Crystallographic Orientation Dependence of Mechanical Responses of FeCrAl Micropillars

: Iron-chromium-aluminum (FeCrAl) alloys are used in automobile exhaust gas purifying systems and nuclear reactors due to its superior high-temperature oxidation and excellent corrosion resistance. Single-phase FeCrAl alloys with a body centered cubic structure plastically deform through dislocation slips at room temperature. Here, we investigated the orientation dependence of mechanical responses of FeCrAl alloy through testing single-crystal and bi-crystal micropillars in a scanning electron microscopy at room temperature. Single-crystal micropillars were fabricated with speciﬁc orientations which favor the activity of single slip system or two slip systems or multiple slip systems. The strain hardening rate and ﬂow strength increase with increasing the number of activated slip system in micropillars. Bi-crystal micropillars with respect to the continuity of slip systems across grain boundary were fabricated to study the e ﬀ ect of grain boundary on slip transmission. The high geometrical compatibility factor corresponds to a high ﬂow strength and strain hardening rate. Experimental results provide insight into understanding mechanical response of FeCrAl alloy and developing the mechanisms-based constitutive laws for FeCrAl polycrystalline aggregates. micro-pillars, we characterized the strain hardening behavior of micropillars associated with the activity of (a) one slip system, (b) two slip systems, and (c) multiple slip systems. Bi-crystal micropillars with respect to the continuity of slip systems across two high-angle GBs were fabricated to study the e ﬀ ect of grain boundary on slip transmission. These results provide insight into understanding mechanical response of FeCrAl alloy.


Introduction
Iron-chromium-aluminum (FeCrAl) alloys was initially developed by General Electric (GE) Corporation in the 1960s. This material exhibits superior high-temperature oxidation and excellent corrosion resistance, and thus were used in automobile exhaust gas purifying systems and nuclear reactors [1,2]. Single-phase FeCrAl alloys with a body centered cubic (BCC) structure plastically deform through dislocation slips. Predominate slip systems include {110}<111> and {112}<111> at room temperature [3,4]. The development of the constitutive laws for FeCrAl polycrystalline aggregates is in urgent demand for designing and predicting mechanical response of FeCrAl-made structural components. Numerous efforts were made to develop constitutive models based on the knowledge of crystal defects, such as dislocations, twins and grain boundaries [5][6][7][8][9][10][11][12]. Yielding strength of a material is determined by the glide of dislocations, in turn, the glide resistance of dislocations associated with different slip systems is the essential parameter. Strain hardening effect is mainly ascribed to dislocation interactions and/or dislocation-grain boundary interactions.
The glide resistance of dislocations, i.e., critical resolved shear stress (CRSS), can be estimated using different methods. First, CRSS can be estimated by analysis of orientation and slip trace on polycrystal sample after macro mechanical tests. In this method, the orientations of grains are analyzed by using transmission electron microscopy (TEM) [13] or electron backscatter diffraction (EBSD) [14]. The slip system of traces and Schmid factors are calculated with help of orientation information. Then the ratio of CRSS can be calculated by counting the frequency of slip traces. Coupled with in situ observation of deformation process, this method can also provide absolute estimation of CRSS [15].

Materials
The FeCrAl alloy tested in the study has a nominal composition of Fe-13Cr-5Al-2Mo-0.2Si-0.05Y (wt.%). The ingot of alloy was prepared by arc-melting under an argon atmosphere using elemental ingredients with a purity above 99.9 at. %. The ingot was homogenized, hot-rolled at 1100 • C, warm-rolled at 800 • C in three steps from its initial thickness~5 mm to a final thickness~2 mm and annealed at 800 • C for 1 h. The grain size of the materials is around 50 µm. The sample was mechanically polished with silicon carbide grinding papers from grit 800# to 4000# and electropolished in a solution of 10 mL perchloric acid and 90 mL methanol at −5 • C for 15 s at 15 V. The following SEM observation and FIB fabrication were conducted on a FEI Helios NanoLab 660 dual beam system. The orientation of polished sample was characterized by using electron backscatter diffraction (EBSD). The orientation information was collected with an EBSD detector from EDAX in this dual-beam system. The OIM software was used to control the data collection process, during which a step size of 0.5 µm was adopted.
Based on the orientation mapping from EBSD, we choose the grain with specific orientation where SF of slip systems with designed interaction are maximized. On these grains, we prepared micropillars by using FIB. The acceleration voltage of Ga + beam was 30 kV. The currents for initial cut and final cut are 64 nA and 0.24 nA respectively. The height-to-diameter ratio of each pillar was 1.5-2.5. The taper angle is within 2 to 5 degrees. The in situ mechanical tests were performed by using a Hysitron PI85 PicoIndentor equipped with a 20-µm flat punch tip. The tests were displacement-controlled while the loading rate was set to reach a strain rate of 10 −3 s −1 . During in situ testing, the indenter was controlled to minimize the misalignment between the tip and the top surface of the pillars, and a minimum of three tests were performed for each type of pillar to ensure the reproducibility of interested phenomena. The in situ compression testing stops when obvious slip bands can be observed on the surface of the samples. Slip trace analysis based on self-developed Matlab program is used to identify the activated slip system in all deformed micropillars. The true stress is estimated using a full width half maximum (FWHM) approach [22,46], where the diameter in the middle of the pillar is estimated from known (1) top surface diameter, (2) taper angle, and (3) total length of the pillar. The true strain is obtained by correcting the engineering strain with the Young's modulus correction formula for a pillar [47,48].
There will be 300 combinations amongst {110}<111> and {112}<111> slip systems, but only 17 configurations of interactions are unique as considering the symmetry of crystal [27]. As depicted in Figure 1b, these dislocations interactions are correspondingly classified into four types, self-, dipolar-, junction-, and collinear-interactions. Most interactions are belonging to junction interaction where both slip plane and slip direction of two slip systems are different. Dipolar interaction is the interaction between dislocations on the same slip plane with different slip vectors, and thus only happen in {110}<111> slip systems because two slip directions are available on a slip plane {110}. Collinear interaction is the interaction between dislocations on two slip planes with same slip direction. Self-interaction refers to the interaction between dislocations on same slip system. For single-crystal micropillars, strain gradients are generally lacking because of free surface [44,53]. When a single slip system is predominately activated in a micropillar, self-interaction is to a great extend reduced, and an obvious yielding and continuous shearing with weak hardening is generally observed. Thus, maximizing the Schmid factor (SF) of one specific slip system can be used to measure the glide resistance of dislocations associated with the slip system. Meanwhile, an apparent strain hardening behavior was expected to occur when the least two slip systems could be activated in the micropillar. Correspondingly, we choose the orientation of micropillars with the following criteria: (a) maximizing the SF of one slip systems in order to assess glide resistance of dislocations in a specific slip system, and (b) maximizing the SFs of two slip systems in order to study the effect of junction interaction on strain hardening. As a comparison, micropillars with multiple activated slip systems were fabricated and tested.
For bi-crystal micropillars, GBs generally act as pinning barriers for impeding dislocation propagation. Dislocation-GB interactions are heavily dependent on the transferability or continuity of slip systems in the two grains across a GB. Geometrical compatibility factor (m') is successfully used to estimate the deformation compatibility across GBs [54][55][56][57][58], where m'=cos(φ)×cos(k), φ is the angle between the slip plane normal directions and k is the angle between the slip directions. We chose bi-crystals with m' varying from 0.44 to 0.84.

Weak Hardening Associated with One Activated Slip System
The self-interaction of dislocations refers to the interaction between dislocations belonging to the same slip system. To study the mechanical response of micropillars with one dominant slip system, we selected grains with specific orientation in a polycrystalline sample according to the SF analysis on each slip system with Euler angle measured from EBSD mapping. As shown in Figure 2a, we chosen a grain with the orientation where [5 1 5] direction is parallel to the loading direction. Under uniaxial loading, the SF of (12-1)[-111] slip system reaches the maximum value of 0.5, the SF of (0-11)[-111] slip system is the second highest and equals 0.438, and SFs of other slip systems are lower than 0.428. Therefore, the (1-1)[-111] slip system would be primarily activated. Similarly, the grain with the orientation where [20 9 2] is parallel to the loading direction and shown in Figure 2b favors [111] slip system, because this slip system has the maximum SF of 0.5, the second highest SF is 0.4683 associated with the slip system (101) , and SFs of other slip systems are lower than 0.435. The orientation of the two grains is demonstrated by the inverse pole figure in Figure 2c. Figure 2d,e show the pillars with initial diameters of 8.9 μm and 8.5 μm. Figure 2f,g show the compressed pillars where the apparent slip traces well match the slip traces on (12-1) plane and (10-1) plane, respectively. For single-crystal micropillars, strain gradients are generally lacking because of free surface [44,53]. When a single slip system is predominately activated in a micropillar, self-interaction is to a great extend reduced, and an obvious yielding and continuous shearing with weak hardening is generally observed. Thus, maximizing the Schmid factor (SF) of one specific slip system can be used to measure the glide resistance of dislocations associated with the slip system. Meanwhile, an apparent strain hardening behavior was expected to occur when the least two slip systems could be activated in the micropillar. Correspondingly, we choose the orientation of micropillars with the following criteria: (a) maximizing the SF of one slip systems in order to assess glide resistance of dislocations in a specific slip system, and (b) maximizing the SFs of two slip systems in order to study the effect of junction interaction on strain hardening. As a comparison, micropillars with multiple activated slip systems were fabricated and tested.
For bi-crystal micropillars, GBs generally act as pinning barriers for impeding dislocation propagation. Dislocation-GB interactions are heavily dependent on the transferability or continuity of slip systems in the two grains across a GB. Geometrical compatibility factor (m') is successfully used to estimate the deformation compatibility across GBs [54][55][56][57][58], where m'=cos(ϕ)×cos(k), ϕ is the angle between the slip plane normal directions and k is the angle between the slip directions. We chose bi-crystals with m' varying from 0.44 to 0.84.

Weak Hardening Associated with One Activated Slip System
The self-interaction of dislocations refers to the interaction between dislocations belonging to the same slip system. To study the mechanical response of micropillars with one dominant slip system, we selected grains with specific orientation in a polycrystalline sample according to the SF analysis on each slip system with Euler angle measured from EBSD mapping. As shown in Figure 2a, we chosen a grain with the orientation where [5 1 5] direction is parallel to the loading direction. Under uniaxial loading, the SF of (12-1)[-111] slip system reaches the maximum value of 0.5, the SF of (0-11)[-111] slip system is the second highest and equals 0.438, and SFs of other slip systems are lower than 0.428. Therefore, the (1-1)[-111] slip system would be primarily activated. Similarly, the grain with the orientation where [20 9 2] is parallel to the loading direction and shown in Figure 2b favors [111] slip system, because this slip system has the maximum SF of 0.5, the second highest SF is 0.4683 associated with the slip system (101) , and SFs of other slip systems are lower than 0.435. The orientation of the two grains is demonstrated by the inverse pole figure in Figure 2c. We thus concluded that (12-1)[-111] slip system and (10-1)[111] slip system were obviously activated in each pillar, respectively. Figure 2h shows the typical stress-strain curves. It is noted there is no apparent strain hardening behavior once continuous plastic flow occurs. Several slight stress drops correspond to shear instability due to free surface. The weak hardening effect is ascribed to the lack of dislocation pileup because the size of the pillar is too small to form dislocation pileup. Videos 1 and 2 record the in situ compression testing of the two pillars. Corresponding to the 0.2% offset yield strengths of 460 MPa and 450 MPa, the glide resistance of dislocations are estimated to be 230 We thus concluded that (12-1)[-111] slip system and (10-1)[111] slip system were obviously activated in each pillar, respectively. Figure 2h shows the typical stress-strain curves. It is noted there is no apparent strain hardening behavior once continuous plastic flow occurs. Several slight stress drops correspond to shear instability due to free surface. The weak hardening effect is ascribed to the lack of dislocation pileup because the size of the pillar is too small to form dislocation pileup. Videos 1 and 2 record the in situ compression testing of the two pillars. Corresponding to the 0.2% offset yield strengths of 460 MPa and 450 MPa, the glide resistance of dislocations are estimated to be 230 MPa and Crystals 2020, 10, 943 6 of 14 220 MPa for the two slip systems {12-1}<-111> and {10-1}<111>, respectively. The similar resistance for the two slip systems is consistent with our previous study [52]. The strain hardening rate is around 1.0 GPa for the two slip systems {12-1}<-111> and {10-1}<111> as the strain exceeds 0.015.

Intermediate Hardening Associated with Two Activated Slip Systems
Micropillars with two orientations were prepared to study the interactions between two {1-21}<111> slip systems and between two {110}<111> slip systems, respectively. When the grain is orientated along the crystallographic direction [1 48 8] Figure 3g shows the stress-strain curves, revealing apparent strain hardening with a hardening rate of~1.9 GPa for the strain exceeding 0.02. MPa and 220 MPa for the two slip systems {12-1}<-111> and {10-1}<111>, respectively. The similar resistance for the two slip systems is consistent with our previous study [52]. The strain hardening rate is around 1.0 GPa for the two slip systems {12-1}<-111> and {10-1}<111> as the strain exceeds 0.015.

Intermediate Hardening Associated with Two Activated Slip Systems
Micropillars with two orientations were prepared to study the interactions between two {1-21}<111> slip systems and between two {110}<111> slip systems, respectively. When the grain is orientated along the crystallographic direction [1 48   When the grain is orientated along the crystallographic direction [- 6 9 -5], the (01-1)<1-1-1> and (-110)<-1-11> slip systems have the largest SFs of 0.399 and 0.344, and other slip systems have the SF smaller than 0.31. Figure 4a and d show two micro-pillars with diameters of 5.9 µm and 8.9 µm. Figure 4h schematically show two sets of slip traces associated with the slip planes (0 1 -1) and (-1 1 0). Apparent slip traces are associated with dislocation motion on the two slip planes (0 1 -1) and (-1 1 0), as observed in the compressed pillars in Figure 4b,e and the magnified images in Figure 4c,f. Especially in Figure 4c, the two slip systems seem equally activated. The stress-strain curves in Figure 4g show apparent strain hardening with a hardening rate around 4.0 GPa for the strain exceeding 0.02. Thus, the strain hardening rate is ascribed to the junction formation interaction between (01-1)[1-1-1] and (-110)[-1-11] slip systems, and is greater than the case associated with the interaction between two {110}<111> slip systems where one slip system is more activated. Video 4 records the in situ compression testing of the pillar with a diameter of 5.9 µm. Corresponding to the 0.2% offset yield strength of 580 MPa in Figure 4c, the critical resistance for dislocation glide is 231 MPa for (01-1)[111] slip family, which is consistent with the results in Section 3.1.
Crystals 2020, 10, 943 7 of 14 on {121} slip planes is calculated to be 212 MPa, which is consistent with the result obtained from Section 3.1. When the grain is orientated along the crystallographic direction [- 6 9 -5], the (01-1)<1-1-1> and (-110)<-1-11> slip systems have the largest SFs of 0.399 and 0.344, and other slip systems have the SF smaller than 0.31. Figure 4a and d show two micro-pillars with diameters of 5.9 μm and 8.9 μm. Figure 4h schematically show two sets of slip traces associated with the slip planes (0 1 -1) and (-1 1 0). Apparent slip traces are associated with dislocation motion on the two slip planes (0 1 -1) and (-1 1 0), as observed in the compressed pillars in Figure 4b,e and the magnified images in Figure 4c,f. Especially in Figure 4c, the two slip systems seem equally activated. The stress-strain curves in Figure  4g show apparent strain hardening with a hardening rate around 4.0 GPa for the strain exceeding 0.02. Thus, the strain hardening rate is ascribed to the junction formation interaction between (01-1)[1-1-1] and (-110)[-1-11] slip systems, and is greater than the case associated with the interaction between two {110}<111> slip systems where one slip system is more activated. Video 4 records the in situ compression testing of the pillar with a diameter of 5.9 μm. Corresponding to the 0.2% offset yield strength of 580 MPa in Figure 4c, the critical resistance for dislocation glide is 231 MPa for (01-1)[111] slip family, which is consistent with the results in Section 3.1.

Strong Hardening Behaviors Associated with Multiple Activated Slip Systems
To reveal hardening behaviors of micropillars associated with multiple activated slip systems, we fabricated two types of micropillars with the crystallographic orientations

Strong Hardening Behaviors Associated with Multiple Activated Slip Systems
To reveal hardening behaviors of micropillars associated with multiple activated slip systems, we fabricated two types of micropillars with the crystallographic orientations  Figure 5e shows the stress strain curves. Although the 0.2% offset yield strength is approximately same about 430 MPa for the two micropillars, the strain hardening behaviors are different. The micropillar with the bigger diameter of 8.5 µm shows a high strain hardening rate varying from 20 GPa to 2.0 GPa as the strain increases from 0.01 to 0.02. A relatively stable strain hardening rate is 2.0 GPa as the strain exceeds 0.025. A homogenous deformation was observed before the strain reaches 0.02, indicating multiple slip systems were activated. Video 5 records the in situ compression testing of the pillar with a diameter of 8.5 µm. The pillar with a diameter of 5.8 µm shows a low strain hardening rate varying from 5.0 GPa to 2.0 GPa for the strain from 0.01 to 0.02. Video 6 records the in situ compression testing of the pillar with a diameter of 5.8 µm, showing homogenous deformation which implies the activation of multiple slip systems. The lower strain hardening rate is thus ascribed to the smaller diameter.  A much stronger hardening behavior was observed in Figure 6a when the micropillar is oriented along the [111]. The strain hardening rate decreases from 35 GPa to 5 GPa as the strain increase from 0.01 to 0.05. Four slip systems, (1-1-2) [1][2][3][4][5][6][7][8][9][10][11], (1-2-1) , (10-1) [1][2][3][4][5][6][7][8][9][10][11] and (1-10)  as shown in Figure 6b, have comparable SFs in the range from 0.32 to 0.35, while other slip systems have SFs less than 0.29. Corresponding to the 0.2% offset yield strength of 600 MPa, these slip systems have the glide resistance of about 213 MPa which is consistent with the results from other tests. Figure 6c shows a dog-bone shaped micro-pillar with the cross-section of 3.3 μm × 3.0 μm. Figure 6d,e shows two snapshots at a strain of 0.075 and 0.085, respectively, indicating homogeneous deformation before cracking takes place. Video 7 records the in situ tension testing of the pillar, showing

Grain Boundary Effects on Mechanical Behavior
Grain boundary (GB) strengthening mechanism is based on the observation that GBs impede dislocation movement. Since the adjacent grains differ in orientation, it requires more energy for a dislocation to change slip direction and slip plane and transfer into the adjacent grain [59,60]. The transferability or continuity of slip systems in the two grains across a GB is described by a geometrical compatibility factor (GCF), m'=cos(φ)×cos(k) [54][55][56][57][58]. The bigger the GCF is, the easier slip transmission happens. φ is the angle between the slip plane normal directions and k is the angle between the slip directions. We examined this in two bi-crystal micropillars.

Grain Boundary Effects on Mechanical Behavior
Grain boundary (GB) strengthening mechanism is based on the observation that GBs impede dislocation movement. Since the adjacent grains differ in orientation, it requires more energy for a dislocation to change slip direction and slip plane and transfer into the adjacent grain [59,60]. The transferability or continuity of slip systems in the two grains across a GB is described by a geometrical compatibility factor (GCF), m'=cos(ϕ)×cos(k) [54][55][56][57][58]. The bigger the GCF is, the easier slip transmission happens. ϕ is the angle between the slip plane normal directions and k is the angle between the slip directions. We examined this in two bi-crystal micropillars.
The bi-crystal 1 has the orientation relation:

Conclusions
In this study, we investigated the mechanical response of single crystal and bi-crystal FeCrAl alloys using in situ micropillar compression and tension testing. According to the EBSD data, we selected grains with specific orientations which favor the type and number of activated slip systems. In order to explicitly envision the influence of the orientation and microstructures on the stress strain responses of micropillars, Figure 8 shows the mechanical responses of single crystal micropillars with one activated slip system, two activated slip systems, and multiple activated slip systems and bi-crystal micropillars. Firstly, it is expected that these micropillars will show different stress strain responses, corresponding to plastic anisotropy associated with crystal plasticity. However, we obtained a very close glide resistance of about 225 MPa for slips on {110} and {112} planes when the 0.2% offset yield strength and the largest Schmid factor were used to estimate the glide resistance. This conclusion is consistent with our systematic study in single crystal micropillars [52]. Secondly, the strain hardening rates derived from these tests clearly indicated that the weakest hardening is associated with pillars with one activated slip system, the largest hardening is observed in pillars with multiple activated slip systems. With increasing the number of activated slip systems, the strain hardening rate increases. Thirdly, the critical strain for reaching a stable strain hardening rate increases with the number of activated slip systems in micropillars and pillars' diameter. Lastly, for the bi-crystal pillars, the strain hardening rate is also related to the geometrical compatibility factor, the higher the factor is, the lower the strain hardening rate and the weaker the strengthening effect are. These results can be used to develop the mechanisms-based meso/micro/macro-scale constitutive laws for FeCrAl polycrystalline aggregates in order to accelerate designing and predicting mechanical response of structural components [61,62].

Conclusions
In this study, we investigated the mechanical response of single crystal and bi-crystal FeCrAl alloys using in situ micropillar compression and tension testing. According to the EBSD data, we selected grains with specific orientations which favor the type and number of activated slip systems. In order to explicitly envision the influence of the orientation and microstructures on the stress strain responses of micropillars, Figure 8 shows the mechanical responses of single crystal micropillars with one activated slip system, two activated slip systems, and multiple activated slip systems and bicrystal micropillars. Firstly, it is expected that these micropillars will show different stress strain responses, corresponding to plastic anisotropy associated with crystal plasticity. However, we obtained a very close glide resistance of about 225 MPa for slips on {110} and {112} planes when the 0.2% offset yield strength and the largest Schmid factor were used to estimate the glide resistance. This conclusion is consistent with our systematic study in single crystal micropillars [52]. Secondly, the strain hardening rates derived from these tests clearly indicated that the weakest hardening is associated with pillars with one activated slip system, the largest hardening is observed in pillars with multiple activated slip systems. With increasing the number of activated slip systems, the strain hardening rate increases. Thirdly, the critical strain for reaching a stable strain hardening rate increases with the number of activated slip systems in micropillars and pillars' diameter. Lastly, for the bi-crystal pillars, the strain hardening rate is also related to the geometrical compatibility factor, the higher the factor is, the lower the strain hardening rate and the weaker the strengthening effect are. These results can be used to develop the mechanisms-based meso/micro/macro-scale constitutive laws for FeCrAl polycrystalline aggregates in order to accelerate designing and predicting mechanical response of structural components [61,62].