 GIA Model: Grain InterAction Model 
Definition:  A statistical
Taylor type model
for the prediction
of deformation
textures.
It can account for
strain
compatibilities
arousing among
grains in a cluster
of eight
monodisperse grains. 
Explanation:  Understanding the
formation of
deformation textures
during forming of
metallic sheets is
of utmost relevance
not only for the
mechanical
properties of a
material but also
for microstructure
development in
subsequent thermal
treatment. The GIA
model predicts
texture
formation
during plastic
deformation by
considering a
statistical ensemble
of eight grain
aggregates, that are
embedded in a
homogeneous matrix.
The aggregate is
subjected to
full constraint
deformation, whereas
free shear
partitioning is
allowed inside the
grains.
Incompatibilities
between the grains
are
compensated by the
introduction of
geometrically
necessary
dislocations (GND).
Additionally,
strain hardening can
be considered by
an incrementally
coupled statistical
model for
dislocation density
evolution. 
Picture / Figure / Diagram: 

Geometry of a single GIA eight grain aggregate, of which an ensemble is simulated.


SFBLink:  The GIA model realizes the smallest possible three dimensional cluster aggregate, with which it is possible to address textures and microstructure (including the dislocation density) evolution of a polycrystalline aggregate. Such nucleation relevant information is used in the recrystallization (→RX) simulations.The amount of orientation dependent strain hardening, approximate intragranular rotation and GND density can be obtained within a computationally efficient and parallelizable framework, that makes the GIA model particularly suitable for industrial applications. 
References:  Crumbach, M.; Pomana, G.; Wagner, P.: A Taylor type deformation texture model considering grain interaction and material properties. Part I – Fundamentals, 1st Joint Int. Conf. on Recryst. and grain growth, Aachen, Germany, (2001) 

