A probabilistic twin nucleation model for HCP polycrystalline metals

by I. J. Beyerlein, and C. N. Tomé

Proceedings AVolume 466(2121):2517-2544

September 8, 2010

©2010 by The Royal Society

Schematic of the process of twin nucleation from a grain boundary: (a) interaction of a dislocation pile-up with an array of grain boundary defects (GBDs), (b) dissociation of GBDs into

twinning partials, and (c) coalescence to form a twin nucleus.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Schematic of the grain boundary surface of an equi-axed grain: each facet corresponds to a boundary that is shared by a neighbouring grain.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Partial grain boundary area of a spherical grain: the relevant area a* is assigned to the area of the spherical cap inscribed by a cone.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Schematic of the multi-scale constitutive model for HCP metals that deform by slip and twinning.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Comparison of the stress–strain predictions from the former model using a deterministic treatment of twinning with the measured stress–strain response at room and liquid nitrogen

temperature.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Basal and prism pole figure of the initial texture of clock-rolled Zr measured by EBSD. Intensity lines are 0.5/1/2/3/4/5 m.r.o.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

(a) Distribution of grain areas of the approximately 9000 grains measured by EBSD. (b) Distribution of grain diameters using the circle area approximation.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Comparison of the predicted and measured stress–strain response of Zr at liquid nitrogen (black) and room temperature (red).

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Comparison of (a) predicted and (b) EBSD measured textures in the form of basal (0002) pole figures at (i) 4%, (ii) 9%, (iii) 14%, and (iv) 19% strain.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

(a) Evolution of twin volume fraction with strain and (b) evolution of the fraction of twinned grains with strain.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Predicted relative activities of each deformation mode during straining in the (a) parent matrix: solid line, prismatic slip; unfilled triangle on a solid line, tensile twinning.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Distribution of twin Schmid factors at (a) 5% strain from the model, (b) 10% strain from the model and (c) 10% strain from EBSD.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Predicted SC factors (equation (4.4)) at the time of twin nucleation for the population of twins present by 10% strain.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

The fraction of twinned grains (grains containing at least one twin) as a function of the highest twin Schmid factor m(1) in the grain at (a) 5% strain from the model, (b) 10% strain from the

model and (c) 10% strain from EBSD. The factor m(1) is calculated...

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

The fraction of twinned grains as a function of grain area in the grain at 10% strain: (a) model prediction and (b) EBSD measurements.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society

Number of twins per grain at 10% strain: (a) model prediction and (b) EBSD measurements.

I. J. Beyerlein, and C. N. Tomé Proc. R. Soc. A 2010;466:2517-2544

©2010 by The Royal Society