Critical Plastic Strain

About the development of the FEM module/workbench.

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HarryvL
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Critical Plastic Strain

Postby HarryvL » Wed Apr 24, 2019 9:16 pm

The issue of what to do with stress concentrations in FEA came up in several posts:

https://forum.freecadweb.org/viewtopic. ... 21#p215672

https://forum.freecadweb.org/viewtopic. ... 31#p220591

https://forum.freecadweb.org/viewtopic. ... 97#p266484

The paradox is that we appear to get punished in “FEM-assisted-design” for more accurate prediction of stress concentrations.

As explained in the above posts, the solution is to take account of plastic strains in the analysis and thereby redistribute peak stresses to lower loaded regions, as will happen in reality.

Then the design question becomes “what is an acceptable plastic strain?” or put differently “will the heavily loaded region crack before the ultimate limit load of the construction detail is reached?”

In my previous posts I recommended to limit the equivalent plastic strain (PEEQ in CCX and ABAQUS terms) to well below 0.05 or 5%.

Now we have fcFEM I can experiment with a more refined check for ductile fracture.

The specification of a critical plastic strain is the topic of active research (see https://www.vtt.fi/inf/julkaisut/muut/2 ... 177-17.pdf and https://www.vtt.fi/inf/julkaisut/muut/2 ... 741-16.pdf) and for the moment design codes make very conservative assumptions; typically eps_cr = 5%.

A better approach (that is both practical and widely accepted) is use of the Stress Modified Critical Strain (SMCS) criterion (see the above reports). It links critical plastic strain (eps_cr) to stress triaxiality (T):

eps_cr = alpha * exp(-beta * T)

where alpha is a material (ductility) parameter, beta=1.5 and T = pressure / sig_von_Mises.

This shows that steel under high isotropic tension (pressure>>0) is much more brittle than steel in pure shear (pressure=0). Alpha factors quoted in literature range for construction steel from 1-5, with the lower values applicable for higher strength steels.

I implemented the SMCS criterion in fcFEM and would like to demonstrate its application for the case of a plate with hole of previous posts.

The design question is: “will the material crack before the plastic limit load of the detail is reached?”. To answer this question I conservatively assume ductility at the lower end of the range (i.e. alpha=1.0) and then increase the load on the detail until the limit load is reached:

fcFEM_Plate_with_Hole_EpsP_Ratio.png
fcFEM_Plate_with_Hole_EpsP_Ratio.png (30.58 KiB) Viewed 206 times

The acceptability of the induced plastic strain can now be reviewed by plotting the ratio of equivalent plastic strain to critical plastic strain in the last load step:

fcFEM_Plate_with_Hole_eps_critical_ratio.png
fcFEM_Plate_with_Hole_eps_critical_ratio.png (114.49 KiB) Viewed 206 times

If the plastic strain ratio is low, so is the risk of ductile fracture. As can be seen from the plot, the maximum plastic strain ratio is of the order 0.02, which is far below the critical value of 1.0.