Failure Theories in Materials Science: Tresca, von Mises, and the Ductile vs Brittle Yielding

Overview

An accessible introduction to predicting when a component will fail under complex loading. The video contrasts ductile yielding with brittle fracture, explains hydrostatic versus deviatoric stresses, and compares the Tresca and von Mises failure criteria with their Mohr-circle representations and yield surfaces. It also touches how experiments determine which theory to apply, how to interpret three dimensional stress states, and how brittle materials require different approaches such as Coulomb-Mohr theory. The goal is to understand where and how failure is predicted in engineering components using simple strength properties and stress analysis data.

Overview

The video introduces the problem of static failure prediction for a bracket under increasing loads and defines what constitutes failure for ductile and brittle materials. It then explains how complex triaxial stress states complicate prediction and why no single universal theory exists. The discussion emphasizes that ductile failure depends on deviatoric (shape-changing) stresses, not hydrostatic (volume-changing) stresses, and introduces the decomposition of any stress state into hydrostatic and deviatoric components. A practical visualization tool, Moore's circle, is used to illustrate how hydrostatic stress shifts the circle without changing yielding, which is why hydrostatic stress does not trigger yielding in ductile materials.

Key Concepts