Microstructural Length Research Articles

Growth competition between columnar dendritic grains – The role of microstructural length scales

The growth competition between columnar dendritic grains is investigated by both phase-field (PF) and cellular automaton (CA) models in a growth regime where the primary dendrite spacing is much larger than the solutal diffusion length. This growth regime favors the formation of highly branched hierarchical dendritic microstructures prevalent in castings. Previous PF and CA studies have shed light on the complex relationship between GB orientation selection and GB bi-crystallography. They showed that, in the CA model, the orientation is governed by the favorably oriented grain (FOG) criterion and the geometrical limit (GL) in the limit of large and small cell size, respectively. The present study focuses on exploring how to quantitatively bridge length scales between PF simulations that resolve the whole solid-liquid interface dynamics and the CA model that resolves the dynamics of the grain envelope under a certain set of assumptions. For this purpose, we study grain boundary (GB) orientation selection as a function of the imposed temperature gradient G under the frozen-temperature approximation, which allows us to vary G-dependent microstructural length scales with a fixed GB bi-crystallography. PF simulations reveal the existence of a transition from FOG to GL dominance with decreasing G at non-degenerate bi-crystallography. Simulations further reveal that this transition can be quantitatively reproduced by the CA model with a choice of the cell size that corresponds, in PF simulations, to the active secondary dendrite arm spacing of the favorably oriented grain preceding the tertiary branching event that gives birth to a new stable primary dendrite. PF simulations are also used to obtain a detailed quantitative characterization of the dynamics of the grain envelope and its internal length scales, thereby providing a quantitative test of the inherent approximations of the existing CA approach and paving the way for its future development.

Microscale size effects in piezomagnetic material for the anti-plane problem

A continuum model of piezomagnetic material with strain, magnetic and piezomagnetic coupling gradient effects is proposed using a variational principle in this work. This model is employed to an anti-plane problem, and a general solution is constructed in polar coordinates. Special attention is paid to microstructural effects on the magnetic and mechanical response in an infinite piezomagnetic medium with a void. It is found that the microstructural length scales have a significant influence on the mechanic and magnetic fields. The three length scales (corresponding to strain, magnetic and piezomagnetic coupling gradients) are indispensable to describe the nonlocal effects of piezomagnetism. Additionally, controlling the direction and magnitude of the magnetic field at the edge of the void can be achieved by adjusting the microstructural length scales of the piezomagnetic medium.

Reflection and transmission of waves at the common interface of piezoelectric half-spaces with microstructure

The present article deals with the reflection and transmission of waves at an interface of piezoelectric (ALN & PZT-5T) half-spaces with microstructures. Unlike the classical piezoelectric material, in the considered media, five coupled waves (2 bulk and 3 surface) [namely the Quasi-longitudinal wave (QP), Quasi-transverse wave (QSV), Electric-acoustic wave (EA), P-type surface wave (SP) and S-type surface wave (SS)] are generated in response to an oblique incident Quasi plane wave. The main objective of this study is to investigate the influence of the characteristic length of microstructure, the inertial characteristic length and flexoelectric coefficients on the reflection and transmission coefficients. For this purpose, the linear algebraic equation, continuity conditions at the common interface are contracted. The linear system of equations comprising the reflection and transmission coefficients is derived, which is solved by using the Cramer's rule. The consequence of this electromechanical phenomenon may be advantageous in certain engineering applications that involve smart nano-composites.

Engineering estimation of the fatigue limit of wrought and defective additively manufactured metals for different load ratios

An empirical bi-parametric model based on the Vickers hardness HV and a proper microstructural length parameter, l, was proposed to estimate the fully reversed threshold-Stress Intensity Factor for long cracks of wrought and additively manufactured (AM) alloys. In this paper, the model has been extended to positive load ratios (R ≅ 0 and ≅ 0.5). Afterwards, experimental results generated from testing AM specimens containing natural defects were taken from the literature and were compared successfully with the estimation based on the El Haddad Smith Topper and the Atzori Lazzarin Meneghetti models defined solely on the basis of the HV and l.

Bauschinger effect and latent hardening under cyclic micro-bending of Ni-base Alloy 718 single crystals: Part I. Experimental analysis of single and multi slip plasticity

Cyclic micro-bending tests on fcc single crystal Ni-base Alloy 718 cantilevers with different crystal orientations were performed to analyze the influence of activated slip systems on dislocation plasticity, latent hardening and the Bauschinger effect. The investigations indicate that plasticity in single crystal micro-cantilevers is significantly influenced by two phenomena - dislocation interaction and dislocation pile-up at the neutral plane. Both phenomena occur at the same time. Their ratio seems to be determined by the activated slip systems. Slip trace analysis indicates that the activation of only one slip system leads to a strong localization of plasticity to a limited number of parallel slip bands. This results in low dislocation interaction and consequently pronounced pile-ups at the neutral plane. In multi slip orientation, the second slip system leads to activation of significantly more dislocation sources, causing a much earlier and more homogeneous elastic-plastic transition zone. In stress-strain hysteresis loops during bending, pronounced dislocation interaction in multi slip orientation leads to a more pronounced latent hardening. The results suggest that on a microstructural length scale, plasticity behavior is strongly affected by activated slip systems, which determine local dislocation phenomena. Based on the results presented in this paper, a finite element analysis of latent hardening and the Bauschinger effect using a single crystal plasticity model with latent kinematic hardening is presented in Part II.

Effect of alkaline treatment on mechanical properties of composites: Unsaturated polyester reinforced ZrO2/jute and sisal

Alkali treated (5 wt. % alkali was used on the total weight of the alkali solution and the treatment time was 2 h) discontinuous cellulosic fiber (jute and sisal were used as cellulosic fibers and 35 wt. % filler content was incorporated) reinforced chemically modified ZrO2 (ZrO2 was used as 10 wt. % of total filler content. In this context, it is worthwhile to mention that when both fillers were used, the fiber content was taken in the weight ratio of 1:1.) dispersed hybrid unsaturated polyester composites were fabricated by a compression molding technique. The mechanical behavior of the fabricated composites was evaluated at the sub-micron scale by nanoindentation (indentation with an applied load on the composites surface at the nano-metric range) or depth-sensing instrumented indentation technique. The significant effect of incorporation of the dispersing phases within the unsaturated polyester matrix with respect to mechanical properties at microstructural length scale was observed. A marked improvement in the nanoindentation-derived parameters viz. , nanohardness, reduced modulus, elastic recovery, and indentation creep was observed which may be attributed due to the influence of fillers inclusion within the unsaturated polyester matrix. An extensive effort was laid to analyze the dynamic mechanical properties using the sinus indentation mode associated with nanoindentation measurements to further correlate the influence of fillers addition with the indentation-derived parameters.

Progress and opportunities in modelling environmentally assisted cracking

Environmentally assisted cracking phenomena are widespread across the transport, defence, energy and construction sectors. However, predicting environmentally assisted fractures is a highly cross-disciplinary endeavour that requires resolving the multiple material-environment interactions taking place. In this manuscript, an overview is given of recent breakthroughs in the modelling of environmentally assisted cracking. The focus is on the opportunities created by two recent developments: phase field and multi-physics modelling. The possibilities enabled by the confluence of phase field methods and electro-chemo-mechanics modelling are discussed in the context of three environmental assisted cracking phenomena of particular engineering interest: hydrogen embrittlement, localised corrosion and corrosion fatigue. Mechanical processes such as deformation and fracture can be coupled with chemical phenomena like local reactions, ionic transport and hydrogen uptake and diffusion. Moreover, these can be combined with the prediction of an evolving interface, such as a growing pit or a crack, as dictated by a phase field variable that evolves based on thermodynamics and local kinetics. Suitable for both microstructural and continuum length scales, this new generation of simulation-based, multi-physics phase field models can open new modelling horizons and enable Virtual Testing in harmful environments.

Enhanced thermal coarsening resistance in a nanostructured aluminum-cerium alloy produced by additive manufacturing

Decreasing microstructural length scales to the nanoscale is a proven way of increasing strength, but the intrinsic metastability of such structures typically makes them susceptible to thermally activated coarsening. Recent advances in additive manufacturing permit bulk-nanostructured materials to be produced through rapid solidification, but like other metastable materials the as-built structures typically coarsen rapidly with even modest thermal exposure. Here, selective laser melting is employed to produce an Al-Ce-based alloy with high mechanical strength arising from the as-built microstructure, which can be controlled by build conditions. In addition, the alloy exhibits extreme resistance to thermal coarsening up to 400 °C and superior strength retention compared to conventional Al alloys after extended thermal exposure. The near-zero solubility of Ce in Al and potent solid solution strengthening of Mg enable this behavior without requiring heat treatment. This result demonstrates that combining insoluble alloying elements with additive manufacturing is a viable method of producing exceptionally stable bulk nanoscale alloys.

Effect of convection on directional solidification in transparent succinonitrile–2.2wt.%(d)camphor alloy

Interaction of melt flow with solidification microstructures is of fundamental interest and technical relevance due to its effect on the selection of characteristic microstructural features and length scales. Here, we report on in-situ optical observation of both melt flow at the solidification front and microstructural evolution in polycrystalline cellular and dendritic microstructures during upwards directional solidification of a transparent succinonitrile-2.2wt.%(d)camphor alloy in a bulk rectangular sample. Melt flows at different flow intensity levels were applied and the microstructures were characterized in terms of morphology, spacing and growth direction.Under unforced or natural convection, transitions from planar to cellular and further to dendritic solid/liquid interface morphology were obtained (having cellular/dendritic spacing with similar trends as reported in literature data). Under forced convection, after a plateau, decreasing dendrite spacing with increasing shear flow intensity was observed. Also, an increasing inclination of cellular and dendritic growth in the downstream direction was established. Furthermore, for the first time a flow-mediated transition from dendritic to seaweed-type microstructures and vice-versa was observed. Finally, an oscillation of dendrite tip positions with fixed frequency was found for a certain parameter range. The results indicate the large variety of flow effects at different length scales and corresponding physical mechanism, which are discussed.

Fractal behavior of surface oxide crack patterns on AISI 4140 high-strength low-alloy steel exposed to the simulated offshore environment

Wear and corrosion are surface-dependent degradation phenomena pertinent to the hostile environment existing in deep-sea oil and gas wells containing aggressive chemical species such as chloride/bromide salts, organic acids, carbon dioxide, and hydrogen sulfide,etc. Apart from the identification of the potential failures of alloys that can occur on a large and devastating scale by its interaction with these deleterious species, it is also essential to comprehend the nature and character, particularly the cracking pattern of the surface oxides formed on alloys undergoing corrosion in a particular environment. This article uses fractal geometry to study the branching of the surface oxide crack patterns in AISI 4140 high-strength low-alloy steel after exposure in a simulated offshore corrosive environment containing aqueous 3.5 wt.% sodium chloride solution. The fractal geometry was evaluated using the box-count technique in three different electrolytic test conditions: Electrochemical Anodic Polarization, Electrochemical Cathodic Polarization, and Immersion Corrosion for 24 h. Our results showed that the magnitude of fractal dimension is highest during immersion corrosion for 24 h and lowest during anodic polarization. Fractals can provide complementary quantifiable information about the surface geometries and fracture crack patterns from macrostructural to microstructural length scales by image analysis. This approach can be leveraged by emerging technologies like Artificial Intelligence (AI), Machine Learning (ML) and Computer Vision (CV), in structural health monitoring of alloys used in exotic and challenging conditions.

Variational-asymptotic homogenization of thermoelastic periodic materials with thermal relaxation

A multi-scale variational-asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement and the micro-temperature fields are rewritten on the transformed Laplace space and expressed as power series of the microstructural length scale, leading to a set of recursive differential problems over the periodic unit cell. The solution of such cell problems leads to the perturbation functions. Up-scaling and down-scaling relations are then defined, and the latter allow expressing the microscopic fields in terms of the macroscopic ones and their gradients. The variational-asymptotic scheme to establish an equivalence between the equations at macro-scale and micro-scale is developed. Average field equations of infinite order are also derived. The efficiency of the proposed technique was tested in relation to a bi-dimensional orthotropic layered body with orthotropy axis parallel to the direction of the layers, where the mechanical and temperature constitutive properties were well established. The dispersion curves of the homogenized medium, truncated at the first order are compared with the dispersion curves of the heterogeneous continuum obtained by the Floquet-Bloch theory. The results obtained with the two different approaches show a very good agreement.

Features of A356 alloy solidified under water cooling conditions

This study focused on using a simple quench method to study the effect of ablation water cooling on microstructural features and heat treatment response of A356 alloy. Molten alloy of a given quantity was solidified in water and the resultant microstructure was characterized and compared with that solidified in metal molds and that reported on ablation castings. It is found that the simple method is suitable in simulating certain features of eutectic solidification during ablation casting. The microstructural length scales obtained in this multicomponent alloy are comparable to that predicted by theories developed for binary alloys. The heat treatment response of the water cooled samples are much faster than that of conventional castings which can be translated into reduced energy consumptions and significant cost savings if the heat treating process is optimized for ablation casting.

Granular micromechanics‐based identification of isotropic strain gradient parameters for elastic geometrically nonlinear deformations

AbstractAlthough the primacy and utility of higher‐gradient theories are being increasingly accepted, values of second gradient elastic parameters are not widely available due to lack of generally applicable methodologies. In this paper, we present such values for a second‐gradient continuum. These values are obtained in the framework of finite deformations using granular micromechanics assumptions for materials that have granular textures at some ‘microscopic’ scale. The presented approach utilizes so‐called Piola's ansatz for discrete‐continuum identification. As a fundamental quantity of this approach, an objective relative displacement between grain‐pairs is obtained and deformation energy of grain‐pair is defined in terms of this measure. Expressions for elastic constants of a macroscopically linear second gradient continuum are obtained in terms of the micro‐scale grain‐pair parameters. Finally, the main result is that the same coefficients, both in the 2D and in the 3D cases, have been identified in terms of Young's modulus, of Poisson's ratio and of a microstructural length.

Strain gradient enhanced chemo-mechanical modeling of fracture in cathode materials for lithium-ion batteries

Next generation lithium-ion batteries (LIBs) cathodes are composed of polycrystalline microstructures where spatial heterogeneity such as grain size is often comparable to the geometric dimension of the cathodes. Incorporating the influence of the aforementioned heterogeneity in a chemo-mechanical continuum description is necessary to address the diffusion induced stress field during electrochemical cycling. Therefore, in the present study, the micro-structural size-dependent characteristic length of the cathode is embedded through a non-classical continuum mechanics approach known as the strain gradient elasticity (SGE) theory. Accordingly, a thermodynamically consistent multi-physics framework is developed where nonlinear diffusion kinetics is included along with the energetic interaction between the lithium-ions and host lattice of the electrode. The coupled governing equations are derived for the spherical cathode, and the generalized differential quadrature (GDQ) method is utilized to build the numerical procedure. The role of material heterogeneity length scale is addressed for strongly coupled chemo-mechanical process. Subsequently, the growth of potential surface flaws is examined under multiple length scales, particle size, and charge rate conditions. Ultimately, a comprehensive fracture map is established to illustrate the regime of flaw insensitivity, partial breakage and complete disintegration. Thus, the present findings can provide a suitable design perspective for fail-safe particulate type composite cathodes.

Modeling Ablation Casting

Research published in open literature on ablation casting has been mainly experimental. Modeling of this innovative technology is scarce. This article describes an initial attempt in modeling ablation casting process. Material properties and boundary conditions were defined for calculating cooling curves and microstructural length scales in A356 alloy castings made using sand casting and ablation casting processes. Model predictions were compared with published data on cooling curves and solidification times in an A356 alloy casting. The validated model was then used to predict unique solidification features associated with the ablation casting process, including the eutectic solidification time, shrinkage porosity formation, eutectic front morphology, the advancing rates of the eutectic front and the associated eutectic silicon morphology. Simulation results indicate that the progressive advancing ablation cooling is capable of reducing secondary dendrite arm spacing, modifying the eutectic silicon phase owing to the water quench effect, and eliminating shrinkage porosity using much smaller risers than usual if the ablation is correctly driven towards the risers.

Fatigue assessment of welded joints at sub-zero temperatures by means of stress averaging approach

ABSTRACT The problem of typical stress-based fatigue assessment methods is that additional influencing factors like temperature effects do not directly influence the respective stress and can thus only be incorporated via modification factors. The stress averaging approach is expected to account for effects that influence the support around notches via the micro-structural support length ρ*. This study thus investigates the applicability of the stress averaging approach for welded joints in engineering structures exposed to sub-zero temperatures. For this purpose, fatigue test results of welded joints in the temperature range of 20°C down to −50°C are assessed. It is shown that it is possible to assess data for different temperature with the same reference fatigue curve while maintaining a small scatter without the need for modification factors.

Mechanical Behaviour of Jute/ZrO2 Based Polyester Composites at Microstructural Scale

Alkali treated jute fibre incorporated silanized ZrO2 based unsaturated polyester composites were synthesized using compression moulding technique. The filler loading was adopted with a progressive wt. %, of 5, 15, 25, 35 and 45 respectively. These samples were further subjected to structural investigation using scanning electron microscope and X-ray diffraction technique to observe the morphological features and crystalline nature of the matrix. The mechanical characterization was accomplished at the microstructural length scale from macro to submicron range. It was observed that the composite with 35 wt. % filler loading resulted in the best properties among the lot.

Modelling and simulation of the freeze casting process with the phase-field method

The freeze casting process is a novel manufacturing method for both near net-shape parts as well as directed porous structures as employed by filters and implants. Depending on the choice of liquid and processing conditions a very wide range of pore shapes and sizes can be achieved. In order to predict the resulting microstructure, a phase-field model is developed on the basis of the grand potential formalism. The model and its parametrization approximate the freeze-casting process of water by linking its thermodynamics with established theory. Directional solidification simulations with varying suspension concentrations, velocities and temperature gradients are carried out. From these, microstructural lengths are determined and linked with the processing parameters, so as to derive linkages between the microstructure and the processing conditions.

Limits of enhanced of macro- and meso-scale continuum models for studying size effect in concrete under tension

The paper investigates a mechanical quasi-static size effect in concrete during splitting tension at the macro- and meso-level. In experiments, five different diameters of cylindrical concrete specimens were tested. Two-dimensional plane strain finite element (FE) simulations were carried out to reproduce the experimental size effect. The size effect in experiments by Carmona et al. was also simulated. Two enhanced continuum concrete models (elasto-plastic and damage) were used which were enriched in softening by a characteristic length of micro-structure with the help of a non-local theory. In macro-level simulations, the effect of crucial geometric and material parameters on the size effect was carefully studied such as the width of loading/supporting strips, concrete fracture energy in tension, concrete compressive strength and stiffness of loading/supporting strips. The focus was on the distribution of primary and secondary strain localization zones. In addition, some 2D size effect calculations were performed within enriched elasto-plasticity at the meso-scale by considering the real heterogeneous meso-structure of concrete from the front side of experimental specimens. The calculated size effect on the splitting tensile strength at the macro- and meso-scale proved to be weaker than in our experiments. Shortcomings of enhanced continuum models for size effect simulations were outlined.

Dispersion and attenuation of shear wave in couple stress stratum due to point source

This study discusses the propagation of a horizontally polarised shear wave in a layered composite structure consisting of couple stress stratum over a functionally graded orthotropic viscoelastic substrate due to point source existing at an imperfect interface of the stratum and substrate. Because of the CS effect in the stratum, the existence of the second kind of dispersive (shear) wave is established along with conventional first kind of a shear wave. The closed-form dispersion equations and damping equations of the first and second kind of a dispersive wave are derived by adopting non-traditional boundary conditions and Green’s function technique. The effect of characteristic length of microstructure, imperfect bonding parameter and functional gradient parameters on velocity profiles and attenuation profiles of the first and second kind of dispersive wave has been computed numerically and delineated graphically. For validation, established results are matched with the classical one.