Deformation texture prediction by statistical models: modelling shear-type
strain heterogeneities by rotational flow.
P. Van Houtte, Department MTM, KU Leuven, Belgium
The most accurate models for polycrystal plasticity are doubtlessly CPFE (crystal plasticity finite
element model [1]) and CP-FFT (crystal plasticity fast Fourier methods [2]). They are very well suited
for capturing the effect of complex patterns of stress and strain distribution occurring in
polycrystalline materials at grain boundaries, triple points, interphase boundaries and so forth. Using
them as multiscale models of plastic deformation of single phase materials in order to predict their
deformation textures and their plastic anisotropy, is a good but computer-intensive method.
'Statistical' models such are much faster instead, and among them, the 'grain interaction models' of
different kinds (GIA, RGC, ALAMEL; see the references in [3], a paper on cluster models that makes
use of the visco-plastic self-consistent model) have also proved to lead to sufficiently reliable
predictions for industrial applications [4]. All these different types of 'relaxed constraints models'
deviate from well-known Taylor theory by allowing the individual grains in some way or another to
deviate from Taylor's assumption of homogeneous plastic strain by adopting additional plastic
shears. In spite of their relative success (good predictions of deformation textures in many cases),
these statistical models are unsatisfactory from the point of view of the prediction of a complete
velocity fields for the polycrystal which are geometrically consistent (not to mention the equilibrium
of the predicted stress field). The results obtained by the CPFEM or CP-FFT models are of course
much more satisfactory from this respect; however, visual inspection of these results does not
provide an easy way of identifying simple improvements that could be brought to the statistical
models. And so the question remains: can a human mind understand how it is possible that
polycrystalline materials find ways to accommodate all these extra plastic strains and this without
requiring excessive extra plastic work? An old idea that could help here is the 'rotational flow' which
was proposed in the past (for example by L.M. Brown [5]) to model the plastic flow around
undeformable particles. The potentiality of this idea to model the effects of misfits caused by plastic
shearing of individual grains as assumed by relaxed-constraints models is explored in this
presentation.
References
[1] F. Roters, P. Eisenlohr, L. Hantcherli, D.D. Tjahjanto, T.R. Bieler, and D. Raabe, Acta Mater., 58
(2010), 1152–1211.
[2] R.A. Lebensohn, A. Rollet, and P. Suquet, JOM 63 (3) (2011) 13–18.
[3] Q. Xie, A. Van Bael, J. Sidor, J. Moerman, P. Van Houtte, Acta Materialia 69 (2014) 175–186.
(Contains references to related work of other groups: RWTH Aachen [23], MPIE Düsseldorf [24-25],
Los Alamos National Laboratory [1-2])
[4] P. Van Houtte, J. Gawad, P. Eyckens, B. Van Bael, G. Samaey, D. Roose, JOM 63 (11) (2011) 37-43.
[5] L.M. Brown, Phil. Trans. R. Soc. Lond. A 355 (1997) 1979-1990.