Complex Heterogeneous Microstructure Research Articles

Extended quasicontinuum methodology for highly heterogeneous discrete systems

SummaryLattice networks are indispensable to study heterogeneous materials such as concrete or rock as well as textiles and woven fabrics. Due to the discrete character of lattices, they quickly become computationally intensive. The QuasiContinuum (QC) Method resolves this challenge by interpolating the displacement of the underlying lattice with a coarser finite element mesh and sampling strategies to accelerate the assembly of the resulting system of governing equations. In lattices with complex heterogeneous microstructures with a high number of randomly shaped inclusions the QC leads to an almost fully‐resolved system due to the many interfaces. In the present study the QC Method is expanded with enrichment strategies from the eXtended Finite Element Method (XFEM) to resolve material interfaces using nonconforming meshes. The goal of this contribution is to bridge this gap and improve the computational efficiency of the method. To this end, four different enrichment strategies are compared in terms of their accuracy and convergence behavior. These include the Heaviside, absolute value, modified absolute value and the corrected XFEM enrichment. It is shown that the Heaviside enrichment is the most accurate and straightforward to implement. A first‐order interaction based summation rule is applied and adapted for the extended QC for elements intersected by a material interface to complement the Heaviside enrichment. The developed methodology is demonstrated by three numerical examples in comparison with the standard QC and the full solution. The extended QC is also able to predict the results with 5% error compared to the full solution, while employing almost one order of magnitude fewer degrees of freedom than the standard QC and even more compared to the fully‐resolved system.

A Machine Learning Approach for Segmentation and Characterization of Microtextured Regions in a Near-α Titanium Alloy

The development of automated segmentation and quantitative characterization of microtextured regions (MTRs) from the complex heterogeneous microstructures is urgently needed, since MTRs have been proven to be the critical issue that dominates the dwell-fatigue performance of aerospace components. In addition, MTRs in Ti alloys have similarities to microstructures encountered in other materials, including minerals and biomaterials. Meanwhile, machine learning (ML) offers new opportunities. This paper addresses segmentation and quantitative characterization of MTRs, where an ML approach, the Gaussian mixture models (GMMs) coupled with density-based spatial clustering of applications with noise (DBSCAN) clustering algorithms, was employed in order to process the orientation data acquired via EBSD in the Matlab environment. Pixels with orientation information acquired through electron backscatter diffraction (EBSD) are divided and colored into several “classes” (MTRs) within the defined c-axis misorientations (i.e., 25°, 20°, 15°, 10°, and 5°), the precision and efficacy of which are verified by the morphology and pole figure of the segmented MTR. An appropriate range of c-axis misorientations for MTR segmentation was derived, i.e., 15~20°. The contribution of this innovative technique is compared with previous studies. At the same time, the MTRs were statistically characterized in the global region.

Peridynamic micromechanical model for damage mechanisms in composites

This study presents a novel three-dimensional (3D) micromechanical peridynamic (PD) model to establish relationships between microstructural features such as shape, size and distribution of fibers, damage initiation, and size-effect relationships. It specifically permits to investigate the effective elastic properties and damage mechanisms in composites. It enables the application of pure strain, pure stress and mixed stress–strain constraints while including the effect of temperature change. Also, it permits the evaluation of effective material properties from a single load case. Periodic boundary conditions are applied naturally by completing the interaction domain using material points from the opposite side of microstructure. Also, this 3D PD micromechanical model does not require any surface correction for both homogenization and dehomogenization. Complex heterogeneous microstructures of composites are constructed and analyzed by state-based PD. Material variability is taken into consideration during the progressive damage analysis to capture more realistic failure mechanisms. Peridynamic predictions recover results available in the literature; thus, verifying the accuracy and effectiveness of the present micromechanical model.

Machine-learning and digital-twins for rapid evaluation and design of injected vaccine immune-system responses

A computational framework is developed that researchers in the field can easily implement and subsequently use as an efficient tool to study the immune-response to a vaccine injection. There are three main components to this work: Part I-Digital-twin construction: An approach is developed that efficiently simulates the time-transient proliferation of cells/antibodies (proteins) and regulator/antigens (deactivated toxin) to an injected vaccine within tissue possessing complex heterogeneous microstructure. Here, we use the terms “cells” and “antibodies”, as well as “regulator” and “antigen” interchangeably. The approach utilizes two strongly-coupled conservation laws: (a) Conservation Law 1: comprises (a) rate of change of cells/antibodies, (b) cellular/antibody migration, (c) cellular/antibody proliferation controlled by a cell/antibody mitosis regulating chemical (antigen), (d) cell/antibody apoptosis and (b) Conservation Law 2: comprises (a) rate of change of the cell/antibody mitosis chemical regulator/antigen, (b) regulator/antigen diffusion, (c) regulator production by cells/antibody and (d) regulator/antigen decay. Part II-Efficient computation: A technique based on a voxel (3D “volume pixels”) representation of tissue microstructures and corresponding digital solution methods is developed for the calculations, which avoids computationally expensive steps involved in usual Finite Element procedures such as topologically conforming meshing, mapping, volume integration, stiffness matrix generation and matrix-based solution methods. The process proceeds by converting the tissue microstructure into voxels. The problem then becomes “digital” on a regular “voxel-grid”, directly manipulating voxel values, allowing extremely fast methods to be used to construct derivatives and to iteratively solve the system with minimal memory requirements. Part III-Machine-learning: The rapid and efficient computation allows for many vaccines to be tested quickly and uses a genomic-based Machine-Learning Algorithm to optimize the system. This is particularly useful for rapid design of next-generation vaccines and boosters for disease strain mutations. Numerical examples are provided to illustrate the results, with the overall goal being to provide a computational framework to rapidly design and deploy a vaccine for a targeted response.

An investigation on the microstructure and mechanical properties of Al0.3CoCrFeNi high entropy alloy with a heterogeneous microstructure

In this study, the Al0.3CoCrFeNi high entropy alloy (HEA) with various heterogeneous microstructures was designed and fabricated through different process histories, such as severely cold-rolled plus annealing at low temperature for a long time (S1), cryo-rolled plus annealing at intermediate temperature (S2), cold-rolled plus annealing at intermediate temperature (S3). The microstructures were analyzed by SEM, EBSD, and TEM. The results showed that the heterogeneous grain structure of S1 alloy was composed of stretched original grains and fine recrystallized grains. Besides, the L12-(Ni, Co)3Al type phase was also observed within the face-centered cubic (FCC) matrix of the S1 alloy. However, the S2 and S3 alloys consisted of stretched original grains, survived original grains, fully recrystallized equiaxed grains, and B2 precipitates. Moreover, a mount of nano-deformation twins was also incorporated in the matrix of S2 alloy. Furthermore, the S2 alloy exhibited a superior balance of high ultimate tensile strength of ∼1019 MPa and high elongation of ∼28% as compared to S1 and S3 alloys due to its complex heterogeneous microstructure. This research would provide guidance for designing the heterogeneous structure in the FCC HEA and facilitate establishing the relationships between the heterogeneous structure and mechanical properties.

Manipulation of Microstructure and Mechanical Properties in N-Doped CoCrFeMnNi High-Entropy Alloys

Herein, we carefully investigate the effect of nitrogen doping in the equiatomic CoCrFeMnNi high-entropy alloy (HEA) on the microstructure evolution and mechanical properties. After homogenization (1100 °C for 20 h), cold-rolling (reduction ratio of 60%) and subsequent annealing (800 °C for 1 h), a unique complex heterogeneous microstructure consisting of fine recrystallized grains, large non-recrystallized grains, and nanoscale Cr2N precipitates, were obtained in nitrogen-doped (0.3 wt.%) CoCrFeMnNi HEA. The yield strength and ultimate tensile strength can be significantly improved in nitrogen-doped (0.3 wt.%) CoCrFeMnNi HEA with a complex heterogeneous microstructure, which shows more than two times higher than those compared to CoCrFeMnNi HEA under the identical process condition. It is achieved by the simultaneous operation of various strengthening mechanisms from the complex heterogeneous microstructure. Although it still has not solved the problem of ductility reduction, as the strength increases because the microstructure optimization is not yet complete, it is expected that precise control of the unique complex heterogeneous structure in nitrogen-doped CoCrFeMnNi HEA can open a new era in overcoming the strength–ductility trade-off, one of the oldest dilemmas of structural materials.

Editors’ Choice—Dealloying-Driven Cerium Precipitation on Intermetallic Particles in Aerospace Aluminium Alloys

Cerium-based compounds have been studied for decades as non-toxic candidates for the protection of aerospace aluminium alloys (AAs) like AA2024-T3. However, the complex heterogeneous microstructure of these alloys has hindered a thorough understanding of the subsequent stages of corrosion protection provided by this class of inhibitors. Thus, this work is devoted to unravelling the interaction mechanisms of different intermetallic particles (IMPs) in AA2024-T3 with cerium nitrate at the nanoscopic scale. This has been fulfilled through detailed top-view and cross-sectional analytical TEM investigations along with electrochemical evaluations. In line with our recent findings, we here report dealloying of IMPs as the main factor governing the rate of local cerium precipitation in contrast to micro-galvanic corrosion between IMPs and the surrounding matrix. Furthermore, we discuss a connection between the electrochemical response of the AA2024-T3 system and the morphological and compositional evolutions of individual IMPs including Al2CuMg, Al2Cu, Al7Cu2Fe(Mn) and Al76Cu6Fe7Mn5Si6 at different stages of a 96-h exposure.

Characterization of meso-scale mechanical properties of Longmaxi shale using grid microindentation experiments

Abstract Mechanical properties, such as the hardness H, Young’s modulus E, creep modulus C, and fracture toughness Kc, are essential parameters in the design of hydraulic fracturing systems for prospective shale gas formations. In this study, a practical methodology is presented for obtaining these properties through microindentation experiments combined with quantitative observations of the mineralogical phases using X-ray diffraction (XRD), scanning electron microscopy (SEM) with backscattered electron (BSE) imaging, and energy-dispersive X-ray spectroscopy (EDS) analyses. We apply this method in the case of three types of Longmaxi shales with different mineralogies (i.e. carbonate-, clay-, and quartz-rich, respectively), which allows us to determine the characteristic indentation depth, hc = 8–10 μm, beyond which the mechanical response of the carbonate-rich shale is homogeneous and independent of its complex heterogeneous microstructure. Moreover, exploiting the results of a large number of indentation tests, we demonstrate that the indentation modulus M of the shale increases as a power-law of hardness H, and its creep modulus C increases linearly with H. We also compute the fracture toughness Kc from the indentation data by assuming a perfectly plastic behavior of the sample. Our results are in good agreement with independent measurements of Kc determined by microscratch tests. Finally, further tests on quartz- and clay-rich samples of the Longmaxi shale suggest further variations in the samples’ mechanical properties depending on their burial conditions and the mechanical properties of their dominant mineral phases.

Improvement of strength-ductility trade-off in a Sn–0.7Cu–0.2Ni lead-free solder alloys through Al-microalloying

The enhancement in strength is generally attended by ductility loss in lead-free solder alloys, which is commonly denoted as strength-ductility trade-off (SDT). This work provides new viewpoint on the design of novel Sn–0.7Cu–0.2Ni (SCN) solders with the notably enhanced SDT, possessing yield stress (YS) of 40.8 MPa, tensile strength (UTS) of 42.9 MPa, and large uniform elongation up to 240%. Such breaking between competing properties of SDT is caused by microstructural modification that comprised with the arrangement of fine and coarse-sized phases in complex heterogeneous microstructures. Toward this end, the heterogeneous structures in SCN solder are produced by Al-microalloying, followed by cold-drawn and temperature-annealing. However, microalloying of 0.1% Al decreases the undercooling of SCN solder while 0.2% Al reduces the eutectic temperature. Our results show that the heterogeneous structure design strategy can offer a new generation of enhanced SDT alloys with boosting elastic compliance and plastic energy chock resistance for mobile products industry.

Crack formation within ceramics via coupled multiscale genome and XFEM predictions under various loading conditions

Because of the complex heterogeneous microstructure of ceramics, predicting crack formation within ceramics is still a challenge. The extended finite element method (XFEM) serves as a good tool for fracture prediction but is incapable of considering heterogeneous microstructure. In this paper, a numerical framework is developed to model cracks within ceramics by coupling a multiscale genome model with XFEM. XFEM is embedded in the formulation of the multiscale genome through the variational asymptotic method for unit cell homogenization (VAMUCH). The implementation of both multiscale genome model and XFEM retains the capabilities of XFEM in modeling fracture while providing accurate predictions by considering heterogeneous microstructure. The crack formation within SiC ceramics under different loading conditions is simulated in comparison with experiments in order to assess the validity of the proposed method. It is shown that the developed model captures the typical characteristics of crack formation within silicon carbide (SiC) ceramics under bending and indentation loadings. The predicted cutting forces and crack depth exhibit a good agreement with the experimental results during machining processes.

Influence of local fatigue damage evolution on crack initiation behavior in a friction stir welded Al-Mg-Sc alloy

Axial loading fatigue tests were carried out in a friction stir welded Al-Mg-Sc alloy. Local strain evolution under fatigue loading was monitored using small strain gages. The weld joint had very complex heterogeneous microstructure and hardness distributions. The cyclic stress-strain responses were strongly dependent on the local hardness distribution. The cyclic plastic strain was observed intensively on the advancing side in the soft stir zone. Transgranular fatigue cracks initiated in the stir zone on the top surface, where high plastic strain was observed. To the contrary, intergranular crack initiations were observed on the bottom surface. The crack initiation was caused mainly by the cyclic plastic straining on the top side. However on the bottom side, the residual initial oxide layer, which was not sufficiently stirred, as well as the local cyclic plastic straining could be attributed to the intergranular crack initiations.

Correlation Study Between 3D Three-Phase Electrode Morphology and Li-Ion Battery Performance: A Case for LiFePO4

It is well known that the microstructure of the Li-ion battery (LIB) electrode can largely impact performance of LIBs. One approach to improve the performance of the LIBs is to gain insight in the correlations between the complex heterogeneous microstructure existing of active material, conductive additive and electrolyte, providing the required electronic and ionic transport. In a recent study we successfully demonstrated a simple and cost effective templating technique utilizing hydrogen carbonate salts to enhance the power density of LiFePO4electrodes without compromising the electrode density [1]. The applied templating method improves the capacity retention at high rates significantly. More importantly, the template only results in a slight increase in the porosity, leading to a combination of large tap density (high volumetric energy density) and large power density. The electrochemical data analysis indicates the better performance of templated electrodes may due to better interconnectivity and tortuosity within electrolyte induced by the template. However, direct evidence to correlate the microstructure of the templating electrode with LIBs performance is still needed. In this work, by combining focused ion beam-scanning electron microscopy (FIB-SEM) and neutron depth profiling (NDP), we have obtained three-phase 3D electrode microstructure and Li-ion concentration profiles to better understand the improved rate performance of the templated LiFePO4 electrodes. Although it is proposed that the hierarchical interconnected porosity in the templated sample can enhance the electrode rate performance, no significant electrolyte tortuosity differences were found between the conventional and carbonate templated LiFePO4 electrodes. Surprisingly, although the same amount of CB was used in the two electrodes, a better electronic conductive CB network was observed for the templated sample (Figure 1 a, b), enhancing the activity of LiFePO4 at near the electrolyte-electrode interface as directly observed with NDP. Moreover, the CB structure in the templated electrode possesses a less tortuous pathway for electron transport, and the tortuosity distribution is less heterogeneous than in the conventional electrode, as shown in Figure 1 c-f. This results from 3D microstructure analysis is consistent with the NDP result where the templated electrodes show enhancing charging/discharging activity near the electrolyte-electrode interface than conventional LiFePO4electrode. The results demonstrate that the templated electrode has better charge transport network, which result in improved performance. [1] Singh, D. P.; Mulder, F. M.; Abdelkader, A. M.; Wagemaker, M. Advanced Energy Materials 2013, 3, 572. Figure 1

Relating the 3D electrode morphology to Li-ion battery performance; a case for LiFePO4

One of the main goals in lithium ion battery electrode design is to increase the power density. This requires insight in the relation between the complex heterogeneous microstructure existing of active material, conductive additive and electrolyte providing the required electronic and Li-ion transport. FIB-SEM is used to determine the three phase 3D morphology, and Li-ion concentration profiles obtained with Neutron Depth Profiling (NDP) are compared for two cases, conventional LiFePO4 electrodes and better performing carbonate templated LiFePO4 electrodes. This provides detailed understanding of the impact of key parameters such as the tortuosity for electron and Li-ion transport though the electrodes. The created hierarchical pore network of the templated electrodes, containing micron sized pores, appears to be effective only at high rate charge where electrolyte depletion is hindering fast discharge. Surprisingly the carbonate templating method results in a better electronic conductive CB network, enhancing the activity of LiFePO4 near the electrolyte-electrode interface as directly observed with NDP, which in a large part is responsible for the improved rate performance both during charge and discharge. The results demonstrate that standard electrodes have a far from optimal charge transport network and that significantly improved electrode performance should be possible by engineering the microstructure.

Microstructural model for the time‐dependent thermomechanical analysis of cast irons

AbstractIn this paper, a multiscale modelling approach is followed for the modelling of time and temperature dependent behaviour of compacted graphite cast iron (CGI) material. Cast irons are often used in heavy duty machinery parts subjected to elevated temperatures for prolonged periods of time. This, in combination with its complex heterogeneous microstructure, plays the crucial role in determining the life time of the material. In this work a 2D microstructural model of CGI is developed. The geometry is based on the micrographs of the material. The pearlitic matrix is modelled with the temperature dependent elasto‐visco‐plastic model calibrated on the pearlitic steel experiments. The graphite particles are modelled as anisotropic elastic. The results of the simulations of tensile and stress relaxation tests at different temperatures between 20 °C and 500 °C show that the macroscopic mechanical behaviour of the ma‐terial deteriorates rapidly above 350 °C. At the microstructural scale, the anisotropic graphite particles act as stress concentrators promoting the formation of strain percolation paths, that become more critical at higher temperatures. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimization of process parameters for plasma arc welding of austenitic stainless steel (304 L) with low carbon steel (A-36)

This research aims to optimize the process parameters of plasma arc welding for welding of dissimilar metals: austenitic stainless steel SS-304 L and low carbon steel A-36. It investigates the effect of welding current and welding speed on the quality of the welded joints. The quality characteristics like bead geometry, microstructure, hardness, ferrite measurement and tensile test are considered for qualification of the welded samples. Welded specimens were prepared both with and without filler material. These specimens were mechanically tested and analyzed using metallographic techniques. Based on the results, suitable welding parameters were found to be 45 A and 2 mm/s for samples prepared with and without filler wire. An all-martensitic weld zone structure was obtained for direct fusion. However, a complex heterogeneous microstructure was obtained by using austenitic stainless steel filler wire E 309 L. Hardness of directly fused sample was observed to be significantly higher compared to filler wire sample.

Effect of Application of Short and Long Holds on Fatigue Life of Modified 9Cr-1Mo Steel Weld Joint

Modified 9Cr-1Mo steel is a heat-treatable steel and hence the microstructure is temperature sensitive. During welding, the weld joint (WJ) is exposed to various temperatures resulting in a complex heterogeneous microstructure across the weld joint, such as the weld metal, heat-affected zone (HAZ) (consisting of coarse-grained HAZ, fine-grained HAZ, and intercritical HAZ), and the unaffected base metal of varying mechanical properties. The overall creep–fatigue interaction (CFI) response of the WJ is hence due to a complex interplay between various factors such as surface oxides and stress relaxation (SR) occurring in each microstructural zone. It has been demonstrated that SR occurring during application of hold in a CFI cycle is an important parameter that controls fatigue life. Creep–fatigue damage in a cavitation-resistant material such as modified 9Cr-1Mo steel base metal is accommodated in the form of microstructural degradation. However, due to the complex heterogeneous microstructure across the weld joint, SR will be different in different microstructural zones. Hence, the damage is accommodated in the form of preferential coarsening of the substructure, cavity formation around the coarsened carbides, and new surface formation such as cracks in the soft heat-affected zone.

Design considerations for achieving simultaneously high-strength and highly ductile magnesium alloys

A comprehensive scheme of phase configuration optimization in the Mg–Zn–Ca(–Zr) system by thermodynamic simulations and microstructural analyses is presented. A composition window of 0.2–0.4 wt% Ca and 5–6 wt% Zn is defined as optimal for establishing a complex heterogeneous microstructure allowing for enhanced ductility and simultaneously high strength of the material. Literature data analysis and our own results confirm the enhanced performance of alloys from this composition window.

Evolutionary optimization of material properties of a tropical seed

Here, we show how the mechanical properties of a thick-shelled tropical seed are adapted to permit them to germinate while preventing their predation. The seed has evolved a complex heterogeneous microstructure resulting in hardness, stiffness and fracture toughness values that place the structure at the intersection of these competing selective constraints. Analyses of different damage mechanisms inflicted by beetles, squirrels and orangutans illustrate that cellular shapes and orientations ensure damage resistance to predation forces imposed across a broad range of length scales. This resistance is shown to be around the upper limit that allows cracking the shell via internal turgor pressure (i.e. germination). Thus, the seed appears to strike an exquisitely delicate adaptive balance between multiple selection pressures.

Novel Development and Applications in Finite Element Technologies. Efficient Modeling of Microscopic Heterogeneity and Local Crack in Composite Materials by Finite Element Mesh Superposition Method.

The finite element mesh superposition method is applied to the two-dimensional crack problem of composite materials. The microscopic heterogeneity involved in the composite materials is modeled by the fixed grid model. On this global mesh, a local mesh that considers the local crack is superimposed without taking care of the matching of nodes and elements of both meshes. The use of the fixed grid model for the global mesh can reduce the time and efforts for the mesh generation to express the complex heterogeneous microstructures. Also it makes the computation and the implementation of the finite element mesh superposition method very easy. The accuracy was verified by comparing with the theory and the calculation by the conventional fine mesh.