Hill 1948 Yield Criterion

[HomerWelsh]

Many of you, I am sure, use Von Mises as a yield criterion to calculate the equivalent stress and strain on your system. I am using Hill 1948 as it provides an anisotropic analysis. However, I am having trouble calibrating Hill48 using the r-values.

Hill constants F,G,H are requal to r0, r90 and r0r90
where r0 is the rolling angle direction and r90 the transverse direction. However, the constants which relate to the 12,13 and 23 stress components: L,M,N and I have no idea. I have repeatedly read Hill's book but I cannot how the L,M or N constants are calculated.

Has anyone any experience of this yield criterion and can offer me some assistance?

Thanks for your time and help,
HW

 

[btrueblood]

have you seen

http://en.wikipedia.org/wiki/Hill_yield_criteria

and

http://en.wikipedia.org/wiki/Lankford_coefficient

 

[HomerWelsh]

Thank you btrueblood for your reply.

Yes, I am aware of those links.

My question more specifically is can L,N,M be defined by solely r-values (lankford coefficients) as F,H and G can?

Best Regards,
HW

 

[btrueblood]

Well, R0, R45 and R90 only come up when talking about thin plates, i.e. a plane stress condition. Is this what you want to discuss?

For plane stress, all of the 13 and 23 direction stress terms are taken to be zero.

Because the plane stress equations use principal stresses assumed to be aligned to the axis of anisotropity, the single remaining shear stress term (tau12) is equal to zero.

Past that, I don't think there is an "easy" way to correlate all of the 3D Hill parameters to simple stress-strain tests. There are a lot of papers describing fairly complex ways to derive them...and I'm not familiar with those.

 

[HomerWelsh]

Thank you Btrueblood for your response. From your advice I have answered my own question and recognised that some of my initial assumptions are incorrect.