Tuesday, January 26, 2010

Limit load analysis

I worked on a 2007 ASME B&PV Code, Section VIII, Div 2 analysis of what was essentially an elbow casting with some additional detail. The more traditional approach would be to use stress linearization on an elastic analysis for stress categorization. However, since the elbow was thick-walled relative to the radius, stress linearization can be non-conservative because the stress distribution is non-linear. Think about the difference between a thick walled cylinder and. thin walled cylinder.

I used the limit load analysis method instead. The limit load analysis has established itself as the preferred method, subject to its limitations, to assess primary sizing (Protection Against Plastic Collapse). The limit load analysis eliminates the need for stress categorization because it is a pass-fail criterion. The material definition is elastic-perfectly plastic. So, the limit load analysis is trying to predict when a plastic hinge forms in a plate an uncontrolled deformation with result with any additional applied load.

Elastic And Inelastic Stress Analysis (Materials Science & Engineering Series)The basis for the limit load is straightforward. A value of 1.5 is applied to the desired load (i.e. design pressure+static head+dead weight). Recall that a plastic hinge is formed in a rectangular cross-section beam with an elastic-perfectly plastic material when the moment is 1.5 X the moment required for initial yield. You can find this discussion in a Continuum Mechanics textbook in a section on Beams. I have the book by Shames and Cozzarelli, "Elastic and Inelastic Stress Analysis," which has a pretty good description of this derivation with lots of pictures. So, if you enter 1.5*S (in some cases 1.5S is equal to yield strength at temperature) as your FEA yield strength, and the model converges, you will not develop a plastic hinge in the component you are analyzing. There will likely be plastic strain, especially at structural discontinuities.

Bottom Line:
Did the analysis model converge at the desired load (i.e.1.5*Design Pressure)? If yes, Section 5.2, Protection Against Plastic Collapse is satisfied. If not, Section 5.2, Protection Against Plastic Collapse is NOT satisfied.

Advances in the capabilities of computers have enabled the method, since the limit load analysis will take longer to run than an elastic stress analysis. However, post-processing effort is reduced to near zero. Also, there is no question about whether or not the stress categorization line (stress cutline) is in the limiting location.

Jeff

6 comments:

  1. I agree. I used the same method for a special flange. And the interpretaion of the results was straight forwared.

    Gurmeet

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  2. Thanks for the comment, Gurmeet. Have you ever used the elastic-plastic stress analysis method (Paragraph 5.5.4) for the fatigue assessment?

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  3. I was reading about the limit-load analysis in ASME, and found it quite hard to follow. Thanks for clearing it up.

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  4. I am currently writing my dissertation and I am exploring the differences between limit load and stress categorization so your article has been extremely useful. Thanks!

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  5. The solver convergence will depend on the setting of the solver also right? For example there may be a limit to the strain,tolerance,no of iterations, etc.How then can one make a decision about the whether the model has converged or not?

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  6. @ Sandhya, Agreed that Convergence of Limit load problem also depends on settings used in the solver (as rightly mentioned % strain increment, no. of substeps/iterations etc.,. However, if you can make the model converge, then to satisfy the DBA (as per Div2), you need also to satisfy another critierion called local strain criterion (5.3- Protection against local failure - using elasticplastic analysis with strain hardening) and hence you are ok. Hope this helps.

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