Barlat's 3- parameter plasticity model is developed in F. Barlat, J. Lian 1 for modeling of sheet under plane stress assumption with
an anisotropic plasticity model. The anisotropic yield stress criterion for plane stress is
defined as:
Where,
is the yield stress,
and
are anisotropic material constants,
exponent and
and
are defined by:
Where,
and
are additional anisotropic material constants. All anisotropic
material constants, except for
which is obtained implicitly, are determined from Barlat width
to thickness strain ratio
from:
The width to thickness ratio for any angle
can be calculated: 1
Where,
is the uniaxial tension in the
direction. Let
= 45°,
Equation 4 gives an equation from which the
anisotropy parameter
can be computed implicitly by using an iterative
procedure:
Note: Barlat's law reduces to Hill's law when using
=2
1 Barlat F. and Lian J.,
Plastic behavior and stretchability of sheet metals,
Part I: A yield function for orthoropic sheets under plane stress conditions
,
International Journal of Plasticity, Vol. 5, pp. 51-66, 1989.