https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_2018047

See attached article

The Lankford value reflects the sheet shape change anisotropy when a flat material is subjected to elasto-plastic deformation.

It is a phenomenological quantification parameter, which indeed - as you point out - includes all / any topologically and microstructurally anisotropic aspects of the material.

This includes for instance the grain shape, the crystallographic texture, the alignment of second phases, anisotropic alignment of sets of precipitates, elongated segregation features etc.

When aiming at a simplified homogenization treatment one can use calculation methods coming from simple Taylor type models or from Bunge's series expansion methods.

When aiming at a more microstructural oriented simulation you can use crystal plasticity models.

Examples are here:

http://www.dierk-raabe.com/sheet-forming-simulation/

http://www.dierk-raabe.com/yield-surface-simulation/

http://www.dierk-raabe.com/large-scale-crystal-plasticity-amd-ansiotropy-simulation/

https://damask.mpie.de

(freeware package to calculate such parameters from microstructures)

Good Luck!

Dear Grzegorz Cios

I appreciate your reply.

Dear Dierk Raabe

Thank you very much for your complete answer.

Of course, your research group is a pioneer in this crystal plasticity modelling.

Are anisotropy and hardening related to one another? Can we model changes in anisotropy during the rolling process by relating it to hardening?

Yours sincerely,

Mozhdeh

Dear Adeyinka Aina

Thank you for your reply.

Yours sincerely,

Mozhdeh

yes, they are connected,

crystal plasticity is always a tensor valued quantity, due to the dyadic nature of the underlying dislocation kinematics.

This means that any quantity derived from them is also anisotropic. Isotropic mechanics in metals is a very very rare exception and does practically not exist.

I agree with Dierk Raabe.