Analysis tipsTips-Tricks

Tips & Tricks: How material edge treatments aid folding plates

Folding thick plates
Sometimes the edges of thick plates can tear when being folded – particularly if high tensile material is used. Whilst working on the floor in a previous role I came across a simple method of preventing this by grinding a small radius on the tensile edge. For this month’s tip and trick we’ll investigate whether part of the reason this works is due to the change in the macro-scale geometry by employing non-linear finite element analysis

bending pic with titles

RA333 1/2 inch (12.7 mm) plate, formed with different edge preparations. Left - Sheared edge ground. Bent 180° flat on itself, no cracks. Middle - Shear burr removed. Bend 90° before cracking. Right- As-sheared, burr up. Cracked at 40° bend angle. Taken from rolledalloys.com.

Hypotheses
Adding a small radius to the extreme edges of a plate in bending reduces the risk of cracking due to a more gradual transition to the free edge/plane stress condition. Ignore localised material changes due to heat affected zones and micro cracks/surface finish effects on the cut edge.
Method
Model a 60mm wide by 16mm thick bar and apply forces sufficient to yield the material (nominally Bis 80). Include a 2mm radius on one side of the bar; top and bottom. Assume a bilinear von Mises plasticity material with the tangent modulus set to E/100. Compare von Mises stresses at edges on face opposite the load application.

thick plate mesh

Results
The image below shows a typical across-width stress distribution of a thick plate in bending. The contour levels have been set to highlight this phenomenon; the actual variance in stress magnitude shown is very low. The stresses away from the edges are lower due to a plain strain condition whereby the surrounding material restrains the strain in the across-width direction, resulting in beneficial hydrostatic stresses that reduce yielding. From this image and the chart below it can be seen that the hypothesis is false; i.e. from a macro scale/geometric perspective, adding a radius makes negligible difference. The benefit gained is most likely due to removal of both heat affect zone material and micro cracks/notches.

thick plate FEA

von Mises stress plot of underside of bar; edge with radius highlighted. Limited stress range shown

thick plate residual stress

Residual stress distribution, actual deformation after unloading

thick plate section

Section adjacent to load application point, 5 X deformation scale. Note arching due to Poisson ratio effect

thick plate results

Comparison of von Mises stresses near opposite plate edges

Conclusion
When I started at Motovated several years ago; I relished the opportunity to test via FEA some of my previous design work. What surprised me was that tricks to reduce stress raisers such as adding extra grooves in shafts near sharp shoulders or drilling holes in front of keyways usually resulted in worse outcomes unless carefully iterated via FEA. I’m not as surprised at the result above, but still really enjoy the insights that engineering analysis can provide. I liken it to illumination; i.e. like “turning the lights on” during design, allowing clarity for robust design decisions.
Leon Daly
Analysis Manager at Motovated
leon@motovated.co.nz
+64 3 382 5282