Zehao Qin

Nan Kang
email: nan.kang@nwpu.edu.cn

Mohamed El Mansori

Zihong Wang

Haoxiang Wang

Xin Lin
email: xlin@nwpu.edu.cn

Jing Chen

Weidong Huang

Anisotropic high cycle fatigue property of Sc and Zr-modified Al-Mg alloy fabricated by laser powder bed fusion

Keywords: Al-Mg-Sc-Zr alloy, Selective laser melting, High cycle fatigue, Anisotropy

Introduction

Laser additive manufacturing (LAM) is a series of technologies with one basic principle for fabrication of complex high-performance components by adding a material layer by layer. Based on the feeding system [START_REF] Liu | Additive manufacturing of structural materials[END_REF][START_REF] Schmidt | Laser based additive manufacturing in industry and academia[END_REF], LAM can be divided into two major categories: (i) laser directed energy deposition (LDED), in which synchronous powder serves as the feeding system; (ii) laser powder bed fusion (LPBF), which based on a powder bed. These manufacturing techniques can realize the 1:1 transformation of a digital model to solid parts through the fixed-point interaction of the laser-induced heat source and powder depending on the digital path objected by a computer [START_REF] Liu | Additive manufacturing of structural materials[END_REF][START_REF] Herzog | Additive manufacturing of metals[END_REF][START_REF] Frazier | Metal additive manufacturing: A review[END_REF][START_REF] Olakanmi | A review on selective laser sintering/melting (SLS/SLM) of aluminium alloy powders: Processing, microstructure, and properties[END_REF]. In addition, the combination of laser-induced heat flux and relatively high travel speed can induce localized transient temperature responses and extremely high temperature gradient (~10 3 -10 7 K/m) in the melt pool, which provides LAM-fabricated parts with nonequilibrium solidification microstructures and excellent mechanical properties [START_REF] Herzog | Additive manufacturing of metals[END_REF][START_REF] Lewandowski | Metal Additive Manufacturing: A Review of Mechanical Properties[END_REF][START_REF] Tan | Inoculation treatment of an additively manufactured 2024 aluminium alloy with titanium nanoparticles[END_REF][START_REF] Xue | Heat-affected coarsening of β grain in titanium alloy during laser directed energy deposition[END_REF].

However, conventional high-strength aluminum alloys, such as 2xxx (Al-Cu), 6xxx (Al-Mg-Si), and 7xxx (Al-Zn-Mg-Cu), have wide freezing temperature intervals and thus are ill-suited to accommodate the rapid solidification characteristics of the LAM technology, wherein high hot-tearing susceptibilities commonly exist and are difficult to eliminate [START_REF] Tan | Inoculation treatment of an additively manufactured 2024 aluminium alloy with titanium nanoparticles[END_REF][START_REF] Bi | Microstructure and mechanical properties of a novel Sc and Zr modified 7075 aluminum alloy prepared by selective laser melting[END_REF][START_REF] Mehta | Additive manufacturing and mechanical properties of the dense and crack free Zr-modified aluminum alloy 6061 fabricated by the laser-powder bed fusion[END_REF][START_REF] Zhang | Effect of Zirconium addition on crack, microstructure and mechanical behavior of selective laser melted Al-Cu-Mg alloy[END_REF][START_REF] Xu | Microstructure, metallurgical defects and hardness of Al-Cu-Mg-Li-Zr alloy additively manufactured by selective laser melting[END_REF]. As a result, the majority of previous studies on LAM-fabricated Al alloys are based on eutectic or near-eutectic Al-Si casting alloys.

Although they have good hot-cracking resistances, their weak mechanical properties restrict their further industrial application of structural relevance [START_REF] Lewandowski | Metal Additive Manufacturing: A Review of Mechanical Properties[END_REF][START_REF] Yang | Porosity formation mechanisms and fatigue response in Al-Si-Mg alloys made by selective laser melting[END_REF][START_REF] Bonneric | Effect of hot isostatic pressing on the critical defect size distribution in AlSi7Mg0.6 alloy obtained by selective laser melting[END_REF][START_REF] Martin | 3D printing of high-strength aluminium alloys[END_REF][START_REF] Beretta | A comparison of fatigue strength sensitivity to defects for materials manufactured by AM or traditional processes[END_REF]. Hence, the development of high-strength aluminum alloys specifically tailored for LAM attracts increasing attention [START_REF] Martin | 3D printing of high-strength aluminium alloys[END_REF][START_REF] Wang | Strength-ductility synergy of selective laser melted Al-Mg-Sc-Zr alloy with a heterogeneous grain structure[END_REF][START_REF] Li | Developing a high-strength Al-Mg-Si-Sc-Zr alloy for selective laser melting: Crack-inhibiting and multiple strengthening mechanisms[END_REF][START_REF] Qi | A high strength Al-Li alloy produced by laser powder bed fusion: Densification, microstructure, and mechanical properties[END_REF][START_REF] Bayoumy | Intensive processing optimization for achieving strong and ductile Al-Mn-Mg-Sc-Zr alloy produced by selective laser melting[END_REF][START_REF] Jia | Selective laser melting of a high strength Al[sbnd]Mn[sbnd]Sc alloy: Alloy design and strengthening mechanisms[END_REF].

Recently, the addition of Sc/Zr elements has been demonstrated as a feasible modification method for LAM-fabricated Al alloys [START_REF] Bi | Microstructure and mechanical properties of a novel Sc and Zr modified 7075 aluminum alloy prepared by selective laser melting[END_REF][START_REF] Mehta | Additive manufacturing and mechanical properties of the dense and crack free Zr-modified aluminum alloy 6061 fabricated by the laser-powder bed fusion[END_REF][START_REF] Zhang | Effect of Zirconium addition on crack, microstructure and mechanical behavior of selective laser melted Al-Cu-Mg alloy[END_REF][START_REF] Li | Developing a high-strength Al-Mg-Si-Sc-Zr alloy for selective laser melting: Crack-inhibiting and multiple strengthening mechanisms[END_REF][START_REF] Jia | Selective laser melting of a high strength Al[sbnd]Mn[sbnd]Sc alloy: Alloy design and strengthening mechanisms[END_REF]. The main modification roles of Sc/Zr can be explained as follows: (i) The coherent Al3(Sc/Zr) precipitates formed during solidification can provide in-situ heterogeneous nucleation sites for α-Al crystallization due to the low lattice misfit with the matrix, forming finer equiaxed grains rather than coarsen columnar grains with epitaxial growth characteristics. The formation of such refined equiaxed grains (EGs) not only solves the problem of thermal cracking by eliminating long intergranular liquid channels between long columnar grains (CGs), but also provides isotropic and improved static mechanical properties; (ii) These Sc/Zr-modified alloys can be further strengthened and promote thermal stability by precipitation of secondary Al3(Sc/Zr) particles through direct aging [START_REF] Croteau | Microstructure and mechanical properties of Al-Mg-Zr alloys processed by selective laser melting[END_REF]; (iii) The unique heterogeneous microstructure, composed of an EG band and CG domain within one molten pool, is a common feature of these alloys and exhibits a superior combination of strength and ductility to those of their homogeneous counterparts [START_REF] Wang | Strength-ductility synergy of selective laser melted Al-Mg-Sc-Zr alloy with a heterogeneous grain structure[END_REF][START_REF] Wu | Heterogeneous materials: a new class of materials with unprecedented mechanical properties[END_REF][START_REF] Kok | Anisotropy and heterogeneity of microstructure and mechanical properties in metal additive manufacturing: A critical review[END_REF][START_REF] Fan | Plastic deformation and fracture of ultrafine-grained Al-Mg alloys with a bimodal grain size distribution[END_REF]. During plastic deformation, the gradient strain distribution at the interface of two grain regions produces geometrically necessary dislocations, resulting in an additional back-stress hardening (more accurately referred to as hetero-deformation-induced hardening) and thus a higher strain-hardening ability [START_REF] Zhu | Perspective on hetero-deformation induced (HDI) hardening and back stress[END_REF].

The literature on the mechanical properties of Sc/Zr-modified Al alloys manufactured by LAM was summarized in Table 1 [START_REF] Bi | Microstructure and mechanical properties of a novel Sc and Zr modified 7075 aluminum alloy prepared by selective laser melting[END_REF][START_REF] Mehta | Additive manufacturing and mechanical properties of the dense and crack free Zr-modified aluminum alloy 6061 fabricated by the laser-powder bed fusion[END_REF][START_REF] Zhang | Effect of Zirconium addition on crack, microstructure and mechanical behavior of selective laser melted Al-Cu-Mg alloy[END_REF][START_REF] Li | Developing a high-strength Al-Mg-Si-Sc-Zr alloy for selective laser melting: Crack-inhibiting and multiple strengthening mechanisms[END_REF][START_REF] Jia | Selective laser melting of a high strength Al[sbnd]Mn[sbnd]Sc alloy: Alloy design and strengthening mechanisms[END_REF][START_REF] Croteau | Microstructure and mechanical properties of Al-Mg-Zr alloys processed by selective laser melting[END_REF][START_REF] Deng | Microstructure and mechanical properties of a combination interface between direct energy deposition and selective laser melted al-mg-sc-zr alloy[END_REF][START_REF] Zhao | Some factors affecting porosity in directed energy deposition of AlMgScZr-alloys[END_REF][START_REF] Wang | Laser powder bed fusion of high-strength Sc/Zr-modified Al-Mg alloy: phase selection, microstructural/mechanical heterogeneity, and tensile deformation behavior[END_REF][START_REF] Zhou | Microstructure and tensile property of a novel AlZnMgScZr alloy additively manufactured by gas atomization and laser powder bed fusion[END_REF][START_REF] Zhou | Process-Dependent Composition, Microstructure, and Printability of Al-Zn-Mg and Al-Zn-Mg-Sc-Zr Alloys Manufactured by Laser Powder Bed Fusion[END_REF][START_REF] Li | Selective laser melting of Al-3.48Cu-2.03Si-0.48Sc-0.28Zr alloy: Microstructure evolution, properties and metallurgical defects[END_REF][START_REF] Wang | Directed energy deposition additive manufacturing of a Sc/Zr-modified Al-Mg alloy: Effect of thermal history on microstructural evolution and mechanical properties[END_REF]. These alloys not only maintain strength-ductility synergy but also exhibit low anisotropies in static mechanical properties owing to the effects of the Sc/Zr modification. In addition, the addition of Sc/Zr elements provides a viable method for in-situ modification of microstructure and properties. For LDED, Wang et al. [START_REF] Wang | Directed energy deposition additive manufacturing of a Sc/Zr-modified Al-Mg alloy: Effect of thermal history on microstructural evolution and mechanical properties[END_REF] reported that the transition of microstructure from an equiaxed grain structure to a bi-modal grain structure can be adjusted by controlling the substrate cooling conditions. Kürnsteiner et al. [START_REF] Kürnsteiner | Control of thermally stable coreshell nano-precipitates in additively manufactured Al-Sc-Zr alloys[END_REF] also showed the potential of making use of the intrinsic heat treatment to change the size and number of precipitates. For LPBF, preheating [START_REF] Shi | Effect of platform temperature on the porosity, microstructure and mechanical properties of an Al-Mg-Sc-Zr alloy fabricated by selective laser melting[END_REF][START_REF] Yang | Columnar to equiaxed transition in Al-Mg(-Sc)-Zr alloys produced by selective laser melting[END_REF], process parameters [START_REF] Shi | Effect of platform temperature on the porosity, microstructure and mechanical properties of an Al-Mg-Sc-Zr alloy fabricated by selective laser melting[END_REF][START_REF] Spierings | Influence of SLM scan-speed on microstructure, precipitation of Al3Sc particles and mechanical properties in Sc-and Zr-modified Al-Mg alloys[END_REF], and rescanning [START_REF] Griffiths | Effect of laser rescanning on the grain microstructure of a selective laser melted Al-Mg-Zr alloy[END_REF] can in-situ alter the grain evolution behavior, thus changing the volume fraction of both grains. Moreover, the high cooling rate of LPBF is favorable for the formation and refinement of bi-modal grain structure and high strength [START_REF] Wang | Strength-ductility synergy of selective laser melted Al-Mg-Sc-Zr alloy with a heterogeneous grain structure[END_REF][START_REF] Deng | Microstructure and mechanical properties of a combination interface between direct energy deposition and selective laser melted al-mg-sc-zr alloy[END_REF].

Currently, many studies, performed on LPBF-fabricated Al alloys, turned to investigate their fatigue behaviors. Most of them focused on Al-Si series alloys. These studies [START_REF] Beretta | A comparison of fatigue strength sensitivity to defects for materials manufactured by AM or traditional processes[END_REF][START_REF] Brandl | Additive manufactured AlSi10Mg samples using Selective Laser Melting (SLM): Microstructure, high cycle fatigue, and fracture behavior[END_REF][START_REF] Tang | Fatigue life prediction for AlSi10Mg components produced by selective laser melting[END_REF] showed that the fine cellular microstructure brings beneficial effects and improved fatigue properties could be achieved by heat treatment. But defects such as pores and lack of fusion led to deteriorated and anisotropic fatigue behavior. Xu et al. [START_REF] Xu | High cycle fatigue performance of AlSi10mg alloy produced by selective laser melting[END_REF] investigated the effects of building direction on fatigue behavior of the LPBF-fabricated AlSi10Mg alloy. The 0° samples show a higher fatigue strength than the 45° and 90° samples because of the smaller defect size distribution of the 0° sample. Wu et al. [START_REF] Wu | The effect of defect population on anisotropic fatigue resistance of selective laser melted AlSi10Mg alloy[END_REF] also reported the low fatigue strength, when the loading direction was parallel to the build direction, was attributed to the larger size of the projected area of LoF defects vertical to the building direction than that along building direction. However, it is still unclear that how the metastable metallurgical features of the LPBF process, especially the rapid solidification, induced defects, heterogeneous grain structure, and precipitates, influence the fatigue properties of the LPBFfabricated Sc/Zr modified Al alloys due to their different metallurgical behavior and heterogeneous structure from Al-Si alloys. On the other hand, the special layer by layer manufacturing procedure will bring new challenges for understanding the metallurgical behavior with emphasis on the building direction. Therefore, this study aims to clarify the effects of multi-scale features on the fatigue properties of LAMfabricated Sc/Zr-modified Al alloys, which is important for the design and application.

In this paper, we introduce Sc/Zr-modified Al alloy specifically tailored for the LPBF, Al-Mg-Sc-Zr alloy, to investigate the effects of Sc/Zr-modified heterogeneous structure characteristics on high-cycle fatigue performances in different deposition directions. The multi-scale heterogeneous structure of the LPBF-fabricated Al-Mg-Sc-Zr alloy was comprehensively characterized, including defects, grain structures, and precipitation phases. Based on the characterization, the effects of these factors on the fatigue crack initiation and propagation were analyzed and their respective mechanisms under dynamic loading conditions were obtained. This study can contribute to the further development of LPBF-fabricated aluminum alloys with isotropic and integrated (monotonic-dynamic) mechanical performances.

Materials and methods

2.1.Powder and sample preparation

A commercially available Al-Mg-Sc-Zr powder, fabricated using a vacuum induction gas atomization process, was used in this study. The chemical compositions of the experimental powder were measured by inductively coupled plasma atomic emission spectrometry according to the American Society for Testing and Materials (ASTM) E3061-17 standard [START_REF]Standard Test Method for Analysis of Aluminum and Aluminum Alloys by Inductively Coupled Plasma Atomic Emission Spectrometry (Performance Based Method), Stand. Test Method Anal. Alum. Alum. Alloy. by Inductively Coupled Plasma At[END_REF], as shown in Table 2. The particle morphology and size distribution of the as-received powder are shown in Fig. 1(a). Most of the powder is spherical. The satellite powder is located at the surface of the larger powder. The D10, D50, and D90 values, which indicate the maximum particle diameters that include 10%, 50%, and 90% of the particles (volume-weighted basis), were determined to be 12.2, 26.0, and 46.8 μm, respectively. All powders were dried under vacuum for 3 h at 120 °C prior to the sample fabrication. 10 × 10 × 10 mm 3 cubic samples, a total of 18 pieces, were fabricated for process parameter optimization (e.g., laser power and scanning speed). The relative densities of the samples were confirmed by the Archimedes method and statistical results of the area of defects using the optical microscope, as shown in the supplement (Fig. S1 andS2). A strip scan strategy with the scanning direction rotation of 67° between the consecutive layers, 80℃ of platform temperature, and an Ar atmosphere with an O concentration below 200 ppm were used. A relative density of ~99.4% was realized using the optimized parameters and remained constant during the fabrication of all samples in this study, as summarized in Table 3. A commercial EOS M280 machine, with a laser beam diameter of 100 μm, was used to deposit two groups of Al-Mg-Sc-Zr samples in the cylindrical form. One of them contains a series of cylindrical rods whose deposition direction is parallel (PD)

to the loading direction (LD), while the other contains cylindrical rods whose deposition direction is transverse (TD) to the LD, as shown in Fig. 1(b). The asdeposited samples were post treated by direct aging in a vacuum furnace before the subsequent machining. The direct aging treatment was carried out at 325 ℃ for 4 h, which ensures the maximum tensile strength of the LPBF-fabricated Al-Mg-Sc-Zr alloy, as reported by Wang et al. [START_REF] Wang | Laser powder bed fusion of high-strength Sc/Zr-modified Al-Mg alloy: phase selection, microstructural/mechanical heterogeneity, and tensile deformation behavior[END_REF]. Both TD and PD cylindrical rod groups included fatigue specimens and tensile specimens with a nominal height of ~108 mm and diameter of ~20 mm and nominal height of ~67 mm and diameter of ~11 mm, respectively, at least to leave the machining allowance of 2 mm. After heat treatment, fatigue specimens and tensile specimens in accordance with GB/T 3075-2008 [START_REF]Metal Material Axial Loading Fatigue Test Method,China National Standard[END_REF] and GB/T 228.1-2010 [START_REF]Metallic Materials-Tensile testing-Part 1: Method of test at room temperature[END_REF], as shown in Fig. 1(c), were obtained by machining work.

Then, all specimens were polished by the numerical control machine tool (K6530) using abrasive paper (2000 #), to achieve a uniform and high surface roughness (Ra < 0.4 μm). Therefore, the effect of surface roughness on the fatigue properties can be ignored. Fatigue specimens of LPBF-fabricated Al-Mg-Sc-Zr alloy, left is TD and right is PD.

2.2.Mechanical properties

The machined and polished tensile specimens under the aging conditions with a gauge length of 30 mm and diameter of 5 mm were used to carry out roomtemperature uniaxial tensile tests using an Instron 3382 universal testing machine. The nominal crosshead displacement rate was 1 mm/min. The tensile properties were averaged by three measurements. To distinguish the differences in the mechanical properties of the EG bands and CG domains under aging conditions, the microhardness was measured using an LM248AT Vickers hardness tester (LECO) with a load of 5 g and holding time of 15 s.

Stress-controlled fatigue tests were conducted at room temperature using an MTS Landmark 200-Hz machine under various stress amplitudes. The stress ratio (R) of the tests was 0.1, while the waveform was sinusoidal with a nominal frequency of 100 Hz. The whole process of testing was based on the Chinese standard GB/T 3075-2008 "Metal Material Axial Loading Fatigue Test Method" [START_REF]Metal Material Axial Loading Fatigue Test Method,China National Standard[END_REF]. The fatigue tests were stopped at specimens that were completely fractured (failed) or loaded for 10 7 cycles (passed). Subsequently, the fracture surfaces of the failed samples were evaluated using scanning electron microscopy (SEM) to investigate the fracture characteristics.

2.3.Characterization

After the fatigue tests, the defect population in the fatigue gauge section of the passed specimens was characterized using X-ray tomography (XRT) using a Zeiss Xradia 520 versa machine. To ensure penetration, a voltage of 120 kV and current of 120 μA were used. The data were collected with a voxel size of 2.51 μm. The twodimensional (2D) projection images were reconstructed into three-dimensional (3D) topography using the DRAGONFLY software.

Before the microstructural characterization, the as-deposited samples were sectioned parallel and transverse to the deposition direction, mechanically ground, and then polished using 600-to 5000-grit SiC papers and 0.25-μm colloidal silica suspension, respectively. The surfaces of the polished specimens were etched with the Keller's reagent (HF:HCl:HNO3:water = 1:1.5:2.5:95) to observe the macrostructure using a GX71 OLYMPUS optical microscope and electropolished at a voltage of 23 V for 10 s with an electrolyte (10 vol.% perchloric acid in a 90-vol.% ethanol solution) using a Struers electrolytic instrument (LectroPol-5) for the observation of the microstructure through an electron back-scatter diffraction (EBSD) test using a FEI Helios Nano-Lab SEM machine with a scanning step size of 0.2 μm. Data were analyzed using the CHANNEL5 software package.

To observe the phase distribution and the dislocation configurations of the fatigue-failed sample through a transmission electron microscopy (TEM) system (double Cs corrector), two methods of preparing thin foils for TEM observation were employed. One of them was cut from the as-deposited sample and ground to a thickness of 50 μm using a 1500-grid SiC paper, and then a φ3-mm foil was prepared via twin jet electrolytic thinning. The other was extracted from the longitudinal plane of the fatigue-failed specimen (the direction of the plane is parallel to the deposition direction, while the extraction location is near the fracture surface) in the TD and PD using an FEI Helios Nano-Lab G4 CX FIB, as shown in Fig.

Results

Microstructure analysis

Defect distribution

Considering the different aspect ratios of the specimens and building times resulting from different building directions, the defects might be diverse [START_REF] Wu | The effect of defect population on anisotropic fatigue resistance of selective laser melted AlSi10Mg alloy[END_REF][START_REF] Du Plessis | Effects of defects on mechanical properties in metal additive manufacturing: A review focusing on X-ray tomography insights[END_REF][START_REF] Sanaei | Defects in Additive Manufactured Metals and Their Effect on Fatigue Performance: A State-of-the-Art Review[END_REF][START_REF] Galy | Main defects observed in aluminum alloy parts produced by SLM: From causes to consequences[END_REF].

The defect characteristics of the LPBF-fabricated Al-Mg-Sc-Zr alloy in the TD and PD were analyzed by XRT. The densities of the samples in the TD and PD estimated by XRT were 99.52% and 99.43%, respectively, which mainly ascribed to more defects in the PD than those for the TD. The longer interval time and the bigger contact area with the substrate of the TD group, compared to the PD group, can increase the cooling rate of the molten pool [START_REF] Afkhami | Fatigue characteristics of steels manufactured by selective laser melting[END_REF]. So, the TD specimen possesses less defects than the PD specimen. The representative spatial distributions of defects in the TD and PD are presented in Fig. 3a andb. Two types of defects with distinct geometric features were identified (insets of Fig. 3a2 andb2). One of them consists of random high-density small spherical defects. These spherical defects were defined as gas pores with smooth edges. The other with a low density, large size, and irregularity is defined as lack of fusing (LoF). The LPBF-fabricated components always contain pores and LoF defects owing to the uncontrollable gas volatilization and improper process parameters. The volatile gas or protective atmosphere trapped in the molten pool forms pores [START_REF] Kumar | High cycle fatigue in selective laser melted Ti-6Al-4V[END_REF]. The unrealized metallurgical bonding was caused by the insufficient heat input and following liquid metal cooled too quickly to fill this gap result in LoFs [START_REF] Galy | Main defects observed in aluminum alloy parts produced by SLM: From causes to consequences[END_REF][START_REF] Xie | Defect-correlated fatigue resistance of additively manufactured Al-Mg4.5Mn alloy with in situ micro-rolling[END_REF]. represents the shape of defects with a higher value meaning more irregular. The Ф and θ, respectively, denote the angle between the longest axis and the Z axis, which is parallel to their building direction, and the Y axis, which is vertical to their building direction. The size distributions of defects show a similar trend in the TD and PD specimens with the equivalent diameters of most defects being below 60 μm (Fig. 4a),

and their shape tends to be regular (Fig. 4b), which mean the pores dominate the population. For the defects (LoFs) with big size (> 60 μm), there is a trend for these defects to be irregular (V/S > 4). So, they are few but are dangerous. A connection between the defects orientation and building direction was found from Fig. 4c, the LoFs prefer to Ф = 0° for the TD specimen and Ф = 90° for the PD specimen.

However, θ randomly distributes from -180° to 180° in both TD and PD specimens.

This phenomenon is mainly because the parts are deposited layer by layer (Fig. 4) and the thermal history between adjacent layers exhibits larger fluctuations [START_REF] Sanaei | Defects in Additive Manufactured Metals and Their Effect on Fatigue Performance: A State-of-the-Art Review[END_REF][START_REF] Wang | Influence of manufacturing geometric defects on the mechanical properties of AlSi10Mg alloy fabricated by selective laser melting[END_REF][START_REF] Balachandramurthi | Influence of defects and as-built surface roughness on fatigue properties of additively manufactured Alloy 718[END_REF],

and the 67° rotation angle can effectively dislocate the orientation of defects at each layer. defects orientation distribution correlated to the Z axis, which is parallel to their loading direction and the X axis, which is vertical to their building direction, respectively.

3.1.2 Bimodal grain structure Fig. 5 shows the macro-and microstructures of the LPBF-fabricated Al-Mg-Sc-Zr specimen. Fig. 5a shows a 3D optical macrodiagram of the specimen under aging conditions, with the laser scanning tracks with a rotation angle of 67°, owing to the track-by-track scanning, on the top surface (XY plane) and fish-scale molten pool, owing to the layer-by-layer accumulation, on the side surface (XZ plane). Fig. 5b andc show microimages in the XY and XZ planes, respectively, obtained by backscatter electrons (BSEs). A heterogeneous grain structure, which comprises fine EG bands at the molten pool boundary and elongated CG domains in the center of the molten pool, is formed in the sample. Fig. 5b andc show a large number of white particles, which are mainly Al3(Sc, Zr) and Al-Mg oxides [START_REF] Croteau | Microstructure and mechanical properties of Al-Mg-Zr alloys processed by selective laser melting[END_REF][START_REF] Spierings | Microstructure characterization of SLM-processed Al-Mg-Sc-Zr alloy in the heat treated and HIPed condition[END_REF], distributed mainly in the EG region and limitedly formed in the CG region. These Al3(Sc, Zr) precipitations are formed during the solidification of the molten pool. Their lattice structure (L12) is similar to α-Al (face-centered cubic (FCC)) [START_REF] Wang | Laser-based directed energy deposition of novel Sc/Zr-modified Al-Mg alloys: columnar-toequiaxed transition and aging hardening behavior[END_REF]. Thus, the precipitation behavior of Al3(Sc, Zr)

during solidification is well correlated to the grain morphology [START_REF] Wang | Directed energy deposition additive manufacturing of a Sc/Zr-modified Al-Mg alloy: Effect of thermal history on microstructural evolution and mechanical properties[END_REF]. This heterogeneous or bimodal grain structure characteristic of the Al-Mg-Sc-Zr alloy is also consistent with the observations by Spierings et al. [START_REF] Spierings | Microstructure characterization of SLM-processed Al-Mg-Sc-Zr alloy in the heat treated and HIPed condition[END_REF]. 6a andc). However, when only the CG region is considered, a stronger solidification fiber texture is formed (Fig. 6a andb). Therefore, the low MUD of the XY plane is mostly attributed to the more visible fraction of disordered EGs. The average grain sizes on the XY and XZ planes are determined to be 0.93 ± 0.79 and 1.06 ± 0.59 μm, respectively (Fig. 6e andf). As the equivalent grain size (the spherical diameter with the same volume as that of the grains) is counted, the average grain size counted by XY is lower because the XY plane is counted for the cross section of a columnar crystal, which has a smaller area.

Precipitation phase

As shown in Fig. 5b andc, numerous precipitates were formed among the Al matrix. To provide insights into the main precipitates in the Al-Mg-Sc-Zr alloy, highresolution (HR) TEM images of these precipitates in the EG and CG regions and corresponding selected-area electron diffraction (SAED) patterns along the [001] zone axis are shown in Fig. 7. As shown in Fig. 7a, a bean-shaped particle with a size of 30-40 nm existed in the EG. The 001-type superlattice reflection was apparent based on the SAED pattern. This particle is considered to be primary Al3(Sc, Zr), which is formed during solidification [START_REF] Wang | Laser powder bed fusion of high-strength Sc/Zr-modified Al-Mg alloy: phase selection, microstructural/mechanical heterogeneity, and tensile deformation behavior[END_REF]. Moreover, the HRTEM image obtained from the CGs (Fig. 7d) shows that some particles were embedded in the α-Al matrix. The corresponding SAED patterns demonstrate their L12 ordered structure and {100} crystal planar space compatible with the α-Al matrix, which indicates their coherency with the α-Al matrix. Owing to the different precipitation kinetics, their sizes vary.

The primary Al3(Sc, Zr) has a larger dimension with a diameter of tens of nanometers, which is a few nanometers for the secondary Al3(Sc, Zr). Thus, these particles are defined as secondary Al3(Sc, Zr) formed during the aging process [START_REF] Spierings | Microstructure characterization of SLM-processed Al-Mg-Sc-Zr alloy in the heat treated and HIPed condition[END_REF]. Mg-Sc-Zr alloy, as confirmed in our previous study [START_REF] Wang | Strength-ductility synergy of selective laser melted Al-Mg-Sc-Zr alloy with a heterogeneous grain structure[END_REF]. Although the heterogeneous deformation will achieve an additional strain hardening under static loading conditions, it seems that it should be avoided under dynamic loading conditions [START_REF] Gao | Training high-strength aluminum alloys to withstand fatigue[END_REF][START_REF] Liu | Exceptional high fatigue strength in Cu-15at.%Al alloy with moderate grain size[END_REF]. The concentration of deformation in small areas reduces the overall fatigue resistance of the material. After the heat treatment, this mechanical inhomogeneity due to the Hell-Petch relationship may be mitigated by secondary Al3(Sc, Zr) phases, which are mainly precipitated in the CG region (Fig. 9). To analyze the extent of mechanical heterogeneity for the directly aged LPBF-fabricated Al-Mg-Sc-Zr alloy, a microhardness test was carried out.

Tensile properties

The tensile engineering stress-strain curves of the LPBF-fabricated Al-Mg-Sc-Zr alloy in the TD and PD under aging conditions are shown in Fig. 10a. The yield strength (YS), ultimate tensile strength (UTS), elongation to failure (εf) and Young's modulus (E) in the TD were determined to be 508. . The UT of the TD specimen is 6979 U slightly lower than that of the PD specimen, 7298 U. The anisotropy is not apparent, which is consistent with the low MUD obtained by the EBSD data (Fig. 6c andd). Similar results were reported by Schmidtke et al. [START_REF] Schmidtke | Process and mechanical properties: Applicability of a scandium modified Al-alloy for laser additive manufacturing[END_REF]. The good mechanical properties, which are comparable to those of traditional high-strength wrought Al alloys and other LPBF-fabricated Al alloys [START_REF] Lewandowski | Metal Additive Manufacturing: A Review of Mechanical Properties[END_REF], are attributed to the high grain boundary and precipitation strengthening. Both PD and TD samples exhibit a yield drop and discontinuous yielding behavior during the uniform plastic deformation stage, which is related to a lack of mobile dislocations. It may result from the pinning effect of the Cottrell atmosphere, grain-refinement (especially for EG), and annealing treatment [START_REF] Wang | Laser powder bed fusion of high-strength Sc/Zr-modified Al-Mg alloy: phase selection, microstructural/mechanical heterogeneity, and tensile deformation behavior[END_REF]. Then, a slighter strain hardening after yield is obtained according to the stressstrain curves in both deposition directions compared to the as-built state [START_REF] Wang | Laser powder bed fusion of high-strength Sc/Zr-modified Al-Mg alloy: phase selection, microstructural/mechanical heterogeneity, and tensile deformation behavior[END_REF], which leads to YS/UTS of 0.965 and 0.972 for TD and PD, respectively, resulting from the less pronounced deformation heterogeneity and thus less dislocation strengthening [START_REF] Li | Mechanical response of dislocation interaction with grain boundary in ultrafine-grained interstitial-free steel[END_REF].

The overviews of fracture morphologies of the TD and PD samples are shown in Fig. S3. Both of them have cup-and-cone fracture surfaces. However, their fibrous zones of tensile fractographs are different, presented in Fig. 10b -d. The TD sample (Fig. 10b andc) shows columnar-like morphology covered with cleavage facets and dimples (diameter around 0.62± 0.16 μm), while the PD sample (Fig. 10d ande)

shows quasi-cleavage features (tearing ridge) with dimples (diameter around 0.

Fatigue properties

The fatigue S-N data of the LPBF-fabricated Al-Mg-Sc-Zr alloy in the TD and PD are presented in Fig. 11a. Two curves fitted well with the Basquin equation as shown in Eq. 1:

𝜎 𝑎 = 𝜎 𝑓 ′ • (2𝑁 𝑓 ) 𝑏 (1)
Where σa and 𝑁 𝑓 are the stress amplitude and the fatigue life, and 𝜎 𝑓 ′ and b are the fatigue strength coefficient and the fatigue strength exponent [START_REF] Basquin | The exponential law of endurance tests[END_REF]. The fatigue data of the TD series shows a higher scatter than the PD series, which can be attributed to their fewer big defects than those for the PD, as shown in Fig. 3 and4. Notably, the fatigue strength (σf) (calculated by the staircase method [START_REF] Dixon | A Method for Obtaining and Analyzing Sensitivity Data[END_REF] and relevant process shown in Fig. S4) of the TD group was 100.5 MPa, considerably higher than σf of the PD group (57 MPa). The fatigue strengths were compared to those of Al-Mg-Sc-Zr alloys prepared by other processes, other LPBF-fabricated Al-based alloys, and traditional high-strength Al, as shown in Fig. 11b. To better synthesize the fatigue strengths under varied stress ratios (R), the values are presented with the effective stress amplitude (σe) at a stress ratio of -1, which were calculated using the Smith-Wastson-Topper's (SWT) model as shown in Eq. ( 1) [START_REF] Smith | A StressStrain Function for the Fatigue of[END_REF]:

𝜎 𝑒 = 𝜎 𝑚𝑎𝑥 √2/(1 -𝑅) (2)
where 𝜎 𝑚𝑎𝑥 is the applied maximum stress and R is the applied stress ratio. The TD specimens exhibited a better combination of σe and UTS than those of the conventional Al-Mg-Sc-Zr alloys and LPBF-fabricated AlSi10Mg alloy [START_REF] Tang | Fatigue life prediction for AlSi10Mg components produced by selective laser melting[END_REF][START_REF] Besel | Fatigue behavior of friction stir welded Al-Mg-Sc alloy[END_REF][START_REF] Estrin | Fatigue behaviour of light alloys with ultrafine grain structure produced by severe plastic deformation: An overview[END_REF][START_REF] Vinogradov | Fatigue life of finegrain Al-Mg-Sc alloys produced by equal-channel angular pressing[END_REF] and similar to that of a wrought 7075-T651 alloy. However, the PD specimens exhibited a relatively low fatigue strength, despite the slightly lower tensile strength than that of the TD specimens. In general, fatigue strength and tensile strength are strongly interdependent in traditional wrought materials [START_REF] Liu | Exceptional high fatigue strength in Cu-15at.%Al alloy with moderate grain size[END_REF]. However, their defects Fig. 12 shows the fracture surfaces in both PD and TD. The whole fatigue fracture surfaces of the TD and PD samples can generally be divided into three regions: crack initiation, crack propagation, and fast fracture regions. The crack is always initiated from the surface and irregular defect, which can be considered a critical defect for crack initiation, as shown in Fig. 12b andd, because of the higher stress concentration of the surface defect than that of the internal defect [START_REF] Gong | Influence of defects on mechanical properties of Ti-6Al-4V components produced by selective laser melting and electron beam melting[END_REF]. The details of these defects shown in Fig. 12b andd (the insets) prove they are LoFs.

Notably, the critical defects of the TD and PD specimens with comparable numbers of cycles share similarities in terms of location, shape, and size, while the difference in σa is 36 MPa. According to the flatness of the fracture surface, the crack propagation areas on both PD and TD samples are subdivided into two regions: crack propagation region (Ⅰ) with a smooth surface and crack propagation region (Ⅱ) with a surface with scratches and grooves, which can also be observed in Fig. 13. This is correlated to the escalated crack driving force [START_REF] Ma | Fatigue short crack propagation behavior of selective laser melted Inconel 718 alloy by in-situ SEM study: Influence of orientation and temperature[END_REF]. When the advancing crack has reached a critical size, the specimen raptures rapidly along the maximum shear stress direction and a shear lip with an angle of 45° with respect to the LD is obtained. 13a andd (insets) shows that the TD specimen has a higher ratio of EG/CG regions. The shape of the molten pool is obtained from Fig. 5a, which is marked by a red line. For the crack propagation region (Ⅱ), Fig. 13c andf show that the crack on the TD sample alternately passes CG and EG regions, while the crack on the PD sample mainly passes CG regions. Therefore, the crack on the TD sample encounters more EG regions than that of the PD sample.

Discussion

Effect of defects on the anisotropic fatigue

The anisotropic fatigue was also observed in other additive manufacturing metallic materials (such as TC4, alloy 718, and steel) [START_REF] Afkhami | Fatigue characteristics of steels manufactured by selective laser melting[END_REF][START_REF] Xu | The influence of building direction on the fatigue crack propagation behavior of Ti6Al4V alloy produced by selective laser melting[END_REF][START_REF] Zhang | Microstructure, surface quality, residual stress, fatigue behavior and damage mechanisms of selective laser melted 304L stainless steel considering building direction[END_REF][START_REF] Ramanathan | Anisotropic fatigue properties of Alloy 718 manufactured by Electron Beam Powder Bed Fusion[END_REF]. A consistent phenomenon is observed where the defect, particularly the LoF with a flattened shape and large volume, contributes to the most adverse effect on the fatigue properties. In addition, these LoFs with flattened shapes are always distributed on the laser track between successive layers, leading to different degrees of surrounding stress concentration in different LDs. Afkhami et al. [START_REF] Afkhami | Fatigue characteristics of steels manufactured by selective laser melting[END_REF] reported that, in vertical samples subjected to an external loading (PD), the sharp corner of the LoF results in a higher stress concentration and lower stress concentration in the horizontal direction (TD). A higher stress concentration implies that the PD samples exhibit a higher true stress around the defect under the same load and are more likely to initiate crack formation.

In addition, Xu et al. [START_REF] Xu | The influence of building direction on the fatigue crack propagation behavior of Ti6Al4V alloy produced by selective laser melting[END_REF] indicated that a large defect projection area on the plane perpendicular to the building direction enhances the probability of main crack connection and accelerates the crack propagation. Thus, a lower fatigue performance can be expected.

Similar shape, size, and distribution of defects were obtained in this study by the XRT results (Fig. 3 and4), which demonstrated that these large irregular LoFs have the most detrimental role in the fatigue properties [START_REF] Murakami | Defect Analysis for Additively Manufactured Materials in Fatigue from the Viewpoint of Quality Control and Statistics of Extremes[END_REF][START_REF] Biswal | Assessment of the effect of isolated porosity defects on the fatigue performance of additive manufactured titanium alloy[END_REF]. Consequently, it is reasonable to consider that they have a crucial role in the anisotropic fatigue properties. For defect and fatigue properties, the Kitagawa-Takahashi diagram (K-T diagram) [START_REF] Kitagawa | Application of fracture mechanics to very small cracks or the cracks in early stage[END_REF] is often used to describe their relationship. The main formula is

∆𝐾 𝑡ℎ = ∆𝜎𝐹 𝑤 √ 𝜋√𝑎𝑟𝑒𝑎 ( 3
)
where ΔKth is the long crack growth threshold [START_REF] Wu | The effect of defect population on anisotropic fatigue resistance of selective laser melted AlSi10Mg alloy[END_REF], Fw is a geometric factor depending on the location of defects (0.5 for internal, 0.65 for surface), Δσ is the stress amplitude applied to the specimens, and √area is the Murakami's parameter [START_REF] Kitagawa | Application of fracture mechanics to very small cracks or the cracks in early stage[END_REF] to express the defect size defined as a smooth contour circumscribing the irregular defects shape as shown in Fig. S5 [START_REF] Sanaei | Defects in Additive Manufactured Metals and Their Effect on Fatigue Performance: A State-of-the-Art Review[END_REF]. To evaluate the value of ΔKth, two points were taken as the critical point: one failed sample (99 MPa, 73.7 μm) with the minimum ΔKth as shown in Table 5 and one run-out sample (112.5 MPa, 60 μm) that defected by XRT in our previous work [76], so that ΔKth = 0.876 MPa m 1/2 .

The relationship between the defect size and stress amplitude is shown in Fig. 14. The surface defect depicted by the red solid line has a lower tolerance than that of the internal defect (black dotted line). This can explain the crack initiation always by a surface defect. As the stress amplitude increased, the Murakami's parameter decreased. The experimental stress amplitudes of the two groups were divided by the line of stress amplitude of 90 MPa. This means that the TD specimens will not fail in the presence of the same-sized surface defects as the PD specimens, which fail during fatigue tests. For example, the critical size of surface defects at fatigue strength (100.5

MPa) on the TD sample is 63 μm, whereas that on the PD sample is 181 μm. Thus, to consider the role of defects in the fatigue anisotropy, the critical defect sizes of the crack initiation (the Marukami's parameter) observed using SEM are presented in Fig. 14. The circles represent the TD group specimens, while the triangles represent the PD group specimens. The TD group is located at the top right of the red solid line, which implies that the defects at crack initiation in these specimens do not support the specimen to undergo 10 7 cycles at the stress amplitude. When the point is more to the right side, the cycle life is shorter. However, for the PD group, although similar defect sizes at crack initiation were observed, they still cause fatigue fracture with similar lifetimes at a lower σa. In particular, the points depicted by the red circle of the PD samples in the safe regime are still ruptured. As the defects on this red line were determined by ΔKth calculated for the TD group, points located in the safe regime imply that ΔKth for the PD group was smaller and that it had a lower resistance to crack initiation and propagation. Therefore, it is reasonable to speculate that other factors affect the anisotropy of the fatigue performance. The Al3(Sc, Zr) phases exhibit an inhomogeneous distribution, with primary Al3(Sc, Zr) precipitating in the EG region, while the secondary Al3(Sc, Zr)

precipitates in the CG region. This inhomogeneous precipitation behavior weakens the hardness gap resulting from the Hall-Petch relationship between the CG and EG regions (Fig. 9). The Al3(Sc, Zr) phases have an L12 ordered structure and are coherent with the α-matrix; the main difference is the size. According to the TEM results (Fig. 7 and8), the size of the primary Al3(Sc, Zr) phase is tens of nanometers, while the size of the secondary Al3(Sc, Zr) phase is smaller than 5 nm. According to the classic precipitation theory, an increase in particle size results in a transition from particle shearing (also referred to as antiphase boundary (APB) mechanism) to Orowan dislocation looping. Watanabe et al. [START_REF] Watanabe | Effects of Al3Sc particle size and precipitate-free zones on fatigue behavior and dislocation structure of an aged Al-Mg-Sc alloy[END_REF] reported that the critical size of the mechanism shift for the Al3(Sc, Zr) phase is approximately 4.8 nm. Therefore, it is reasonable to speculate that the resistance of the primary Al3(Sc, Zr) to dislocation is the Orowan mechanism and APB mechanism for the secondary Al3(Sc, Zr). This leads to the different resistances of the two types of particles to cyclic loading. For the APB mechanism, planar slip, a feature of the APB mechanism, results in dislocations continuously passing particles along a single plane and simultaneously disrupting the short-range order (SRO) structure of Al3(Sc, Zr) particles [START_REF] Gerold | On the origin of planar slip in f.c.c. alloys[END_REF]. Thus, cyclic softening occurred. This has been demonstrated in Al-Mg-Sc alloys with Al3Sc (4 nm) [START_REF] Watanabe | Low-cycle fatigue behavior and dislocation structure of an Al-Mg-Sc alloy[END_REF].

For the Orowan mechanism, the dislocation loop in the second phase with the SRO structure is unbroken. Thus, no cyclic softening occurred [START_REF] Watanabe | Effects of Al3Sc particle size and precipitate-free zones on fatigue behavior and dislocation structure of an aged Al-Mg-Sc alloy[END_REF]. This difference leads to the EG region possessing a better resistance to cyclic loading than the CG region in the aged LPBF-fabricated Al-Mg-Sc-Zr alloy.

In addition, the microtextures of the two grain regions are important to the crack propagation process because the twist and tilt angles of the crack-plane deflection at grain boundaries are the main factors affecting the fatigue crack growth [START_REF] Zhai | Crystallographic mechanism for fatigue crack propagation through grain boundaries[END_REF]. The crack path tilting reduces the effective driving force, while the twisting controls the fractured area for cracks to pass through the grain boundaries [START_REF] Zhai | Crystallographic mechanism for fatigue crack propagation through grain boundaries[END_REF][START_REF] Balachandramurthi | Microstructural influence on fatigue crack propagation during high cycle fatigue testing of additively manufactured Alloy 718[END_REF]. The EBSD results (Fig. 6) show that the CG region has a preferred orientation, while the EG region does not have preferred orientation. This implies that the EG region possesses larger tilt and twist angles than those of the CG region. Therefore, the resistance to crack propagation in the EG region is higher than that in the CG region. The EG region has better fatigue properties than the CG region because it has a slight cyclic softening effect and strong crack deflection effect. Moreover, the percentage of EGs encountered by the crack is larger on the TD sample than on the PD sample, as shown in Fig. 13. Therefore, the TD group had a better fatigue performance than that of the PD group.

CG orientation

According to the above EBSD analysis, the average grain size of the EG region is 0.6 ± 0.2 μm, while that of the CG region is 1.8 ± 0.5 μm. Most grains in the EG region are UFGs (0.1-1 μm) without formation of dislocation configuration, which can store the strain in the case of static tension [START_REF] Li | Mechanical response of dislocation interaction with grain boundary in ultrafine-grained interstitial-free steel[END_REF][START_REF] Kumar | Critical grain size for change in deformation behavior in ultrafine grained Al-Mg-Sc alloy[END_REF][START_REF] Sun | Influence of boundary characters on the tensile behavior of sub-micron-grained aluminum[END_REF]. To clarify the mechanism of fatigue, the dislocation configurations were determined in the EG and CG regions on the TD and PD samples, as shown in Fig. 15. The EG regions on the TD and PD samples lack dislocations, as shown in Fig. 15a andc. The dislocation configuration and intergranular cracking in the CG region are not the same for the TD and PD FIB foils, which were obtained from the near fatigue fracture surface, as shown in Fig. 15a-d. Dislocations and few intergranular cracks are visible in the TD section, whereas an inverse phenomenon appears in the PD section. As mentioned above, the presence of numerous secondary Al3(Sc, Zr) phases forces the dislocation motion by the APB mechanism so that the planar slip mode is suggested for dislocation glide [START_REF] Gerold | On the origin of planar slip in f.c.c. alloys[END_REF]. Furthermore, the deformation leads to nucleation and multiplication of dislocation within grains. With a sufficient deformation, the dislocation rearranges in a subgrain boundary and saturates to a certain value. The microstructural characteristic of saturated subgrains is such that the interior of the subgrain is almost free from dislocation and dislocation concentrates in 2D subgrain boundaries at steady-state deformation [START_REF] Kumar | Critical grain size for change in deformation behavior in ultrafine grained Al-Mg-Sc alloy[END_REF][START_REF] Hayes | Deformation and activation volumes of cryomilled ultrafine-grained aluminum[END_REF]. The dislocation configuration is well correlated with the distance between dislocation sources and sinks, which is equal to the size of the subgrain (w), which can be calculated by [START_REF] Kumar | Critical grain size for change in deformation behavior in ultrafine grained Al-Mg-Sc alloy[END_REF]

𝑤 = 𝑘 𝑤 𝑏 𝐺 𝜎 𝑡 , (4)
where 𝑘 𝑤 is a numerical factor, 28 for the Al-Mg alloy [START_REF] Kapoor | High strain rate behavior of ultrafinegrained Al-1.5 Mg[END_REF][START_REF] Kumar | Additivity of strengthening mechanisms in ultrafine grained Al-Mg-Sc alloy[END_REF], 𝑏 is the magnitude of the Burgers vector (0.286 nm for Al), G is the shear modulus (26.2 GPa for Al), and 𝜎 𝑡 is the true stress. Considering the plastic zone at the crack tip of the aluminum alloy, the stress concentration was limited to the yield strength. The steadystate deformation of grains under fatigue conditions was between the yield and fatigue. Thus, by substituting 𝜎 𝑡 with the average value of the yield strength and fatigue strength (304.8 MPa for TD and 280 MPa for PD) into Eq. 3, the sizes of the subgrains were determined to be 0.71 μm for the TD sample and 0.77 μm for the PD sample.

However, it is not sufficient to explain the different dislocation patterns in the CG regions of the TD and PD samples (Fig. 15c ande) through the relationship between w and grain size, which can be attributed to the grain size in the CG region.

The sizes of the subgrains of the TD and PD specimens are similar. However, the angle between the slip plane and long axis of the CG affects the distance between the dislocation source and sink. The size of the subgrains of the TD and PD samples conforms to the short axis of the CG and is smaller than the long axis of the CG.

Thus, it is reasonable to speculate that, if the dislocation moves along the short axis of the CG, it will be absorbed by the grain boundary, while the dislocation moving along the long axis will be hardly absorbed by the grain boundary.

To discuss this mechanism, it is necessary to understand the relationship between the slip plane and grain orientation. Fig. 16 shows the grains with < 100 >, < 110 >, and < 111 > crystal orientations along the building direction (angle < 20°) according to the EBSD data (Fig. 6b). The grain orientation is random in the EG, while the grains have grown preferentially in the CG. The major crystal direction of CGs was < 100 > || BD, followed by the grains with the < 110 > || BD orientation.

where 𝜎 is the external stress, 𝛼 is the angle between the normal direction of the slip plane and direction of the external stress, 𝛽 is the angle between the direction of the slip direction and direction of the external stress, and cos (𝛼)cos (𝛽) is the Schmid factor (ms). Considering the 12-slip system in an FCC crystal, 12 different Schmid factors were obtained. The crystal orientation, Schmid's factors, and corresponding slip systems are shown in Fig. 17e. For the PD specimen, the directions of the slip system of the < parallel to the short axis of the grain, as illustrated in Fig. 17f. For the TD specimen, the < 100 > || BD grain has a slip direction with a high ms inclined at 45° with respect to the short axis, while for the < 110 > || BD grain, its crystal growth direction can be used as an effective slip system for dislocation motion. For example, for grain A, ms of the [110] grain growth direction is 0.45, which is the highest in its 12-slip system.

Therefore, after emission from the source, the dislocation slipped along the long axis of the CG, encountering the boundary of the subgrain.

This potential mechanism was also demonstrated in the crack propagation region (I). Fig. 18 shows the fractographs of the TD and PD samples with clear fatigue striations, which are parallel to each other and perpendicular to the local crack propagation direction. In the CG region of the PD specimen (Fig. 18d), the main crack truncates the CG and shows a circular surface. In addition, the fatigue striations are distributed parallel to the surface, as indicated by the red dashed lines. The intergranular cracks at the grain boundaries parallel to the fatigue striations are visible (also observed in Fig. 15f), which represents the formation of dislocations emanated from one side of the grain boundary and subsequently absorbed by the other side of one grain. Cracking becomes an important manner to accommodate the deformation of grains that cannot accommodate dislocations [START_REF] Zhai | Crystallographic mechanism for fatigue crack propagation through grain boundaries[END_REF]. For the TD specimen, the crack propagation direction defined by the fatigue striations is parallel to the long axis of the CG. Unlike the single plane for crack propagation of the CG on the PD sample, a dual-plane is formed with the formation of a secondary crack in the vicinity, which implies a complex stress state in the CGs of the TD sample.

Therefore, dislocations are absent in the CGs of the PD sample. This results in irreversible deformation, cyclic softening [START_REF] Li | Mechanical response of dislocation interaction with grain boundary in ultrafine-grained interstitial-free steel[END_REF][START_REF] Estrin | Fatigue behaviour of light alloys with ultrafine grain structure produced by severe plastic deformation: An overview[END_REF][START_REF] Sun | Influence of boundary characters on the tensile behavior of sub-micron-grained aluminum[END_REF][START_REF] Kapoor | High strain rate behavior of ultrafinegrained Al-1.5 Mg[END_REF][START_REF] Yamakov | Dislocation processes in the deformation of nanocrystalline aluminium by moleculardynamics simulation[END_REF], and absence of formation of multiple slip planes, which can disperse the crack driving force. Therefore, the PD group exhibited a lower crack propagation resistance than that of the TD group.

Conclusions

This study was focused on the anisotropic high-cycle fatigue mechanism

Fig. 1 .

 1 Fig. 1. (a) Secondary electron image and particle size distribution (the inset) of Al-

Fig. 2 .

 2 Fig. 2. Schematic diagrams of positioning and extracting a TEM thin foil from

Fig. 3 .

 3 Fig. 3. Reconstructed X-ray tomographic images of specimen of Al-Mg-Sc-Zr

Fig. 4

 4 Fig. 4 Defects features statistics of TD and PD specimens. (a) Size distribution. (b)

Fig. 5 .

 5 Fig. 5. (a) 3D light optical image of LPBF-fabricated Al-Mg-Sc-Zr alloy. The red

Fig. 6 .

 6 Fig. 6. EBSD maps showing the heterogeneous grain structure, pole figure and grain

Fig. 7 .

 7 Fig. 7. Bright field (BF) images showing EG (a) and CG (c) regions of Al-Mg-Sc-Zr

Fig. 8 .

 8 Fig. 8. STEM-EDS mapping (left) HAADF images showing EG (a) and CG (b) regions

3. 2

 2 Static mechanical properties 3.2.1 Microhardness According to the Hall-Petch relation, the grain size has a crucial influence on the static mechanical properties of the material, which inevitably results in a nonuniform deformation between the coarse and fine grain regions of the LPBF-fabricated Al-

Fig. 9 .

 9 Fig. 9. Overall microhardness images, local enlargement showing the difference of

  69 ± 0.23 μm). Both of them indicate a mixed mode of ductile and brittle fracture. It is reminiscent of the microstructure distribution in Fig. 6a and b, which suggests that the crack initiation and propagation are aided by the microstructure.

Fig. 10 .

 10 Fig. 10. (a) Representative engineering stress-strain curve of LPBF-fabricated Al-

  and microstructure are more homogeneous and present less detrimental effects compared to the pore, the LoF, and the inhomogeneous microstructure in the LPBFfabricated Al-Mg-Sc-Zr alloy. Therefore, the exceptionally low fatigue strength might indicate an underlying mechanism that can accelerate the fatigue failure in the PD group. The anisotropy of the fatigue strength is crucial for the design and manufacturing of engineering parts. Therefore, it is necessary to clarify the mechanism for the anisotropy of the LPBF-fabricated Al-Mg-Sc-Zr alloy.

Fig. 11 .

 11 Fig. 11. (a) S-N curves of LPBF-fabricated Al-Mg-Sc-Zr alloy in TD and PD. (b)

Fig. 12 .

 12 Fig. 12. An overview of fracture morphologies of failed Al-Mg-Sc-Zr specimen and

Fig. 13 shows

 13 Fig.13shows the crack propagation path and detailed EBSD maps. Similar to

Fig. 13 .

 13 Fig. 13. OM images and EBSD maps of the crack propagation in TD (a, b and c) and

Fig. 14 .

 14 Fig. 14. Calculated stress amplitude (σa) as a function of Murakami's parameter for

Fig. 15

 15 Fig. 15 depicts the difference of the fatigue striations between EG and CG regions

Fig. 15

 15 Fig. 15 Fatigue striations in TD (a, b and c) and PD (d, e and f). (b) and (e) showing the

Fig. 16 .

 16 Fig. 16. Dislocation configuration in EG and CG regions in TD (a, b) and PD (d, e).

Fig. 17

 17 Fig. 17. The grains with < 100 >, < 110 >, and < 111 > crystal orientations along the

  Fig. 17. The grains with < 100 >, < 110 >, and < 111 > crystal orientations along the

Fig. 18 .

 18 Fig. 18. The overview of FIB-foil image and corresponding EBSD maps, which is

Fig. 19 .

 19 Fig. 19. Fractographs of samples in TD (a, b) and PD (c, d). (b) and (d) representing

Fig. 20 .

 20 Fig. 20. Schematic of effects of defect and microstructure on anisotropic fatigue. (a)

  responsible for crack initiation and propagation in LPBF-fabricated Al-Mg-Sc-Zr alloys. The fatigue properties of the aged LPBF-fabricated Al-Mg-Sc-Zr showed a surprising anisotropy. The fatigue strength of the TD sample was 100.5 MPa, while that of the PD sample was 57 MPa. The following mechanisms were proposed. (i) With respect to defects, based on the features of defects analyzed X-ray tomography, the LoF defects in the LPBF-fabricated Al-Mg-Sc-Zr are more important to the fatigue performance than the pores. The LoF defects have irregular shape with longest axis distributing predominantly vertical to the building direction. This feature of LoF resulted in a higher stress concentration in the PD sample than that of the TD sample in the crack initiation stage. (ii) With respect to the heterogeneous structure, owing to the significant cyclic softening and indistinctive crack deflection of the CG region, it became soft with the decrease in fatigue resistance. Furthermore, the different crack propagation directions led to different CG/EG area ratios for the anisotropic fatigue properties. (iii) With respect to the CG orientation, in the TD samples, the presence of the CGs with the < 110 > || BD orientation led to a higher fatigue resistance of the TD sample than in the PD sample, owing to the exceptional dislocation formation.

Table 1

 1 Literature review on tensile performance of Sc/Zr-modified Al alloys fabricated by LAM (TD represents deposition direction is transverse to loading direction and PD is parallel to loading direction).

			Yield strength
	Refs.	Material		UTS (MPa)	εf (%)	Heat treatment	Orientation	Process
			(MPa)
			453 ± 20	530 ± 12	9 -10		TD	LPBF
	[43]	Al-Mg-Sc-Zr				Aging
			450 ± 9	515 ± 16	9 -10		PD	LPBF
	[29]	Al-Mg-Sc-Zr	510 ± 2	531 ± 2	15.0 ± 0.3	Aging	TD	LPBF
	[44]	AA5083 + Zr	309 -325	380 -399	13.9 -14.5	Aging	-	LPBF
	[30,31]	AlZnMgScZr	418 ± 3	436 ± 3	11 ± 1	T6	-	LPBF
	[18]	Al-Mg-Si-Sc-Zr	-	506 -550	8-17	Aging	-	LPBF
			556 ± 11	-	18±1.6		TD	LPBF
	[21]	Al-Mn-Sc				Aging
			530 -550	-	12-14		PD	LPBF
			349 ± 15	383 ± 5	19.5 ± 4.4		PD	LPBF
	[22]	Al-Mg-Zr				Aging
			365 ± 11	389 ± 4	23.9 ± 4.4		TD	LPBF

Table 2

 2 The chemical compositions of the experimental powder (wt.%).

	Si	Mg	Mn	Fe	Sc	Zr	Al
	0.09	4.74	0.47	0.10	0.70	0.32	Bal.
	Table 3 Constant process parameters for LPBF-fabricated Al-Mg-Sc-Zr alloy.
	Process	Laser power	Scanning speed	Layer thickness	Hatch space
	parameter	(W)		(mm/s)		(μm)	(mm)
	Value	370		1000		30	0.12

  4 MPa, 536.3 MPa, 13.7%, and 72.7 GPa, respectively, while those of the PD sample were 502.4 MPa, 530.2 MPa, 14.4%, and 72.8 GPa, respectively, as listed in Table 4. The deformation energies

(UT) of two sample series were also calculated by using the area underneath the tensile curve: UT = ∫ 𝜎𝑑𝜀 𝜀𝑓 0

Table 4

 4 Mechanical properties of LPBF-fabricated Al-Mg-Sc-Zr alloy in TD

				and PD
	Sample YS (MPa) UTS (MPa)	εf (%)	E (GPa) UT (U) σf (MPa)
	TD	509 ± 2	536 ± 1	14.5 ± 0.8 72.1 ± 2.4 6979	100.5
	PD	503 ± 2	530 ± 2	14.9 ± 0.5 72.2 ± 1.5 7298	57

Table 5

 5 Information about fatigue tests and characteristics of defects

	TD
	group

* It was not included in the staircase calculation. ** The fracture surface was damaged. 4.2 Effect of the microstructure on the anisotropic fatigue properties 4.2.1 Heterogeneous structure

Acknowledgements

This work was supported by National Key Research and Development Plan of China (2016YFB1100102) and National Natural Science Foundation of China (52005411) and the Research Fund of the State Key Laboratory of Solidification Processing (NPU) (2020-tz-02). The authors also appreciate the help from Dr. Ying Ding at Analytical & Testing Center of NPU for FIB milling.

CRediT authorship contribution statement

Jing Chen: Funding acquisition. Weidong Huang: Supervision.