The term "principle stress theory" is not commonly used in materials science or mechanics. However, I believe you are referring to the concept of the "Maximum Shear Stress Theory" or "Tresca Criterion," which is one of the failure criteria used in mechanics to predict the failure of materials under certain loading conditions.
The Maximum Shear Stress Theory states that failure occurs when the maximum shear stress in a material reaches a critical value. It assumes that failure occurs along planes where the shear stress is maximum.
While this theory can be useful for predicting the failure of brittle materials, it is not applicable to ductile materials for a couple of reasons:
Ductile materials deform plastically before failure: Ductile materials, like most metals, have the ability to undergo significant plastic deformation before failing. In the case of ductile materials, they tend to deform and yield before reaching the maximum shear stress criteria. Their ability to undergo plastic deformation enables them to redistribute the stress and dissipate energy, which makes the Maximum Shear Stress Theory less appropriate.
Multiple failure mechanisms: In ductile materials, failure can occur through various mechanisms, such as necking, void growth, and coalescence. These mechanisms are influenced by different stress components and depend on the material's microstructure and properties. The Maximum Shear Stress Theory does not account for these complex failure mechanisms.
To address the limitations of the Maximum Shear Stress Theory in ductile materials, engineers and researchers use other failure criteria, such as the Von Mises Criterion or the Tresca-Hencky Criterion. These criteria are more suitable for ductile materials as they consider both normal and shear stress components and take into account the material's ability to undergo plastic deformation before failure. The Von Mises Criterion, in particular, is widely used for ductile materials because it correlates well with experimental data and is well-suited for predicting plastic deformation and yielding.