Polycrystalline Microstructure Research Articles

An alternate approach for estimating grain-growth kinetics

Rate of grain growth, which aides in achieving desired properties in polycrystalline materials, is conventionally estimated by measuring the size of grains and tracking its change in micrographs reflecting the temporal evolution. Techniques adopting this conventional approach demand an absolute distinction between the grains and the interface separating them to yield an accurate result. Edge-detection, segmentation and other deep-learning algorithms are increasingly adopted to expose the network of boundaries and the associated grains precisely. An alternate approach for measuring grain-growth kinetics, that curtails the need for advanced image-processing treatment, is presented in this work. Grain-growth rate in the current technique is ascertained by counting the number of triple-( and quadruple-) junctions, and monitoring its change during the microstructural evolution. The shifted focus of this junction-based treatment minimises the significance of a well-defined grain-boundary network, and consequently, the involvement of the sophisticated techniques that expose them. A regression-based object-detection algorithm is extended to realise, and count, the number of junctions in polycrystalline microstructures. By examining the change in the number of junctions with time, the growth rate is subsequently determined. Growth kinetics estimated by the present junction-based approach, across a wide-range of multiphase polycrystalline microstructures, agree convincingly with the outcomes of the conventional treatment. Besides offering a novel technique for grain-growth measurement, the analysis accompanying the current work unravels a trend, compatible with the topological events, in the progressive evolution of the triple-junctions count. The present approach, through its underlying algorithm, provides a promising option for monitoring grain-growth during in-situ investigations.

Outstanding shape memory effect and thermal stability of Cu–Al–Ni-based high temperature shape memory alloys achieved by Gd and Mn doping

In this paper, the effects of Mn element and rare earth element Gd on the microstructure, thermal stability, mechanical properties and shape memory effect of polycrystalline Cu-12.0Al-4.0Ni and Cu-12.0Al-4.0Ni-1.5Mn-xGd high-temperature shape memory alloy were investigated. The results show that the Cu-12.0Al-4.0Ni alloy exhibits millimeter-sized grain, dual-phase structure with coexistence of 18R and 2H martensite and poor thermal stability. When the Mn and Gd element was added to Cu-12.0Al-4.0Ni alloys, the grain size can be refined by an order of magnitude, and the 2H martensite disappeared completely, accompanied by the formation of the AlCu4Gd phase, meanwhile, thermal stability is significantly improved. The grain refinement improves the mechanical properties and shape memory effect of Cu-12.0Al-4.0Ni-1.5Mn-xGd alloys. When x = 0.3, the compressive fracture stress, compressive fracture strain and recoverable strain can reach 969 MPa, 15 % and 8 %, respectively.

A parallel and performance portable implementation of a full-field crystal plasticity model

We have developed a parallel implementation of an Elasto-Viscoplastic Fast Fourier Transform-based (EVPFFT) micromechanical solver to enable computationally efficient crystal plasticity modeling for polycrystalline materials. Our primary focus lies in achieving performance portability, allowing a single EVPFFT implementation to run optimally on various homogeneous architectures, including multi-core Central Processing Units (CPUs), as well as on heterogeneous computer architectures comprising multi-core CPUs and Graphics Processing Units (GPUs) from different vendors. To accomplish this goal, we have leveraged MATAR, a C++ software library that simplifies the creation and utilization of multidimensional dense or sparse matrix and array data structures. These data structures are designed to be portable across diverse architectures through the use of Kokkos, a performance-portable library. Additionally, we have employed the Message Passing Interface (MPI) to efficiently distribute the computational workload among processors. The heFFTe (Highly Efficient FFT for Exascale) library is used to facilitate the performance portability of the fast Fourier transforms (FFTs) computation. The computational performance of EVPFFT is evaluated and presented in terms of parallel scalability and simulation runtime on different high-performance computing (HPC) architectures. The utility of the developed framework to efficiently simulate the micro-mechanical fields in polycrystalline microstructures in engineering applications is discussed. Program summaryProgram Title: EVPFFTCPC Library link to program files:https://doi.org/10.17632/2k8579fyyv.1Developer's repository link:https://github.com/lanl/FierroLicensing provisions: BSD 3-Clause LicenseProgramming language: C++External routines/libraries: MPI, Kokkos, MATAR, HeFFTe, HDF5Nature of problem: EVPFFT is a crystal plasticity code designed to compute micro-mechanical fields within a polycrystalline representative volume element (RVE) and predict the macroscale response of the RVE.Solution method: EVPFFT uses the periodic Green's function method in Fourier space to solve the field equations of static stress equilibrium in a periodic spatial domain.

Direct modeling of non-uniform strain field of heterogeneous materials

Engineering materials have a heterogeneous microstructure that induces non-uniform deformations (NUDs) even under uniform stress. Therefore, the development of NUDs in heterogeneous materials under a macroscopically non-uniform stress is characterized by the interactions between micro- and macroscopic NUDs. In this study, we attempt to directly describe microscopic NUDs by introducing a constitutive equation for the strain field. Using polycrystalline metal, which is a well-known heterogeneous material, we performed the uniaxial tensile tests on specimens with curved gauge sections. During modeling, the constitutive equation without nonlocal effect was first fitted based on the distribution of the local equivalent stress and strain. The strain calculated using the fitted equation was regarded as the strain for the homogeneous material, whereas the strain deviating from the fitted equation was assumed to be induced by the microscopic heterogeneity of the material. The respective strains were represented using different constitutive models, and the parameters employed in the models were fitted separately using the experimentally measured strain field. The plastic compliance gradient was employed as a material parameter quantifying the microscopic NUDs. Subsequently, a multiaxial elastoplastic nonlocal constitutive equation was formulated based on the nonlocally extended J2 flow theory. Finite element method simulations introducing the proposed nonlocal effect indicated that a scale-dependent NUD characterized by the interactions between micro- and macro-NUDs could be represented using the proposed model. Furthermore, the proposed model could predict the experimentally observed strain field characterized by a polycrystalline microstructure, such as the dispersion of the strain concentration at the curved gauge section and the appearance of NUDs even under uniform stress.

Coupled crystal plasticity and damage model for micro crack propagation in polycrystalline microstructures

Coupled crystal plasticity and damage model for micro crack propagation in polycrystalline microstructures

Raster approach to modelling the failure of arbitrarily inclined interfaces with structured meshes

AbstractThis paper presents an approach to evaluate the failure of arbitrarily inclined interfaces using FE models with structured spatial discretization, providing accurate prediction of crack propagation along paths known a priori that are not constrained to the element boundaries. The combination of algorithms for the generation of structured discretization of representative polycrystalline microstructures with novel cohesive element formulations allow modelling the failure of complex topologies along rasterised boundaries, with noticeably higher computational efficiency and comparable accuracy. Two formulations of raster cohesive elements are presented, adopting either elastic-brittle or Tvergaard–Hutchinson traction separation laws. The formulations proposed are first validated comparing the failure of the interface within bi-crystal structures discretised using hexahedral elements either within a structured mesh (i.e. with rasterised boundaries) or an unstructured mesh (i.e. with planar boundary). Subsequently, the effectiveness of the formulations is demonstrated comparing the inter-granular crack propagation within complex polycrystalline microstructures. The behaviour of the novel cohesive element formulation in structured meshes consisting of regular hexahedral elements is in excellent agreement with the deformation and failure of classic cohesive element formulations placed along the planar boundaries of unstructured meshes consisting of tetrahedral elements. The higher computational cost of the raster cohesive elements is more than compensated by the increase in computational efficiency of structured meshes when compared to unstructured meshes, leading to a reduction of the simulation time of up to over 200 times for the simulations presented in the paper, thus allowing the simulation of large domains.

Nitrogen doped single layer graphene for CZTS-based thin film solar cells

CdS thin films are commonly utilized as a buffer layer in chalcopyrite thin-film solar cells. However, due to the toxic nature of Cadmium (Cd), ongoing efforts are being directed towards exploring alternative options. In this contribution, doped graphene film with remarkable optical and electrical properties has been introduced for the first time as an alternative buffer layer, replacing CdS in CZTS thin-film solar cell application. In this study, nitrogen-doped graphene (N-doped graphene) film was utilized as a substitute buffer layer in the CZTS thin-film solar cell structure, replacing the conventional CdS thin film. For comparative analysis, CZTS/N-doped graphene and CZTS/CdS traditional solar cell structures were fabricated and separately characterized. The CZTS thin films produced were examined through EDX, XRD, SEM, Raman, optical transmission and PL spectroscopy measurements. According to performed analyses, the Cu-poor and Zn-rich kesterite CZTS thin films exhibited a uniform and dense polycrystalline microstructure as observed in surface and cross-sectional SEM images. XRD spectra of the kesterite CZTS thin film displayed predominant peaks corresponding to the (112), (220/204), and (312/116) diffraction planes of the kesterite CZTS phase. Raman spectra showed a dominant peak at ∼336 cm−1 associated with the kesterite CZTS phase. PL emission spectra indicated transitions from the conduction band to defect levels. The CVD-grown doped graphene film exhibited a 3.43 I2D/IG ratio and a 25 cm−1 FWHM of the 2D peak, indicating a single-layer graphene according to Raman analysis. Permanent nitrogen doping with a 2% atomic concentration was confirmed by XPS measurement. The optical transmission measurement of the single layer doped graphene film showed a 95% transmittance value. Nitrogen doping was contributed to decrease the sheet resistance of the graphene film. The Glass/Mo/CZTS/N-doped graphene/i-ZnO/ITO/Al solar cell displayed a VOC of 0.267 V, JSC of 24.6 mA/cm2, FF of 36.46, and η of 2.37%, showing higher FF and Jsc values but lower conversion efficiency compared to the Glass/Mo/CZTS/CdS/i-ZnO/ITO/Al traditional solar cell structure. Hence, the superior working function and transparency properties position the N-doped graphene film as a competitive buffer layer for use in CZTS-based thin-film solar cells.

Tomography-based digital twin of Nd-Fe-B permanent magnets

Many functional materials have been designed at the multiscale level. To properly simulate their physical properties, large and sophisticated computer models that can replicate microstructural features with nanometer-scale accuracy are required. This is the case for permanent magnets, which exhibit a long-standing problem of a significant offset between the simulated and experimental coercivities. To overcome this problem and resolve the Brown paradox, we propose an approach to construct large-scale finite element models based on the tomographic data from scanning electron microscopy. Our approach reconstructs a polycrystalline microstructure with actual shape, size, and packing of the grains as well as the individual regions of thin intergranular phase separated by triple junctions. Such a micromagnetic model can reproduce the experimental coercivity of ultrafine-grained Nd-Fe-B magnets along with its mechanism according to the angular dependence of coercivity. Furthermore, a remarkable role of thin triple junctions as nucleation centers for magnetization reversal is revealed. The developed digital twins of Nd-Fe-B permanent magnets can assist their optimization toward the ultimate coercivity, while the proposed tomography-based approach can be applied to a wide range of polycrystalline materials.

Abnormal Grain Growth and Pseudoelasticity of Industrially Processed Fe–Mn–Al–Ni Shape Memory Alloy Joined by Metal Inert Gas Welding

The effect of metal inert gas welding on the microstructure, abnormal grain growth and the pseudoelastic properties of industrially processed Fe–Mn–Al–Ni shape memory alloy sheets were studied. Square-butt welds were manufactured using similar filler material. The influence of alternating mean arc linear energy on the microstructure of the individual zones is shown. A correlation between the process parameters, the associated heat input, the grain morphology and the α/γ-ratio could be deduced. As the mean arc linear energy increases, the α/γ-ratio in the fusion zone and the heat-affected zone increases. To evaluate the influence of the welding process on abnormal grain growth, a post-weld cyclic heat-treatment was carried out. Although no loss of major alloying elements in the fusion zone was observed after welding, metal inert gas welding has a significant effect on grain growth upon cyclic heat treatment. While abnormal grain growth occurred in the base material, a polycrystalline microstructure characterized by significantly smaller grain sizes was visible in the former fusion zone. Incremental strain tests revealed severe plastic deformation near the grain boundaries in the former fusion zone. However, the grain boundaries of the bamboo-like grown grains in the base material turned out to be more critical for structural failure.

Generative adversarial network (GAN) enabled Statistically equivalent virtual microstructures (SEVM) for modeling cold spray formed bimodal polycrystals

Image-based micromechanical models, necessary for the development of structure-property-response relations, are far from mature for complex microstructures with multi-modal distributions of morphological and crystallographic features, such as those occurring with cold spray-formed (CSF) aluminum alloys. These materials have a bimodal polycrystalline microstructure composed of recrystallized ultra-fine grains (UFGs) and deformed coarse grains (CGs) within prior particles. A prime reason is the lack of robust approaches for generating statistically equivalent virtual microstructures (SEVM) capturing the statistics of characteristic morphological and crystallographic features, such as grain size, crystallographic orientations, and misorientations. This paper introduces an approach, strategically integrating Generative Adversarial Network-based approaches for producing bimodal CSF AA7050 alloy microstructures, with the synthetic microstructure builder Dream3D for packing prior particles with CGs having statistically equivalent morphological and crystallographic descriptors to electron backscatter diffraction (EBSD) maps. An efficient finite element (FE) simulation approach is developed for the SEVMs to generate local and overall response functions through the creation of sub-volume elements (SVEs).

Effect of bias voltage on the structural properties of WN/NbN nanolayer coatings deposited by cathodic-arc evaporation

In this work, WN/NbN nanolaminate coatings were synthesized by cathodic-arc physical vapor deposition (CA-PVD) technique on a stainless-steel substrate. The paper reports the microstructure, cross-sectional morphology, surface roughness, and adhesion strength changes caused by variations in the absolute values of the negative substrate bias voltage, Us , in the 50-200 V range. Synthesized coatings were analyzed by Grazing incidence X-ray diffraction (GI-XRD), scanning transmission electron microscopy (STEM), scanning electron microscopy (SEM), laser scanning confocal microscopy (LSCM), and Daimler-Benz test. The phase analysis revealed that multilayer coatings had complex polycrystalline microstructure. They consisted of face-cantered cubic (fcc) β-W2N, fcc δ-NbN, and hexagonal ε-NbN phases. The total thickness and surface roughness had a descending trend with an increase in the absolute value of the negative bias voltage. Moreover, the WN/NbN coating deposited at Us = -50 V demonstrated the best adhesion strength to the substrate, suitable for protective coatings.

Automated Reconstruction and Conforming Mesh Generation for Polycrystalline Microstructures from Imaging Data

A new algorithm named PolyCISAMR is introduced to automatically generate high-fidelity conforming finite element (FE) meshes for two-dimensional polycrystalline microstructures. PolyCISAMR extends the capabilities of the Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) algorithm, which transforms a structured grid overlaid on the domain geometry into a high-quality conforming mesh. The PolyCISAMR approach uses a segregated meshing strategy, where CISAMR is used to discretize each grain independently and the resulting matching meshes are merged to form the final FE model. In addition, this article presents a set of integrated algorithms for processing low-resolution images of a polycrystal, reconstructed using DREAM.3D software (Version 6.5.121), to generate NURBS characterizations for each grain prior to mesh generation. Example problems demonstrate the effectiveness of PolyCISAMR in creating high-quality meshes for various polycrystalline metallic microstructures along with corresponding crystal plasticity finite element (CPFE) simulations.

Mechanical properties of Al2O3–LaPO4 composites with eutectic microstructure produced by flash sintering

AbstractThe mechanical properties of Al2O3–LaPO4 composites with varying microstructures produced by flash sintering and conventional sintering are evaluated. Specifically, Vickers and Knoop hardness values were measured and calculated for different resultant microstructures, including eutectic microstructures with varying layer thickness, polycrystalline (noneutectic) microstructures, and single‐phase samples of Al2O3, LaPO4, and 8YSZ. The findings indicate that eutectic microstructures exhibited higher hardness values than polycrystalline counterparts on the flash‐sintered sample. However, the hardness values of eutectic microstructures with varying layer thicknesses show no significant or systematic variation. The grain size, indentation size, eutectic colony size, indentation shape (elastic recovery in Knoop indentations), and crack propagation pathways in the indented samples are also discussed. Overall, the results suggest that Al2O3–LaPO4 eutectic composites have higher hardness than their polycrystalline counterparts and have great potential as abradable coatings with high machinability and durability.

Microstructural effects in rate-dependent responses of smooth and notched magnesium bars

We perform three-dimensional crystal plasticity simulations of smooth and notched bar geometries made of polycrystalline hexagonal close-packed material representing a magnesium alloy. The polycrystalline microstructure is explicitly resolved to investigate the combined effect of initial texture and grain size on the rate-dependent macroscopic responses and their micromechanical underpinnings under uniaxial and multiaxial stress states. The simulations reveal that in addition to the textural effect recently investigated by Ravaji et al. (2021), grain size plays an important role in the anisotropy of macroscopic responses. For a given texture, the lateral deformation anisotropy increases with grain size refinement for all strain rates considered here. The load-deformation responses exhibit a synergistic strengthening effect in microstructures with stronger initial textures and finer grain sizes, which is enhanced with increasing notch acuity. A transition from a conventional power-law type load-deformation response to a sigmoidal load-deformation response may occur, which depends on the imposed strain rate. It is a result of the interaction between textural weakening and grain size refinement that influence extension twinning together with an equitable landscape of the different slip mechanisms. We discuss possible implications of the net material plastic anisotropy due to texture and grain size on macroscopic failure using a micromechanical basis.

Stieltjes functions and spectral analysis in the physics of sea ice

Abstract. Polar sea ice is a critical component of Earth’s climate system. As a material, it is a multiscale composite of pure ice with temperature-dependent millimeter-scale brine inclusions, and centimeter-scale polycrystalline microstructure which is largely determined by how the ice was formed. The surface layer of the polar oceans can be viewed as a granular composite of ice floes in a sea water host, with floe sizes ranging from centimeters to tens of kilometers. A principal challenge in modeling sea ice and its role in climate is how to use information on smaller-scale structures to find the effective or homogenized properties on larger scales relevant to process studies and coarse-grained climate models. That is, how do you predict macroscopic behavior from microscopic laws, like in statistical mechanics and solid state physics? Also of great interest in climate science is the inverse problem of recovering parameters controlling small-scale processes from large-scale observations. Motivated by sea ice remote sensing, the analytic continuation method for obtaining rigorous bounds on the homogenized coefficients of two-phase composites was applied to the complex permittivity of sea ice, which is a Stieltjes function of the ratio of the permittivities of ice and brine. Integral representations for the effective parameters distill the complexities of the composite microgeometry into the spectral properties of a self-adjoint operator like the Hamiltonian in quantum physics. These techniques have been extended to polycrystalline materials, advection diffusion processes, and ocean waves in the sea ice cover. Here we discuss this powerful approach in homogenization, highlighting the spectral representations and resolvent structure of the fields that are shared by the two-component theory and its extensions. Spectral analysis of sea ice structures leads to a random matrix theory picture of percolation processes in composites, establishing parallels to Anderson localization and semiconductor physics and providing new insights into the physics of sea ice.

Inverse design of dual-phase steel microstructures using generative machine learning model and Bayesian optimization

The design of optimal microstructures requires first, the identification of microstructural features that influence the material’s properties and, then, a search for a combination of these features that give rise to desired properties. For microstructures with complex morphologies, where the number of features is large, deriving these structure–property relationships is a challenging task. To address this challenge, we propose a generative machine learning model that can automatically identify low-dimensional descriptors of microstructural features that can be used to establish structure–property relationships. Based on this model, we present an integrated, data-driven framework for microstructure characterization, reconstruction, and design that is applicable to heterogeneous materials with polycrystalline microstructures. The proposed method is evaluated on a case study of designing dual-phase steel microstructures created with the multi-level Voronoi tessellation method. To this end, we train a variational autoencoder to identify the descriptors from these synthetic dual-phase steel microstructures. Subsequently, we employ Bayesian optimization to search for the optimal combination of the descriptors and generate microstructures with specific yield stress and low susceptibility for damage initiation. The presented results show how microstructure descriptors, determined by the variational autoencoder model, act as design variables for an optimization algorithm that identifies microstructures with desired properties.

Characterizing polycrystalline microstructures by reconstructing grain boundaries and velocity map from ultrasonic surface wave field

An ultrasonic material characterization method is proposed to reconstruct the polycrystalline microstructures from the field-measurement of ultrasonic surface waves. Two wavenumber–frequency domain filters are developed to extract specific wave components for the reconstructions. One is the evanescent-pass filter that can be used to reconstruct the grain boundaries. The other is the directional filter to map the surface wave velocity along a specific direction. The method is validated by numerical simulations, as well as by experiments, on an additively manufactured sample. Sub-wavelength resolution can be achieved by the proposed method if sufficient data is captured spatially within one wavelength of the surface wave.

Achieving high efficiency in reduced order modeling for large scale polycrystal plasticity simulations

Reduced order models for the nonlinear response of heterogeneous microstructures typically require a construction (or training) stage to build the reduced order basis. In this manuscript, an efficient model construction strategy for the eigenstrain homogenization method (EHM) is presented. The proposed strategy relies on a parallel, element-by-element, conjugate gradient solver. Near linear scaling has been achieved with respect to the number of degrees of freedom used to resolve the microstructure. Linear scaling with respect to the number of pre-analyses required to construct the reduced order model (ROM) follows from the EHM formulation. Furthermore, a parallel implementation for fast evaluation of the constructed ROM has been developed using shared memory parallelization. It has been shown that for large microstructures with ≈10,000 grains, the total computational cost of evaluating the nonlinear response of a polycrystal could be reduced by approximately an order of magnitude using 32 cores with respect to serial ROM simulation. The present methodology has been verified using an additively manufactured polycrystalline microstructure of a nickel-based superalloy, Inconel 625. The capability of the developed framework to construct a ROM for such large microstructures, as well as the ability of the ROM to predict average and local quantities of interest has been demonstrated.

Proper orthogonal decomposition assisted eigendeformation-based mathematical homogenization method for modeling cracks in 3D polycrystalline microstructures

In this manuscript, a reduced order model (ROM) is proposed for full three-dimensional (3D) polycrystalline microstructures with tortuous short cracks. The model reformulates eigendeformation-based homogenization method (EHM) assisted with the proper orthogonal decomposition (POD) method to account for local plastic deformation and crack separation fields. A constrained optimization problem is formulated with reduced order objective functions and un-reduced constraints to solve for the separation. To make the optimization process more feasible, an integrated form of the constraint is introduced, enabling the use of only one constraint regardless of the crack morphology. The model is verified against direct numerical simulations (DNS) with crystal plasticity as the constitutive relation. The use of priori knowledge in building crack separation field basis functions as well as sampling strategies in the absence of prior knowledge are discussed. The performance and accuracy of the ROM are assessed under various loading conditions and different crack configurations.

Formation process, microstructure, and mechanical properties of an ultrafine dual-phase alloy formed through phase transition of 18R-type long-period stacking ordered in Mg85Zn6Y9 under high pressure

The 18R-type long-period stacking ordered (LPSO) structure in Mg85Zn6Y9 exhibits phase transition into D03 and α-Mg (D03/α-Mg) before it transforms into a liquid phase with the increase in temperature at 7.8 GPa. First-principles calculations suggest that the energy barrier between 18R-type LPSO and D03/α-Mg decreases with pressure. A further increase in the temperature decreases the energy difference between LPSO and D03/α-Mg. Therefore, the free energy variations due to the effects of both pressure and temperature cause phase transition. The D03/α-Mg phases formed at high pressure can be recovered at 0.1 MPa and room temperature. The phase transition from 18R-type LPSO structure to D03/α-Mg causes inner-grain diffusion and generates a lamellar structure. The thickness of the lamellar structure decreases with the increasing pressure until it reaches 65 nm at 15 GPa. Moreover, the alloy solidified above 5 GPa also comprises D03/α-Mg phases. The alloy solidified at 5 GPa exhibits a typical eutectic lamellar structure. However, spherulite-like polycrystalline microstructures containing ultrafine grains are obtained when the alloys are solidified at 10 and 15 GPa. The microstructure variations are caused by an increase in the degree of supercooling due to atomic diffusion suppression with the increasing pressure. The alloys containing D03/α-Mg exhibit both low modulus and ultrahigh strength. The Young’s modulus is related to the presence of the D03 and α-Mg phases in the alloy structure. In contrast, the increase in σy can be attributed to the grain refinement strengthening.