According to the von Mises Yield Criterion, when does material yield?

The von Mises Yield Criterion is an essential concept in material science and engineering that helps predict the yielding of materials under complex loading conditions. According to this criterion, material will yield when the von Mises stress reaches a specific critical value, which is defined as the yield strength of the material.

This criterion operates on the fundamental principle that yielding is determined not by the magnitude of the individual stresses, but rather by a combination of them that relates to how they distort the material. The von Mises stress is a derived value that combines the effects of multiple types of stress (like tensile and shear stress) into a single effective stress value. When this effective stress equals the yield strength of the material, it indicates that the material has reached its yield point – meaning it will start to deform plastically and will not return to its original shape after the load is removed.

Thus, the correct answer highlights this relationship between the von Mises stress and the yield strength, which is crucial for accurately predicting material behavior under load, ensuring structures are designed safely and effectively.