- The Tresca criterion measured the loads required to extrude metals through dies of various shapes sigma _(1)-sigma _(3)=sigma _(Y) (4.14) where sigma _(1)geqslant sigma _(2)geqslant sigma _(3) and sigma _(Y) is the yield stress That is, the equivalent stress. sigma _(e) is given by sigma _(e)=sigma _(1)-sigma _(3) (4.15)

The Tresca criterion is a yield criterion used in the field of plasticity to predict the onset of yielding in a material. It states that yielding occurs when the difference between the maximum and minimum principal stresses exceeds the yield stress of the material.In the given equation, , , and represent the principal stresses, and is the yield stress of the material. The Tresca criterion can be expressed as: This equation implies that yielding will occur when the difference between the maximum and minimum principal stresses is equal to the yield stress of the material.The equivalent stress, , is also given by the equation: This equation represents the Tresca criterion in terms of the equivalent stress, which is a measure of the overall stress state in a material. The equivalent stress is used to predict the yield behavior of the material, taking into account the different stress components.It is important to note that the Tresca criterion assumes that yielding occurs when the maximum shear stress exceeds the yield stress of the material. This criterion is widely used in the analysis of plastic deformation and failure of materials under complex stress states.