# Plastic failure evaluation of steel using FEM

I would like to evaluate failure in steel using FEM, especially in geometries with stress concentrations (notches etc.).

One possibility is to calculate the stress distribution using a purely linear equation of state (elastic = Hooke's law) and evaluate the von Mises stress, using appropriate stress concentration factors (plastische Stützzahlen in German). The drawback is that you need to know (or approximate) the appropriate stress concentration factor(s).

Another possibility is to calculate the stress distribution using a nonlinear equation of state. For steel I read that the bilinear elasto-plastic model is realistic enough for most cases. However, I'm unclear what to evaluate as failure criterion. I noticed that when I change the load to a certain model by a factor of two, the maximum von Mises stress does not change significantly (once it is in the plastic region). I suppose this is due to the values of the two moduli (elastic modulus and tangent modulus) being at least one order of magnitude apart (210 GPa vs. 1-10 GPa). My assumption is that I can use the maximum strain or maximum plastic strain as failure criterion, however I was unable to find a reference supporting this assumption.

Please note that I am interested in failure from a single loading event only. I understand that the fatigue failure mechanisms (when load cycles are applied) are quite different.

So the question is: What can I use as failure criterion, and why? Please support your answer with a (link to a) book chapter or publication - thanks.

• Timoshenko - Strength of Materials is always a good place to start. Jan 14, 2018 at 9:55
• @SolarMike Thanks for the start; especially part II is of interest. In chapter 9, sections 75 and 76, there are phenomenological arguments towards using plasting strain as failure criterion. Chapter 8, section 67 also gives some arguments why the maximum von Mises stress does not change significantly once the stresses are above the yield limit. However, does anybody know of some more recent investigation, that probably also includes FEM as application? Jan 15, 2018 at 8:11