Equivalent plastic strain will not converge at an inside corner. Equivalent stress will converge at the plastic limit. Equivalent principle stresses will not converge. It’s hard to find places where this is written down explicitly – many people know about the stress singularity with elastic analysis, but seem unaware of the strain singularity with elastic-plastic analysis. Of course, if it were not true, we would not need elastic-plastic fracture mechanics. It is also very easy to prove to yourself. Make a small 2D model with a sharp corner, decrease the mesh size several times, and make a plot of log(element edge length) vs equivalent plastic strain. The divergence should be obvious. If you use an elastic-perfectly plastic material, it will be more obvious with a coarser mesh, but it will also show up with a strain hardening material model.
Arturs Kalnins sort of mentions this in “Fatigue Analysis in Pressure Vessel Design by Local Strain Approach: Methods and Software Requirements,” but he doesn’t come out and say the strain is singular: “The local strain approach is applicable to cases in which all structural features that affect fatigue damage are defined and can be modeled with sufficient accuracy. It is not applicable to cases in which some structural detail is known to affect fatigue damage but cannot be modeled, either because its geometry is unknown (e.g., flaws at the weld toe of an untreated weld) or because its model is unreliable (e.g., very sharp notch). Such cases require approaches that incorporate the unmodelable details in the test data, such as, for example, those described by Maddox for weld joint classes, and more recently by Dong et al.”
Thankfully for fatigue analysis, there has been an enormous amount of experimental and numerical research to come up with the statistical fatigue strength of weldments based on local stress analysis. Follow Kalnins' advice and the advice of previous posters and use a method based on an SN curve fit to test data (master SN method, smooth bar method with linearization and FSRF, PD5500 structural stress, etc). If you use the smooth bar curve with FSRF, read WRC 432 and pay attention to the data they used. It only went up to about 500k cycles, right before the SN curve changes slope. You might also read BS7608 Annex C. If the stress field isn’t amenable to linearization (e.g., rapid thermal transient with nonlinear temperature gradients through the thickness at the weld), you could consider surface stress extrapolation (though if you are doing a Div 2 design, that code doesn’t recognize this method). Alternatively, grind the weld to a known radius and use the local notch stress.
In areas other than fatigue and collapse, technology has not come as far. The plastic strain limit for ‘local failure’ in Div 2 will not converge at a sharp inside corner. Same with stress intensity at the ends of a semi-elliptical crack calculated with the weight function method for an arbitrary stress profile. This, unfortunately, requires a heavy dose of judgement (i.e. guesswork). Failures due to high hydrostatic test are not particularly common, but cracks at weld toes unfortunately are.
In general, if you’re not certain that your model is converged, run a convergence study. Weld toes are a particularly sticky wicket when it comes to local effects, but an elastic-plastic model can also overestimate the collapse load if the mesh is too coarse. Run a convergence study, and then you’ll know, because the internet is often wrong.
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