Eigen stress refers to self-equilibrated internal stresses within a body that is free from external forces and surface constraints. These stresses arise due to eigenstrains, which are internal strains that don't require an external force to be generated. These eigenstrains can come from various sources and are the root cause of eigenstress. The key is that these internal stresses are balanced within the body and do not result in any net external force or moment.
Understanding Eigenstrains and Eigenstress
What are Eigenstrains?
Eigenstrains are internal strains within a body that don't result from applied external forces. They are inherent strains, or changes in the material's structure.
How Eigenstrains Lead to Eigenstress:
When a material experiences eigenstrains, it attempts to change its shape according to those strains. However, since the material is constrained by its own structure, it can't freely deform. This conflict leads to the development of internal stresses which are what is called eigenstress. These stresses are self-equilibrated, meaning that the tension in one area is balanced by compression in another.
The Role of Incompatibility:
The incompatibility of these eigenstrains, meaning they cannot all be accommodated simultaneously without causing stress, is the fundamental reason for eigenstress.
Key Characteristics of Eigenstress
- Self-Equilibrated: The stresses are internally balanced; there is no net force or moment acting on the body because of them.
- No External Force/Constraint Required: These stresses develop in the absence of external loads or surface constraints.
- Arise from Eigenstrains: They are a consequence of incompatible eigenstrains within the material.
Examples of Eigenstress
| Example | Explanation |
|---|---|
| Thermal Expansion/Contraction | If parts of an object heat or cool at different rates or magnitudes, they experience differential expansion or contraction. If the object's structure prevents this deformation from occurring freely, it will result in eigenstress. |
| Phase Transformations | When a material undergoes a phase change, such as from liquid to solid or changes in crystal structure, it can lead to volume changes that generate eigenstress in the solid material |
| Residual Stress from Manufacturing | Processes like welding, casting, or machining can introduce residual eigenstresses into the material. These are self-equilibrated stresses left after manufacturing. |
| Plastic Deformation | During forming of materials such as bending or drawing, the different parts of the material undergo different plastic strains. These strains do not require external forces to sustain them but they cause eigenstresses to appear in the material structure. |
Practical Implications and Solutions
- Component Integrity: Understanding eigenstress is crucial for predicting the performance and lifespan of components. Unmanaged eigenstress can contribute to premature failure.
- Stress Engineering: Intentional introduction of eigenstress is used for strengthening materials, for example compressive surface stresses introduced by shot peening or case hardening
- Mitigation Strategies: Various techniques like stress relief annealing are employed to reduce unwanted residual eigenstresses caused by manufacturing processes.
In summary, eigenstress is a result of the material's attempt to accommodate internal strains called eigenstrains which creates internal balanced stress fields. These stresses are not due to external loads and can be significant for the structural integrity of materials and components.
