ES 246 project: Plane Strain Extrusion - Slip-line Field Solution vs. FEM Solution

Due to maturity of FEM package, slip-line field theory is not widely used these days. However, we shall keep in mind that slip-line field analysis can provide analytical solutions to a number of very difficult problem which may involve huge deformations or velocity discontinuities, e.g. many metal forming processes. To evaluate these two analytical and numerical methods for plasticity I will try a simple example, compare these two solutions and finally get into a conclusion of my own.

Following figure shows an example of metal-forming process known as Plane Strain Extrusion (Hill). I will first use slip-line field analysis to show that the force on the punch is given by P=2k(π/3+1/2)H. And then use ABAQUS/CAE to find out the numerical relation of P(H). If time permits I may also use ABAQUS/Explicit to dynamic analysis.

Journal articles:

[1] KOBAYASHI S, PLANE-STRAIN SLIP-LINE FIELDS FOR METAL-DEFORMATION PROCESSES, JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME 50 (3): 702-702 1983

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It might also be interesting

It might also be interesting to consider unsymmetrical extrusions with ABAQUS. There is a paper by A.P. Green which proposes slip-line fields and extrusion pressures for unsymmetrical extrusion through a sqare die. I don't know how difficult it would be to move the extrusion opening on your ABAQUS model, but it would be neat to see how the results compare to Green's work.

GREEN AP, ON UNSYMMETRICAL EXTRUSION IN PLANE STRAIN, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 3 (3): 189-196 1955

It's very interesting to

It's very interesting to compare the analytical results from slip-line field theory to the numerical solutions of FEM software. A problem you may encounter in this project is the model's material property. The slip-line field theory assumes a plastic-rigid material, which has an infinite Young's modulus below the yield point and no hardening upon yielding. As Prof. Vlassak mentioned in class, the numerical model with plastic-rigid material may lead to divergence. One possible solution to this problem might be to approximate the plastic-rigid condition as high Young's Modulus, reasonable yield stress, and very low hardening. Moreover, large distortions of elements may occur in your numerical model. If so, you may consider the ALE option for adaptive remeshing in ABAQUS.

can abaqus give out the slip lines?

Can abaqus give out the slip lines?

I'm not sure

Hi George,

The slip line is given by theoretical analysis here and I don't think ABAQUS can explicitly draw the slip lines for you. But with the given stress field maybe you'll be able to figure out the slip line field manually.

non-perfect plasticity

How accurate is the perfect plasticity for metal forming?
How is the slip-line defined for a non-perfect plasticity?

As far as I know

Because I also used rigid plasticity in my ABAQUS model I can not tell how accurate perfect plasticity can be used to simulate real metal forming process.

One assumption of slip-line field theory is the perfect plasticity.

How can i get the slip-line field from the stress filed solution?

with Ms. Lu's permission...

Can I propse Mr. Hosford's book to draw a simple slf under compression test ? If your question is just draw a simple net, it will helpfull I think.

Thanks a lot, i will chekc it out

i will check it out

The slip line field is given by theoretical analysis

Actually slip line field is given by theoretical analysis. It is just an assistant to determine the stress field eventually. If you can figure out the stress field directly from FEM why do you insist to get the slip line field?

Hi,