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Research Papers

# On Predicting Nucleation of Microcracks Due to Slip-Twin Interactions at Grain Boundaries in Duplex Near $γ-TiAl$

[+] Author and Article Information
D. Kumar, T. R. Bieler, M. A. Crimp

Chemical Engineering and Materials Science, Michigan State University, East Lansing, MI 48824

P. Eisenlohr, F. Roters, D. Raabe

Max-Planck-Institut für Eisenforschung, 40237 Düsseldorf, Germany

D. E. Mason

Mathematics and Computer Science, Albion College, Albion, MI 49224

Student t-distribution based hypothesis tests on comparative means were conducted using EXCEL ™ (assuming unequal variances, normal distributions with two tails).

Hence, omitting the Schmid factor from the fip is possible as long as the Schmid factor is used to choose the appropriate twin systems to be evaluated in the other terms.

The deviations from $Σ$ are in the $2–4deg$ range, giving them a significantly higher energy than a perfect $Σ$ boundary.

J. Eng. Mater. Technol 130(2), 021012 (Mar 13, 2008) (12 pages) doi:10.1115/1.2841620 History: Received July 19, 2007; Revised January 09, 2008; Published March 13, 2008

## Abstract

Simkin (2003, “A Factor to Predict Microcrack Nucleation at Gamma-Gamma Grain Boundaries in TiAl  ,” Scr. Mater., 49(2), 149–154) proposed a relationship for predicting crack initiation in $γ-TiAl$ in a scenario where a mechanical twin interacts with a grain boundary. This correlation (quantified using a fracture initiation parameter or fip) was based only on the geometry of the Burgers vectors as they are related to slip transfer across the grain boundary and the Mode I type opening force experienced by the grain boundary. Generally, a fip is a mathematical combination of factors that allow weak boundaries to be probabilistically identified in the context of a state of stress. This paper further develops this approach by considering the inclusion of the mismatch between the slip planes in the grain boundary and a parameter that accounts for the different elastic properties in adjoining grains. Also, the significance of primary twin (slip) systems versus secondary slip systems is assessed. When compared to fips that can be constructed through a variety of other combinations of nine geometrical parameters that could affect grain boundary damage nucleation, the fip obtained by multiplying Simkin’s original parameter by $Emin∕Emax$, the ratio of Young’s modulus in the stress direction in the two grains, is best able to distinguish between cracked and intact grain boundary populations. Cracked and intact boundaries are also characterized to assess tilt and twist character and whether they are low $Σ$ (or coincident site lattice) boundaries (using a cubic criterion). It is also shown that fips based on $Σ$ values or the tilt and twist character of the boundary lead to an unacceptably high probability of incorrectly distinguishing between cracked and intact grain boundaries, implying that these are not critical parameters affecting crack nucleation at the grain boundary in duplex near-$γ$ TiAl. The paper closes with a discussion on how combined microscopic and crystal plasticity finite element analyses provide insights on local stress-strain relationships that can be used to evaluate a fip in the context of heterogeneous deformation in multigrain ensembles.

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## Figures

Figure 1

(a) Unit cell of TiAl: OD, ordinary dislocation, Tw, mechanical twin; SD, superdislocations on a given (111) plane, c∕a∼1.02 and (b) number of available ⟨110] OD and ⟨112¯] twin systems with Schmid factor m>0.25

Figure 2

Angles used to evaluate the geometrical efficiency of strain transfer at a grain boundary

Figure 3

Two microcracks between Grains 7 and 8 are correlated with mechanical twins in Grain 8. No cracks developed in the boundary between Grains 8 and 6, which followed the same trajectory to the left for another 20μm. In (b), ellipses represent unit circles on the slip plane where slip and twin Burgers vectors (gray, dashed) are labeled with their Schmid factors (based on global stress state). Twinning in Grain 8 had the highest fip value and second highest Schmid factor for twinning.

Figure 4

2D schematic of crack nucleation at a concentrated band of slip or twinning

Figure 5

Histograms of components of fips (a)–(f), and four examples of particular fips (g)–(j)

Figure 6

∣b̂tw⋅ĉ∣ is plotted with ∣b̂tw⋅t̂∣, illustrating a more complex relationship between them than is able to separate intact and cracked boundaries

Figure 7

Special boundaries (based on a cubic assumption) are not common, nor do they reveal any pattern regarding slip based grain boundary strength

Figure 8

Electron channeling contrast image (ECCI) of microcracks formed between Grains 14 and 15, while boundaries between Grains 13 and 16, and between 14 and 17 (an annealing twin) remained intact after a surface strain of about 1.4%. The microstructure within the larger box in the upper figure was modeled with a FEM mesh; the smaller box is enlarged to show three microcracks correlated with twin grain boundary intersections.

Figure 9

Flow behavior used for ordinary and superdislocation slip and twinning systems in the finite element crystal plasticity model of near-γ TiAl. Experimental data are from Ref. 50.

Figure 10

Crystal plasticity FEM model of region in Fig. 8. Shears on the two dominant twin systems are plotted spatially in Grain 14 ((b) and (c)), and with increment at the location where cracks were observed (d), indicating that cracks occurred in a region where much higher twin shear occurred on the secondary twin system (lower global Schmid factor). Most other cracked boundaries were correlated with the primary twin system, but in this case, the secondary twin system was locally more active where cracks were observed.

Figure 11

White orientations will activate ODs preferentially and prevent thick twins from developing that could cause microcrack nucleation. Black areas have either a high Schmid factor for twinning and/or are about 40deg from the Burgers vectors for twinning. The black areas in the middle are susceptible to preferential twinning in compression.

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