Distortion Energy Theory:
The distortion energy theory says that failure occurs due to distortion of a part,
not due to volumetric changes in the part (distortion causes shearing, but
volumetric changes due not).
As examples:
Rocks below the earth's surface. Pressure exerted on them is essentially
uniform and well beyond their compressive ultimate strengths, yet the rocks are
able to withstand the pressure of the water without fracture. The explanation for
their survival is that because the shape of the rock is not distorted, there is no
shearing, therefore no failure.
Failure will occur if
σ ' = σ1 + σ 2 + σ3 − σ1σ 2 − σ 2σ3 − σ1σ3 ≥ Sy
2
2
2
In terms of applied stresses
σ =
'
(σ
(
(
(
− σ y ) + σ y − σz ) + σz − σxy ) + 6 τ xy + τ yz + τ zx
2
x
2
2
2
2
2
)
2
σ’is called the Von Mises effective stress.
σ2
σ1
For the case of pure shear, i.e., σ1=τ=− σ3,σ2=0
S 2 y = σ 21 − σ1σ3 + σ3 = 3σ 21 = 3τ 2 max
2
σ1 =
Sy
3
= 0.577 S y = τ max
Shear yield strength, Ssy = 0.577 Sy
Distortion Energy Theory is less conservative than Maximum Shear Strength
Theory, but more conservative than the Maximum Normal Stress Theory
MNST
DET
MSST
Determine whether or failure is predicted with the Distortion Energy Theory for
the shaft loaded as shown
y
L= 6.0’’
x
z
a = 8.0’’
F=1000