The Mohr-Coulomb stress criterion is based on the Mohr-Coulomb theory
also known as the Internal Friction theory.
This criterion is used for brittle materials with different tensile
and compressive properties. Brittle materials do not have a specific yield point and
hence it is not recommended to use the yield strength to define the limit stress for
this criterion.
The theory predicts failure to occur when the combination of the maximum
tensile principal stress σ1 and the minimum compressive principal stress
σ3 exceeds their respective stress limits.
For the principal stresses σ1, σ2, and σ3
ordered such as σ1 > σ 2 > σ3, the Mohr-Coulomb
theory predicts failure to occur in the following cases:
| State of Principal Stresses |
Failure Criterion |
FOS |
| All principal stresses in tension: σ1 > 0 and σ3 >
0
|
σ1 > σTensile Limit
|
(σ1 / σTensile Limit
)-1 |
All principal stresses in compression: σ 1< 0 and σ 3 <
0 σ3 is the
principal compressive stress with the largest magnitude.
For example, σ1 = -5 MPa > σ2 =
-10 MPa > σ3 = -30 MPa.
|
|σ3| > σCompressive
Limit |
(|σ3| / σCompressive
Limit)-1 |
| First principal stress in tension σ1 > 0,
and third principal stress in compression σ3 < 0.
For example, σ1 = 5 MPa, σ2 = -10 MPa, and
σ3 = -30 MPa. |
σ1 / σTensile Limit +
|σ3| / σCompressive Limit >
1 |
(σ1 / σTensile Limit +
|σ3| / σCompressive
Limit)-1
|
When the third principal stress σ3 is in
compression (negative), both values for σ3 and the material's
compressive limit have positive signs for the FOS calculation.