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At least 73 records · Page 4

Mesoscale crystal plasticity modeling of nanoscale Al–Al 2 Cu eutectic alloy

Nanolaminated composites composed of alternate metal and intermetallic or ceramic lamellae exhibit high strength, high strain hardening rate and measurable plasticity at ambient and elevated temperatures. Due to the difference in plastic deformation capability between the two phases, structural instability occurs in hard lamellae associated with buckling when a compression strain is applied parallel to the lamellae. Taking nanoscale Al–Al 2 Cu eutectic alloy as a model system, we develop a mesoscale crystal plasticity (CP) model based on the confined layer slip (CLS) mechanism (referred to as CLS-CP) to understand the buckling behavior of the nanolaminates. In the CLS-CP model, buckling in Al 2 Cu lamellae is constrained by the elastic-plastic deformation of Al lamellae. The critical resolved shear stress for dislocation slip in Al lamellae varies with layer thickness, estimated by the CLS mechanism. To capture the essential features of confined layer slip mechanism that dislocations propagate within the layer and are deposited at the interfaces, plastic deformation in each lamella is the same through the layer thickness. The variation of elastic deformation through the layer thickness is captured through dividing each Al lamella into three or more elements that have the same plastic deformation through the thickness. In comparison, we also conduct standard crystal plasticity modeling in which plastic deformation in the three elements through the layer thickness is calculated individually according to phenomenological power law. In these simulations, plasticity in Al 2 Cu lamellae is modeled with slips on {121} planes due to the slip continuity across the interface, which have been observed in our recent experiments. The CLS-CP model is able to predict mechanical properties of nano-scale lamellar materials. In contrast, the standard CP model is more suitable to study deformation behavior of sub-micro scale lamellar materials. In conclusion, the CLS-CP model calculations reveal that critical compression strain corresponding to buckling increases as layer thickness decreases, which agree with micro-pillar compression tests.

36 MATERIALS SCIENCE↗

Czochralski crystal growth: Modeling study

The modeling study of Czochralski (Cz) crystal growth is reported. The approach was to relate in a quantitative manner, using models based on first priniciples, crystal quality to operating conditions and geometric variables. The finite element method is used for all calculations.

Dudukovic, M. P.↗

Revisiting Néel 60 years on: The magnetic anisotropy of L1 0 FeNi (tetrataenite)

The magnetocrystalline anisotropy energy of atomically ordered L1 0 FeNi (the meteoritic mineral tetrataenite) is studied within a first-principles electronic structure framework. Two compositions are examined: equiatomic Fe 0.5 Ni 0.5 and an Fe-rich composition, Fe 0.56 Ni 0.44 . It is confirmed that, for the single crystals modeled in this work, the leading-order anisotropy coefficient K 1 dominates the higher-order coefficients K 2 and K 3 . To enable comparison with experiment, the effects of both imperfect atomic long-range order and finite temperature are included. While our computational results initially appear to undershoot the measured experimental values for this system, careful scrutiny of the original analysis due to Néel et al. [J. Appl. Phys. 35, 873 (1964)] suggests that our computed value of K 1 is, in fact, consistent with experimental values, and that the noted discrepancy has its origins in the nanoscale polycrystalline, multivariant nature of experimental samples, that yields much larger values of K 2 and K 3 than expected a priori. These results provide fresh insight into the existing discrepancies in the literature regarding the value of tetrataenite’s uniaxial magnetocrystalline anisotropy in both natural and synthetic samples.

36 MATERIALS SCIENCE↗

Fully implicit crystal plasticity models representing orientations with modified Rodrigues parameters

Here, this work describes a crystal plasticity formulation combining several mathematical, numerical, and implementation choices to produce a highly efficient model. Specifically, the key choices in the implementation are (1) representing orientations with modified Rodrigues parameters, (2) implementing a fully coupled implicit time integration for the elastic stretch, the crystal orientations, and the model internal variables, (3) implementing the model in the NEML2 constitutive modeling framework, based on PyTorch, to vectorize the calculations and port the computation to GPUs and other hardware accelerators, and (4) an exact implementation of the consistent tangent matrix, even for arbitrary coupling to other field variables beyond the displacements, like temperature, neutron fluence, etc. The first two features of the model are, to our knowledge, novel. The paper considers each of these choices individually as well as the final model as a whole. This includes a full description of modified Rodrigues parameters, their advantages over other representations of orientations, the mathematical formulae and tools required to implement a model with modified Rodrigues parameters, and a detailed description of the geometry of the space of modified Rodrigues parameters (in an appendix). It also includes a description of a fully implicit time integration scheme for the orientations and the advantages in representing orientations with modified Rodrigues parameters in implementing such a model. The work then assess, via numerical examples, the advantages of fully coupled implicit time integration versus more common decoupled and explicit time integration schemes. These studies demonstrate the computational advantages of fully coupled integration versus other time integration algorithms, though the performance of the competing models depends on the complexity of the underlying single crystal model. The study concludes by demonstrating that the choice of time integration method affects the sharpness of the predicted texture, with explicit methods for integrating the orientations overestimating texture sharpness and implicit methods underestimating texture sharpness.

Crystal plasticity↗

Identification of crystal plasticity model parameters by multi-objective optimization integrating microstructural evolution and mechanical data

Crystal plasticity models evolve a polycrystalline yield surface using meso-scale descriptions of deformation mechanisms. The activation of deformation mechanisms is governed by crystallography and a set of model parameters, which are typically calibrated through the fitting of mechanical data such as stress–strain curves and elastic lattice strains. Microstructural data such as phase fractions and texture evolution are used for verifying crystal plasticity parameters. In this study, we use a multi-objective genetic algorithm to identify hardening parameters from flow stress curves with an option to incorporate texture into the optimization approach. Robust, generalized objective functions are developed and used to identify sets of parameters pertaining to dislocation density-based hardening laws in visco-plastic and elasto-plastic self-consistent (VPSC and EPSC) homogenization models. First, the parameters are identified for pure Nb directly from texture using an objective function based on generalized spherical harmonics. Since texture evolution is driven by the relative contribution of active slip systems, the parameters governing the evolution of slip resistance ratios can be recovered from fitting discrete textures at a series of strains. Next, a comprehensive set of load reversal data for dual phase (DP) 780 steel is used to fit a hardening law and a back-stress law in EPSC. Finally, parameters pertaining to a complex hardening law for the evolution of slip and twinning in pure α-Ti are identified. Remarkably, using texture as an objective in combination with stress–strain objectives constrains the model of Ti to fully reproduce not only stress–strain and texture evolution but also hierarchical twinning measurements as a function of initial grain size and texture. Furthermore, given an appropriate model fit to representative experimental texture evolution, underlying twin volume fractions contributing to texture evolution can be predicted.

42 ENGINEERING↗

Evaluation of a Thermodynamic Ice Crystal Icing Model Using Experimental Ice Accretion Data

This paper presents the evaluation of a thermodynamic ice crystal icing model, previously presented to describe the possible mechanisms of icing within the core of a turbofan jet engine. It has been proposed that there are two types of distinct ice accretions based on a surface energy balance: freeze-dominated icing and melt-dominated icing. In the former, ice accretion occurs where a freeze fraction (0 to 1) of melted ice crystals freezes on a surface, along with the existing ice of the impinging water and ice mass. This freeze-dominated icing is characterized by having strong adhesion to the surface. In the latter, icing occurs from accumulated unmelted ice on a surface, where a melt fraction (0 to 1) dictates the amount of unmelted impinged ice. This melt-dominated icing is characterized by weakly bonded surface adhesion. The experimentally observed ice growth rates suggest that only a small fraction of the impinging ice remains on the surface, implying a mass loss mechanism such as splash, runback, bounce, or erosion. This mass loss parameter must be determined in conjunction with the fraction of freezing liquid water or fraction of melting ice on an icing surface. This loss parameter, however, along with the freeze and melt fraction, are the only experimental parameters that are currently not measured directly. Using reported icing growth rates from published ice crystal icing experiments, a methodology is proposed to determine these unknown parameters. This work takes reported ice accretion data from tests conducted by the National Aeronautics and Space Administration (NASA) in 2016 and tests NASA collaborated on with the National Research Council (NRC) of Canada in 2012 that examined the fundamental physics of ice crystal icing. Those research efforts sought to generate icing conditions representative of those that occur inside a jet engine when ingesting ice crystals. This paper presents the fundamental equations of the thermodynamic model, the methodology used to determine the aforementioned unknown icing parameters, and results from model evaluation using experimental data. In addition, this paper builds on the previously proposed model by adding a transient conduction term to explain ice growth behavior at the onset of experimental tests that was observed to be different from steady-state ice growth that occurred later in the test run.With the addition of this energy term, this becomes a quasi-steady model. A key finding from this work suggests that mass loss fractions can exceed 0.90 for steady ice growth periods. In addition, due to conductive heat fluxes when using a warmer-than-freezing airfoil, lower mass loss fraction values were calculated during the initial transient period.

Ice-Crystal Ice Accretion↗

Bridging microscale to macroscale mechanical property measurements of FeCrAl alloys by crystal plasticity modeling

FeCrAl alloys are candidates for accident tolerant fuel cladding of light water reactors. In this work, a microstructure- and temperature-dependent crystal plasticity model is employed to bridge microscale to macroscale mechanical property measurements of FeCrAl alloys. With the visco-plastic self-consistent (VPSC) polycrystal plasticity framework, a mechanism-based single crystal plasticity (MSCP) model adopts the Arrhenius type rate equation to describe the dependence of the critical resolved shear stress for dislocation slips on their temperature-dependent intrinsic frictional resistance and the microstructure-dependent irradiation hardening. The intrinsic frictional resistance associated with {110}<111> and {112}<111> slip systems were measured by in-situ micromechanical testing on unirradiated/irradiated samples at 25-500 °C. The irradiation hardening is estimated by the Bacon-Kocks-Scattergood (BKS) model with density and size of radiation-induced defects measured from microstructural characterization. Several features associated with thermo-mechanical behavior of unirradiated/irradiated polycrystalline FeCrAl alloys are captured. High density of deformation-induced dislocations and radiation-induced defects results in obvious hardening at room temperature, which is weakened at high temperature, and facilitates damage evolution during deformation. Moreover, both high temperature and radiation-induced defects, which facilitate dislocation multiplication, trigger large hardening rate. Finally, the proposed method together with application of accelerator-based ion irradiation technique is a surrogate approach to simulate neutron damage, improving the efficiency associated with evaluation of mechanical properties of FeCrAl alloys exposed to temperature, stress and radiation conditions.

36 MATERIALS SCIENCE↗

Deformation behavior of HCP titanium alloy: Experiment and Crystal plasticity modeling

The deformation behavior of commercially pure titanium is studied using experiments and a crystal plasticity model. Compression tests along the rolling, transverse, and normal-directions, and tensile tests along the rolling and transverse directions are performed at room temperature to study the activation of slip and twinning in the hexagonal closed packed titanium. A detailed EBSD based statistical analysis of the microstructure is performed to develop statistics of both {10-12} tensile and {11-22} compression twins. A simple Monte Carlo (MC) twin variant selection criterion is proposed within the framework of the visco-plastic self-consistent (VPSC) model with a dislocation density (DD) based law used to describe dislocation hardening. In the model, plasticity is accommodated by prismatic, basal and pyramidal slip modes, and {10-12} tensile and {11-22} compression twinning modes. Thus, the VPSC-MC model successfully captures the experimentally observed activation of low Schmid factor twin variants for both tensile and compression twins modes. The model also predicts macroscopic stress-strain response, texture evolution and twin volume fraction that are in agreement with experimental observations.

36 MATERIALS SCIENCE↗

A crystal plasticity model with an atomistically informed description of grain boundary sliding for improved predictions of deformation fields

Crystal plasticity (CP) is a powerful meso-scale technique for deformation modeling in polycrystalline materials. Crystal plasticity models typically do not include an explicit description of grain boundary (GB) sliding, which could lead to inaccurate predictions of strain distributions, especially in the vicinity of GBs. In the present study, a CP model is developed that includes GB sliding as an additional deformation mechanism and models the interaction between slip and GB sliding. Atomistic simulations are used to formulate the constitutive model for GB sliding and its interaction with incident slip. The deformation fields and structure of the GBs are obtained directly from experimental characterization and are faithfully reproduced as bicrystal systems for molecular dynamics simulations. The GBs are modeled as random-type (non-coincidence, asymmetrical) boundaries as observed from experimental data. The underlying atomistic-scale mechanism for pure sliding of random GBs was found to be analogous to fluid-flow. The interaction between incident slip and a sliding GB caused local increases in stress concentration, which further led to a momentary increase in the local sliding rate. The displacement profiles at the sliding GBs computed from the CP model with sliding accommodation are 38% more accurate than the baseline CP model as quantified by the mean squared error between the simulations and experiment. Here these results help improve the sophistication and accuracy of deformation modeling by including physics-based descriptions for GB sliding and its interaction with slip, eventually leading to more reliable predictions of micromechanical quantities.

36 MATERIALS SCIENCE↗

A crystal plasticity model for body-centered cubic molybdenum: Experiments and simulations

Here, a physics-based finite strain crystal plasticity constitutive model for body-centered-cubic (BCC) single crystals is developed to capture the strong temperature, rate, and orientation dependence of mechanical behavior. The key features of the model include twinning-anti-twinning asymmetry of shearing resistance, a yield criterion that incorporates atomistics-informed non-Schmid effects, and a flow rule formulated based on the theory of thermally activated motion of screw dislocations via nucleation of double kinks. The implementation of the constitutive model in a finite-element program is briefly discussed. The material constants in the model are determined by calibrating the model against literature-based experimental data on single-crystal Molybdenum subjected to uniaxial compression and uniaxial tension. Experiments of uniaxial compression on a single crystal specimen with a hole were performed for validation of the calibrated model for BCC Molybdenum. Measurements of deformations in the vicinity of the hole were used to assess the ability of the model in predicting localized deformation patterns around the hole. Lastly, the model is able to effectively describe the anisotropic and temperature-dependent stress-strain response of a molybdenum crystal up to a homologous temperature of 0.3.

36 MATERIALS SCIENCE↗

A dislocation-based crystal viscoplasticity model with application to micro-engineered plasma-facing materials

We report materials developed with special surface architecture are shown here to be more resilient to the transient thermomechanical environments imposed by intermittent exposures to high heat flux thermal loading typical of long-pulse plasma transients. In an accompanying article, we present experimental results that show the relaxation of residual thermal stresses in micro-engineered W surfaces. A dislocation-based model is extended here within the framework of large deformation crystal plasticity. The model is applied to the deformation of single crystals, polycrystals, and micro-engineered surfaces composed of a uniform density of micro-pillars. The model is utilized to design tapered surface micro-pillar architecture, composed of a Re core and W coatings. Residual stresses generated by cyclic thermomechanical loading of these architectures show that the surface can be in a compressive stress state, following a short shakedown plasma exposure, thus mitigating surface fracture.

36 MATERIALS SCIENCE↗

Deformation behavior of CP-titanium under strain path changes: Experiment and crystal plasticity modeling

The deformation behavior of commercially pure rolled titanium subjected to strain path changes is studied using experiments and a crystal plasticity model. Four different loading combinations are performed at room temperature to study the activation of slip, twinning, de-twinning and double-twinning in hexagonal closed packed titanium. The strain paths considered are: rolling direction compression (RDC) followed by normal direction compression (NDC), RDC followed by transverse direction compression (TDC), NDC followed by RDC, and NDC followed by TDC. An EBSD-based analysis of the distribution of boundary misorientation angles before and after reload was developed to analyze the evolution of {$10\bar{1}2$} tensile and {$11\bar{2}2$} compression twins. This analysis supports the model results concerning the treatment of twin reorientation. A de-twinning and double-twinning model accounting for back stress effects, an important feature of strain path changes, is implemented within the framework of the visco-plastic self-consistent (VPSC) model along with a dislocation density (DD) based hardening scheme. In the model, plasticity is accommodated by prismatic $\langle$a$\rangle$, basal $\langle$a$\rangle$ and pyramidal $\langle$c+a$\rangle$ slip modes, and {$10\bar{1}2$} tensile and {$11\bar{2}2$} compression twinning modes. The VPSC model predicts the evolution of twinning, de-twinning and double-twinning processes for both tensile and compression twinning modes under strain path change. The model predicts macroscopic stress-strain response, texture evolution, and twin volume fraction that are in agreement with experimental observations. The evolution of texture is investigated in detail by separately analyzing the twinned domains, rather than the evolution of the global texture.

36 MATERIALS SCIENCE↗

Numerical modeling of crystal growth on a centrifuge for unstable natural convection configurations

The fluid mechanics associated with crystal growth processes on centrifuges is modeled using 2D and 3D models. Two-dimensional calculations show that flow bifurcations exist in such crystal growth configurations where the ampoule is oriented in the same direction as the resultant gravity vector and a temperature gradient is imposed on the melt. A scaling analysis is formulated to predict the flow transition point from the natural convection dominated regime to the Coriolis force dominated regime. Results of 3D calculations are presented for two thermal configurations of the crystal growth cell: top heated and bottom heated with respect to the centrifugal acceleration. In the top heated configuration, a substantial reduction in the convection intensity within the melt can be attained by centrifuge operations, and close to steady diffusion-limited thermal conditions can be achieved over a narrow range of the imposed microgravity level. In the bottom heated configuration the Coriolis force has a stabilizing effect on fluid motion by delaying the onset of unsteady convection.

Ramachandran, N.↗

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. As a result, the utility of the developed framework to efficiently simulate the micro-mechanical fields in polycrystalline microstructures in engineering applications is discussed.

36 MATERIALS SCIENCE↗

A Crystal-Physical Model of Electrotransfer in the Superionic Conductor Pb{sub 1–} {sub x}Sc{sub x}F{sub 2+} {sub x} (x = 0.1)

The frequency (ν = 10{sup –1}–107 Hz) dependences of electrical conductivity σ(ν) of single crystals of superionic conductor Pb{sub 0.9}Sc{sub 0.1}F{sub 2.1} (10 mol % ScF{sub 3}) with fluorite type structure (CaF{sub 2}) in the temperature range 153–410 K have been investigated. The static bulk conductivity σ{sub dc} =1.5 × 10{sup –4} S/cm and average hopping frequency ν{sub h} = 1.5 × 10{sup 7} Hz of charge carriers (mobile ions F{sup −}) at room temperature (293 K) have been defined from the σ{sub dc}(ν) experimental curves. Enthalpies of thermoactivated processes of ionic conductivity σ{sub dc}(T) (ΔH{sub σ} = 0.393 ± 0.005 eV) and dielectric relaxation ν{sub h}(T) (ΔH{sub h} = 0.37 ± 0.03 eV) coincide within their errors. A crystal-physical model of fluorine-ion transport in a Pb{sub 0.9}Sc{sub 0.1}F{sub 2.1} crystal lattice has been proposed. The characteristic parameters of charge carriers have been calculated: concentration n{sub mob} = 2.0 × 10{sup 21} cm{sup −3}, the distance of the hopping d ≈ 0.5 nm and mobility μ{sub mob} = 4.5 × 10{sup −7} cm{sup 2}/s V (293 K).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Crystal plasticity modeling for the strengthening effect of multilayered copper–graphene nanocomposites

The paper explores plastic deformation mechanisms in metal–graphene nanocomposites, illustrating their material strengthening effects through a crystal plasticity finite element (CPFE) model. This model is compared with published experimental results, which have previously shown that the two-dimensional shape of graphene effectively controls dislocation motion and significantly enhances the strength of metals. Simulated nanopillar compression tests, using a physics-based CP model that incorporates surface nucleation and single-arm source dislocation mechanisms, help us understand dislocation motions at submicron length scales. The crystal plasticity models are applied to nanolayered composites with copper grain layers and monolayer graphene, featuring repeat layer spacings of 200 nm, 125 nm, and 70 nm, respectively. This study quantifies the accumulation of dislocations at the graphene interfaces, contributing to the ultra-high strength of copper–graphene composites. Furthermore, a Hall–Petch-like correlation is established between yield strength and the number of embedded graphene layers.

36 MATERIALS SCIENCE↗