Engineering stress vs true stress, difference significant

Engineering Stress vs True Stress: Understanding the Significant Difference in Materials Science

In materials science, stress is a fundamental concept that describes the internal forces per unit area within an object under external loads or constraints. However, there exist two distinct types of stress measurements used to quantify these forces - engineering stress and true stress.

The primary difference between engineering stress and true (or actual) stress lies in how they account for changes in cross-sectional area due to plastic deformation during the testing process. This crucial distinction has significant implications for interpreting material properties, designing structures, and predicting their behavior under various loads.

Engineering Stress: A Simplistic Approach

Engineers often resort to using engineering stress as a quick and easy method of analysis due its simplicity and ease of calculation. Engineering stress is defined as the ratio of the applied force (F) divided by the original cross-sectional area (A0), regardless of any changes in area that may occur during testing.

This approach assumes that no plastic deformation takes place, meaning the material behaves elastically throughout the entire loading process. However, this assumption rarely holds true in real-world applications where materials are frequently subjected to significant stress beyond their elastic limits.

True Stress: Accounting for Real-World Deformations

On the other hand, true (or actual) stress provides a more accurate representation of the internal forces within an object by taking into account changes in cross-sectional area due to plastic deformation. True stress is calculated as the ratio of applied force divided by the current or instantaneous cross-sectional area (A), which may differ from its original value.

True Stress vs Engineering Stress: A Numerical Example

Consider a cylindrical bar made of steel with an initial diameter of 10mm and length of 1000mm, subjected to a tensile load until it reaches failure. Assuming no plastic deformation occurs during the test:

- The engineering stress can be calculated as:

F / (π x D^2 /4) = 500MPa

- However, if we account for an approximately 20% reduction in diameter due to necking near failure,

true stress would then become:

F' / A' = (500x0.8)/(3.14x5^2/4)

≈ 648 MPa

As evident from this example, the difference between engineering and true stresses can be substantial - nearly a third in this case! This stark contrast highlights why neglecting material strain hardening effects through the use of engineering stress alone may lead to gross underestimation or overestimation of an object's actual strength capabilities.

In conclusion, when working with materials science applications it is crucially important to differentiate between engineering and true stresses. Failure to do so can result in serious consequences ranging from structural failure down to inaccurate prediction of material properties for subsequent design phases. Therefore, engineers must always carefully consider which type of stress measurement best suits their specific needs based on the nature of loading conditions being considered within any given problem context.

By understanding these fundamental differences between engineering and true stresses, materials scientists can ensure that they make informed decisions regarding both experimental setup design as well as post-processing analysis techniques used throughout entire lifecycle stages - from initial testing through final product deployment.

Engineering stress vs true stress, difference significant