White Paper: Role of Grain Boundaries in Polycrystal Deformation
by
OSU Group: R. H. Wagoner (prof.), H. Lim (post-doc)
BYU Group: B. L. Adams (prof.), D.T. Fullwood (prof.), E.R. Homer (ass. prof.)
Note: This White Paper follows 6 successive regular proposals*declined by NSF/DMR, extensive bootlegged work by the collaborators over 7 years, and a current EAGER award that made rapid progress and
publications possible. One or more reviewers for each proposal has had great difficulty understanding the
complex, novel, collaborative project, and rated it accordingly. Others have understood the concept and
have rated the work as excellent or very good. Discussions with NSF program directors suggested that the
problem may lie with the multi-disciplinary/ multi-scale nature of the work among materials (metals), solid
mechanics, and physics. We hope to get advice on this topic, and to be better able to explain the concepts
using peer-reviewed papers from the group that have just appeared in the literature.
The Concept: Use two breakthroughs, as outlined below, to determine, for the first time, the
slip propagation strength at local grain boundaries in metals (p). (One of these breakthroughs is
also a principal motivating factor to determine a verified value p.) This elusive quantity is
essential to understanding and predicting the role of grain boundaries and inter-grain
misorientation on mechanical properties. The work will pursue a “top-down” approach, i.e.
working from measured dislocation characters and densities. The alternative, a “bottom-up”
approach, would rely on atomic simulations of dislocation-grain boundary interactions. The
bottom-up approach, while conceptually appealing and simple, has been judged impractical by
several reviewers for bcc polycrystals, although this opinion is controversial. We will continue
to seek to work with groups that specialize in such methods to supplement the proposed project.
The goal of the proposed work is to determine the slip propagation strength, which is required to
to operate deformation between compatible, adjacent grains, and use such a value in larger-scale
simulations. At present, the exact mechanism behind the operation of such deformation is not
resolved, notwithstanding the many proposed ideas on the controlling mechanisms and their
relationship to bulk properties such as the Hall-Petch effect. While it is not the principal goal of
this work, it is expected that the experiments will provide some insight on possible mechanisms
that generate, obstruct, and propagate dislocation slip at grain boundaries.
The Breakthroughs: The technical approach leverages two fundamental breakthroughs made in
recent years, most recently under the auspices of the current EAGER award:
1. Novel high-resolution EBSD techniques can now resolve dislocation densities (and their
tensor characters) as low as 1012/m2 with typical limits of 1013/m2. These resolution
limits are two orders of magnitude better than with the best standard EBSD techniques.
Using sufficiently small step sizes (e.g. 20 nm) allows the resolution of single
dislocations to be approached. The EBSD techniques utilize image cross-correlation and
*
Proposals: DMR 1104700 (2010), DMR 0936340 (2009), DMR 0806731 (2008), DMR 0705090 (2007), DMR
0604459 (2005), DMR 0504411(2004).
solution of boundary-value problems to reveal all of the stress and strain tensor
components and the lattice curvature. (Primary responsibility: BYU. References: 1 and
2, provided.)
2. A unique multi-scale simulation “Superdislocation” model makes possible for the first
time the prediction of the Hall-Petch effect in metallic polycrystals. No arbitrary length
scales (such as with strain-gradient formulations or composite models) are invoked. No
non-physical/not observed mechanisms (such as isolated planar dislocation pile-ups with
lengths proportional to grain size) are required. The only critical parameter in the model
is p. Because this is the first simulation method to predict Hall-Petch slopes based on
local grain interactions, it motivates the need for knowing and verifying values for p
(Primary responsibility: OSU. Reference: 3, provided.)
Technical Landscape: The proposed work falls into the broad “hot topic” of scale effects in
materials. Nonetheless, a clear distinction needs to be made. Recent results in that broad area
have focused on very small specimens, typically single crystals with sizes on the order of a
micron. The mechanisms† proposed from that work are based on discrete dislocation generation
and annihilation of small numbers of dislocations, as influenced by very local free surfaces.
Heterogeneous deformation is integral to those special, small-scale phenomena. None of the
mechanisms proposed to explain the small-scale results appear to govern bulk material behavior,
a fact confirmed by changes of slope and even reversals of Hall-Petch behavior at these small
scales.
The proposed work is aimed at a different scale regime: bulk specimens (mm scale and up – i.e.
at least 1000 times larger) and “normal” grain sizes (micron size and larger). These correspond
to virtually every practical structural metal in use today, and it is for such materials that the HallPetch effect has been widely measured and verified. Such materials deform heterogeneously on
the macro scale (i.e. requiring compatible deformation among many grains), the deformation
involving the cooperative motion of ~ 1014 dislocations per square meter.
A Critical Experiment: Goal 1 is to measure p for several grain boundaries, and then to
codify those results in a simple equation to reproduce p, for that material and for any
combination of grain boundary and grain misorientation. Goal 2 is to simulate coarse-grained
polycrystals using the p equation, and to compare such simulations with mechanical and EBSD
experiments.
†
Examples of such mechanisms include source truncation, exhaustion hardening, and dislocation starvation. See
Reference 4, provided.
Figure 1: Schematic of a tensile specimen for the “Critical Experiment”
The idealized experiment will look something like that shown in Figure 1. Several steps will be
involved in the experiment and analysis:
1. A columnar bicrystal (or a bicrystal region of a multicrystal) will be fully characterized
with regular EBSD (for orientations) and Hi-Res EBSD (for original dislocation content
near the grain boundary).
2. The bicrystal will be deformed in tension to a given strain (say 5%) and will be recharacterized using EBSD along a primary slip plane, as shown. The local stress tensor
along such a scan line will be revealed using the Hi-Res EBSD patterns (using methods
presented in References 2 and 3).
3. The variation of the measured local stresses will be extrapolated to the boundary location
to obtain a trial value of p for that slip system, that boundary, and that crystal
misorientation. (This procedure is a meso-scale extension of one presented in the
literature for a discrete dislocation pile-up observed in TEM. See Reference 5, provided.)
4. Using the estimated value of p and an assumed equation relating it to the corresponding
one for other slip systems for that boundary (See Reference 5, provided), and using the
simulation method (Breakthrough 2), the full dislocation distribution (tensor character
and density) of the bicrystal sample will be predicted.
5. The predicted dislocation content will be compared with Hi-Res EBSD measurements to
refine the value for p, and its variation for other slip systems.
6. After iterating on steps 4 and 5 to obtain an improved determination of p, EBSD pattern
simulations based on the simulated stresses and dislocation contents throughout the
bicrystal will be used to further probe the agreement. (Details of the EBSD images that
are not used to obtain dislocation content or stresses provide a richer test of the
superdislocation simulations.)
7. Steps 1-6 will be repeated for several grain and grain boundary orientation to test the
existing model of p, and to verify or improve it.
References:
1.
C. J. Gardner, B. L. Adams, J. Basinger, D. T. Fullwood: EBSD-Based Continuum
Dislocation Microscopy, Int. J. Plast., 2010, vol. 26, pp. 1234-1247.
Link: http://mt.seas.upenn.edu/Stuff/RHW/Upload/Ref1IJPEBSD2010.pdf
2. T. Hardin, B.L. Adams, D. T. Fullwood, R. H. Wagoner: Estimation of the Full Nye Tensor
by EBSD-Based Dislocation Microscopy, ICOTOM16 (submitted for publication).
Link: http://mt.seas.upenn.edu/Stuff/RHW/Upload/Ref2ICOTOM16.pdf
3. H. Lim, M.G. Lee, J.H.Kim, B.L. Adams, R. H. Wagoner: Simulation of Polycrystal
Deformation with Grain and Grain Boundary Effects, Int. J. Plast., 2011, vol. 27, pp. 13281354. Link: http://mt.seas.upenn.edu/Stuff/RHW/Upload/Ref3IJPPolyXLH-P.pdf
4. Series of articles in JOM, 2009, Vol. 61(3), pp. 14-41:
Link: http://mt.seas.upenn.edu/Stuff/RHW/Upload/Ref4JOM2009.pdf
a. D. Kiener, K. Durst, M. Rester, A. M. Minor: Revealing Deformation Mechanisms with
Nanoindentation, pp. 14-23
b. D. S. Gianola, C. Eberl: Micro- and Nanonscale Tensile Testing of Materials, pp. 24-35.
c. M. D. Uchic, P. A. Shade, D. M. Dimiduk: Micro-Compession Testing of FCC Metals:
A Selected Overview of Experiments and Simulations, pp. 36-41
5. Z. Shen, R. H. Wagoner, and W. A. T. Clark: Dislocation and Grain Boundary Interactions
in Metals, Acta Metall., 1988, Vol. 36, pp. 3231-3242.
Link: http://mt.seas.upenn.edu/Stuff/RHW/Upload/Ref5SWC1988.PDF