Understanding True Stress and True Strain vs. Engineering Stress and Engineering Strain

In the realm of materials science and engineering, understanding the difference between true stress and true strain, and their counterparts, engineering stress and engineering strain, is crucial. These concepts vary in their physical meaning and calculation methods, making them essential for accurate analysis of material behavior under stress.

Introduction to Engineering Stress and Engineering Strain

Engineering stress and engineering strain are fundamental concepts in the study of materials and structures. Engineering stress is defined as the force applied to a material divided by the original cross-sectional area. Engineering strain is the change in length of a material divided by its original length. These values are computed using dimensions before any deformation has occurred.

Understanding True Stress and True Strain

True stress and true strain differ from engineering stress and engineering strain in that they are calculated based on dimensions after or during the deformation of the material. This distinction becomes particularly important in situations where significant deformation, such as necking in ductile materials, occurs. Let's explore how these differences manifest in practice.

Example: Tension Test on a Circular Bar

Consider a circular bar loaded axially in tension. Initially, the cross-sectional area of the bar is denoted as A. When a tensile force P is applied, the engineering stress is calculated as P/A, and this value remains constant as the load is increased, assuming the cross-sectional area does not change.

However, if the material is ductile, it will experience necking, where the minimum cross-sectional area decreases as the material stretches. In this case, the true stress, which takes into account the reduced cross-sectional area, will be greater than the engineering stress. The ratio of true stress to engineering stress increases as the area reduction due to necking progresses with increasing load.

Engineering Strain vs. True Strain

Similarly, when measuring strain during a tension test, if the deformation is small, the engineering strain is the displacement of two reference points divided by the initial length between them. This value is straightforward to measure.

However, with increasing deformation, the distance between the reference points increases, leading to a decrease in the ratio of deformation to the original length. This is because engineering strain does not account for the change in length that occurs during the deformation.

Making a Judgment: Which is More "True"?

The question of which is more "true" is a matter of perspective. All of these measures are accurate within their respective contexts:

Engineering Stress and Engineering Strain: Useful for initial analysis and standard engineering practice before any significant deformation occurs. True Stress and True Strain: More accurate for describing the deformation behavior of materials, especially for ductile or materials undergoing significant strain hardening.

Beyond these technical definitions, stress and strain can also have broader implications. Emotional stress and strain, experienced by humans, are just as valid and real as any physical stress. However, measuring these emotional strains can be extremely challenging, as they often manifest in subtle and complex ways, typically only affecting health indicators rather than direct, measurable outcomes.

Practical Applications

The concepts of stress and strain have wide-ranging practical applications:

Tension and Compression Tests: These tests are fundamental for determining the strength and deformation characteristics of materials. In tension tests, materials are pulled to observe how they resist deformation and eventually break, while compression tests observe how materials change under crushing forces.

Conclusion

In summary, while engineering stress and engineering strain remain the standard in basic material analysis, true stress and true strain provide a more precise description of material deformation, especially in ductile materials. Understanding and applying these concepts correctly is essential for accurate engineering design and analysis.