic rearrangement.
  4. Time Duration:
    • The longer the constant strain is maintained, the more stress will relax over time.
  5. Microstructure:
    • Grain size, dislocation density, and the presence of impurities influence how easily atoms can move, affecting relaxation rate.
  6. Environmental Conditions:
    • Exposure to corrosive environments or radiation can enhance atomic diffusion, increasing stress relaxation.

Examples of Stress Relaxation in Engineering Applications

  1. Bolted Joints:
    • Bolts and fasteners under tension lose preload over time due to stress relaxation.
    • This can cause joint loosening if not properly designed.
  2. Springs and Elastic Elements:
    • Springs operating at elevated temperatures gradually lose force because of relaxation.
  3. Seals and Gaskets:
    • Rubber gaskets under constant compression lose sealing pressure over time due to molecular rearrangement.
  4. Welded Joints:
    • Residual stresses generated during welding gradually reduce when the component is kept at a high temperature (called stress-relief heat treatment).
  5. Polymers and Plastics:
    • Plastic materials used in electronic housings or medical devices exhibit stress relaxation during long-term use.

Measurement of Stress Relaxation

Stress relaxation can be measured experimentally by keeping a specimen under constant strain and recording the reduction in stress over time. The test is conducted using a stress relaxation testing machine at constant temperature.

A graph of stress (σ) versus time (t) is plotted. The curve typically shows a steep decrease in stress at the beginning followed by a gradual flattening, indicating that stress approaches a constant value after a certain period.

Prevention and Control of Stress Relaxation

  1. Material Selection:
    • Choose materials that have high resistance to stress relaxation under expected operating conditions.
    • For example, high-temperature alloys for turbine components.
  2. Proper Heat Treatment:
    • Stress-relieving or annealing processes help reduce residual stresses before service.
  3. Use of Coatings:
    • Protective coatings can prevent oxidation and diffusion-related relaxation in metals.
  4. Design Modifications:
    • Reducing high stress concentrations and allowing flexibility in design can minimize the impact of relaxation.
  5. Operating Condition Control:
    • Avoid prolonged high-temperature exposure or constant deformation whenever possible.
Conclusion

Stress relaxation is a gradual reduction in internal stress in a material kept under constant strain over time. It occurs because of atomic or molecular rearrangements that allow the material to reach equilibrium. This phenomenon is influenced by temperature, time, and material type. While metals show stress relaxation mainly at high temperatures, polymers and rubbers can exhibit it even at room temperature. In engineering, it is important to consider stress relaxation when designing joints, seals, springs, and other components to ensure long-term reliability and dimensional stability.