Linear Relation between Stress and Strain

The linear relationship between stress and strain is an important concept in the field of material science and engineering. It helps us understand how a material deforms under the application of stress and provides valuable information about its mechanical properties. However, this linear relationship is only valid up to a certain point, beyond which the material starts to exhibit non-linear behavior.

The Proportional Limit

The point at which the linear relationship between stress and strain ends is known as the proportional limit. It represents the maximum stress that a material can withstand while still maintaining a linear stress-strain relationship. In other words, it is the highest stress at which Hooke's law is valid. Hooke's law states that stress is directly proportional to strain within the elastic limit of a material.

Elastic Limit

Beyond the proportional limit, the material enters the elastic region. The elastic limit represents the maximum stress that a material can sustain without undergoing permanent deformation. If the stress exceeds the elastic limit, the material will undergo plastic deformation and will not return to its original shape once the load is removed. The stress-strain relationship in the elastic region is still linear, but the material exhibits a degree of non-recoverable strain.

Ultimate Stress

As the stress increases further, the material reaches its ultimate stress or ultimate tensile strength. This is the maximum stress that a material can withstand before failure occurs. At this point, the material starts to deform significantly and necking may occur. The stress-strain relationship in this region is non-linear and the material undergoes significant plastic deformation.

Fracture Stress

Finally, when the stress exceeds the ultimate stress, the material experiences failure and fractures. This is known as the fracture stress. It represents the stress at which the material breaks apart. The stress-strain relationship in the fracture region is non-linear and the material undergoes rapid and catastrophic deformation.

Conclusion

In summary, the linear relationship between stress and strain is valid until the proportional limit of a material. Beyond this point, the material enters the elastic region, followed by the ultimate stress region, and finally the fracture stress region. Understanding these different regions is crucial for designing and analyzing the behavior of materials under various loading conditions.