Microstructural Length Scale Research Articles

Multiscale prediction of microstructure length scales in metallic alloy casting

Microstructural length scales, such as dendritic spacings in cast metallic alloys, play an essential role in the properties of structural components. Therefore, quantitative prediction of such length scales through simulations is important to design novel alloys and optimize processing conditions through integrated computational materials engineering (ICME). Thus far, quantitative comparisons between experiments and simulations of primary dendrite arms spacings (PDAS) selection in metallic alloys have been mainly limited to directional solidification of thin samples and quantitative phase-field simulations of dilute alloys. In this article, we combine casting experiments and quantitative simulations to present a novel multiscale modeling approach to predict local primary dendritic spacings in metallic alloys solidified in conditions relevant to industrial casting processes. To this end, primary dendritic spacings were measured in instrumented casting experiments in Al–Cu alloys containing 1 wt.% and 4 wt.% of Cu, and they were compared to spacing stability ranges and average spacings in dendritic arrays simulated using phase-field (PF) and dendritic needle network (DNN) models. It is first shown that PF and DNN lead to similar results for the Al-1 wt.%Cu alloy, using a dendrite tip selection constant calculated with PF in the DNN simulations. PF simulations cannot achieve quantitative predictions for the Al-4 wt.%Cu alloy because they are too computationally demanding due to the large separation of scale between tip radius and diffusion length, a characteristic feature of non-dilute alloys. Nevertheless, the results of DNN simulations for non-dilute Al–Cu alloys are in overall good agreement with our experimental results as well as with those of an extensive literature review. Simulations consistently suggest a widening of the PDAS stability range with a decrease of the temperature gradient as the microstructure goes from cellular-dendrites to well-developed hierarchical dendrites.

The Role of Lengthscale in the Creep of Sn-3Ag-0.5Cu Solder Microstructures

Creep of directionally solidified Sn-3Ag-0.5Cu wt.% (SAC305) samples with near-<110> orientation along the loading direction and different microstructural lengthscale is investigated under constant load tensile testing and at a range of temperatures. The creep performance improves by refining the microstructure, i.e. the decrease in secondary dendrite arm spacing (λ2), eutectic intermetallic spacing (λe) and intermetallic compound (IMC) size, indicating a longer creep lifetime, lower creep strain rate, change in activation energy (Q) and increase in ductility and homogeneity in macro- and micro-structural deformation of the samples. The dominating creep mechanism is obstacle-controlled dislocation creep at room temperature and transits to lattice-associated vacancy diffusion creep at elevated temperature ( frac{T}{{T_{M} }} > 0.7 to 0.75). The deformation mechanisms are investigated using electron backscatter diffraction and strain heterogeneity is identified between β-Sn in dendrites and β-Sn in eutectic regions containing Ag3Sn and Cu6Sn5 particles. The size of the recrystallised grains is modulated by the dendritic and eutectic spacings; however, the recrystalised grains in the eutectic regions for coarse-scaled samples (largest λ2 and λe) is only localised next to IMCs without growth in size.

Effect of cooling rate on microstructure and microhardness of hypereutectic Al–Ni alloy

High solidification cooling rates during unsteady-state conditions of solidification of Al-based alloys can induce different microstructural length scales or metastable phases, leading to improved properties. The present study aims to characterize the microstructural arrangement of the hypereutectic Al–8 wt%Ni alloy, unidirectionally solidified in unsteady-state heat flow conditions, examining the influence of the cooling rate in the development of the Al–Al3Ni eutectic and the primary phase. A columnar-to-equiaxed macrostructural transition is shown to occur at a solidification cooling rate (Ṫ) of about 4.8 °C/s, with different microstructures associated with each morphological zone. The observation of microstructures of hypoeutectic, eutectic and hypereutectic Al–Ni alloys, has permitted an asymmetric coupled zone diagram to be proposed. The microstructural interphase spacings of the Al–8 wt%Ni alloy are experimentally determined and correlated to Ṫ, and the Vickers microhardness (HV) is shown to decrease with the increase in such spacings. The higher experimental HV profile of the examined hypereutectic alloy as compared to that of the eutectic Al–Ni alloy is attributed to the formation of a supersaturated solid solution of Ni in α-Al.

On the heterogeneous cooling rates in laser-clad Al-50Si alloy

Abstract The local microstructural heterogeneities in a single layer of laser clad hypereutectic Al-50Si alloy over Al7075 substrate has been studied over different applied laser powers. The general microstructure of the laser clad layer, irrespective of the applied laser power, could be described by three distinctive regions from the deposited bead/substrate interface to the top – i) columnar primary Al-dendritic region, ii) Al-Si near-eutectic region, and iii) non-equilibrium three phase region composed of Si primary particles, fine Al-rich dendrites and interdendritic Al-Si eutectic. A spatial heterogeneity in the cooling rates is inferred within the single clad layer based on the microstructural length scales – the bulk Al-Si shows two orders of magnitude higher cooling rate than interface. A distinct difference in the orientation of the clad microstructure near the bead/substrate interface and size and distribution of Si particles in the deposited layer is seen with different applied laser power. Such microstructural differences have been explained on the basis of the melt pool solidification conditions of the hypereutectic alloy under different laser power.

Ablation Casting: Solidification Characteristics, Microstructure Formation, and Mechanical Properties

Ablation casting is an emerging sand casting technology that achieves high cooling rates in a casting during its solidification, especially its eutectic solidification of the metal, resulting in an extremely fine eutectic microstructure, reduced levels of defect, and enhanced mechanical properties of the casting. The technology is creating extensive interest in the industry for its capability in producing castings with high mechanical properties and internal integrity. However, scientific research lags behind the industrial applications of this new technology. There is a lack of scientific understanding on the solidification features of the castings made using ablation casting. Experimental data on the microstructural length scales seem inconsistent. This article aims at interpreting the experimental data available in the literature by considering the solidification characteristics of ablation casting. The paper also discusses certain research needs to further exploring the potential of the ablation casting process.

Static analysis of cutout microstructures incorporating the microstructure and surface effects

This article develops a nonclassical model to analyze bending response of squared perforated microbeams considering the coupled effect of microstructure and surface stress under different loading and boundary conditions, those are not be studied before. The corresponding material and geometrical characteristics of regularly squared perforated beams relative to fully filled beam are obtained analytically. The modified couple stress and the modified Gurtin-Murdoch surface elasticity models are adopted to incorporate the microstructure as well as the surface energy effects. The differential equations of equilibrium including the Poisson's effect are derived based on minimum potential energy. Exact closed form solution is obtained for bending behavior of the proposed model considering the classical and nonclassical boundary conditions for both uniformly distributed and concentrated loads. The proposed model is verified with results available in the literature. Influences of the microstructure length scale parameter, surface energy, beam thickness, boundary and loading conditions on the bending behavior of perforated microbeams are investigated. It is observed that microstructure and surface parameters are vital in investigation of the bending behavior of perforated microbeams. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams that commonly used in nanoactuators, nanoswitches, MEMS and NEMS systems.

Nonlinear analysis of thermal-mechanical coupling bending of clamped FG porous curved micro-tubes

A nonlinear analysis on the thermal-mechanical coupling bending behavior of functionally graded porous curved micro-tubes is performed in this research. The case of curved micro-tubes with doubly-clamped boundary conditions resting on nonlinear elastic foundation is considered. Based on the modified couple stress theory, curved micro-tubes under uniformly distributed transverse pressure and uniform temperature rise are analyzed. It is assumed that the material properties of the curved micro-tube are temperature-dependent and graded across the radius of cross-section. The governing equations of the curved micro-tube are established within the framework of higher-order shear deformation theory and the von Kármán kinematic assumptions. These equations are reformulated for the case of curved micro-tubes with even distributed porosities based on the uncoupled thermoelasticity theory. The system of nonlinear differential equations governing the equilibrium position of curved micro-tubes is solved using the two-step perturbation technique. The analytical solutions are given in this study to obtain the large deflection in curved micro-tubes as an explicit function of the thermal/mechanical load. The influences of porosity volume fraction, power law index, microstructural length scale parameter, foundation stiffness, and geometrical parameters on the thermomechanical deflection of curved micro-tubes are investigated.

Competing Interactions between Mesoscale Length-Scales, Order-Disorder, and Martensitic Transformation in Ferromagnetic Shape Memory Alloys

In the present work, the effects of composition and heat treatments and the resulting microstructural changes on the martensitic transformation and ferromagnetic transition have been investigated in NiCoMnIn metamagnetic shape memory alloys. In this shape memory alloy system, it is observed that upon heat treatments at a wide temperature range, the onset temperature of the martensitic transformation follows a non-monotonic behavior with respect to heat treatment time, and the nature of the non-monotonic behavior is also a function of composition. This behavior cannot be attributed to well-known factors such as precipitation, change in local composition due to the precipitation and/or global degree of order. In this work, a systematic investigation through synthesis, thermal processing and characterization via thermo-physical measurements, transmission electron microscopy and in-situ synchrotron x-ray diffraction experiments has been used to correlate the non-monotonic dependence of the martensitic transformation and ferromagnetic transition temperatures to the evolution of L21 domains arising from a order/disorder phase transition. A thermodynamic model for the magneto-structural transition is combined with classical nucleation theory to further ascertain the role of microstructural length-scales on the onset of the martensitic transformation. This work thus provides understanding of the thermodynamic and kinetic factors that can be controlled to tune the coupled magneto-structural transformations in NiCoMnIn metamagnetic shape memory alloys.

A novel particle-filled carbon-fibre reinforced polymer model composite tailored for the application of digital volume correlation and computed tomography

This paper presents the development of novel Carbon-Fibre Reinforced Polymer (CFRP) laminates, tailored for the application of Digital Volume Correlation (DVC) and Computed Tomography (CT) to experimental mechanics analyses of these materials. Analogous to surface-based Digital Image Correlation (DIC), DVC is a relatively novel volumetric method that utilizes CT data to quantify internal three-dimensional (3D) displacements and implicit strain fields. The highly anisotropic and somewhat regular/self-similar microstructures found in well-aligned unidirectional (UD) materials at high fibre volume fractions are intrinsically challenging for DVC, especially along the fibre direction at microstructural length-scales on the order of a few fibre diameters. To permit the application of DVC to displacement and/or strain measurements parallel to the fibre orientation, the matrix was doped with a sparse population of sub-micrometre particles to act as displacement trackers ( i.e. fiducial markers). Barium titanate particles (400 nm, ∼1.44 vol. %) were found to offer the most favourable compromise between contrast in CT images and the ability to obtain a homogeneous distribution in 3D space with sufficient particle compactness for local DVC analyses. This property combination was selected following an extensive Micro-focus Computed Tomography (µCT)-based qualitative assessment on a wide test matrix, that included 38 materials manufactured with a range of possible particle compositions, mean sizes and concentrations. By comparing the tensile behaviour of the particle-adapted material alongside its particle-free counterpart, we demonstrate through the application of in situ Synchrotron Radiation Computed Tomography (SRCT) that the macro- and micromechanical responses of the newly developed CFRP are consistent with standard production materials indicating its suitability as a model system for mechanistic investigations.

Solute trapping in rapid solidification

Abstract

Thermal vibration characteristics of pre/post-buckled bi-directional functionally graded tapered microbeams based on modified couple stress Reddy beam theory

This paper investigates the nonlinear vibration characteristics of pre- and post-buckled nonuniform bi-directional functionally graded (BDFG) microbeams subjected to nonlinear thermal loading. The formulations derived herein are based on thermoelastic constitutive relations of the higher-order Reddy beam theory in conjunction with the modified couple stress theory, von Karman nonlinear strains, and physical neutral plane concept, for the first time. Power-law model is employed to describe the continuous variation of temperature-dependent thermomechanical material properties of BDFG in both the thickness and length directions. Variable microstructure length scale parameter and Poisson’s ratio in both directions are considered. The variable coefficient nonlinear governing equations and associated boundary conditions of nonuniform BDFG microbeam in the thermal environment are derived utilizing the Hamilton principle. The obtained equations are discretized using the differential quadrature method accounting for various boundary conditions, and iterative Newton’s method is adopted to solve the resulting nonlinear algebraic equations. The developed model and solution procedure are validated by comparing the predicted results with those in the available literature. To this end, extensive parametric studies are carried out to explore the influence of linear and nonlinear temperature profiles, microstructure length scale parameter ratio, microstructure length scale parameter-to-thickness ratio, gradient indices in thickness and length directions, material-temperature dependency, and taperness parameters on the nonlinear vibration response and higher-order mode frequencies of tapered BDFG microbeams accounting different boundary conditions.

Copper Surfaces with Bimodal Nanoporosity by Microstructural Length Scale Controlled Dealloying of a Hypereutectic Al-Cu Alloy

Copper (Cu) surfaces with bimodal nanoporosity can be used for a variety of applications. This research shows that bimodal nanoporous Cu surfaces can be fabricated by dealloying of an as-cast hypereutectic alloy Al75Cu25 (at.%) alloy, which solidifies as pre-eutectic Al2Cu (micrometre-scaled) and eutectic lamella of α-Al/Al2Cu (nanoscaled). The bimodal nanoporous Cu surface is a result of a microstructural length scale controlled dealloying process: In the beginning, the micrometre-scaled Al2Cu acts as a cathode enabling the preferential dissolution of α-Al (anode) for larger pores to form. Afterwards, the nanosize effect of α-Al overrides the intrinsic difference in electrochemical potential allowing for subsequent simultaneous dealloying leading to finer pores. The assessment of the in situ Synchrotron XRD data of the formation of bimodal nanoporous Cu surfaces revealed a two-stage kinetic process, closely related to the formation of bimodal pores during the microstructural length scale controlled dealloying process. The underlying rationales and implications are discussed.

Effects of Silver Content and Cooling Rate on Electrical Conductivity and Tensile Properties of Al-Si(-Ag) Alloys

In recent years, new designing of components provided by electronics and automotive industries has required higher mechanical properties and electrical conductivity. Some of the examples are mobile phone frames, automotive powertrain components and new aluminum (Al) housing components. Silver (Ag) and Al have similarities in terms of crystal lattices and atoms diameters. Consequently, the addition of Ag in Al alloys may result in improved properties. The present research focuses on better understanding of the effects of Ag additions and cooling rate variations on the length scale of the dendritic microstructure constituting a Al-5 wt.% Si alloy. One of the factors to be considered during examination of as-cast Al-Si(-Ag) alloys microstructures is the interdendritic spacing. This factor, in combination with the second phases and solid solution, is able to control the application properties. In the present investigation, the ultimate tensile strength increases from 142 MPa for the Al-5 wt.% Si-0.1 wt.% Ag alloy to 154 MPa for the Al-5 wt.% Si-2.0 wt.% Ag alloy. This difference is not observed for ductility, which is preserved essentially unchanged into an improved value of 22% for both Ag-containing alloys. The less Ag-modified alloy samples (0.1 Ag) enhanced electrical conductivity by about 2% and 4% IACS as compared to those of the Al-5 wt.% Si and the Al-5 wt.% Si-2.0 wt.% Ag alloys samples, respectively.

In-plane surface wave in a classical elastic half-space covered by a surface layer with microstructure

Surface layers with microstructures are widely used in many engineering fields. The mechanical behavior of microstructures in solids can be described by gradient elasticity theories. [One of them is the couple stress theory (Mindlin and Tiersten in Arch. Ration. Mech. Anal. 11:415–448, 1962).] In the present paper, we study the in-plane surface wave propagating in a classical elastic half-space covered by a surface layer described by the couple stress theory. We firstly develop the full solution for the above configuration. Since our primary objective is to introduce the couple stress theory (or strain-gradient elasticity theory) into the surface elasticity model (Gurtin and Murdoch in Arch. Ration. Mech. Anal. 57:291–323, 1975), we are particularly interested in the case that the surface layer is very thin. Therefore, as our second step, by employing the Kirchhoff thin plate model, we establish the surface elasticity model considering couple stresses and derive the isotropic surface elasticity solution of the present problem. Thirdly, by employing the second-order strain-gradient model (Aifantis in Int. J. Eng. Sci. 30:1279–1299, 1992), we derive the dispersion equation of the surface wave for the case that the microstructure length scale is larger than the layer thickness. The last two solutions are compared with the full solution numerically for the lowest mode of the surface wave. It should be pointed out that the present study involves multi-field knowledge of surface waves, couple stress theory, and surface elasticity theory.

Strain rate sensitivity and deformation mechanism of nano-lamellar γ-Ni/Ni5Zr eutectic at room temperature

Abstract

Implications of post-processing induced microstructural changes on the deformation and fracture response of additively manufactured Ti–6Al–4V

Ti–6Al–4V parts fabricated via electron beam melting (EBM) powder bed fusion are often subjected to hot isostatic pressing below the β-transus temperature to mitigate defects. During which the pressure aids in pore closure and the thermal exposure results in coarsening of α phase while retaining the columnar prior-β phase grain morphology present in the as-fabricated condition. The same post-processing treatment can also be carried out above β-transus temperature which is an effective way to modify both the grain morphology and the associated α textures. The objective of this work is to correlate thermally induced microstructural changes to the deformation and fracture response of the EBM processed Ti–6Al–4V. To this end, we have carried out both sub-transus and super-transus heat-treatments of the as-fabricated material. The mechanical response of the as-fabricated and all heat-treated materials are characterized by in-situ tensile tests under a high-resolution digital optical microscope. This enabled us to capture large-scale panoramic images of the deforming microstructure, and overcome the trade-off between the image resolution and the field of view during in-situ experiments. The series of images captured throughout the imposed deformation are subsequently used to perform microstructure-based digital image correlation to measure microstructural-scale strains over a large area. The results of the in-situ tests together with detailed fractographic analyses are then used to elucidate how the heterogeneous deformation spanning over multiple microstructural length-scales, for example, at the scale of lamellae, colonies of lamellae and grain boundaries, affect the overall deformation and fracture response of the post-processed materials.

Design of lattice structures with direct multiscale topology optimization

The structure of latticed/cellular materials is often designed with the lack of information about macro-material. Material information of each macro-element is realized by reducing the scale, homogenizing the microstructure, and calculating the properties of an equivalent material for the macro-element. The lattice structure is simultaneously optimized at both the macro- and microstructural levels with additional connectivity constraints, while finite element analysis (FEA) and design variable updates are required twice (at the macro- and micro-levels) for each optimization loop. This approach requires significant storage and has a substantial computational cost. In addition, when the size of the unit cell is quite large compared to the macrostructure, the homogenization method could fail to provide sufficient accuracy. To deal with these issues, in this work, we propose a new multiscale topology optimization approach for the direct and simultaneous design of lattice materials, without material homogenization at the microscale, using adaptive geometric components. The adaptive geometric components are projected onto macro- and micro-element density fields to calculate the effective densities of grid elements. Macro-and microstructures are simultaneously optimized, considering the load and boundary conditions of the overall structure without any additional constraints. FEA and design variable updates are required only once for each optimization loop. Furthermore, the minimum length scales of the macrostructure and the length scales of microstructures can be simultaneously controlled explicitly by simply adjusting the bounds of the size parameters. Some benchmark structures are topologically optimized with different types of lattice materials (such as square, diamond, and triangle) to verify the effectiveness of the proposed method.

Size-dependent analysis of a functionally graded piezoelectric micro-cylinder based on the strain gradient theory with the consideration of flexoelectric effect: plane strain problem

In this study, a size-dependent analysis of functionally graded piezoelectric (FGP) micro-rotating cylinder is presented based on the plane strain condition and strain gradient theory, which is a non-classical theory capable of capturing the size effect in microscaled structures. The present model is used to analyze the FGP micro-rotating cylinder with the consideration of flexoelectric effects exposed to a symmetric magneto-electro-mechanical loading. All mechanical and electrical properties are assumed to be graded in the thickness direction according to a power-law distribution. With respect to the fifth-order strain gradient coefficient and electromechanical coupling, the constitutive equations are obtained from electric Gibbs free energy density, which is a function of strain, second-order deformation gradient and electric field. By substituting the constitutive equations in electric and mechanical equilibrium equations, two coupled electromechanical governing differential equations in terms of radial displacement and electric potential are derived considering centrifugal force and Lorentz magnetic force obtained from Maxwell’s relations. The generalized differential quadrature method is proposed to solve the coupled governing differential equations. Numerical results attained from the strain gradient elasticity reveal the effects of flexoelectric, microstructural length scale, non-homogeneity constant, rotation and magnetic field on the response of the FGP micro-rotating cylinder.

Superconducting Cu/Nb nanolaminate by coded accumulative roll bonding and its helium damage characteristics

A very broad distribution of microstructural length scales spanning few nm- to the μm-scale has proven effective to achieve exceptional materials properties. Here, we fabricate a Cu/Nb two-phase composite made of a hierarchically layered structure by modifying the conventional accumulative roll bonding (ARB) technique, where fresh Nb sheets are inserted and bonded during a repeated stacking and rolling process. This barcode-like multilayer with a designed hierarchical length scale distribution possesses densely distributed phase boundaries and rich interfacial structures. The composite demonstrates similar superconductivity characteristics as pure Nb, but is 3 × stronger, has theoretically better oxidation resistance, and retains considerable ductility. Under the helium irradiation environment, the unique interfacial structures featuring chemical intermixing zones (3-dimensional) are more immune to the formation of large helium clusters than atomically sharp interfaces (2-dimensional), screening them from radiation damage and improving their long-term mechanical integrity. This work signifies an effective strategy of constructing hierarchical laminates to achieve high-performance materials, which holds promise in fusion and fission energy applications.

Microstructural dependence of the incipient to homogeneous flow transition in metallic glass composites

As ductile derivatives of amorphous alloys, metallic glass composites balance high strength with the ability to mitigate catastrophic shear localization, which has long plagued monolithic metallic glasses. In this study, we employ a bonded-interface indentation technique coupled with strain field mapping to identify the governing yield criterion in metallic glass composites as a function of their microstructural length scales. A crossover from the shear plane to maximum shear stress yield criterion is uncovered at a crystalline fraction of approximately 60%, thus signaling an effective transition from incipient to homogeneous flow as the dominant deformation mode of the composite microstructure.