The Fundamentals of Metalworking (PDF)

Tresca yield criterion
Yielding occurs when the maximum shear stress ττττ max reaches
the value of the shear stress in the uniaxial-tension test, ττττ o .
σ 1 −σ
3
τ max =
2
…Eq.17
Where σσσσ 1 is the algebraically largest
and σσσσ 3 is the algebraically smallest
principal stress.
For uniaxial tension, σσσσ 1 = σσσσ o , σσσσ 2 = σσσσ 3 = 0, σ 1 − σ 3 σ o
τ max = = τ o =
and the shearing yield stress ττττ o = σσσσ o /2. 2 2
Therefore the maximum - shear
stress criterion is given by σ 1 −σ 3 = σ o
In pure shear, σσσσ 1 = -σσσσ 3 = k , σσσσ 2 = 0,
τ = 0.
5σ
ττττ max = ττττ y y
o
***
…Eq.12
…Eq.13
…Eq.14
Suranaree University of Technology Tapany Udomphol
Jan-Mar 2007