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Modified-Mohr Brittle Material Failure Theory



  • Introduction

    The modified-Mohr failure theory is a commonly used failure theory for uneven brittle materials under static loading conditions [1]. The modifed-Mohr theory matches well with empirical strength measurements. An uneven material is a material that has an ultimate compressive strength that is higher than its ultimate tensile strength. Common examples of uneven brittle materials are concrete and cast iron. The modified-Mohr failure theory can be used to predict a factor of safety to failure based on a material's ultimate tensile strength, Sut, and its ultimate compressive strength, Suc. The diagram below shows the modified-Mohr failure theory envelope. Loading conditions that lie within the shaded area are below the failure threshold, where a loading point's x-position is determined by its most tensile principal stress, σ1, and its y-position is determined by its most compressive principal stress, σ3.

    The factor of safety to failure can be calculated by determining the relative distance to the boundary of the modified-Mohr failure theory envelope as outlined in [1]. The remainder of this sheet goes through this calculation. The loads and material properties can be edited for your particular case.


    Define the Loading Condition

    The principal stress are defined below:









  • Material Properties

    The material can be chosen from the table below [1]. Notice that the ultimate compressive strength values are significantly higher than the ultimate tensile strength values.



  • Gray Cast Iron, Class 20, as cast
    Gray Cast Iron, Class 30, as cast
    Gray Cast Iron, Class 40, as cast
    Gray Cast Iron, Class 50, as cast
    Gray Cast Iron, Class 60, as cast


  • Modified-Mohr Effective Stress Calculation

    Dowling [2] developed a set of equations to determine the effective stress that can be used to calculate the factor of safety to failure:









  • The maximum of the set C1, C2, C3, σ1, σ2, and σ3 is taken as the effective stress. If all of these values are zero, than zero is taken as the effective stress:





  • Factor of Safety Calculation

    Finally, the effective stress can be used to calculate the factor of safety to failure:







  • [1] Norton, R.L. "Machine design, A integrated approach, 5th Editi." (2013).

    [2] Dowling, N.E., "Mechanical Behavior of Materials." (1993).