Orientation Distribution Function Research Articles

Thermal Cycling Behavior of Aged FeNiCoAlTiNb Cold-Rolled Shape Memory Alloys

Fe–Ni–Co–Al-based systems have attracted a lot of interest due to their large recoverable strain. In this study, the microstructure and thermal cycling behaviors of Fe41Ni28Co17Al11.5Ti1.25Nb1.25 (at.%) 98.5% cold-rolled alloys after annealing treatment at 1277 °C for 1 h, followed by aging for 48 h at 600 °C, were investigated. From the electron backscatter diffraction results, we see that the texture intensity increased from 9.4 to 16.5 mud and the average grain size increased from 300 to 400 μm as the annealing time increased from 0.5 h to 1 h. The hardness results for different aging heat treatment conditions show the maximum value was reached for samples aged at 600 °C for 48 h (peak aging condition). The orientation distribution functions (ODFs) displayed by Goss, brass, and copper were the main textural features in the FeNiCoAlTiNb cold-rolled alloy. After annealing, strong Goss and brass textures were formed. The transmission electron microscopy (TEM) results show that the precipitate size was ~10 nm. The X-ray diffraction (XRD) results show a strong peak in the (111) and (200) planes of the austenite (⁠⁠γ, FCC) structure for the annealed sample. After aging, a new peak in the (111) plane of the precipitate (⁠⁠γ′, L12) structure emerged, and the peak intensity of austenite (⁠⁠γ, FCC) decreased. The magnetization–temperature curves of the aged sample show that both the magnetization and transformation temperature increased with the increasing magnetic fields. The shape memory properties show a fully recoverable strain of up to 2% at 400 MPa stress produced in the three-point bending test. However, the experimental recoverable strain values were lower than the theoretical values, possibly due to the fact that the volume fraction of the low-angle grain boundary (LABs) was small compared to the reported values (60%), and it was insufficient to suppress the beta phases. The beta phases made the grain boundaries brittle and deteriorated the ductility. On the fracture surface of samples after the three-point bending test, the fracture spread along the grain boundary, and the cross-section microstructural results show that the faces of the grain boundary were smooth, indicating that the grain boundary was brittle with an intergranular fracture.

Reconstruction of intra- and extra-neurite conductivity tensors via conductivity at Larmor frequency and DWI data patterns

The developed magnetic resonance electrical properties tomography (MREPT) techniques visualize the internal conductivity distribution at Larmor frequency by measuring the B1 transceive phase data. In biological tissues, electrical conductivity is influenced by ion concentrations and mobility. To visualize the anisotropic conductivity tensor of biological tissues, we use the Einstein–Smoluchowski equation, which links the diffusion coefficient to particle mobility. By assuming a correlation between ion mobility and water diffusivity, we aim to decompose the internal isotropic conductivity at Larmor frequency into anisotropic conductivity tensors within the intra- and extra-neurite compartments. The multi-compartment spherical mean technique (MC-SMT), utilizing both high and low b-value diffusion-weighted imaging (DWI) data, characterizes the diffusion of water molecules within and across the intra- and extra-neurite compartments by analyzing the microstructural intricacies and the foundational architectural arrangement of the brain’s tissues. By analyzing the relationships between the measured DWI data, the microscopic diffusion signal, and the fiber orientation distribution function, we predict the DWI data for the intra- and extra-neurite compartments using spherical harmonic decomposition. Using the predicted DWI data for the intra- and extra-neurite compartments, we develop a conductivity tensor imaging method that operates specifically within the separated compartments. Human brain experiments, involving four healthy volunteers and a brain tumor patient, were performed to assess and confirm the reliability of the proposed method.

Changes in diffusion MRI and clinical motor function after physical/occupational therapies in toddler-aged children with spastic unilateral cerebral palsy.

Diffusion-weighted magnetic resonance imaging (DMRI) is a potential tool to assess changes in brain connectivity and microstructure resulting from physical and occupational therapy in young children with cerebral palsy. This works was carried out to assess whether DMRI can detect changes after 36 weeks of physical and occupational therapy in the microstructure and connectivity of the brains of children with cerebral palsy and determine whether imaging findings correlate with changes in clinical measures of motor function. Five children underwent anatomical MRI and DMRI and evaluations of motor function skills at baseline and after 36 weeks of intensive or once-weekly physical and occupational Perception-Action Approach therapies. Diffusion tensor imaging and constrained spherical deconvolution methods were used to calculate fractional anisotropy (FA) and fiber orientation distribution functions (fODFs), respectively. The fODFs were used to generate tractograms of the cerebrospinal tract (CST). After 36 weeks of physical and occupational therapy, all children showed increases in motor function. No changes were observed in anatomical MRI before and after therapy but CST tractography did show small differences indicating possible altered microstructure and connectivity in the brain. FA values along the CSTs, however, showed no significant changes. Reliable longitudinal DMRI can be employed in toddler-aged children with CP and DMRI has the potential to monitor neuroplastic changes in white matter microstructure. However, there is a high variability between subjects and clinical improvements were not always correlated with measures of FA along the CST.

Shale anisotropic rock-physics model incorporating the effect of compaction and nonplate mixtures on clay preferred orientation

Compared with other sedimentary rocks, the strong elastic anisotropy of shale is extremely prominent, which is mainly caused by the preferred orientation and platy nature of its clay minerals. Especially in seismic reservoir characterization, a suitable and correct estimation of the shale elastic anisotropy can improve the accuracy of the shale seismic inversion and prediction. Due to the long-term compaction of shale and the rearrangement of minerals, its microstructure and macrostructure are more complex, resulting in obvious anisotropic characteristics of shale. Existing methods do not incorporate the impact of nonplate particles on clay platelets, or indirectly incorporate it through empirical formulas, resulting in poor applicability and errors in the rock-physics models. To reveal the main causes of the anisotropy of clay minerals, a theoretical model incorporating the effect of compaction and nonplate particles on the preferred orientation of clay platelets is developed using experimental data and electronic scanning results. Based on theoretical analysis, an orientation distribution function (ODF) based on the effect of compaction and nonplate particles is derived, which not only incorporates the influence of compaction but also further incorporates the effect of other nonplate particles, such as quartz, which makes the established shale anisotropic rock-physics model more reasonable and accurate. Then, an improved anisotropic shale rock-physics model is developed using the compaction and nonplate particles-based ODF. The prediction results indicate that the presence of nonplate particles has an inhibitory effect on the preferred orientation of clay platelets, which is verified by the measured experimental data and indicates that our method is reliable and effective.

Heat treatment, microstructure, texture, and mechanical properties of electron beam melted Ti6Al4V

The findings from the microstructural and textural analysis of as-printed and heat-treated electron beam melted Ti-6Al-4V (EBM-Ti64) samples are discussed in this work. The initial microstructures of both samples were characterized precisely. The as-printed microstructure exhibits aligned grain boundaries parallel to the building direction, with the presence of α platelets. In contrast, the heat-treated microstructure reveals a lamellar α/β structure with a considerably wide interlamellar spacing. This work addresses the transformations from β→α+ά and ά→α+β occurring when materials are heated up to below the β-transus temperature. While the ά→α˝+β transformation is deemed unlikely to take place, the process can still occur through spinodal decomposition of β,β→βV−poor+βV−rich→α˝+βV−rich where α˝ eventually transforms into α+β. A thorough characterization of three primary morphologies of the α phase was revealed. Due to exposure to high temperatures, as experienced in the environment of a rocket engine fan, it was necessary to conduct isothermal hot compression experiments on the homogenized EBM-Ti64 alloy. These experiments aim to investigate the hot deformation behavior within the temperature range of 250–350 °C and a strain rate of 10 s−1. The findings indicate that the modified Johnson-Cook constitutive model and its corresponding numerical simulation, based on stress-strain and work-hardening characteristics, effectively predict the flow behavior of this microstructurally complex alloy. Microstructure and mechanical properties of deformed as-printed and heat-treated samples at 250 ℃, 300 ℃, and 350 ℃ show that although dynamic recrystallization is not feasible under these conditions, we observe grain refinement and decreasing interlamellar spacing. These findings align with mechanical properties, where higher total strain and lower ultimate compression strength were noted as the testing temperature increased. Additionally, heat-treated materials exhibited inferior mechanical characteristics under each testing circumstance. Texture rotation (90 degrees) after deformation is evident in all pole figures. Considering the orientation distribution function maps, more intense <0001> fibre and {101̅0} <0001> textures were formed. Assessments of the slip systems revealed that the basal slip system has the lowest activity when considering texture orientations. Conversely, the most significant deformation contribution, particularly in the c-axis, comes from contraction twin and <c+a> 1st order pyramidal.

Microstructure and properties of Al-4.8Cu-0.45Mn-0.19Cd-0.18Ti-0.17Zr-0.14V aluminum alloy extrusion bar

The mechanical properties, texture transformation, and mechanism of Al–Cu–Mn alloy during annealing were studied using three-dimensional orientation distribution function (ODF), electron backscatter diffraction (EBSD), and transmission electron microscopy (TEM). The results showed that the increase in yield strength after annealing at 200 °C is due to the decrease in the proportion of P and M textures and the increase in the proportion of Goss texture. The increase in the change rate of mechanical properties observed during annealing at 250 and 350 °C can be attributed to the higher proportion of M and P textures and the reduced proportion of Goss textures. Among them, the proportion of M texture increased significantly, and the Goss texture decreased significantly after annealing at 350 °C. This is because the structural energy density (Ev) value of the Goss texture is higher than that of the M texture at 250 °C and 350 °C. The Goss texture is in an unstable state of high energy order. The deformed Goss texture is unstable at high temperatures, leading to conversion into M and other textures. The EBSD and TEM analysis revealed that the hardness is mainly related to the change in dislocation density. When the annealing temperature is increased from 250 to 350 °C, the hardness is significantly reduced from 62 HV to 52 HV, and the dislocation density is reduced from 4.0 × 1014 ρ/m−2 to 2.4 × 1014 ρ/m−2.

Microstructural evolution and hot tensile deformation behaviors below δ-solvus temperature of IN718 alloy fabricated by plasma arc additive manufacturing

Plasma arc additive manufacturing (PAAM) stands out for its remarkable efficient utilization and good performance reliability, making it a highly favored additive manufacturing technique. This study delves into the tensile deformation below δ-solvus temperature of PAAM IN718 alloy with complete heat treatment. The results show that the peak stresses are decreased from 1069 to 1189 MPa at 550 °C to 620–1059 MPa at 750 °C. Through the orientation distribution function, the domain textures for hot deformation were identified as cube texture <100> and Rt-Goss texture {110}<110>. The results of the observations on the substructure and grain boundary components of the deformed alloy confirmed that the onset temperature of recrystallization in PAAM alloy is approximately 750 °C. The recrystallization nucleation mechanism of PAAM IN718 alloys was identified as discontinuous dynamic recrystallization. A deformation constitutive equation for hot deformation was established using the Zener-Hollomon parameter, with an average activation energy of 508.93 kJ/mol. A processing map for the hot working of PAAM alloy was developed, and the reasonable processing domains are located at a temperature 700–750 °C/strain rate 10−2–10−1 s−1 with a power dissipation efficiency range of 0.41–0.47. The high-temperature fracture mechanism of PAAM alloy was discussed, identifying the important inducements for high-temperature fracture failure including carbides, residual Laves phase, and δ phase in the PAAM alloy.

Bundle-specific tractogram distribution estimation using higher-order streamline differential equation

Streamline tractography locally traces peak directions extracted from fiber orientation distribution (FOD) functions, lacking global information about the trend of the whole fiber bundle. Therefore, it is prone to producing erroneous tracks while missing true positive connections. In this work, we propose a new bundle-specific tractography (BST) method based on a bundle-specific tractogram distribution (BTD) function, which directly reconstructs the fiber trajectory from the start region to the termination region by incorporating the global information in the fiber bundle mask. A unified framework for any higher-order streamline differential equation is presented to describe the fiber bundles with disjoint streamlines defined based on the diffusion vectorial field. At the global level, the tractography process is simplified as the estimation of BTD coefficients by minimizing the energy optimization model, and is used to characterize the relations between BTD and diffusion tensor vector under the prior guidance by introducing the tractogram bundle information to provide anatomic priors. Experiments are performed on simulated Hough, Sine, Circle data, ISMRM 2015 Tractography Challenge data, FiberCup data, and in vivo data from the Human Connectome Project (HCP) for qualitative and quantitative evaluation. Results demonstrate that our approach reconstructs complex fiber geometry more accurately. BTD reduces the error deviation and accumulation at the local level and shows better results in reconstructing long-range, twisting, and large fanning tracts.

Predicting Effective Transport Properties of Randomly Oriented Polycrystalline Li-Ion Battery Electrodes

Widely practiced Li-ion battery models, such as pseudo-two-dimensional (P2D) models [1-3], use representative spherical electrode particles with assumed isotropic transport properties. Electrode particles, such as NMC, are typically composites that are comprised of numerous randomly oriented crystallites. Each of the single-crystal primary particles that compose secondary particle can have strongly anisotropic transport properties that affect the intercalation process. The empirically approximated effective properties (e.g., diffusion coefficients) as reported in literature vary by as much as six orders of magnitude. In many cases, the effective diffusion coefficients are determined as a part of a parameter-fitting procedure to represent battery polarization measurements.The present approach develops both analytical and computational homogenization methods that derive effective properties based upon the intrinsic single-crystal properties of the crystallites. Homogenization techniques are computationally effective methods to predict macroscale behavior based on microscale properties.As illustrated in Fig. 1, the computational approach begins by assembling over 1000 randomly oriented single-crystal primary particles, with each crystallite having anisotropic properties associated with the crystal lattice. The dodecahedron-shaped primary particles are tightly assembled into a secondary particle that is approximately spherical. A three-dimensional finite-element model predicts transient Li-intercalation fractions throughout a secondary particle during charge or discharge processes. In graphite, the transverse and normal diffusion coefficients differ by approximately six orders of magnitude. Based on the cut plane in Fig. 1, and despite extreme anisotropy within the crystallites, the homogenized macroscopic behavior is nearly isotropic.The analytical approach extends a self-consistent method (SCM) for polycrystalline materials first presented by Ponte-Castañeda and Willis [4], which mathematically combines tensors describing diffusion pathways for every primary particle. The present study considers the concentration-dependent and anisotropic diffusion parameters collected by Persson et al. [5] and Zhou et al. [6] for graphite and NMC, respectively. Another homogenization method is the use of an orientation distribution function (ODF) [7], which predicts the effective diffusion parameters based on the statistical average of every possible primary particle orientation. Fig. 2 shows the predicted effective diffusion coefficients bounded by Hashin-Shtrikman bounds for anisotropic composites proposed by Willis [8] and the experimentally determined diffusion coefficients. The predicted effective diffusion coefficients are lower than the experimentally determined values in transverse direction but are significantly larger than the values in the normal direction. Additionally, the in-plane diffusion dominates the curvature of the predicted effective properties.[1] M. Doyle, T. F. Fuller, and J. Newman. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. J. Electrochem. Soc., 140:1526–1533, 1993.[2] T. F. Fuller, M. Doyle, and J. Newman. Simulation and optimization of the dual lithium ion insertion cell. J. Electrochem. Soc., 141:1–10, 1994.[3] M. Doyle, J. Newman, A. S. Gozdz, C. N. Schmutz, and J.-M. Tarascon. Comparison of modeling predictions with experimental data from plastic lithium ion cells. J. Electrochem. Soc., 143:1890–1903, 1996[4] P.P.- Castañeda and J.R. Willis. The effect of spatial distribution on the effective behavior of composite materials and cracked media. J. Mech. Phys. Solids, 43:1919–1951, 1995[5] K. Persson, V. A. Sethuraman, L. J. Hardwick, Y. Hinuma, Y. S. Meng, A. van der Ven, V. Srinivasan, R. Kostecki, and G. Ceder. Lithium diffusion in graphitic carbon. J. Phys. Chem. Lett., 1:1176–1180, 2010[6] H. Zhou, F. Xin, B. Pei, and M. S. Whittingham. What limits the capacity of layered oxide cathodes in lithium batteries? ACS Energy Lett., 4:1902–1906, 2019[7] S. Nemat-Nasser, M. Hori, and J. D. Achenbach. Micromechanics: Overall properties of heterogeneous materials. In Micromechanics, volume 37. Elsevier Science I& Technology, The Netherlands, 1993[8] J.R. Willis. Bounds and self-consistent estimates for the overall properties of anisotropic composites. J. Mech. Phys. Solids, 25:185–202, 1977 Figure 1

Piezoresistive modeling of orthotropic 3D-printing composite line extrusions with non-affine reorientation of fibers

This work introduces a micromechanical semi-analytical model to estimate piezoresistive constants in 3D-printable short-fiber composites, extending the Mori–Tanaka scheme with two innovative components. Firstly, the model incorporates non-affine reorientation of fibers, controlled by a parameter η, which significantly impacts texture coefficients. This parameter introduces an additional layer of complexity, modifying texture coefficients beyond traditional affine fiber reorientations. Observational data illustrate a linear relationship between piezoresistivities and η, leading to the development of a statistical model that calculates η based on the fiber aspect ratio. Secondly, the model accounts for preferential fiber orientation in the undeformed state, resulting in an orthotropic material model. This anisotropy is quantified using an Orientation Distribution Function (ODF) derived from X-ray scans, which is parameterized to maintain symmetry across three orthogonal planes. Initial investigations indicate that the inherent anisotropy introduced by the printing process substantially affects the initial resistivity of 3D-printed composites. Utilizing a Gaussian transversely isotropic model, we find that neglecting this anisotropy could lead to significant errors in understanding and predicting piezoresistive behavior. The model’s incorporation into advanced nanocomposite frameworks offers preliminary reconciliation with experimental data. Additionally, our results emphasize the necessity to refine wavy fiber models by incorporating non-affine rotations, particularly crucial for fibers with small aspect ratios, thereby enhancing predictive accuracy. The findings lay a robust foundation for future research, emphasizing the need for comprehensive experimental validation and setting the stage for nuanced applications in piezoresistive composite materials.

Reconstruction of the Orientation Distribution Function for Materials with Low Lattice and Sample Symmetry Using the Harmonic Method

Reconstruction of the Orientation Distribution Function for Materials with Low Lattice and Sample Symmetry Using the Harmonic Method

Texture tomography, a versatile framework to study crystalline texture in 3D.

Crystallographic texture is a key organization feature of many technical and biological materials. In these materials, especially hierarchically structured ones, the preferential alignment of the nano constituents heavily influences the macroscopic behavior of the material. To study local crystallographic texture with both high spatial and angular resolution, we developed Texture Tomography (TexTOM). This approach allows the user to model the diffraction data of polycrystalline materials using the full reciprocal space of the crystal ensemble and describe the texture in each voxel via an orientation distribution function, hence it provides 3D reconstructions of the local texture by measuring the probabilities of all crystal orientations. The TexTOM approach addresses limitations associated with existing models: it correlates the intensities from several Bragg reflections, thus reducing ambiguities resulting from symmetry. Further, it yields quantitative probability distributions of local real space crystal orientations without further assumptions about the sample structure. Finally, its efficient mathematical formulation enables reconstructions faster than the time scale of the experiment. This manuscript presents the mathematical model, the inversion strategy and its current experimental implementation. We show characterizations of simulated data as well as experimental data obtained from a synthetic, inorganic model sample: the silica-witherite biomorph. TexTOM provides a versatile framework to reconstruct 3D quantitative texture information for polycrystalline samples; it opens the door for unprecedented insights into the nanostructural makeup of natural and technical materials.

The impact of annealing temperature and time on the grain distribution and texture evolution of cold-rolled electric-furnace annealed low-carbon steel

This study investigated the effect of annealing temperature and time on the grain distribution and textural development of commercial-grade low-carbon steel that undergone cold rolling and subsequent electric-furnace annealing at either 700 or 800 °C for 5 and 10 min. Scanning electron microscopy and electron backscatter diffraction analyses of the annealed samples revealed equiaxed microstructures with cementite at the ferrite grain boundaries. The samples annealed at 700 °C for 5 and 10 min exhibited a bimodal grain distribution, while larger ferrite grains formed at 800 °C. The orientation distribution function texture of the sample annealed at 700 °C for 5 min exhibited both a γ-fiber ND//〈111〉 and a cube texture ND//〈001〉 . Raising the annealing temperature and time reduced the intensity of cube texture and strengthened the γ-fiber, increasing tensile elongation from 8 to 38 %.

Stress relaxation following sudden cessation of steady shearing from polymer rotarance theory

Deriving rheological material functions from rotarance theory proceeds in two steps. We first solve the general diffusion equation to get the polymer orientation distribution, then we integrate the result in phase space to get the material functions. Rotarance theory thus relies entirely on polymer orientation to explain the elasticity of a polymeric liquid and, thus, to explain how such complex fluids depart from Newtonian behavior. We are attracted to rotarance theory by virtue of its versatility. The rheological behavior can be deduced, from first principles, from the structure of the macromolecule. However, of the 13 canonical rheological material functions, 5 are still unknown. We devote this paper to stress relaxation following cessation of steady shear flow. We arrive at analytical expressions for the relaxation of the orientation distribution function and then integrate this to get expressions for the relaxation of the shear stress, along with both normal stress differences.

ODF-based model considering compressive stress for modeling the magnetic properties of Grain-oriented electrical steels

Grain-oriented electrical steels (GOES) are widely used in the manufacturing of high efficiency energy conversion systems thanks to their excellent magnetic properties along the rolling direction. Nevertheless, on the one hand, GOES exhibit strong magnetic anisotropy, resulting in distinct magnetic properties regarding the direction of the applied magnetic field to the rolling direction. On the other hand, GOES undergoes changes in their magnetic properties due to the industrial manufacturing process and mechanical constraints during operation. In general, stress, and particularly compressive stress, deteriorates magnetic properties. This paper deals with the modeling of the magnetic behavior of GOES under compressive stress. The orientation distribution function (ODF) based approach recently applied to describe the B-H first magnetization curves of a conventional GOES without stress as well as under applied uniaxial mechanical tensile stress is extended to account for the effect of compressive stress, with different considerations of modeling. The magnetic properties and the sensitivity of the ODF-based model to the magnetization direction as well as to the applied compressive stress are analyzed. Oscillation issues inherent to the ODF-based model are also discussed.

Effect of HIP Treatment on the Evolution of Texture and Microstructure of LBPF Fabricated Pure Ni

Microstructure and texture analysis were conducted employing electron backscatter diffraction (EBSD) technique on laser powder bed fusion (LPBF) fabricated pure Ni. The texture analysis of the hot isostatic pressed (HIP) and as-printed (AP) samples were done utilizing orientation distribution function (ODF) maps. The AP sample comprises mostly of &amp;lt;110&amp;gt;||BD fiber texture with insignificant presence of twins. In contrast, the HIP sample has &amp;lt;111&amp;gt;||BD grains. It was found that the development of the texture &amp;lt;111&amp;gt;||BD was due to the deformation linked to the HIP process. In addition, HIP generated a substantial fraction of Σ3 coincident site lattice boundaries (CSL) because of pure Ni which is a medium stacking fault energy (SFE) element.

AtomTex: texture characterization software for atomic configurations

A software named AtomTex has been developed for characterizing texture/orientation of atomic configurations. The software currently can generate orientation distribution functions, Miller indices, pole figures, inverse pole figures and angle-axis pairs between grains. Utilizing AtomTex, one can explicitly trace orientation evolution of a given atom, resembling an in situ probe with atomic scale resolution, which is expected to significantly deepen understanding how microstructure evolves upon various thermomechanical treatments.

Accurate distances measures and machine learning of the texture-property relation for crystallographic textures represented by one-point statistics

The crystallographic texture of metallic materials is a key microstructural feature that is responsible for the anisotropic behavior, e.g. important in forming operations. In materials science, crystallographic texture is commonly described by the orientation distribution function, which is defined as the probability density function of the orientations of the monocrystal grains conforming a polycrystalline material. For representing the orientation distribution function, there are several approaches such as using generalized spherical harmonics, orientation histograms, and pole figure images. Measuring distances between crystallographic textures is essential for any task that requires assessing texture similarities, e.g. to guide forming processes. Therefore, we introduce novel distance measures based on (i) the Earth Movers Distance that takes into account local distance information encoded in histogram-based texture representations and (ii) a distance measure based on pole figure images. For this purpose, we evaluate and compare existing distance measures for selected use-cases. The present study gives insights into advantages and drawbacks of using certain texture representations and distance measures with emphasis on applications in materials design and optimal process control.

Microstructure evolution and local mechanical properties of friction stir additively manufactured (FSAM) AA5083/AA6061/AA7075 gradient composite

The current study is focused on the successful fabrication and characterization of microstructure and properties gradient composite made of 3 mm thick sheets of AA5083-O, AA6061-T6, and AA7075-T6 alloys using friction stir additive manufacturing (FSAM) technique. Two combinations of four layered FSAM builds (6756 and 7567) were fabricated successfully without any major defects at the optimized process parameters of 850 rpm (tool rotational speed) and 55 mm/min (tool transverse speed). The material mixing, interfacial bonding features, microstructure evolution, and mechanical performance within the stir zones (SZ) were thoroughly examined using advanced characterization techniques. Electron backscatter diffraction (EBSD) analysis confirmed a gradient microstructure along the build depth in both FSAM builds, with average grain sizes decreasing from 52 μm (AA5083), 46 μm (AA6061), and 40 μm (AA7075) in base metals to ∼ 4–7 μm within the SZ. The remarkable grain refinement within the SZ was mainly attributed to the dominant presence of the continuous dynamic recrystallization (CDRX) mechanism. Texture analysis corresponding to pole figures (PFs) and orientation distribution function (ODF) plots reveals the crystallographic texture evolution along the build depth. The prevalent existence of B/ B‾ and C textures throughout all regions of the FSAM builds affirms the presence of ample shear strain during the FSAM procedure. Through thickness miniature tensile and microhardness tests depict the gradient in mechanical performance for both the FSAM builds along the build depth. Microhardness gradients in the range from ∼ 80 HV0.1 to ∼ 145 HV0.1 were observed along the build depth. The axial sample in the build direction shows appreciable strength (265 MPa and 224 MPa) and uniform elongation (28 % and 24 %) for 6756 and 7567 FSAM build, respectively. Furthermore, remarkable strain hardening behaviour corresponding to hardening capacity (Hc) and hardening exponent (n) was noticed for both the axial build samples compared to AA6061-T6 and AA7075-T6 base metals. These findings underscore the potential of FSAM in fabricating functionally gradient composite materials tailored to specific functional requirements.

Analytical modelling of the orientation dependency of 3D printed SHCC at increasing levels of scale

3D printable strain hardening cementitious composites (3DP-SHCC) stand out for their high ductility and increase in tensile strength after initial cracking. Due to the printing process, which includes the pumping and extruding of the material, the fibres are not uniformly orientated in the material but have an orientation dependency due to the specific printing process applied. Three different cases for the fibre orientation distribution functions are presented with increasing levels of relation to the printing process. These three cases have been used in a micro-mechanical model to verify with experimental stress-crack opening results (single crack). Furthermore, a spring model is used to give insight into the potential to develop pseudo strain hardening behaviour (multiple cracking) in various printing directions. The method is also used to model the experimentally obtained spread in uni-axial tensile dogbone test results. From these experimental dogbone tests, average stress-strain relations are determined in two directions. Finally, a multi-layer method is used on the component level to validate the use of these average stress-strain relations for modelling the bending behaviour of printed elements in multiple directions.