- Email: [email protected]
TiAl composites
Accepted Manuscript Strain partitioning behavior of in situ Ti5Si3/TiAl composites Hao Wu, Jinfeng Leng, Xinying Teng, Guohua Fan, Lin Geng, Zhenhua Liu PII:
S0925-8388(18)30528-0
DOI:
10.1016/j.jallcom.2018.02.087
Reference:
JALCOM 44963
To appear in:
Journal of Alloys and Compounds
Received Date: 5 January 2018 Revised Date:
6 February 2018
Accepted Date: 8 February 2018
Please cite this article as: H. Wu, J. Leng, X. Teng, G. Fan, L. Geng, Z. Liu, Strain partitioning behavior of in situ Ti5Si3/TiAl composites, Journal of Alloys and Compounds (2018), doi: 10.1016/ j.jallcom.2018.02.087. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Strain partitioning behavior of in situ Ti5Si3/TiAl composites
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Hao Wu a,*, Jinfeng Leng a, Xinying Teng a, Guohua Fan b,*, Lin Geng b, Zhenhua Liuc
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a
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China
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b
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Harbin, 150001, China
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c
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Co., Ltd., Jinan, 250306, China
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* Corresponding author E-mail: [email protected], [email protected]
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Technical Division, Jinan Foundry & Metalforming Machinery Research Institute
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School of Materials Science and Engineering, Harbin Institute of Technology,
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School of Materials Science and Engineering, University of Jinan, Jinan, 250022,
Abstract
For a particle-reinforced composite, strain attribute at both sides of the interface is a
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critical factor influencing the mechanical properties. Here, we applied transmission
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electron microscope (TEM) and geometrical phase analysis (GPA) to Ti5Si3/TiAl
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composites, and demonstrated that strain compatibility and geometric continuity of
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these two components primarily relied on interfacial shear deformation. This
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approach is expected to be applied in other traditional composites for nanoscale strain
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analysis and performance optimization.
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Keywords: Interfaces; Particulate reinforced composites; Precipitation; Strain field;
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Transmission electron microscopy (TEM).
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1. Introduction
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Intermetallic compound based on γ-TiAl has great potential in automotive and
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aerospace industries owing to its low density, high strength and stiffness [1]. However
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the insufficient oxidation and creep resistance limits its high-temperature (above 700
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o
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that minor amounts of elemental Si could improve the resistance to oxidation and
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creep, although silicon additions might induce the precipitation of ζ-Ti5Si3 phase [3,
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4]. The orientation relationship between ζ-Ti5Si3 precipitate and γ-TiAl matrix has
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been reported as <0-11> γ // <41-50> ζ, {111} γ // {0002} ζ [5, 6]; nevertheless, the
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nanoscale strain level of either component in the Ti5Si3/TiAl composite is still unclear.
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The strain distribution in the vicinity of the interface is of great significance in
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determining the mechanical properties of metal matrix composite, ultrafine eutectic
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alloys, or other heterogeneous materials [7]. Generally, the influence of heterogeneous
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interfaces on strain accommodation can be understood in terms of three kinds of
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interface-mediated plastic deformation modes as proposed in as-casted Al81Cu13Si6
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eutectic alloys [8]. In order to further improve the mechanical performance,
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dispersing strain by tailoring the chemical constituent or microstructural morphology
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seems plausible to elevate the strain gradient and work hardening capacity [9-11], thus
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promoting the uniform plastic deformation by decreasing the degree of strain
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localization at the interfaces, grain boundaries, or shear bands [12-14]. In particular,
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understanding the strain distribution at the nanoscale is very useful but mainly
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depends on molecular dynamics simulations, while experimental measurements are
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commonly incomplete [15]. Fortunately, the technology of geometrical phase analysis
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(GPA) was developed rapidly in recent years, which enables direct strain
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measurement at an extremely high spatial resolution, i.e., at the atomic or nanoscopic
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C) structural applications [2]. Considerable efforts have been made, and it is found
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The aim of this work is to provide direct visualization of nanoscale strain field of
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Ti5Si3/TiAl composites by applying GPA, and to enrich current understanding of the
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behavior of strain compatibility between these two components. Our finding is
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expected to be utilized for guiding the design of next-generation high-performance
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structural materials.
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2. Experimental procedure
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The Ti5Si3/TiAl composites used in this study were fabricated by reaction annealing
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of elemental Ti and SiCp/Al foils as described in our previous work [19]. A FEI Tecnai
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F30 field emission gun transmission electron microscope (TEM), operated at 300 kV,
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was employed for microstructure observation and phase analysis, and the sample was
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prepared by traditional mechanical grinding and ion-thinning. The technology of
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geometrical phase analysis (GPA) was applied and produced nanoscale strain maps
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with color contours which directly illustrated the position of the relative strain. In this
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paper, two non-collinear g-vectors used for strain calculations have been marked in
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the section of Appendix, and a scale range of -0.1 to +0.1 was applied to all strain
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maps for consistency.
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3. Results
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Fig. 1 shows the morphology and distribution of ζ-Ti5Si3 particles in the Ti5Si3/TiAl
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composite. The γ-TiAl matrix was in situ synthesized by diffusion annealing of pure
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Ti and SiCp/Al foils with almost equal thicknesses via the chemical reaction of Ti + Al
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→ TiAl3 (at ~ 660 oC) → TiAl3 + TiAl + Ti3Al (at ~ 1200 oC) → TiAl. The
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diffusion-mediated phase transformation has been well elucidated in our previous
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work [19, 20]. At the same time, SiC particles were selected as a silicon carrier for the
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formation of ζ-Ti5Si3 precipitates. Due to the different solid solubility of Si in Ti-Al 3
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ζ-Ti5Si3 precipitates with dimensions of less than 2 µm were detected at the triple
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junction (intergranular precipitation caused by Si segregation at grain boundaries [22])
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or in the interior of equiaxed γ-TiAl matrix (cooling-induced intragranular
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precipitation, local concentration fluctuation of Si element in γ-TiAl grain interior
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[23]).
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Fig. 1. Bright field image of in situ Ti5Si3/TiAl composites, showing the morphology
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and spatial distribution of ζ-Ti5Si3 particles embedded in γ-TiAl matrix. Events of
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intragranular precipitation, as well as intergranular precipitation, of ζ-Ti5Si3 were
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found. A series of dislocation lines were generated for strain accommodation.
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Reproduced with permission from Ref. [19], Elsevier.
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It is also found that dislocations were generated for strain accommodation. These
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dislocations are seemingly emitted from the interface between ζ-Ti5Si3 precipitate and
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γ-TiAl matrix, propagated within the γ-TiAl interior, and finally arrested at or
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penetrated through the grain boundary (Fig. 1). Actually, the formation of dislocations
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implied that the coarsening of ζ-Ti5Si3 precipitates has already destroyed the coherent 4
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relationship produced at the initial precipitation stage as mentioned in the section of
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Introduction. Here, we tilted the incident electron beam to <-1100> ζ zone axis, in
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order to take the lattice fringes of low-indexed crystallographic planes of ζ-Ti5Si3
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phase for nanoscale strain analysis. Atomic-scale characterization of two-dimensional strain distribution can be
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determined directly from the local structural displacements of lattice fringes [18]. The
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strain fields are represented by strain tensor components εxx, εyy, and γxy, in such a way
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that x // [11-20] ζ, y // [0001] ζ. A scale range of -0.1 to +0.1 was applied to all strain
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components for consistency. Lattice atoms are colored according to the strain scale:
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color for positive value represents compressive strain, while that for negative value
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represents tensile strain. Note that the strain analysis was performed in the interior of
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ζ-Ti5Si3 particles, from which the strain distribution of γ-TiAl matrix can be
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extrapolated.
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Strain partitioning behaviors are measured at a series of specific sites as plotted by
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squares 1~6 in Fig. 2a. In order to obtain an acceptable precision of these three strain
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components, they are averaged over a square area with a dimension at least greater
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than the spatial resolution of the technology of GPA and TEM; in the current case,
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squares of 3 × 3 nm2 were chosen. Results of εxx, εyy, and γxy are summarized in Table
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1 and plotted in Fig. 3a, in which a roughly gradual decrease in local normal stresses
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along the two directions was presented when moving towards ζ-Ti5Si3 precipitates.
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We also observed that ζ-Ti5Si3 precipitates withstood a smaller amount of normal
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compressive strains, i.e., εxx and εyy. The positive εxx and εyy values are probably due to
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the limitation of two-dimensional in-plane strain characterization. For γxy strain
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component normalized by an average shear strain, as shown in Fig. 3b, it is found that
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the shear strain in the interior of γ-TiAl matrix and ζ-Ti5Si3 precipitate approximately
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highlighted here that a positive normalized shear strain appeared in the Ti5Si3 side
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near the interface (Square 3 marked in Fig. 2a), while an opposite trend was exhibited
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in the TiAl part.
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Fig. 2. Lattice fringe and strain field of in situ Ti5Si3/TiAl composites. (a) High
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resolution transmission electron microscope image. The white squares represent areas
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for which corresponding strain tensor levels are summarized in Table 1. (b-d) Strain
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tensor components, εxx, γxy, εyy, respectively, obtained by GPA: x // [11-20] ζ, y // [0001]
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ζ. 6
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Fig. 3. Strain partitioning behavior of six white squares indicated in Fig. 2a. True
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strain levels are plotted in (a), while the vertical coordinate in (b) denotes the strain
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amplitude, normalized by respective average strain.
Site
εxx
Mean Region 1
γxy
0.0173±0.0010
0.0345±0.0015
-0.0131±0.0011
0.0340±0.0012
0.0733±0.0021
-0.0125±0.0015
0.0279±0.0013
0.0589±0.0018
-0.0190±0.0014
Region 3
-0.0018±0.0005
0.0124±0.0013
-0.0088±0.0009
Region 4
0.0086±0.0006
0.0104±0.0013
-0.0086±0.0006
0.0083±0.0008
0.0223±0.0011
-0.0128±0.0007
0.0219±0.0010
0.0220±0.0013
-0.0123±0.0009
Region 5
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Region 2
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Table 1 Strain partitioning determined from the regions (3 × 3 nm2) plotted in Fig. 2.
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Fig. 4 shows a profile of real shear strain along the direction of <0001> ζ and
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averaged over the width of the rectangle (with black border). The phenomenon of
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strain partitioning behavior, taking shear strain for example, was clearly revealed: (i)
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both the maximum and minimum shear strains peaked near the interface (marked by
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green dotted line in Fig. 4b); (ii) ζ-Ti5Si3 precipitate was subjected to a larger positive
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shear strain compared to γ-TiAl matrix, in good consistence with experimental results
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Fig. 4. Strain profile of γxy along the longitudinal direction and averaged over the
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width of the rectangle (black border, length: 8.6 nm, width: 2.4nm). (a) γxy strain
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tensor component. The scanning direction has been particularly shown by black
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dotted arrow. (b) Strain partitioning. The area in light pink represents a compressive
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strain, as opposed to the lower part colored by light orange.
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4. Discussion
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For a particulate-reinforced composite, the strain distribution of either component
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at a fine microstructural scale is a key factor influencing the mechanical properties of
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the composite [13]. In the past few years, the residual compressive stress was
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deliberately introduced to suppress the crack initiation and propagation by means of
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phase transformation [24], thermomechanical processing [25], etc.. In the present
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work, brittle ζ-Ti5Si3 particles are found to be compressed when precipitated from
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γ-TiAl matrix after furnace cooling, being a good candidate as strengthening phases.
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The strain compatibility and geometric continuity across the interface are sustained by
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experimentally observed shear deformation (Fig. 4), which distorts the lattice
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arrangements in the vicinity of interfaces and impedes the dislocation transmission
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from one grain to the next [26]. Additionally, the spherical or ellipsoidal morphology
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precipitates compared to cuboidal-shaped ones for a fixed volume fraction [27], thus
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increasing the critical stress required for dislocation motion and contributing to the
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hardening effect according to the classical Orowan formula [28]. It should be
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mentioned here that at the current grain size of a few microns (Fig. 1), ζ-Ti5Si3
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precipitate is hard to be sheared by gliding dislocations [29], and optimizing
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performance by tailoring the distribution and morphology of Ti5Si3 particles seems
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plausible [30], for example, finer Ti5Si3 particles embedded in TiAl matrix are
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recommended for engineering application whereby particle shearing partially
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alleviates the mismatched stress at the interface.
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5. Conclusions
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In summary, a combination of TEM and GPA was applied in the Ti5Si3/TiAl
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composite to investigate the behavior of strain distribution of ζ-Ti5Si3 particle and
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γ-TiAl matrix. Our work demonstrated that strain compatibility between these two
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components mainly depends on interfacial shear deformation. This finding is expected
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to be widely applied in other traditional structural materials for nanoscale strain
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analysis and performance optimization.
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Acknowledgements
H.W. and X.T. are grateful for financial support from the Shandong Provincial
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Natural Science Foundation, China (Grant No. ZR2017BEM001), National Natural
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Science Foundation of China (Grant No. 51701081, 51571102), the scientific and
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technological project supported by the Science Foundation from the University of
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Jinan (Grant No. XKY1713, 511-1009406). G.F. is funded by National Natural
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Science Foundation of China (Grant No. 51571070, 51571071), and Key Laboratory 9
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of Micro-systems and Micro-structures Manufacturing of Ministry of Education,
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Harbin Institute of Technology (Grant No. 2015KM002).
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Appendix
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Fig. A1. (a) Lattice image of Ti5Si3/TiAl composites projected along the <-1100>
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zone axis. (b) Fourier transform image taken from the ζ-Ti5Si3 side. The g-vectors
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marked by red circles are used for calculating the strain tensor components.
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Figure and table captions
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Fig. 1. Bright field image of in situ Ti5Si3/TiAl composites, showing the morphology
281
and spatial distribution of ζ-Ti5Si3 particles embedded in γ-TiAl matrix. Events of
282
intragranular precipitation, as well as intergranular precipitation, of ζ-Ti5Si3 were
283
found. A series of dislocation lines were generated for strain accommodation.
284
Reproduced with permission from Ref. [19], Elsevier.
285
Fig. 2. Lattice fringe and strain field of in situ Ti5Si3/TiAl composites. (a) High
286
resolution transmission electron microscope image. The white squares represent areas
287
for which corresponding strain tensor levels are summarized in Table 1. (b-d) Strain
288
tensor components, εxx, γxy, εyy, respectively, obtained by GPA: x // [11-20] ζ, y // [0001]
289
ζ.
290
Fig. 3. Strain partitioning behavior of six white squares indicated in Fig. 2a. True
291
strain levels are plotted in (a), while the vertical coordinate in (b) denotes the strain
292
amplitude, normalized by respective average strain.
293
Fig. 4. Strain profile of γxy along the longitudinal direction and averaged over the
294
width of the rectangle (black border, length: 8.6 nm, width: 2.4nm). (a) γxy strain
295
tensor component. The scanning direction has been particularly shown by black
296
dotted arrow. (b) Strain partitioning. The area in light pink represents a compressive
297
strain, as opposed to the lower part colored by light orange.
298
Fig. A1. (a) Lattice image of Ti5Si3/TiAl composites projected along the <-1100>
299
zone axis. (b) Fourier transform image taken from the ζ-Ti5Si3 side. The g-vectors
300
marked by red circles are used for calculating the strain tensor components.
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Table 1 Strain partitioning determined from the regions (3 × 3 nm2) plotted in Fig. 2.
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ACCEPTED MANUSCRIPT Highlights The method of geometrical phase analysis (GPA) was applied.
Strain partitioning behavior was observed in Ti5Si3/TiAl composites
Interfacial shear deformation sustained the strain compatibility.
This approach can be applied in other composites for strain analysis.
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S0925-8388(18)30528-0
DOI:
10.1016/j.jallcom.2018.02.087
Reference:
JALCOM 44963
To appear in:
Journal of Alloys and Compounds
Received Date: 5 January 2018 Revised Date:
6 February 2018
Accepted Date: 8 February 2018
Please cite this article as: H. Wu, J. Leng, X. Teng, G. Fan, L. Geng, Z. Liu, Strain partitioning behavior of in situ Ti5Si3/TiAl composites, Journal of Alloys and Compounds (2018), doi: 10.1016/ j.jallcom.2018.02.087. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Strain partitioning behavior of in situ Ti5Si3/TiAl composites
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Hao Wu a,*, Jinfeng Leng a, Xinying Teng a, Guohua Fan b,*, Lin Geng b, Zhenhua Liuc
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a
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China
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b
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Harbin, 150001, China
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c
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Co., Ltd., Jinan, 250306, China
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* Corresponding author E-mail: [email protected], [email protected]
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Technical Division, Jinan Foundry & Metalforming Machinery Research Institute
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School of Materials Science and Engineering, Harbin Institute of Technology,
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School of Materials Science and Engineering, University of Jinan, Jinan, 250022,
Abstract
For a particle-reinforced composite, strain attribute at both sides of the interface is a
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critical factor influencing the mechanical properties. Here, we applied transmission
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electron microscope (TEM) and geometrical phase analysis (GPA) to Ti5Si3/TiAl
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composites, and demonstrated that strain compatibility and geometric continuity of
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these two components primarily relied on interfacial shear deformation. This
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approach is expected to be applied in other traditional composites for nanoscale strain
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analysis and performance optimization.
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Keywords: Interfaces; Particulate reinforced composites; Precipitation; Strain field;
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Transmission electron microscopy (TEM).
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1. Introduction
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Intermetallic compound based on γ-TiAl has great potential in automotive and
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aerospace industries owing to its low density, high strength and stiffness [1]. However
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the insufficient oxidation and creep resistance limits its high-temperature (above 700
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o
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that minor amounts of elemental Si could improve the resistance to oxidation and
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creep, although silicon additions might induce the precipitation of ζ-Ti5Si3 phase [3,
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4]. The orientation relationship between ζ-Ti5Si3 precipitate and γ-TiAl matrix has
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been reported as <0-11> γ // <41-50> ζ, {111} γ // {0002} ζ [5, 6]; nevertheless, the
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nanoscale strain level of either component in the Ti5Si3/TiAl composite is still unclear.
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The strain distribution in the vicinity of the interface is of great significance in
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determining the mechanical properties of metal matrix composite, ultrafine eutectic
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alloys, or other heterogeneous materials [7]. Generally, the influence of heterogeneous
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interfaces on strain accommodation can be understood in terms of three kinds of
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interface-mediated plastic deformation modes as proposed in as-casted Al81Cu13Si6
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eutectic alloys [8]. In order to further improve the mechanical performance,
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dispersing strain by tailoring the chemical constituent or microstructural morphology
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seems plausible to elevate the strain gradient and work hardening capacity [9-11], thus
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promoting the uniform plastic deformation by decreasing the degree of strain
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localization at the interfaces, grain boundaries, or shear bands [12-14]. In particular,
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understanding the strain distribution at the nanoscale is very useful but mainly
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depends on molecular dynamics simulations, while experimental measurements are
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commonly incomplete [15]. Fortunately, the technology of geometrical phase analysis
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(GPA) was developed rapidly in recent years, which enables direct strain
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measurement at an extremely high spatial resolution, i.e., at the atomic or nanoscopic
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C) structural applications [2]. Considerable efforts have been made, and it is found
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The aim of this work is to provide direct visualization of nanoscale strain field of
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Ti5Si3/TiAl composites by applying GPA, and to enrich current understanding of the
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behavior of strain compatibility between these two components. Our finding is
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expected to be utilized for guiding the design of next-generation high-performance
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structural materials.
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2. Experimental procedure
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The Ti5Si3/TiAl composites used in this study were fabricated by reaction annealing
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of elemental Ti and SiCp/Al foils as described in our previous work [19]. A FEI Tecnai
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F30 field emission gun transmission electron microscope (TEM), operated at 300 kV,
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was employed for microstructure observation and phase analysis, and the sample was
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prepared by traditional mechanical grinding and ion-thinning. The technology of
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geometrical phase analysis (GPA) was applied and produced nanoscale strain maps
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with color contours which directly illustrated the position of the relative strain. In this
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paper, two non-collinear g-vectors used for strain calculations have been marked in
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the section of Appendix, and a scale range of -0.1 to +0.1 was applied to all strain
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maps for consistency.
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3. Results
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Fig. 1 shows the morphology and distribution of ζ-Ti5Si3 particles in the Ti5Si3/TiAl
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composite. The γ-TiAl matrix was in situ synthesized by diffusion annealing of pure
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Ti and SiCp/Al foils with almost equal thicknesses via the chemical reaction of Ti + Al
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→ TiAl3 (at ~ 660 oC) → TiAl3 + TiAl + Ti3Al (at ~ 1200 oC) → TiAl. The
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diffusion-mediated phase transformation has been well elucidated in our previous
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work [19, 20]. At the same time, SiC particles were selected as a silicon carrier for the
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formation of ζ-Ti5Si3 precipitates. Due to the different solid solubility of Si in Ti-Al 3
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ζ-Ti5Si3 precipitates with dimensions of less than 2 µm were detected at the triple
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junction (intergranular precipitation caused by Si segregation at grain boundaries [22])
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or in the interior of equiaxed γ-TiAl matrix (cooling-induced intragranular
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precipitation, local concentration fluctuation of Si element in γ-TiAl grain interior
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[23]).
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Fig. 1. Bright field image of in situ Ti5Si3/TiAl composites, showing the morphology
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and spatial distribution of ζ-Ti5Si3 particles embedded in γ-TiAl matrix. Events of
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intragranular precipitation, as well as intergranular precipitation, of ζ-Ti5Si3 were
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found. A series of dislocation lines were generated for strain accommodation.
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Reproduced with permission from Ref. [19], Elsevier.
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It is also found that dislocations were generated for strain accommodation. These
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dislocations are seemingly emitted from the interface between ζ-Ti5Si3 precipitate and
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γ-TiAl matrix, propagated within the γ-TiAl interior, and finally arrested at or
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penetrated through the grain boundary (Fig. 1). Actually, the formation of dislocations
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implied that the coarsening of ζ-Ti5Si3 precipitates has already destroyed the coherent 4
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relationship produced at the initial precipitation stage as mentioned in the section of
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Introduction. Here, we tilted the incident electron beam to <-1100> ζ zone axis, in
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order to take the lattice fringes of low-indexed crystallographic planes of ζ-Ti5Si3
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phase for nanoscale strain analysis. Atomic-scale characterization of two-dimensional strain distribution can be
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determined directly from the local structural displacements of lattice fringes [18]. The
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strain fields are represented by strain tensor components εxx, εyy, and γxy, in such a way
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that x // [11-20] ζ, y // [0001] ζ. A scale range of -0.1 to +0.1 was applied to all strain
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components for consistency. Lattice atoms are colored according to the strain scale:
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color for positive value represents compressive strain, while that for negative value
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represents tensile strain. Note that the strain analysis was performed in the interior of
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ζ-Ti5Si3 particles, from which the strain distribution of γ-TiAl matrix can be
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extrapolated.
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Strain partitioning behaviors are measured at a series of specific sites as plotted by
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squares 1~6 in Fig. 2a. In order to obtain an acceptable precision of these three strain
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components, they are averaged over a square area with a dimension at least greater
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than the spatial resolution of the technology of GPA and TEM; in the current case,
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squares of 3 × 3 nm2 were chosen. Results of εxx, εyy, and γxy are summarized in Table
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1 and plotted in Fig. 3a, in which a roughly gradual decrease in local normal stresses
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along the two directions was presented when moving towards ζ-Ti5Si3 precipitates.
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We also observed that ζ-Ti5Si3 precipitates withstood a smaller amount of normal
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compressive strains, i.e., εxx and εyy. The positive εxx and εyy values are probably due to
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the limitation of two-dimensional in-plane strain characterization. For γxy strain
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component normalized by an average shear strain, as shown in Fig. 3b, it is found that
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the shear strain in the interior of γ-TiAl matrix and ζ-Ti5Si3 precipitate approximately
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highlighted here that a positive normalized shear strain appeared in the Ti5Si3 side
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near the interface (Square 3 marked in Fig. 2a), while an opposite trend was exhibited
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in the TiAl part.
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Fig. 2. Lattice fringe and strain field of in situ Ti5Si3/TiAl composites. (a) High
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resolution transmission electron microscope image. The white squares represent areas
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for which corresponding strain tensor levels are summarized in Table 1. (b-d) Strain
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tensor components, εxx, γxy, εyy, respectively, obtained by GPA: x // [11-20] ζ, y // [0001]
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Fig. 3. Strain partitioning behavior of six white squares indicated in Fig. 2a. True
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strain levels are plotted in (a), while the vertical coordinate in (b) denotes the strain
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amplitude, normalized by respective average strain.
Site
εxx
Mean Region 1
γxy
0.0173±0.0010
0.0345±0.0015
-0.0131±0.0011
0.0340±0.0012
0.0733±0.0021
-0.0125±0.0015
0.0279±0.0013
0.0589±0.0018
-0.0190±0.0014
Region 3
-0.0018±0.0005
0.0124±0.0013
-0.0088±0.0009
Region 4
0.0086±0.0006
0.0104±0.0013
-0.0086±0.0006
0.0083±0.0008
0.0223±0.0011
-0.0128±0.0007
0.0219±0.0010
0.0220±0.0013
-0.0123±0.0009
Region 5
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Table 1 Strain partitioning determined from the regions (3 × 3 nm2) plotted in Fig. 2.
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Fig. 4 shows a profile of real shear strain along the direction of <0001> ζ and
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averaged over the width of the rectangle (with black border). The phenomenon of
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strain partitioning behavior, taking shear strain for example, was clearly revealed: (i)
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both the maximum and minimum shear strains peaked near the interface (marked by
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green dotted line in Fig. 4b); (ii) ζ-Ti5Si3 precipitate was subjected to a larger positive
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shear strain compared to γ-TiAl matrix, in good consistence with experimental results
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Fig. 4. Strain profile of γxy along the longitudinal direction and averaged over the
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width of the rectangle (black border, length: 8.6 nm, width: 2.4nm). (a) γxy strain
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tensor component. The scanning direction has been particularly shown by black
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dotted arrow. (b) Strain partitioning. The area in light pink represents a compressive
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strain, as opposed to the lower part colored by light orange.
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4. Discussion
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For a particulate-reinforced composite, the strain distribution of either component
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at a fine microstructural scale is a key factor influencing the mechanical properties of
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the composite [13]. In the past few years, the residual compressive stress was
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deliberately introduced to suppress the crack initiation and propagation by means of
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phase transformation [24], thermomechanical processing [25], etc.. In the present
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work, brittle ζ-Ti5Si3 particles are found to be compressed when precipitated from
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γ-TiAl matrix after furnace cooling, being a good candidate as strengthening phases.
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The strain compatibility and geometric continuity across the interface are sustained by
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experimentally observed shear deformation (Fig. 4), which distorts the lattice
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arrangements in the vicinity of interfaces and impedes the dislocation transmission
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from one grain to the next [26]. Additionally, the spherical or ellipsoidal morphology
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precipitates compared to cuboidal-shaped ones for a fixed volume fraction [27], thus
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increasing the critical stress required for dislocation motion and contributing to the
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hardening effect according to the classical Orowan formula [28]. It should be
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mentioned here that at the current grain size of a few microns (Fig. 1), ζ-Ti5Si3
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precipitate is hard to be sheared by gliding dislocations [29], and optimizing
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performance by tailoring the distribution and morphology of Ti5Si3 particles seems
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plausible [30], for example, finer Ti5Si3 particles embedded in TiAl matrix are
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recommended for engineering application whereby particle shearing partially
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alleviates the mismatched stress at the interface.
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5. Conclusions
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In summary, a combination of TEM and GPA was applied in the Ti5Si3/TiAl
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composite to investigate the behavior of strain distribution of ζ-Ti5Si3 particle and
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γ-TiAl matrix. Our work demonstrated that strain compatibility between these two
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components mainly depends on interfacial shear deformation. This finding is expected
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to be widely applied in other traditional structural materials for nanoscale strain
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analysis and performance optimization.
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Acknowledgements
H.W. and X.T. are grateful for financial support from the Shandong Provincial
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Natural Science Foundation, China (Grant No. ZR2017BEM001), National Natural
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Science Foundation of China (Grant No. 51701081, 51571102), the scientific and
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technological project supported by the Science Foundation from the University of
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Jinan (Grant No. XKY1713, 511-1009406). G.F. is funded by National Natural
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Science Foundation of China (Grant No. 51571070, 51571071), and Key Laboratory 9
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of Micro-systems and Micro-structures Manufacturing of Ministry of Education,
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Harbin Institute of Technology (Grant No. 2015KM002).
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Appendix
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Fig. A1. (a) Lattice image of Ti5Si3/TiAl composites projected along the <-1100>
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zone axis. (b) Fourier transform image taken from the ζ-Ti5Si3 side. The g-vectors
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marked by red circles are used for calculating the strain tensor components.
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Figure and table captions
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Fig. 1. Bright field image of in situ Ti5Si3/TiAl composites, showing the morphology
281
and spatial distribution of ζ-Ti5Si3 particles embedded in γ-TiAl matrix. Events of
282
intragranular precipitation, as well as intergranular precipitation, of ζ-Ti5Si3 were
283
found. A series of dislocation lines were generated for strain accommodation.
284
Reproduced with permission from Ref. [19], Elsevier.
285
Fig. 2. Lattice fringe and strain field of in situ Ti5Si3/TiAl composites. (a) High
286
resolution transmission electron microscope image. The white squares represent areas
287
for which corresponding strain tensor levels are summarized in Table 1. (b-d) Strain
288
tensor components, εxx, γxy, εyy, respectively, obtained by GPA: x // [11-20] ζ, y // [0001]
289
ζ.
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Fig. 3. Strain partitioning behavior of six white squares indicated in Fig. 2a. True
291
strain levels are plotted in (a), while the vertical coordinate in (b) denotes the strain
292
amplitude, normalized by respective average strain.
293
Fig. 4. Strain profile of γxy along the longitudinal direction and averaged over the
294
width of the rectangle (black border, length: 8.6 nm, width: 2.4nm). (a) γxy strain
295
tensor component. The scanning direction has been particularly shown by black
296
dotted arrow. (b) Strain partitioning. The area in light pink represents a compressive
297
strain, as opposed to the lower part colored by light orange.
298
Fig. A1. (a) Lattice image of Ti5Si3/TiAl composites projected along the <-1100>
299
zone axis. (b) Fourier transform image taken from the ζ-Ti5Si3 side. The g-vectors
300
marked by red circles are used for calculating the strain tensor components.
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Table 1 Strain partitioning determined from the regions (3 × 3 nm2) plotted in Fig. 2.
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ACCEPTED MANUSCRIPT Highlights The method of geometrical phase analysis (GPA) was applied.
Strain partitioning behavior was observed in Ti5Si3/TiAl composites
Interfacial shear deformation sustained the strain compatibility.
This approach can be applied in other composites for strain analysis.
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