Failure Theories in Pressure Vessels

Stresses occurs in pressure vessels and other structures are always compared to a failure theory. In this section I will discuss 3 of the failure theories commonly used with ductile material.

1. Maximum principal stress theory

• This theory stands as the oldest, most utilized, and simplest to implement.
• ASME Section VIII, Division 1 employs it as a foundational element for design.
• This theory straightforwardly posits that yielding occurs when the most significant principal stress matches the yield strength.
• Stresses acting in other directions are dismissed for this criterion.

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2. Maximum Shear Stress Theory

• According to this theory, yielding occurs when the largest difference in shear stress matches the shear yield strength.
• Based on this theory, the initiation of yielding takes place at a specific point when the highest shear stress at that location attains half of the uniaxial yield strength.

3. Distortion Energy Theory (Von Misses)

• This theory asserts that the total strain energy is composed of two parts; the strain energy required for hydrostatic strain and the strain energy required for distortion.
• In this theory, it is assumed that yielding will begin when the distortion component is equal to the uniaxial yield strength.
• This theory exhibits a stronger correlation with ductile test specimens compared to the two other theories.
• The updated (2007 version and later) ASME Section VIII, Division 2, Part 5, employs the distortion energy theory to determine the equivalent stress in an elastic analysis.
• In the previous edition (before 2007), this calculation was accomplished using the maximum shear stress theory.

- The Question now is which theory of failure to be used?

To reply to this question it’s important to understand the difference between the hydrostatic stress & deviatoric stress.

In a three-dimensional stress state, such as that experienced by an object submerged in a fluid or subjected to external forces, the total stress at a point can be decomposed into two main components:

• Hydrostatic Stress (known as mean stress or volumetric stress): This component represents the uniform pressure acting on a material in all directions, causing changes in volume but not shape. Hydrostatic stress is typically isotropic and does not contribute to material deformation through shearing.
• Deviatoric Stress: This component represents the difference between the actual stress acting on a material and the hydrostatic stress. Deviatoric stress is responsible for changes in the shape or distortion of the material without affecting its volume. It plays a crucial role in causing shear deformation and is associated with the material's response to shear forces.

-Deviatoric stress is particularly important in the study of material failure and plastic deformation because it is the component of stress responsible for yielding and the initiation of fractures or shearing within a material, so the failure theory which most catches the deviatoric stresses are the most accurate that's why Von misses stress theory is the one which correlate more to the test specimens.

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