The Mohr-Coulomb Stress Safety Tool is based on the Mohr-Coulomb theory for brittle materials, also known as the internal friction theory.
The theory states that failure occurs when the combination of the Maximum, Middle, and Minimum Principal equal or exceed their respective stress limits. The theory compares the maximum tensile stress to the material's tensile limit and the minimum compressive stress to the material's compressive limit. Expressing the theory as a design goal:
where σ1 > σ2 > σ3: σ3 and the compressive strength limit assume negative values even though you must actually enter positive values for these quantities. Also, a given term is only used if it includes the correct sign. For example, σ1 must be positive and σ3 must be negative. Otherwise, the invalid term is assumed to be negligible.
Note that the Mohr-Coulomb Stress Safety tool evaluates maximum and minimum principal stresses at the same locations. That is, this tool does not base its calculations on the absolute maximum principal stress and the absolute minimum principal stress occurring (most likely) at two different locations in the body. The tool bases its calculations on the independent distributions of maximum and minimum principal stress. Consequently, this tool provides a distribution of factor or margin of safety throughout the part or assembly. The minimum factor or margin of safety is the minimum value found in this distribution.
For common brittle materials such as glass, cast iron, concrete and certain types of hardened steels, the compressive strength is usually much greater than the tensile strength, of which this theory takes direct account.
The design goal is to limit the maximum and minimum principal stresses to their ultimate strength values by means of the brittle failure relationship:
An alternative but less common definition compares the greatest principal stresses to the yield strengths of the material:
The theory is known to be more accurate than the maximum tensile stress failure theory used in the Maximum Tensile Stress Safety tool, and when properly applied with a reasonable factor of safety the theory is often considered to be conservative.
Options
Define the tensile stress limit in the Details under Tensile Limit Type. Use either , or , or enter a . By default, Tensile Limit Type equals .
Define the compressive stress limit in the Details under Compressive Limit Type. Use either , or , or enter a . By default, Compressive Limit Type equals .
Select one of the following Stress Tool results from the Result group of the Stress Tool tab or by right-clicking and selecting > [result type]:
Safety Factor
Safety Margin
Stress Ratio
Notes
The use of a yield strength limit with brittle materials is not recommended since most brittle materials do not exhibit a well-defined yield strength.
For ductile and some other types of materials, experiments have shown that brittle failure theories may be inaccurate and unsafe to use. The brittle failure theories may also be inaccurate for certain brittle materials. Potential inaccuracies are of particular concern if the accuracy of calculated answers is suspect.
The reliability of this failure criterion is directly related to treatment of stress risers (peak stresses). For brittle homogeneous materials such as glass, stress risers are very important, and it follows that the calculated stresses should have the highest possible accuracy or significant factors of safety should be expected or employed. If the calculated results are suspect, consider the calculated stresses to be nominal stresses, and amplify the nominal stresses by an appropriate stress concentration factor Kt. Values for Kt are available in many strength of materials handbooks. For brittle nonhomogeneous materials such as gray cast iron, stress risers may be of minimal importance.
If a part or structure is known or suspected to contain cracks, flaws, or is designed with sharp notches or re-entrant corners, a more advanced analysis may be required to confirm its structural integrity. Such discontinuities are known to produce singular (that is, infinite) elastic stresses: if the possibility exists that the material might behave in a brittle manner, a more rigorous fracture mechanics evaluation must be performed. An analyst skilled in fracture analysis can use the Mechanical APDL application to determine fracture mechanics information.
The proper selection and use of a failure theory relies on your engineering judgment. Refer to engineering texts such as Engineering Considerations of Stress, Strain, and Strength by R. C. Juvinall (McGraw-Hill) and Mechanical Engineering Design by J. E. Shigley (McGraw-Hill) for in-depth discussions on the applied theories.