Dislocation Mediated Plasticity and Strengthening in Crack-Resistant ZnAlMg Coatings Notes

Introduction

ZnAlMg coatings, produced by hot-dip galvanizing (HDG), are commonly used for steel sheet protection in corrosive environments. However, Mg-alloyed zinc coatings have low cracking resistance during deformation. This is due to detrimental phases and incompatible plastic deformation from insufficient activated slip systems, leading to early microstructural damage and cracking.

The key is to reduce cracking by creating a microstructure with a good balance of strength and ductility. Prior research has focused on microstructure, chemical composition, phase formation, oxidation, and corrosion properties. There is a need to improve the cracking resistance of ZnAlMg coatings to enhance their formability and durability.

Compared to galvanized pure zinc (GI) coatings, ZnAlMg coatings have a more complex deformation behavior because of their multiphase and anisotropic microstructure. Early-stage cracks significantly alter the local stress/strain state, making it challenging to determine deformation mechanisms at the grain level.

This study examines the plastic deformation performance of a tailored binary eutectic (BE)-free ZnAlMg coating, comparing it to a BE-containing ZnAlMg coating. The goal is to eliminate damage/crack incidents in the binary eutectics. The study uses correlative in-situ SEM tensile testing, orientation image microscopy (OIM), scanning transmission electron microscopy (STEM), and in-situ micro-digital image correlation (µ-DIC) tests to reveal deformation mechanisms, microstructural scale plasticity, strain/slip transfer, and strengthening mechanisms. The research demonstrates how microstructure control can hinder cracking and improve the overall plasticity of ZnAlMg coatings on steel substrates.

Materials and methods

Two types of ZnAlMg coatings were produced using a hot-dip annealing simulator (HDS) on interstitial-free (IF) steel substrates: a reference ZnAlMg coating (1.7-2 wt.% Al, 1.7-2 wt.% Mg) containing binary eutectic (ZnMgAl-ref) and a BE-free ZnAlMg coating (2.9 wt.% Al, 1.9 wt.% Mg). The mean thicknesses of the coatings were measured as 13 µm and 15 µm, respectively.

Tensile test samples were mechanically polished using 1 µm diamond and water-free lubrication suspension. The surface quality was improved using a JEOL IB-19520CCP ion polisher for high-quality EBSD maps. Surface microstructures were examined using a scanning electron microscope (SEM, Philips XL30-FEG ESEM).

In-situ tensile tests were performed using a Kammrath & Weiss tensile module in a Tescan LYRA SEM–FIB dual-beam microscope to assess real-time cracking tendency. Yttria-stabilized zirconia nano-particles were sprayed on the sample surfaces as nanometer-sized markers to achieve appropriate image contrast for precise DIC study. Post-processing of the DIC data was conducted using GOM Correlate software.

OIM analyses were carried out before straining and during in-situ tests using a Philips XL30 ESEM equipped with an EBSD detector. High-resolution EBSD patterns were acquired using an acceleration voltage of 30 kV and a scanning step size of 150 nm. EDAX-TSL OIMTM Analysis 8 software was used to analyze the EBSD data. Taylor factor maps were obtained by inputting Zn slip systems (basal, prismatic, and pyramidal) with estimated CRSS ratios and the deformation gradient into the OIM Analysis software.

STEM characterizations were conducted using a Thermo Fisher Scientific Themis ZTM scanning transmission electron microscope (S/TEM) operating at 300 kV. A two-beam condition approach and a collection angle of 5-10 mrad were used to capture dislocations in the bright field (BF) STEM mode. A 100 nm thick TEM lamella was extracted from selected grains in the BE-free ZnAlMg coating after a true strain of \varepsilon = 0.1 using focused ion beam (FIB) in an FEI Helios G4 CXTM dual beam microscope.

Results and discussion

Microstructure control

Fig. 1a shows the microstructure of the ZnMgAl-ref coating, which includes three components: primary zinc, binary eutectic, and ternary eutectic. The binary eutectic, shown in Fig. 1b, consists of coarse lamellae of zinc and MgZn2 with a dendrite structure. EDS analysis of the binary eutectic was reported in a previous study (Ahmadi et al., 2020), identifying it as a detrimental constituent for plastic deformation and a site for crack initiation.

The microstructure of the BE-free coating, shown in Fig. 1c, consists of primary zinc and ternary eutectic. The refined structure of the ternary eutectic, magnified in Fig. 1d, incorporates fine grains of zinc (Zn), aluminum (Al), and ZnxMgy intermetallic. The ternary eutectic component is examined in detail in Section 3.5.1. Image analysis quantified the area fraction of the constituents in the BE-free ZnAlMg coating, finding less than 1% binary eutectic (Fig. 2b), compared to almost 20% in the ZnMgAl-ref coating (Fig. 2a).

Deformation and cracking behavior

Interrupted in-situ SEM tensile tests were conducted to examine the deformation/cracking behavior of the two coatings. Fig. 3 represents the true stress-strain curves for the two coatings on the same interstitial-free (IF) steel substrates.

SEM micrographs captured at different strain values for the reference coating and the BE-free coating are shown in Fig. 4 and Fig. 5, respectively. The true global strain values are shown in the upper right corner of the images. Early microcracks nucleate in the binary eutectic of the ZnMgAl-ref coating at a strain value as low as 0.05 (Fig. 4b). The number and size of the cracks increase significantly with increasing global strain. The cracking mechanism in ZnAlMg coatings with binary eutectic was described in an earlier work (Ahmadi et al., 2020).

The number and density of cracks are significantly reduced in the BE-free coating. Almost no cracks with large openings are observed in the BE-free coating, even at high strain values (Fig. 5). The presence of tiny micro-cracks (<5 µm in length) is attributed to the retained binary eutectic (less than 1%). Eliminating the detrimental binary eutectic improves the ductility of the coating substantially due to very low crack density and small crack openings. Primary zinc and ternary eutectic exhibit higher micro-ductility (Ahmadi et al., 2020), delivering an enhanced collective response in terms of plastic deformation and crack resistance compared to the reference ZnAlMg coating containing binary eutectic.

Another contributing factor is the geometrical parameter. The finer fiber-like ternary eutectic, compared to the coarse lamellar-shape binary eutectic, can accommodate the applied strain and results in additional strengthening. Detailed EBSD and DIC analyses are conducted on the BE-free coating to further analyze the plasticity mechanism and scrutinize the underlying phenomena of the observed ductility enhancement.

Identification of the deformation mechanisms

Understanding the role of crystallographic orientation can elucidate the mechanical behavior of a hexagonal close-packed (HCP) polycrystalline metal. The EBSD results of a selected area in the BE-free coating prior to deformation are illustrated in Fig. 6. Specifically, high-quality [001] inverse pole figure (IPF) plus image quality (IQ) map, IQ plus crystallographic plane traces of the selected region, and Zn slip systems are depicted in Figs. 6a-c, respectively.

The crystallographic orientation of the ternary eutectic is normally aligned with that of the adjacent primary zinc grain, but this is not true for the entire microstructure (Fig. 6a). The coating exhibits a relatively random texture and several twins. The pole figures for the selected region in Fig. 6 and for another area of the coating demonstrating the random textures are given in the supplementary data, Fig. S2. Based on the EBSD result, all possible slip plane traces of the HCP zinc grains are defined and categorized with colored lines (basal, prismatic, 1st order pyramidal, and 2nd order pyramidal) overlaid on the corresponding grains in Fig. 6b. The plane traces are considered in order to identify the activation of the possible slip systems after imposing plastic deformation.

Identification of the activated slip systems as a function of the orientation of primary zinc grains can shed light on understanding the plasticity mechanism of the BE-free coating. The BE-free coating was subjected to a uniaxial tensile test, and the SEM micrographs of the selected region (where EBSD was conducted) at a global strain \varepsilon = 0.1 are given in Fig. 7. By comparing the EBSD results and SEM images, the slip traces generated within each grain were detected. The plane traces associated with each grain (given in Fig. 6b) and recognizing the slip traces revealed after deformation allows to capture the activated slip systems.

For an individual grain, the slip trace line after deformation (see Fig. 7) is compared to the reference plane trace families (see Fig. 6b) obtained by orientation data. For instance, if the slip trace line fits on the reference trace of the basal plane, the basal slip system has been activated. This procedure is repeated for all the grains in the selected area of the BE-free coating, and the total activated slip systems are designated with colored lines in Fig. 7a. The notations in Fig. 7a correspond to the following deformation mechanisms: white arrows: twinning, red lines: basal, blue lines: prismatic, yellow lines: 1st order pyramidal, and green lines: 2nd order pyramidal slip systems. The quantity (number) of the activated deformation mechanisms was calculated, and the results are provided in Fig. 7d. Note that the patterns generated on the grains due to ion polishing should not be confused with the slip traces. Also notice that the grains exhibiting no twinning or slip traces are left blank. For instance, grain no. 4 (G4) has not generated any slip or deformation trace, whereas grain no. 3 (G3) clearly exhibits slip traces of the 2nd order pyramidal system as depicted in Fig. 7c.

As Fig. 7d shows, five types of deformation systems are activated within the coating microstructure. Based on the von Mises criterion, in order to achieve a compatible plastic deformation in a polycrystal, at least five independent deformation/slip systems need to be activated. Therefore, by fulfilling this criterion, the coating exhibits compatible plastic deformation. Twinning is detected as the most abundant deformation event within the deformed BE-free coating. The most important outcome is the activation of 2nd order and 1st order pyramidal

Since the primary zinc grains and ternary eutectics possess higher micro-ductility (Ahmadi et al., 2020) compared to the binary eutectics, an enhanced homogenous deformation is accomplished in the BE-free coating. It is essential to evaluate the collective response of the microstructure after the deformation using an in-depth EBSD analysis.

GND and Taylor factor quantifications

The EBSD technique can assist in estimating the dislocation density distribution within deformed polycrystalline metals. The EBSD analyses were performed on the same selected region given in Fig. 6 after applying a true global strain \varepsilon = 0.1. [001] IPF plus image quality, geometrically necessary dislocation (GND) density map, Taylor factor map (associated with all the slip systems), SEM image, and GND distributions are given in Figs. 8a-e, respectively.

GND density has been calculated based on local misorientations considering both screw and edge dislocation types on all the available slip systems of HCP zinc. As can be observed in Fig. 8b, some of the grains exhibit high GND density (revealed by yellow and red colors), while a few of the grains have low GND density (revealed in blue). This is mostly attributed to the crystallographic orientation of the grains with respect to the applied load direction. The Taylor factor (M) is a useful parameter for determining the extent of microplastic deformation within the grains in a polycrystalline metal.

The Taylor factor (M) is described as:

M = \sum \Delta\gamma \Delta\varepsilon (1)

where \Delta\gamma is the summation of the slip shears on all the available slip systems and \Delta\varepsilon is the applied microscopic strain increment. The Taylor factor (M) is a strictly geometrical parameter that takes into account the collective grains’ orientation rather than a single grain response. Accordingly, some specific grains are labeled for further analysis. As can be perceived in Fig. 8c and Fig. 8e, grains (G1 and G4) with a higher Taylor factor (close to 2.4) deliver lower in-grain GND density, while grains (G2 and G3) with a lower Taylor factor (close to 2) deliver a higher extent of GND density. The in-grain GND density is found almost 4-5 times higher for G2 and G3 compared to G1 and G4. These results illuminate the pronounced inconsistent behavior in the deformation mechanisms discussed in Section 3.3. In particular, G1 with an orientation close to [1010] exhibits a higher Taylor factor but lacks the activation of the slip systems. Consequently, no slip trace was detected for G1 as shown in Fig. 7b.

STEM characterization

EDS elemental mapping

For further understanding, a TEM lamella containing G3 and G4 (see Figs. 9a-c) was sliced using the FIB method. G3 and G4 grains were selected because they exhibit a good contrast in terms of Taylor factor and crystallographic orientation. Figs. 9d-l demonstrate the STEM energy dispersive x-ray spectroscopy (EDS) results on the designated region in Fig. 9c encompassing the ternary eutectic and G3.

As can be noticed in the overlaid elemental image provided in Fig. 9h, the ternary eutectic is composed of three elements: Zn, Al, and Mg. By attaining the atomic percentage along the indicated arrow given in Fig. 9i, the distribution of the elements in the selected region is found and illustrated in Fig. 9l. Based on the atomic fractions, the observed fibrous nanostructure in the ternary eutectic is therefore composed of Mg2Zn11 and Al in the matrix of zinc. A remarkable observation is the presence of nano-sized Al precipitates within the primary zinc grains (here G3) as shown and magnified in Fig. 9j. As the selected area diffraction pattern (SAED) given in Fig. 9k confirms, the FCC Al nano-sized precipitates are dispersed in the primary zinc matrix. Due to the higher Al content in the BE-free coating, Al is supersaturated in the liquid zinc resulting in nano precipitation in the final coating.

Dislocation density determination

Although the EBSD technique provides an indicative and statistical representation of dislocation density distribution via GND calculations, there still exist some inaccuracies in this method when it comes particularly to dislocations in complex microstructures. Scanning transmission electron microscopy (STEM) has been utilized to explore the dislocation characteristics in polycrystalline materials. STEM delivers the possibility to capture the dislocations in a few microns field of view. In addition, nano-scale features of the microstructure can also be characterized by means of STEM technique. Fig. 10 demonstrates the STEM characterization results on the thin foil specimen. The imaging locations on G3 and G4 are indicated in Fig. 10a. Fig. 10b shows the [001] IPF combined with image quality map attained by conducting transmission electron backscatter diffraction (t-EBSD) on the same foil sample. Figs. 10c-d display the bright field (BF) STEM image of dislocations within G3 and G4, respectively. The lattice orientation of each grain acquired by t-EBSD are given in the upper right corner of the BF-STEM images. The zone axis plane of each imaging set associated with G3 and G4 are highlighted on the unit cells. Corresponding high-angle annular dark-field (HAADF) images of the same regions are presented in Figs. 10 e-f. Fast Fourier transform (FFT) images of the grains are given in the bottom right of the HAADF micrographs showing the zone axes of [0002] and [0110] for imaging of G3 and G4 respectively.

Dislocations in the G3 and G4 primary zinc grains can be observed with good contrast in the BF-STEM images in Figs. 10c-d using two beam condition. However, G3 and G4 exhibit quite different dislocation patterns in terms of spatial density, size and structure. The dislocations are not clearly visible in the HAADF mode imaging as Figs. 10e-f demonstrate. As Fig. 10c and Fig. 10d show, abundant and quite dense dislocations are revealed in G3, whereas the dislocations in G4 are sparse and mostly isolated with less density. In both grains, dislocations have interacted with the existing Al-rich precipitates. In the case of G3, several dense dislocation tangles as well as the dislocation pile-ups (arrays) are formed. These results are in good agreement with the previous findings on G3 and G4 given in Section 3.4. In particular, G3 exhibits one of the favorable orientations for dislocation slip (c-axis of HCP unit cell is perpendicular to the loading direction) and thus hinders cracking (Ahmadi et al., 2020). G3 possesses a Taylor factor M = 2.1, leaving clear slip traces behind after a true strain of 0.1 (see Fig. 7c), whereas G4 exhibits M = 2.4 without generating slip traces. It is positively confirmed by BF-STEM imaging that the orientation of G3 facilitates dislocation motion and generates a high dislocation density within G3. G4 on the other hand, exhibiting an HCP c-axis close to loading direction, does not provide abundant slip systems and therefore leads to a much lower dislocation density within the grain.

In order to image the dislocations in G3 and G4, two beam condition in STEM imaging was performed by tilting the lamella. To assure that the observed contrasts are attributed to the dislocations, invisibility criterion g.b (g and b are diffraction and Burgers vectors) was applied on the studied lamella. Fig. 11a presents the in-zone axis [0002] imaging of a selected area in G3 showing dark dislocation contrasts in BF mode when g.b /= 0. These contrasts nearly disappear by tilting the sample to around 30◦ as depicted in Fig. 11b. This indicates that, the Burgers vectors of the dislocation are in line with imaging direction (i.e. [1123]) providing no diffraction contrast and thus dislocations are invisible at g.b = 0. Therefore, considering the Zn HCP unit cell, this orientation configuration corresponds to pyramidal dislocations (b = 1/3[1123]) which are dominantly present in Fig. 11a. The bright regions of the HAADF in [0002] zone axis imaging seem to also disappear after tilting the foil as shown in Fig. 11d.

In a quantitative manner, the intersection method can be used in order to evaluate the dislocation density using TEM (\rho_{TEM}) as follows:

\rho{TEM} = \frac{N}{Ld t} (2)

where N is the number of intersections of arbitrarily drawn lines with the dislocations in a micrograph, \Ld is the total length of these lines, and t represents the TEM foil thickness. By applying this method on the STEM images taken from the specimen, the average \rho{TEM} values are found as 112 \times 10^{12} m^{-2} and 26 \times 10^{12} m^{-2} for G3 and G4, respectively. These results affirm that the dislocation density of G3 is nearly four times greater than that of G4, signifying much higher activated dislocation slip in G3. To compare the quantitative dislocation density values obtained by STEM characterization and GND densities achieved by EBSD, the latter values were measured for G3 and G4 as 160 \times 10^{12} m^{-2} and 38 \times 10^{12} m^{-2} on average from the EBSD results given in Fig. 8. The dislocation densities found using EBSD are slightly higher than those of STEM, yet their ratio is quite comparable to those measured by STEM. These findings might attribute to the fact that GND analysis is measured based on local misorientations differences. Hence, any feature or artifact in the surface or within the microstructure may alter the misorientation distributions. Given that the EBSD data are attained by backscattered electrons reflected from the vicinity of the sample surface, and bearing in mind the presence of the precipitates within the Zn grains, local misorientations may be overestimated, which leads to higher GND density values. Moreover, it is likely that the total dislocations are not fully captured during STEM characterizations, for instance due to the foil thinning stage as demonstrated recently.

Strengthening mechanisms

Quantifying the plasticity and strengthening mechanisms of the coating materials using experimental tests is usually more challenging compared to bulk materials. Since the hot-dip coatings are produced on a steel substrate, the mechanical properties attained by the tensile test are mainly governed by the much thicker steel substrate. Here, by employing all (quantitative) analyses using SEM, EBSD, and STEM, the strengthening mechanisms active in the ZnAlMg coatings can be unraveled. Considering additive strengthening, the contribution of each strengthening mechanism in the flow stress (\sigma_{\varepsilon}) can be expressed as follows:

\sigma{\varepsilon} = \sigma0 + \Delta\sigma{GB} + \Delta\sigma{dis} + \Delta\sigma_{pr} (3)

where \sigma0, \\Delta\sigma{GB}, \Delta\sigma{dis}, and \Delta\sigma{pr} are friction stress, grain boundary strengthening, dislocation strengthening, and precipitation hardening. \Delta\sigma_{GB} can be described as the classical Hall-Petch model for the dominant zinc phase as follows:

\Delta\sigma_{GB} = K d^{-1/2} (4)

where K is a constant and found to be 8.5 MPa mm1/2 for Zn. d represents the grain size, which is measured by the EBSD result as 13 µm on average for the Zn grains (including both primary Zn and ternary eutectic zinc constituent) in the investigated area shown in Fig. 8. Consequently, the contribution of grain boundary strengthening is found to be 74.5 MPa. \Delta\sigma_{dis} can be achieved using Taylor model:

\Delta\sigma_{dis} = \alpha M G b \rho^{1/2} (5)

where \alpha is a constant and is reported normally as 0.2, M is the Taylor factor (average value of M = 2.32), G represents the shear modulus equals to 40 GPa for Zn. The magnitude of Burgers vector is denoted by b that should be calculated based on the corresponding activated dislocation slip set. Based on the Thomson tetrahedron bi-pyramid, b for perfect dislocations of basal, prismatic and pyramidal slip equals to a, c and \sqrt{a^2 + c^2}, respectively, where a and c are the lattice parameters of HCP Zn found to be 0.267 nm and 0.495 nm (c/a = 1.856), respectively, using high-resolution (HR) STEM imaging. Thus, the magnitude of Burgers vector for the studied region accounts to 0.52 nm on average. denotes the dislocation density of a polycrystalline material. The average dislocation density can be estimated by EBSD results. The actual dislocation density is modified as \rho{TEM} \cong 0.7 \rho{EBSD} based on the results of this study. Subsequently, \rho = 81 \times 10^{12} m^{-2} was attained and used in the Eq. 5. The contribution of dislocation forest strengthening is therefore revealed as \Delta\sigma{dis} = 86.8 MPa. Owing to the dispersion of nano-sized Al precipitates in the primary Zn grains, the precipitation hardening (\Delta\sigma{pr}) driven by dislocation-precipitate interactions can be quantified next. The dislocations are dominantly bowed by the precipitates. Therefore the Orowan mechanism can be employed as follows:

\Delta\sigma{pr} = \frac{M G b}{2 \pi \bar{\lambda} \sqrt{1 - \upsilon}} ln \frac{dp}{r_0} (6)

where \lambda is the effective inter-precipitate spacing which is measured as 340 nm by using the STEM micrographs. Poisson’s ratio \upsilon is 0.25 for Zn. dp is the mean precipitate diameter accounts to 72 nm and r0 is the dislocation core radius assumed to be equal to the magnitude of Burgers vector. By inserting all the known parameters into Eq. 6, \Delta\sigma{pr} is found to be 127.8 MPa. Hence, by knowing all the strengthening contributions required for the Eq. 3 and when \sigma0 = 23 MPa for Zn, the flow stress \\sigma_{\varepsilon} is then calculated as 312.1 MPa. The results reveal that the BE-free ZnAlMg coating is substantially strengthened by precipitation hardening of Al nano-sized precipitates with a dominant contribution of 41%, followed by 28% and 24% contributions of dislocation and grain boundary strengthening mechanisms.

The global stress obtained by tensile test on BE-free ZnAlMg coated steel at \varepsilon = 0.1 in Fig. 3 is found to be 302 MPa. The coating flow stress found by additive strengthening mechanism is quite close to the overall stress of the coating and the substrate. This can signify an important insight that, the plasticity of the coating is comparable to that of the steel substrate, which means that the coating and substrate would deform homogeneously. This can further avoid possible extreme shear deformation at the interface of the coating-steel substrate and hinders localization of stress/strain and adverse micro-cracking.

Although the zinc component of the ternary eutectics has been considered in the Hall-Petch model, it is important to notice that the ternary eutectic can contribute more to the total strengthening of the coating. It exhibits a very fine fiber-like structure (in contrast to the coarse platelets in the binary eutectics) that by itself is essentially influential on the observed strengthening of the coating. In our previous study (Ahmadi et al., 2020) by extensive nanoindentation tests, it was found that the ternary eutectic possesses a higher yield strength (i.e. 310 MPa) average compared to that of primary Zn grains (i.e. 98 MPa) owing to its hard intermetallic phase component. Therefore, the ternary eutectic can be highly stressed but less strained during the deformation. It is thus very probable that the ternary eutectic further gives rise to the overall strength of the coating due to its fine morphology and high hardness. Nevertheless, considering the complex structure of the ternary eutectic (i.e. Zn, Al, and Mg2Zn11 grains), an accurate quantitative determination of such contribution may require separate experimental or computational studies to realize a more composite-type strengthening/plasticity model. It is interesting to employ a self-consistent numerical modeling in addition to the experimental findings on the plasticity of such multiphase HCP alloys.

Grain boundary slip transfer analysis

In addition to in-grain responses, grain boundary characteristics can elaborate further on the plasticity of a polycrystalline material. Theoretically, grain boundary characteristics can be generally categorized into two different cases as follows:

• The impenetrable boundary: the boundary that resists against slip transfer and does not allow dislocation transmission, leading to dislocation pileup and local stress/strain concentration at the boundary.
• The transparent boundary: the boundary that facilitates the fully transmission of the dislocations on a slip system between two adjacent grains.

Identifying the implication of the interface features within the coating microstructure can further illuminate the corresponding ductility behavior. Luster and Morris have addressed the slip transfer along the grain boundaries and defined a quantitative/geometrical parameter as following:

m' = cos\kappa \cdot cos\psi (7)

where m' is the slip transfer parameter, \kappa is the angle between slip directions, and \\psi is the angle between plane normals of the two neighboring grains. m' = 1 means complete slip transfer, and the grain boundary is fully transparent to dislocation motion. If m' approaches zero, the grain boundary tends toward an impenetrable boundary for dislocation motion. Therefore, the closer the m' value to 1 (mostly > 0.8), the easier the slip transfer will occur. By implementing the EBSD data in a modified Matlab code for HCP zinc crystals, grain boundary slip transfer parameters were calculated for the area indicated in Fig. 8a at \varepsilon = 0.1. The results of m' values for basal, prismatic, 1st order pyramidal, and 2nd order pyramidal slip systems are given in Fig. 12a-d, respectively.

As can be observed in Fig. 12a, the grain boundaries slip transfer for basal slip systems is quite low, exhibiting the average value of m' = 0.31. Moreover, as Fig. 12b displays, in the case of prismatic slip transfer, the boundaries also show a low average value (m' = 0.52). On the other hand, for the sets of 1st order and 2nd order pyramidal slip systems, grain boundaries deliver pretty high m'-values (m' =0.91 and m' =0.87 in average, respectively), signifying transparent grain boundary behavior. These findings imply that the ductility enhancement of the binary eutectic-free coating is promoted by the easy slip transfer through grain boundaries mostly govern by 1st and 2nd order pyramidal slip transfer mechanisms. Comparison of m'-values associated with G1 and G2 provided in Fig. 12 offers additional insights regarding the interplay between crystallographic orientation, GND density, and grain boundary slip transfer. As previously unveiled in Fig. 8, G1 exhibits a high Taylor factor and subsequently possesses low in-grain GND density. The m' values of G1 grain boundary are measured as 0.18, 0.38, 0.73, 0.65 for basal, prismatic, 1st order, and 2nd order pyramidal systems, respectively (m' =0.48 in average). The low m' values of the G1 grain boundary indicate that it is impenetrable. As a result, the dislocation motions are obstructed at the interphase of G1, leading to a low GND density within this grain (see Fig. 8e). In contrast, for the case of the G2 boundary, the m'-values are measured as 0.5, 0.72, 0.97, 0.96 for basal, prismatic, 1st order, and 2nd order pyramidal systems, respectively (m' =0.8 in average). The higher values of m' for the G2 grain boundary, specifically those of non-basal systems, facilitate slip transfer through this grain leading to high in-grain GND density. It should be mentioned that only the dominant Zn phase of the ternary eutectic is considered for these analyses.

Local deformation mapping and strain transfer by DIC/EBSD

Full-field strain mapping via DIC accompanied by EBSD analysis can cast light on the deformation state and accurate determination of the local strain distribution at the individual grain level. In particular, the interrelationship between crystallographic orientation and strain accumulation within the coating is assessed next. To achieve this, EBSD analysis was performed on a selected region before the tensile test (see Fig. 13a), followed by the decoration of the same region with zirconia nanoparticles for µ-DIC as illustrated in Fig. 13c. The Taylor factor map of the selected region is also calculated and provided in Fig. 13b. The selected area of the coating subjected to in-situ tensile test was tracked accordingly, and the test was interrupted at the global strain values of 0.01, 0.06, and 0.1. By DIC analysis, the local strain distributions on the selected area at the mentioned global strain values are demonstrated in Figs. 13d-f, respectively.

As the results in Figs. 13d-f indicate, the measured value of actual (local) strain within the coating is quite comparable to the global strain. Although the microstructure exhibits strain distribution contrast, a compatible deformation takes place among the phases. In particular, the primary zinc grains carry the majority of the applied strain within the coating. This pronounced observation is attributed to the higher micro-ductility of the primary zinc grains in comparison with the ternary eutectic. In contrast to the reference ZnAlMg coating containing binary eutectic, the BE-free coating accommodates the applied strain without early severe localization and cracking (Ahmadi et al., 2020). From another perspective, not all the primary zinc grains have accommodated the same strain values. For instance, G1 with a relatively low Taylor factor has accommodated relatively higher strain during deformation (revealed in red in Figs. 13d-f), whereas G2 exhibiting a high Taylor factor has not contributed to the total strain accommodation (revealed in blue in Figs. 13d-f). Therefore, the orientation of the primary zinc grains determines the extent of plasticity and obviously the tendency to carry the local strain. Another significant observation in the DIC/EBSD results is the exchange of strain in some adjacent primary zinc and/or ternary eutectics. In particular, in some specific regions of the microstructure, strain is transferred toward the neighboring grains. Having discussed the ability of various grain boundaries to facilitate slip transmission, it is possible to apply the approach to analyze the strain transfer at the grain level. Two different areas designated in Fig. 13f are selected for assessing the grain/phase boundary characteristic. These two areas are further magnified and shown in Fig. 14 accompanied by their corresponding IPF map. The grain boundary slip transfer parameter (m') of the indicated areas are calculated and given in Table 1. It should be noted that only the zinc phase (the dominant constituent) of the ternary eutectic is considered in these calculations.

As can be observed in Fig. 14a, a high strain accumulation exists along GB1. The grain boundary slip transfer results in Table 1 imply that GB1 exhibits very high m' values (quite close to 1) associated with all the available slip systems. Hence, this grain boundary is able to transmit the incoming dislocations leading to easy slip and strain transfer. On the contrary in Fig. 14b, the measured strain in the vicinity of the grain boundary (GB2) is found quite low. Considering the results of GB2 in Table 1, one can perceive that the boundary is almost impenetrable by delivering very low m' values for all the available slip systems. Therefore, the strain is trapped within the grain, and almost no significant strain transfer has occurred along the boundary.

In summary, the findings of this work deliver insightful approaches on unraveling the mechanisms of plastic deformation and crack resistance in zinc alloy coatings. Proper microstructure control has been shown to induce dislocation-driven plasticity and strengthening and consequently reduce undesirable crack nucleation and propagation significantly.

Conclusions

A comprehensive analysis of the crack-resistance mechanism of ZnAlMg coatings has been carried out in the present study. We have revealed the dislocation and grain boundary mediated plasticity/strengthening mechanisms utilizing the combination of correlative electron microscopy and in-situ mechanical testing techniques. The most important findings of the present work can be derived as follows:

1. By eliminating the detrimental binary eutectic, the ductility and formability of ZnAlMg coatings can be significantly improved.
2. Slip trace analysis using correlative SEM-EBSD indicates the activation of five independent slip/twinning systems leading to compatible deformation within the BE-free ZnAlMg coating. Twining and pyramidal slipping are revealed as the dominant deformation mechanisms of the BE-free ZnAlMg coating.
3. Non-basal activated slip systems including 2nd order pyramidal slip promote high ductility and compatible deformation in the BE-free coating. Slip/strain transfer across grain boundaries is mostly governed by pyramidal slip transfer.
4. Via the quantitative dislocation density determination using EBSD and STEM techniques, it has been unveiled that the grains with lower Taylor factor are deformed more easily by slip mechanisms generating higher dislocation densities.
5. Strengthening mechanisms in the BE-free ZnAlMg coating are