Anisotropic plasticity - data input 1

[JanPipora]

Dear experienced ABAQUS users,

as well as I'm not familiar with the ABAQUS, I have a big problem with ansiotropic data input. I have got true stress/strain curves as well as Lankford coefficients for the 0°,45° and 90°direction. There are few notes in ABAQUS Analysis User's manual Vol III. - materials on the page 18.2.6-2 - 18.2.6-6, but it is not so clear for me. What the coef. Rxx really mean? How to apply them to the ABAQUS/CAE. The same coef. F,G,H,L,M and N ? I will be very happy to receive any hints or examples. Thanks a lot.
J. Pipora

 

[Janus3]

I am not that experienced however I have faced similar problems half a year ago. The coefficients Rxx, Ryy, Rxy etc. are ratios of measured yield stress to the reference yield stress and represent application of Hill's potential function into abq code without need to use UMAT.
You can calculate them easily as: in terms of Rvalues,
assuming the yield stress ratio in the rolling direction is 1:
R11=1, R22=rootsquare((r90.(r0+1))/(ro.(r90+1)))..etc
Got to run today but will be back tomorrow with the rest.

 

[JanPipora]

Thank you very much for you kind replay. I'm really interested on the rest of your hint.
Jan

 

[Janus3]

Hi, sorry for the abrupt end yesterday.
There is the rest:
R33=square root [(r90.(r0+1))/(r0+r90)],
finally R12=square root[(3.(r0+1).r90))/(2.r45+1).(r0+r90)]
Assuming that your r-values has been derived from a simple tensile test.
I forgot to mention that the above data were derived for thin metal sheets where the plane stress condition can be assumed.
For another case you can try to derive them by yourself if you express Hill's criterion in rectangular Cartesian stress components and 1, 2, and 3 represent the rolling, transverse and normal directions, respectively.
F,G,H, L,M, and N can be defined by means of the coefficients R11, R22, R33 and R12. Than from flow rule and definition of r-value the coefficients could be established.
Post back if you do not understand the explanation.