Theory of failure in Piping Stress Analysis

There are three generally accepted criteria which deal with the deviatoric stress components to predict the onest of yielding in a material :

Method 1 - Von Mises, or Distortion Energy, or Octahedral Shear Theories. Plastic deformation occurs in a three-dimensional stress state whenever the octahedral shear stress exceeds (√2)/3 σ_yield.

Method 2 - Maximum Shear, or Tresca Theory. Plastic deformation occurs in a three-dimensional stress state whenever the maximum shear stress exceeds σ_yield /2.

Method 3- Maximum Stress or Rankine Theory. The problem to be dealt with by these criteria is to relate an arbitrary three dimensional stress state in a material to the uniaxial stress state found in a tensile specimen. This is because it is the tensile test that is used to determine the allowable strength of all commonly used materials.

Maximum Stress or Rankine Criteria "Failure occurs when the maximum tensile stress in a body is equal to the maximum tensile stress at yield in a uniaxial tension test". The maximum tensile stress is the largest, positive principal stress, σ₁ ( By definition, σ₁ is always the largest of the principal stresses).

For uniaxial tension (as above), when the specimen is at the point of yielding :

σ₁ = σ_yield & σ₂ = σ₃ = 0, therefore σ₁ = σ_yield

Plastic deformation occurs in a three-dimensional stress state whenever the maximum principal stress exceeds σ_yield.

Whatever the method used, the ASME code define exactly the allowable tensile strength of material to be applied in design equations in accordance with the related rules.

Please visit the following sites:

• Materials Failure Analysis

• Failure Theories

• Scholarly articles for Theory of failure in Piping Stress Analysis

• STRESS ANALYSIS FOR PROCESS PIPING

• Piping Design Central: Piping Design Theory

In piping its PD/4t + M/Z= longitudinal principle stress

compared with allowable based on uniaxial yield stresses (max. principle stress theory).