Journal Club for October 2023: Dynamic Behavior of Ceramics, Ceramic Composites, and Structures: Experimental and Computational Mechanics to Inform Advanced Manufacturing

Journal Club for October 2023:Dynamic Behavior of Ceramics, Ceramic Composites, and Structures: Experimental and Computational Mechanics to Inform Advanced Manufacturing

Authors (alphabetical by last name): James D. Hogan*, Haoyang Li, Saman Sayahlatifi, Sara Sheikhi, Zahra Zaiemyekeh, and Jie Zheng

Centre for Design of Advanced Materialsat theUniversity of Alberta

*For further information or interest, please email Jamie Hogan atjdhogan@ualberta.ca

I. Introduction and motivation

The development of better-performing advanced ceramics and ceramic-based composites is important in defence, aerospace and space, energy production and storage, biomedical, and manufacturing industries, where light-weight and chemically stable ceramic-based materials with favorable mechanical and thermal properties are widely used in harsh environments (e.g., high-speed tool wear, protective armor for human and carriers, space debris shielding, and high-temperature barriers for heat exchangers and nuclear reactors). Recent advancements in advanced manufacturing (e.g., cold spraying, stereolithography) allows for flexibility in designing geometrically-complex and multi-functional ceramic-based materials with controlled failure behaviors and improved performances. This is accomplished by tailoring the mechanical properties and microstructures through control of feedstock powders (e.g., size), and printing and post-processing parameters (e.g., laser energy). At the core of advancing the design of next-generation ceramic-based materials is experimental and computational mechanics, whose fields have been driven recently by developments in new advanced in situ diagnostics (e.g., laser-based probes), multi-scale physics-based modelling approaches (e.g., phase-field, micro-mechanical modelling with real or synthetic microstructures benefited from rapid growth in computational power), and atomistic simulations (e.g., quantum-mechanical modelling, molecular dynamics). In addition, machine learning-assisted materials science, either physically-informed or based on regression, has been a growing research field given its capacity to largely reduced computational cost while providing sufficient accuracy in predicting mechanical responses.

This iMechanica post will outline recent progress in advancing both applied and fundamental knowledge of experimental and computational mechanics of ceramic-based materials at the Centre for Design of Advanced Materials (website:https://sites.ualberta.ca/~jdhogan/) at the University of Alberta, Canada; this is shown in Section II. The emphasis of this article is on understanding the dynamic failure mechanisms (e.g., intergranular and transgranular fracture, plastic flow, thermal cracking) and process (e.g., structural collapse) through experimental and computational mechanics approaches, and then linking this knowledge back to how we can control mechanisms and processes via design and manufacturing. Section II categorizes ceramic material systems based on their fabrication techniques (e.g., hot pressing, spraying, 3D printing), and attempts to emphasize the efforts by the authors while highlighting recent progress in literature. The following sub-sections build up in complexity of the interplay between material responses (e.g., damage, micro-failure mechanisms) and structural responses (e.g., stress-strain relationship, failure modes), and this represents how the research at theCentre for Design of Advanced Materialshas evolved since 2015. The post concludes with an outlook (Section III) focusing on the advancing of machine learning-assisted experimental and computational mechanics with higher spatial-temporal-resolution, in conjunction with new material systems development.

II. Experimental and computational mechanics of ceramic-based materials

实验和计算力学的马特里als research focuses on understanding structure-property-performance relationships in materials. The goal is to determine the length-scale- and time-scale-dependent failure mechanisms within materials for a given loading situation (e.g., ballistic impact). Once understood, we seek to improve material performance by controlling how they fail, and this is accomplished through design and manufacturing on either the material or structure level. In some applications, one seeks to promote failure in a controlled manner to improve performance (e.g., transparent ceramic windshields), while in other cases one seeks to suppress failure in order to improve performance (e.g., armor).

In the following sub-section of this post, we will provide some insights on the multi-scale experimental and computational mechanics of advanced ceramics (see Section II.1). Next, we will highlight some recent works encompassing the fabrication, experimentation, and advanced micro-mechanical modelling of a cold-sprayed ceramic-metal composite (see Section II.2); this section concludes with suggested future efforts on numerically-computed damage quantification and data-driven constitutive modelling. Lastly, we will discuss the advantages and limitations of multi-functional ceramic-based structures fabricated by additive manufacturing (see Section II.3), while showcasing our most recent results on additively manufactured alumina ceramics.

1. Multi-scale mechanics in advanced ceramics: insights on state-of-the-art testing and modelling

Advanced ceramics have become indispensable in various engineering applications (e.g., aerospace, automotive, and defence) due to their exceptional properties, such as low density, high hardness, and high wear resistance [1 – 5]. Existing ceramic materials can be broadly categorized into two groups: oxide-dense ceramics (e.g., alumina (Al2O3), zirconia (ZrO2), and titania (TiO2)) and non-oxide ceramics, which include carbides, nitrides, and borides (e.g., silicon carbide (SiC), silicon nitride (Si3N4), and boron carbide (B4C)). In this section, we explore research involving experimental and computational mechanics used for establishing relationships between the microscale characteristics (e.g., grain sizes and flaws) and macroscale performance (e.g., mechanical properties and failure mechanisms) of advanced ceramic materials.

a. State-of-the-art experimental studies of advanced ceramics

获得了大规模的深入了解mechanical properties and failure mechanisms of advanced ceramics, controlled stress-state experiments, such as uniaxial compression [4, 6], confined compression [5, 7], compression-shear [4], bending [8], and Brazilian disk testing [9] are conducted coupled with advanced diagnostic techniques, such as high-speed imaging [1 – 11]. These experiments have demonstrated that properties and failure of ceramic materials are sensitive to stress-state [4, 9, 13]; for example, an increase in confinement pressure enhances the compressive strength due to suppression of fracture propagation [13]. In addition, advanced ceramics exhibit strain-rate-dependent mechanical behaviors attributed mainly to the activated failure mechanisms, fracture propagation rate, and inertial effects [14]. Various experimental methods are used to achieve a wide range of strain rates that are relevant in engineering application, including servo hydraulic machines [15], drop towers [16], split-Hopkinson pressure bars [17], plate impact tests [3], ballistic impact tests [18], and laser shock methods [19]. Fig. 1a (on left) shows the split-Hopkinson pressure bar system for testing the dynamic stress–strain response of advanced ceramics at the Centre for Design of Advanced Materials (CDAM).

Figure 1: Length-scale dependent experimental and numerical research efforts by the authors:分离式霍普金森压杆系统动态tests. b) Electron Backscatter Diffraction (EBSD) image of an alumina ceramic. c) Transmission Electron Microscopy (TEM) image of an alumina ceramic. d) A hybrid finite-discrete element model simulating a Brazilian disk loading experiment of an alumina ceramic. e) Phase field modelling of twinning in boron carbide (B4C). f) Atomic model of alumina (Al2O3) with a spherical void in the center used in molecular dynamics simulations, and a unit cell of Al2O3 used in first-principle calculations such as DFT.

The mechanical properties of ceramics at the macro-scale (e.g., density, modulus, strength, fracture mode) are largely influenced by their microstructure [20]. For instance, in fine-grained alumina (e.g., 6 μm grain size), crack propagation is primarily intergranular [1], [9], whereas in alumina with a coarse grain size of 53 μm, the crack path is predominantly transgranular [21]. Fig. 1b is a representative grain structure of an alumina ceramic, acquired through electron backscatter diffraction (EBSD) technique [4]. Such ceramic materials typically comprise of randomly oriented crystallographic grains, ranging in size from a few nanometers to the micrometers scale, and flaws (e.g., pores, micro-cracks, and impurities) typically dispersed around grain boundaries [4, 9]. Fig. 1c shows a transmission electron microscopy (TEM) image of and alumina grain boundary used for studying the nanoscale structure, morphology, crystallography, and defects of the material. Notably, the microstructure (e.g., pore size, grain size, impurity content) can be tailored using various manufacturing techniques (e.g., sintering, additive manufacturing methods) in response to external stimuli such as sintering temperature, dwell time, pressure, manufacturing additives, and powder size [22]. Some of these concepts are discussed later.

b. Multi-scale modeling of advanced ceramics

The experimental observed failure phenomena have also promoted the development of modeling approaches for the purpose of investigating their initiation and growth, including physical-based and phenomenological models. The wing crack model is a widely adopted physical-based model for compression loading scenarios, which shows that activated cracks propagate parallel to the uniaxial compressive loading direction [10]. Moreover, various stress-state-dependent micro-cracking models have been proposed based on the wing-crack model, such as crack interaction, dilatancy, and coupled sliding and damage models [23]. Phenomenological models, including continuum damage mechanics (CDM), the extended Finite Element Method (XFEM), the virtual crack closure technique (VCCT), the cohesive zone method (CZM), and the phase field model (PFM) [24 - 26], have also been developed for ceramic materials. The CDM method uses damage parameters to describe failure behavior, with well-known approaches such as the JH1, JH2, JH2-V, and JHB models being popularly used to solve dynamic problems [3,14]. The XFEM, VCCT, CZM, and PFM methods are commonly used to investigate fracture behavior such as crack branching and interaction [24 - 26]. For example, Fig. 1d shows the fracture pattern in simulations of a Brazilian disk experiments produced using a hybrid finite-discrete element model with CZM. Additionally, Fig. 1e illustrates the phase field modeling of twin propagation in boron carbide under a plain strain condition [27].

在分子和原子,原子论的同时ations, including molecular dynamics (MD) [29], Monte Carlo simulation (MC) [30], and density functional theory (DFT) [31] are often employed to study the fundamental interactions between atoms, so that to inform properties (e.g., mechanical, electrical, magnetic) for an “ideal” material (i.e., perfect crystal structure). Recent work from the authors in Chang et al. [32] shown in Fig. 1f demonstrates an alumina unit cell and supercell with a spherical void that is studied in molecular dynamic simulation under uniaxial, bi-axial, and tri-axial tension. These simulations capture the elaborate details of the material's atomic and electronic structure, bonding, and defects [33]. By simulating the electronic structure of atoms and interactions between the atoms and molecules, we can understand the fundamental mechanisms that define the properties of materials (e.g., atomistic simulations can reveal how atoms move, bond, and react under different conditions [33]). Utilizing first principle calculations such as DFT, the variation of total energy versus the cell volume are found, and this can be used to determine the stable structures of the materials [37]. In addition, the combined effects of temperature and volume on energy and elastic properties calculated using DFT allow for the establishment of elastic property-temperature relationship [31,37]. This is motivated by the relatively unexplored territory of estimating the Cij coefficients at elevated temperatures. This allows for a more comprehensive understanding of how the elastic behavior of advanced ceramics varies with temperature and understanding the temperature-dependent behavior of these materials is crucial for stability, mechanical response, and engineering applications (e.g., nuclear reactors [38], aerospace [39], and thermal barrier coatings [40]).

Altogether, the integration of atomistic simulations, mesoscale modelling, continuum simulations, and experimental observations enables researchers to understand the complex behavior of ceramic materials across multiple length and time scales. This multi-scale approach enables the prediction of materials’ microstructure-property-performance relationships, facilitating the design and optimization of ceramics for various applications, ranging from structural materials in aerospace engineering to functional materials in electronics and energy storage.

2. Ceramic-based composites:computational-assisted materials design for dynamic applications

Building upon the conventional advanced ceramics, ceramic-ceramic composites have gained popularity for high strain rate applications [41-43] as their ceramic constituents synergistically contribute their desirable properties to enhance the performance of the material system (e.g., the incorporation of ZrO2 in a CMC for increasing ductility [44] to absorb higher energy under ballistic impacts). While these multi-phase ceramic materials offer superior weight-specific stiffness and strength, low ductility and catastrophic failure may limit their use in dynamic applications [45]. As a remedy, ceramic-metal composites [46] were introduced to combine the hardness and strength of ceramics with the high fracture toughness of metallic binders, and this synergy idealizes them for dynamic impact scenarios [47-49]. The dynamic failure of ceramic-metal composites is a complex phenomenon across multiple length scales (i.e., involving matrix/ceramic interface debonding and ceramic particle fracture at micro scale [50] to the coalescence of meso-scale shear bands [51]) that necessitates the development of multiscale computational frameworks [52,53] and in situ experimental testing [54,55] to inform on the manufacturing of the material with an optimized/tailored performance through controlling the evolution of failure mechanisms.

a. Advanced manufacturing of ceramic-metal composites

如图2所示,通过作者在邵et al. [56] fabricated Al-46wt.% Al2O3 composites with a minimal porosity of 0.17±0.03 vol.% via cold-spray additive manufacturing (CSAM) [56], where the size of the feedstock powders was informed by a finite element (FE) model to reach a theoretically pore-free composite. These CSAM ceramic-metal composites were found to outperform the conventionally made counterparts by powder metallurgy [57] and casting [58] in terms of hardness and compressive yield strength, as seen in Fig. 2b. The superior mechanical properties of this ceramic-metal composite are attributable to the multi-level strengthening mechanisms, including grain refinement mechanism (i.e., the Hall-Petch (H-P) relationship [59]), work hardening mechanism as a result of the increase in the density of dislocations [60], and particle dispersion mechanism that transfers the load from the Al matrix to the Al2O3 ceramic particles [61]. This synergistic strengthening effect is enabled by the CSAM where the grain refinement and work hardening mechanisms are mainly induced by the impacting high-velocity ceramic particles during the cold spray deposition process [62]. The contribution of these strengthening mechanisms is identifiable by a microstructure-informed representative volume element (RVE) modeling framework [63] which enables the manufacturing of higher performing composites by tuning the contribution of these mechanisms through microstructural tailoring (see Figure 3).

Figure 2: (a) Cold-spray additive manufacturing (CSAM) of high-performing Al-Al2O3 ceramic-metal composites with minimum porosity [56]. (b) Superior mechanical properties of the CSAM Al-Al2O3 composites in terms of hardness and yield strength compared to conventionally made counterparts in the literature. (c) Achieving Al-Al2O3 composites with ultra-high hardness and strength by synthesizing a nano-structured Al matrix via high-throughput CSAM [65].

Very recently, via a high-throughput mode of design [64], Shao et al. [65] synthesized CSAM Al-Al2O3 composites with a nanostructured-Al matrix that showed the highest hardness and compressive strength compared to the counterparts in the literature (see Fig. 2c) due to a nanocrystalline metallic binder (i.e., a grain size of 43.1 ± 12.4 nm) and the precipitate strengthening mechanism [66] by the inclusion of alloying elements. As shown in Fig. 3a, thein situdigital image correlation (DIC) shows that the CSAM Al-46wt.% Al2O3 composites fail under compression due to the localization of strain in nearly 45° shear bands with respect to the loading direction. In addition, the post-mortem SEM imaging of the sample shown in Fig. 3a reveals the microscale failure mechanisms, including matrix failure, Al2O3 particle cracking, and matrix/particle debonding. While these advanced characterization and diagnostic experimental approaches inform on the material failure, multiscale numerical frameworks are needed to provide insights into the evolution of failure mechanisms across different length scales; this is one of the main thrusts at the CDAM.

图3:(a)成立与实验方法rizing the failure behavior of CSAM Al-Al2O3 composites across different length scales, includingin situDIC technique and post-mortem SEM imaging [50,65]. (b) Development of microstructure-informed FEM models accounting for experimental particle size distribution and porosity. (c) Quantitative and qualitative history of the evolution of failure mechanisms of the CSAM Al-46wt.% Al2O3 composite under uniaxial compression through experimentally-validated microscale FEM modeling [63].

b. Micromechanical finite element and data-driven modeling of ceramic-metal composites

To better understand the initiation and interaction of these failure mechanisms, work by the authors in Sayahlatifi et al. [63] have recently developed a microscale FE modeling framework to quantitatively track the evolution of failure mechanisms. Here, RVEs of the composite informed by the microstructural data in terms of porosity, particle weight fraction, and size distribution, as shown in Fig. 3b. The Al matrix and ceramic particles were constitutively modelled by a stress-state-dependent ductile failure model [67], and a viscosity-regularized plasticity model for ceramics [68] via VUMAT subroutines in Abaqus software. The interface between the particles and matrix was modelled by surface-based cohesive zone model (CZM) approach with a bi-linear traction-separation law. As shown in Fig. 3c, the experimentally validated model reveals the sequence of the initiation of failure mechanisms when the Al-46wt.% Al2O3 composite is under uniaxial compression: 1. matrix/particle debonding, 2. particle cracking, and 3. matrix failure. Debonding as the first mechanism is initiated almost prior to yielding, demonstrating the impact of interfacial properties on the yield strength of ceramic-metal composites. Upon the activation of the particle cracking mechanism at a strain of ~ 1%, the stress-bearing capacity follows closely a plateau up to the onset of the softening regime, and this is attributable to the simultaneous evolution of the debonding mechanism, particle cracking, and the accumulation of plastic strain in the Al binder. Next, matrix failure is triggered when ~ 4% of interfaces are failed and ~20% of particles are cracked at a global strain of ~ 4%. At the onset of the softening regime at a strain of ~ 10%, the volume of matrix cracking exceeds ~ 1% and grows with an ascending rate along with the other two mechanisms, accelerating the softening regime. As shown in Fig. 3c, the model also qualitatively reproduces the SEM-observed features of failure, including the debonding at the sharp asperities of the interfaces, cracking of ceramic particles parallel to the compression direction, and the formation of shear cracks in the matrix with an angle of ~ 45° with respect to the loading direction. Lastly. the numerical visualization of fully damaged regions in Fig. 3c shows that matrix cracking is mainly initiated in the vicinity of fractured particles ascribed to the unloading of the cracked particle, implying that the spatial distribution of cracked particles plays an important role on the morphology of the fracture surface of CSAM ceramic-metal composites.

Finally, in addition to providing a better understanding of the evolution of failure in the material, the current micromechanical computational model is being leveraged for generating datasets for training/validating of computationally efficient machine learning (ML)-based models [69-72] to correlate the macro-scale response of the CSAM ceramic-metal composites (e.g., stress-strain curves) to their microstructural characteristics (e.g., porosity, particle content, and size). These ML-based models will be incorporated into the design process to accelerate the fabrication of high-performing ceramic-metal composites by controlling the evolution of failure. In addition, the current RVE modeling and quantification of failure mechanisms will lead to the development of data-driven ML-enabled constitutive models [73,74] that allows bridging the length scales. The integration of these ML-based constitutive models into FE solvers or physics-informed neural network (PINN) will significantly accelerate the design of next-generation ceramic-metal composites where the manufacturing process is informed by these computationally efficient models.

3. Design of multi-functional structures through advanced manufacturing

考虑到很多好处(例如,优越的压缩ion strength and hardness) of advanced ceramics to be used in extreme environments (see Section 1), the conventional manufacturing processes of ceramics (e.g., dry pressing [82], and injection molding [83]) are complex, time-consuming, and need post-processing (i.e., machining) [84]. As such, additive manufacturing (AM) methods are gaining high popularity and progress for the fabrication of ceramic structures with flexibility in the design of customized geometries [85-87]. AM methods are based on using material deposition to fabricate 3D parts by adding material, usually layer-by-layer directly from computer-based models [88]. Based on the pre-processed feedstock prior to printing, AM methods are categorized into powder-based (e.g., 3DP [89], and SLS [90]), slurry-based (e.g., SLA [91], and DLP [92]), and bulk solid-based (e.g., FDM [93]) techniques. Powder-based methods (i.e., SLS, and SLM) rely on melting processes (usually by lasers) that induce residual stresses generated by thermal gradients under fast laser heating and cooling rates, and these are major factors contributing to the formation of defects (e.g., cracks) [93-95]. Beyond powder-based methods, slurry-based photopolymerization techniques (i.e., SLA, and DLP) have shown more promise for the fabrication of ceramic structures with high density and surface quality due to the achievement of controllable feature resolution [95]. Specifically, the SLA technique has been extensively used in recent years owing to high forming accuracy, high resolution, and high-quality surface finish when compared to other AM technologies [96]. In the SLA technology, the solidification process is repeated in a layer-by-layer pattern to produce a 3D geometry. The as-printed samples are then thermally processed to remove the resin binder and sinter the ceramics [96].

a. Experimental characterization of the dynamic behavior of AM ceramics

而传统的力学行为de ceramics under different stress states and strain rates is well-studied in literature [4, 9, 11, 97-99], very limited efforts have been made toward those of AM ceramics [100-103]. More recently, the authors have focused on exploring the strain-rate-dependent mechanical behavior of alumina ceramics additively manufactured with the SLA method (see Fig. 4a), and the material was tested under uniaxial compression across different strain rates ranging from 10-4 to 103 s-1. Fig. 4b shows the strength versus strain rate response of the AM alumina ceramics when compared to that of the conventionally made counterparts in the literature. As shown, the strength of the AM alumina ceramic is lower than that of the conventional ones by ∼ 40% and ∼ 25% under quasi-static and dynamic rates, respectively, and this observation agrees with previous studies on AM ceramics of DeVries et al. [101]. The lower strength of the current AM ceramics is attributable to the manufacturing-induced microstructural defects (e.g., pores and weak grain boundaries) leading to localized failure zones that result in the loss of structural integrity of the specimen [104]. Shown in Fig. 4c and d are SEM images of the fractured surface of the AM alumina used to unravel the micro-scale failure mechanisms under quasi-static and dynamic loading, respectively. It is believed that a combination of intergranular and transgranular failure mechanisms govern the failure process of the material under dynamic loading, while the intergranular failure mechanism contributes more predominantly under quasi-static conditions. To achieve similar or better performance for the AM ceramics, it requires further advanced in multi-scale experimental testing (e.g., in situ SEM imaging [104], synchrotron X-ray time-resolved imaging [105, 106]), and cross-scale computational frameworks to better understand the dynamic failure of the material and inform the manufacturing route through the control of failure initiation and evolution.

Figure 4: (a) AM alumina sample. (b) A comparison of the rate-dependent compressive strength of AM and conventional-made alumina ceramics in the literature. (c) and (d) SEM images showing the fracture surface of the material and failure mechanisms under quasi-static and dynamic uniaxial compression loading, respectively.

b. Multi-scale modeling of AM ceramics: Micromechanical and machine learning modeling

To unravel the time-resolved evolution of failure mechanisms and inform dominant factors in material failure, a multiscale computational model is recently being developed by the authors in which RVEs of the AM alumina ceramics are generated in the Neper software informed by the microstructural characteristics, including grain size distribution and grain orientations from the EBSD analysis, and porosity features, as shown in Fig. 5a. The alumina grains are constitutively modeled by a viscosity-regularized form of the JH2 material model (i.e., JH2-V [14, 68, 108]) accounting for the random crystallographic orientation of grains implemented via a VUMAT subroutine in Abaqus/Explicit FE solver. To account for the intergranular failure mechanism, the interfaces between the grains are modeled by a bi-linear cohesive law implemented through a surface-based cohesive zone modeling (CZM) approach [109]. Fig. 5b shows that the predicted stress-time history is in reasonable agreement with those of the experiments for dynamic loading at a rate of 690 s-1 represented by the shaded area. Next, to explore the growth of failure with the experimentally validated model, the transgranular and intergranular mechanisms were quantified in terms of the fraction of fully damaged elements and fully debonded interfacial nodes, respectively. As shown in Fig. 5b, the intergranular failure as the first mechanism is initiated and grows at a higher rate than the transgranular mechanism up to the peak stress and then follows a plateau, indicating the important role of grain boundary properties (e.g., cohesion strength) on the global strength of the AM ceramic material. At the onset of softening, the transgranular mechanism exponentially evolves and mainly governs the degradation of the load-bearing capacity of the material, while the intergranular mechanism is nearly stabilized. The current micromechanics-based computational model could be leveraged to inform the manufacturing of AM ceramics with enhanced properties where the evolution of failure is numerically tailored by microstructural tuning. Fig. 5c and d show the 3D contour of the transgranular mechanism represented by the JH2-V damage parameter and the intergranular mechanism on the interfaces between the grains by the CZM damage parameter corresponding to the maximum strain level in Fig. 5b, respectively. As seen, the transgranular mechanism (fully damaged areas are in red) is mainly triggered and evolved in the vicinity of pores at the initial defect zones demonstrating the important role of porosity in the overall performance of AM ceramics. The damage distribution reflects a diffusive pattern that aligns with the nature of the dynamic loading phenomenon where dynamic fracture and fragmentation are typically observed at the macro scale. In addition, the intergranular mechanism is mainly initiated and coalesced at the junction of grains where maximum stress concentration is present.

While AM ceramics are mainly studied in terms of mechanical properties [100-103], there is still a gap in our understanding of the relationships between their microstructural characteristics (e.g., the volume fraction of pores and their size distribution, properties of the grain boundaries) and the behavior of the material at structural scale (e.g., strength). Here, current multiscale computational models developed by the authors coupled with experimental testing could be further extended to discover these links under different stress states and strain rates. Additionally, the developed multiscale computational models are used for unveiling the correlation between the microstructure and macro-scale behavior of ceramics (e.g., strength as a function of grain size and porosity). The generated data sets by these microscale models that cover the space of stress states and strain rates could be leveraged for training and validation of ML-based models [111] to bridge length scales by establishing the microstructure-property-performance relationships to inform the accelerated design and development of next-generation AM ceramics with higher performance for dynamic applications [111, 112].

Figure 5: (a) The polycrystalline model of the AM alumina generated in Neper software. (b) The numerical and experimental stress–time history of AM alumina ceramic under dynamic uniaxial compression loading at a rate of 690 s-1 with quantification of failure mechanisms considering the effect of void volume fraction (VVF) from 0% to 10%. (c) and (d) The 3D contour of the transgranular and intergranular failure mechanisms in the material, respectively. In the numerical legend, SDV10 and CSQUADSCRT represent the damage parameters of the JH2-V model and debonded interfaces, respectively.

III. Outlook and future areas of research

Further advancements in ceramic-based materials development will be driven by improvements in multi-scale computational design tools, and their wider adoption into industry. Computationally, models need to be faster, contain more physics across length scales, and be more robustly validated with experiments. To address challenges with having faster models, open-source platforms (e.g., FEniCS, GROMACS 4.5) offer opportunities for highly parallelized and computationally-efficient numerical algorithms that are more industry-friendly. To refine these models, efforts are needed to address challenges with passing information from the sub-element to multi-element scales (e.g., implicit damage to explicit fracture; discrete to continuum behaviors), where machine learning-based approaches offer a promising means for scale-bridging and homogenization. For instance, the development of multiscale ML-based constitutive models based on FE micromechanical models could account for stress-state- and strain-rate-dependent behaviors, and its incorporation into the numerical FE solver for higher scale structural simulations would offer computationally efficient scale-bridging with the relevant physics captured. When completed, these higher fidelity multi-scale models will provide new insights into the important mechanisms that govern performance of ceramic-based materials, and, in turn, can guide design of better-performing advanced materials with tailored micro- and macro-structures.

Once models are developed, efforts are needed to improve the robustness of model validation using experimental data by, for example, comparing temporally- and spatially resolved field measurements (e.g., temperature), and better evaluating and appreciating inherent variability and stochasticity in both experiments and models (e.g., real microstructures accounting for grain and boundary features). In the meantime, gaps in our knowledge on failure evolution during history-dependent loading and multi-functional behaviors (e.g., coupled thermal-mechanical) need to be addressed before use in most industrial applications. To bolster experimental validation, concerted efforts are needed to develop and support national research facilities with specialized in situ measurement capabilities at increasingly smaller length scales and faster time scales needed to overcome gaps with our fundamental understanding of material behaviors (e.g., synchrotron, SEM-assisted micro-mechanical testing).

产品开发所引起的lopment of advanced computational and experimental toolboxes, new material systems with better performance or distinct mechanisms can be explored. In this post, we provide one of the new ceramic classes termed high entropy ceramics (HEC), where Fig. 7 shows some examples of their potential in achieving high performing thermal, mechanical, electrical, or magnetic properties [116 – 121]. Most recently, rare-earth elements (e.g., Y, Nd, Sm, Tb) have been introduced into high entropy alloys and high entropic ceramics, with some successful findings on significantly improved properties [122 – 126]. In addition, research on fabricating these new material systems using advanced manufacturing techniques is underway [127], where considerations regarding improving grain boundary cohesion, reducing printing defects, and obtaining a good understanding of the trade-offs between complex design and multi-functionality still need to be addressed. Overall, we are optimistic about the development of new additively manufactured ceramic-based materials informed by advances in experimental and computational mechanics.

Figure 6: Exploring the potential of high entropy ceramics: characterization of (Hf0.2Zr0.2Ta0.2Nb0.2 Ti0.2)C through (a) X-ray diffraction [113], (b) scanning electron microscopy and associated chemical analysis [113]; enhanced properties of HECs compared to low and medium entropy materials: (c) yield and failure strength [114], (d) oxidation resistance [115], and (e) thermal conductivity and Young’s modulus [116].

References

[1]Zheng, Jie, Haoyang Li, and James D. Hogan. "Strain-rate-dependent tensile response of an alumina ceramic: Experiments and modeling."International Journal of Impact Engineering173 (2023): 104487.

[2]Pisavadia, Harshil, Geneviève Toussaint, Patricia Dolez, and James D. Hogan. "Cohesive zone failure modeling of polymeric adhesives used in ceramic/metal armor."International Journal of Impact Engineering170 (2022): 104364.

[3]Yang, Alex, Dan Romanyk, and James D. Hogan. "High-velocity impact study of an advanced ceramic using finite element model coupling with a machine learning approach."Ceramics International49, no. 7 (2023): 10481-10498.

[4]Zheng, Jie, Min Ji, Zahra Zaiemyekeh, Haoyang Li, and James D. Hogan. "Strain-rate-dependent compressive and compression-shear response of an alumina ceramic."Journal of the European Ceramic Society42, no. 16 (2022): 7516-7527.

[5]Nicewicz, Piotr, Peter Peciar, Oliver Macho, Tomoko Sano, and James D. Hogan. "Quasi‐static confined uniaxial compaction of granular alumina and boron carbide observing the particle size effects."Journal of the American Ceramic Society103, no. 3 (2020): 2193-2209.

[6]Hogan, James David, Lukasz Farbaniec, Nitin Daphalapurkar, and K. T. Ramesh. "On compressive brittle fragmentation."Journal of the American Ceramic Society99, no. 6 (2016): 2159-2169.

[7]Hogan, James D., Lukasz Farbaniec, Matt Shaeffer, and K. T. Ramesh. "The effects of microstructure and confinement on the compressive fragmentation of an advanced ceramic."Journal of the American Ceramic Society98, no. 3 (2015): 902-912.

[8]Liu, Haiyan, Lihong Liang, Yingbiao Wang, and Yueguang Wei. "Fracture Characteristics and Damage Evolution of Coating Systems Under Four‐Point Bending."International Journal of Applied Ceramic Technology13, no. 6 (2016): 1043-1052.

[9]Ji, Min, Haoyang Li, Jie Zheng, Shuo Yang, Zahra Zaiemyekeh, and James D. Hogan. "An experimental study on the strain-rate-dependent compressive and tensile response of an alumina ceramic."Ceramics International48, no. 19 (2022): 28121-28134.

[10]Koch, Brendan ML, Calvin Lo, Haoyang Li, Tomoko Sano, Jonathan Ligda, and James David Hogan. "Two-dimensional dynamic damage accumulation in engineered brittle materials."Engineering Fracture Mechanics244 (2021): 107539.

[11]Koch, Brendan ML, Calvin Lo, Haoyang Li, Tomoko Sano, Jonathan Ligda, and James David Hogan. "Dynamic mechanical response of damaged alumina AD995."Journal of the European Ceramic Society41, no. 3 (2021): 2034-2048.

[12]Sano, Tomoko, Lionel Vargas-Gonzalez, Jerry LaSalvia, and James David Hogan. "Dynamic failure and fragmentation of a hot-pressed boron carbide."Journal of Dynamic Behavior of Materials3 (2017): 548-556.

[13]Farbaniec, L., J. D. Hogan, K. Y. Xie, M. Shaeffer, K. J. Hemker, and K. T. Ramesh. "Damage evolution of hot-pressed boron carbide under confined dynamic compression."International Journal of Impact Engineering99 (2017): 75-84.

[14]Zaiemyekeh, Zahra, Haoyang Li, Saman Sayahlatifi, Min Ji, Jie Zheng, Dan L. Romanyk, and James D. Hogan. "Computational finite element modeling of stress-state-and strain-rate-dependent failure behavior of ceramics with experimental validation."Ceramics International49, no. 9 (2023): 13878-13895.

[15]Lo, Calvin, Tomoko Sano, and James D. Hogan. "Deformation mechanisms and evolution of mechanical properties in damaged advanced ceramics."Journal of the European Ceramic Society40, no. 8 (2020): 3129-3139.

[16]Williams, Stephanie. "Impact tests for ceramics."Advanced Materials & Processes167, no. 5 (2009): 37-39.

[17]Koch, Brendan ML, Haoyang Li, Calvin Lo, Jonathan Ligda, and James David Hogan. "Damage accumulation mechanisms during dynamic compressive failure of boron carbide."Journal of the European Ceramic Society42, no. 13 (2022): 5522-5537.

[18]Hogan, James David, Lukasz Farbaniec, Debjoy Mallick, Vladislav Domnich, Kanak Kuwelkar, Tomoko Sano, James W. McCauley, and Kaliat T. Ramesh. "Fragmentation of an advanced ceramic under ballistic impact: Mechanisms and microstructure."International journal of impact engineering102 (2017): 47-54.

[19]Zhang, Chaoyi, Yalin Dong, and Chang Ye. "Recent developments and novel applications of laser shock peening: A review."Advanced Engineering Materials23, no. 7 (2021): 2001216.

[20]Farbaniec, L., J. D. Hogan, and K. T. Ramesh. "Micromechanisms associated with the dynamic compressive failure of hot-pressed boron carbide."Scripta Materialia106 (2015): 52-56.

[21]Chevalier, Jérome, and Gilbert Fantozzi. "Slow crack propagation in ceramics at the nano-and micro-scale: effect of the microstructure." InFracture Mechanics of Ceramics: Active Materials, Nanoscale Materials, Composites, Glass and Fundamentals, pp. 173-190. Boston, MA: Springer US, 2005.

[22]Parsazadeh, Mohammad, Shashank Sharma, and Narendra Dahotre. "Towards the next generation of machine learning models in additive manufacturing: A review of process dependent material evolution."Progress in Materials Science(2023): 101102.

[23]Ahmadi, Mohammad Hossein, and Hamed Molladavoodi. "A micromechanical sliding-damage model under dynamic compressive loading."Periodica Polytechnica Civil Engineering63, no. 1 (2019): 168-183.

[24]Amirian, Benhour, Hossein Jafarzadeh, Bilen Emek Abali, Alessandro Reali, and James David Hogan. "Phase-field approach to evolution and interaction of twins in single crystal magnesium."Computational Mechanics70, no. 4 (2022): 803-818.

[25]Amirian, Benhour, Bilen Emek Abali, and James David Hogan. "The study of diffuse interface propagation of dynamic failure in advanced ceramics using the phase-field approach."Computer Methods in Applied Mechanics and Engineering405 (2023): 115862.

[26]Zheng, Jie, Haoyang Li, and James D. Hogan. "Hybrid Finite-Discrete Element Modeling of the Mode I Tensile Response of an Alumina Ceramic."Modelling4, no. 1 (2023): 87-101.

[27] Amirian, Benhour, Hossein Jafarzadeh, Bilen Emek Abali, Alessandro Reali, and James David Hogan. "Thermodynamically-consistent derivation and computation of twinning and fracture in brittle materials by means of phase-field approaches in the finite element method."International Journal of Solids and Structures252 (2022): 111789.

[28] Horstemeyer, Mark F. "Multiscale modeling: a review."Practical aspects of computational chemistry: methods, concepts and applications(2010): 87-135.

[29] Li, Jun, and Qi An. "Nanotwinning-induced pseudoplastic deformation in boron carbide under low temperature."International Journal of Mechanical Sciences242 (2023): 107998.

[30] Dodd, L. R., and D. N. Theodorou. "Atomistic Monte Carlo simulation and continuum mean field theory of the structure and equation of state properties of alkane and polymer melts."Atomistic modeling of physical properties(2006): 249-281.

[31] Shang, Shun-Li, Yi Wang, DongEung Kim, and Zi-Kui Liu. "First-principles thermodynamics from phonon and Debye model: Application to Ni and Ni3Al."Computational Materials Science47, no. 4 (2010): 1040-1048.

[32]Chang, Junhao, Zengtao Chen, and James D. Hogan. "Molecular Dynamics Simulations Correlating Mechanical Property Changes of Alumina with Atomic Voids under Triaxial Tension Loading."Modelling4, no. 2 (2023): 211-223.

[33] Handley, Chris M., and Paul LA Popelier. "Potential energy surfaces fitted by artificial neural networks."The Journal of Physical Chemistry A114, no. 10 (2010): 3371-3383.

[34] Yao, Sanxi, Qin Gao, and Michael Widom. "Phase diagram of boron carbide with variable carbon composition."Physical Review B95, no. 5 (2017): 054101.

[35] Mishin, Y. "Machine-learning interatomic potentials for materials science."Acta Materialia214 (2021): 116980.

[36] Behler, Jörg. "Perspective: Machine learning potentials for atomistic simulations."The Journal of chemical physics145, no. 17 (2016).

[37] Shang, Shun-Li, Hui Zhang, Yi Wang, and Zi-Kui Liu. "Temperature-dependent elastic stiffness constants of α-and θ-Al2O3 from first-principles calculations."Journal of Physics: Condensed Matter22, no. 37 (2010): 375403.

[38] Subramanian, C., A. K. Suri, and T. S. R. C. Murthy. "Development of Boron-based materials for nuclear applications."Barc Newsletter313 (2010): 14-22.

[39]Varshney, Vikas. "Molecular dynamics methodologies for predicting thermal transport in aerospace polymers and their composites." In混合量子材料的界面设计Functionality, pp. 19-34. Elsevier, 2021.

[40]Madhavi, G., Naik Kishan, and C. R. Raghavendra. "A review on recent approaches in the field of surface coating."Materials Today: Proceedings52 (2022): 403-406.

[41]Lo, Calvin, Haoyang Li, Geneviève Toussaint, and James D. Hogan. "On the evaluation of mechanical properties and ballistic performance of two variants of boron carbide."International Journal of Impact Engineering152 (2021): 103846.

[42]Song, Qi, and Zhitao Cheng. "Dynamic response of the TiB2–SiC/B4C composite ceramic under dynamic loading."International Journal of Applied Ceramic Technology(2023).

[43]Chen, Daimeng, Kuibao Zhang, Jianjun Zeng, Haiyan Guo, and Bo Li. "High‐strength TiB2‐B4C composite ceramics sintered by spark plasma sintering."International Journal of Applied Ceramic Technology19, no. 4 (2022): 1949-1955.

[44]Pan, Shouxu, Gang Shao, Hongtian He, Rui Zhao, Chao Ma, Hongxia Lu, Hongliang Xu, Hailong Wang, Rui Zhang, and Linan An. "Effects of strain rate and current density on plastic deformation of zirconia ceramics under a high electric field."Ceramics International(2023).

[45]Andraskar, Nikhil D., Gaurav Tiwari, and Manmohan Dass Goel. "Impact response of ceramic structures-A review."Ceramics International(2022).

[46]Hu, Yingbin, and Weilong Cong. "A review on laser deposition-additive manufacturing of ceramics and ceramic reinforced metal matrix composites."Ceramics International44, no. 17 (2018): 20599-20612.

[47]Lee, Hyungsoo, Jin Hyeok Choi, Min Chul Jo, Donghyun Lee, Sangmin Shin, Ilguk Jo, Sang-Kwan Lee, and Sunghak Lee. "Effects of SiC particulate size on dynamic compressive properties in 7075-T6 Al-SiCp composites."Materials Science and Engineering: A738 (2018): 412-419.

[48]王,杨、羌族刘表,Haoqian张Zhaoxin Zhong, Jian Ye, Yuhan Ren, Liying Shen, Feng Ye, and Wen Wang. "Mechanical response and damage evolution of bio-inspired B4C-reinforced 2024Al composites subjected to quasi-static and dynamic loadings."Materials Science and Engineering: A840 (2022): 142991.

[49]Jo, Min Chul, Jin Hyeok Choi, Jisung Yoo, Donghyun Lee, Sangmin Shin, Ilguk Jo, Sang-Kwan Lee, and Sunghak Lee. "Novel dynamic compressive and ballistic properties in 7075-T6 Al-matrix hybrid composite reinforced with SiC and B4C particulates."Composites Part B: Engineering174 (2019): 107041.

[50]Sayahlatifi, Saman, Chenwei Shao, André McDonald, and James Hogan. "3D microstructure-based finite element simulation of cold-sprayed Al-Al 2 O 3 composite coatings under quasi-static compression and indentation loading."Journal of Thermal Spray Technology(2021): 1-17.

[51]Lee, Hyungsoo, Seok Su Sohn, Changwoo Jeon, Ilguk Jo, Sang-Kwan Lee, and Sunghak Lee. "Dynamic compressive deformation behavior of SiC-particulate-reinforced A356 Al alloy matrix composites fabricated by liquid pressing process."Materials Science and Engineering: A680 (2017): 368-377.

[52]Peng, Peng, Minqiang Gao, Enyu Guo, Huijun Kang, Honglan Xie, Zongning Chen, and Tongmin Wang. "Deformation behavior and damage in B4Cp/6061Al composites: An actual 3D microstructure-based modeling."Materials Science and Engineering: A781 (2020): 139169.

[53]Amirian, B., H. Y. Li, and J. D. Hogan. "The mechanical response of a α2 (Ti3Al)+ γ (TiAl)-submicron grained Al2O3 cermet under dynamic compression: Modeling and experiment."Acta Materialia181 (2019): 291-308.

[54]Yang, Zhiyu, Jianzhong Fan, Yanqiang Liu, Ziyue Yang, Yonglin Kang, and Junhui Nie. "Effect of combination variation of particle and matrix on the damage evolution and mechanical properties of particle reinforced metal matrix composites."Materials Science and Engineering: A806 (2021): 140804.

[55]Ye, S. J., B. X. Bie, Z. M. Zhang, X. J. Zhao, T. Sun, K. Fezzaa, J. Y. Huang, X. H. Yao, and S. N. Luo. "Rate-dependent strength and deformation heterogeneity of B4C-reinforced Al composite: Time-resolved imaging with synchrotron X-rays."Ceramics International47, no. 11 (2021): 16141-16151.

[56]Shao, Chenwei, Calvin Lo, Kapil Bhagavathula, André McDonald, and James Hogan. "High strength particulate aluminum matrix composite design: Synergistic strengthening strategy."Composites Communications25 (2021): 100697.

[57]Rahimian, Mehdi, Nader Parvin, and Naser Ehsani. "Investigation of particle size and amount of alumina on microstructure and mechanical properties of Al matrix composite made by powder metallurgy."Materials Science and Engineering: A527, no. 4-5 (2010): 1031-1038.

[58]Ezatpour, H. R., M. Torabi-Parizi, and Seyed Abdolkarim Sajjadi. "Microstructure and mechanical properties of extruded Al/Al2O3 composites fabricated by stir-casting process."Transactions of Nonferrous Metals Society of China23, no. 5 (2013): 1262-1268.

[59]Hansen, Niels. "Hall–Petch relation and boundary strengthening."Scripta materialia51, no. 8 (2004): 801-806.

[60]Chen, Chaoyue, Yingchun Xie, Shuo Yin, Wenya Li, Xiaotao Luo, Xinliang Xie, Ruixin Zhao et al. "Ductile and high strength Cu fabricated by solid-state cold spray additive manufacturing."Journal of Materials Science & Technology134 (2023): 234-243.

[61]Kim, Chang-Soo, Il Sohn, Marjan Nezafati, J. B. Ferguson, Benjamin F. Schultz, Zahra Bajestani-Gohari, Pradeep K. Rohatgi, and Kyu Cho. "Prediction models for the yield strength of particle-reinforced unimodal pure magnesium (Mg) metal matrix nanocomposites (MMNCs)."Journal of Materials Science48 (2013): 4191-4204.

[62]He, Lewei, and Mostafa Hassani. "A review of the mechanical and tribological behavior of cold spray metal matrix composites."Journal of Thermal Spray Technology29 (2020): 1565-1608.

[63]Sayahlatifi, Saman, Zahra Zaiemyekeh, Chenwei Shao, André McDonald, and James D. Hogan. "Micromechanical damage analysis of Al-Al2O3 composites via cold-spray additive manufacturing."International Journal of Mechanical Sciences259 (2023): 108573.

[64]Curtarolo, Stefano, Gus LW Hart, Marco Buongiorno Nardelli, Natalio Mingo, Stefano Sanvito, and Ohad Levy. "The high-throughput highway to computational materials design."Nature materials12, no. 3 (2013): 191-201.

[65]Shao, Chenwei, Haoyang Li, Yankun Zhu, Peng Li, Haoyang Yu, Zhefeng Zhang, Herbert Gleiter, André McDonald, and James Hogan. "Nano-additive manufacturing of multilevel strengthened aluminum matrix composites."International Journal of Extreme Manufacturing5, no. 1 (2022): 015102.

[66]Sun, Wenwen, Yuman Zhu, Ross Marceau, Lingyu Wang, Qi Zhang, Xiang Gao, and Christopher Hutchinson. "Precipitation strengthening of aluminum alloys by room-temperature cyclic plasticity."Science363, no. 6430 (2019): 972-975.

[67]Zhou, Jun, Xiaosheng Gao, James C. Sobotka, Bryan A. Webler, and Brian V. Cockeram. "On the extension of the Gurson-type porous plasticity models for prediction of ductile fracture under shear-dominated conditions."International Journal of Solids and Structures51, no. 18 (2014): 3273-3291.

[68]Simons, E. C., J. Weerheijm, and Lambertus J. Sluys. "A viscosity regularized plasticity model for ceramics."European Journal of Mechanics-A/Solids72 (2018): 310-328.

[69]Eghtesad, Adnan, Qixiang Luo, Shun-Li Shang, Ricardo A. Lebensohn, Marko Knezevic, Zi-Kui Liu, and Allison M. Beese. "Machine learning-enabled identification of micromechanical stress and strain hotspots predicted via dislocation density-based crystal plasticity simulations."International Journal of Plasticity166 (2023): 103646.

[70]Dai, Wei, Huamiao Wang, Qiang Guan, Dayong Li, Yinghong Peng, and Carlos N. Tomé. "Studying the micromechanical behaviors of a polycrystalline metal by artificial neural networks."Acta Materialia214 (2021): 117006.

[71]Nascimento, Anderson, Sharan Roongta, Martin Diehl, and Irene J. Beyerlein. "A machine learning model to predict yield surfaces from crystal plasticity simulations."International Journal of Plasticity161 (2023): 103507.

[72] Miguel A. Bessa, “Journal Club for February 2020: Machine Learning in Mechanics: simple resources, examples & opportunities | iMechanica.”//m.limpotrade.com/node/23957(accessed Jun. 19, 2023).

[73]Moritz, Flaschel, and Kumar Siddhant. "Discovering plasticity models without stress data."NPJ Computational Materials8, no. 1 (2022).

[74]Jan Niklas Fuhg,克雷格·m·哈默尔凯尔·约翰逊,再保险ese Jones, and Nikolaos Bouklas. "Modular machine learning-based elastoplasticity: generalization in the context of limited data."Computer Methods in Applied Mechanics and Engineering407 (2023): 115930.

[75] He, Zeming, J. Ma, Hongzhi Wang, G. E. B. Tan, Dongwei Shu, and Jian Zheng. "Dynamic fracture behavior of layered alumina ceramics characterized by a split Hopkinson bar."Materials Letters59, no. 8-9 (2005): 901-904.

[76] Pittari III, John, Ghatu Subhash, James Zheng, Virginia Halls, and Phillip Jannotti. "The rate-dependent fracture toughness of silicon carbide-and boron carbide-based ceramics."Journal of the European Ceramic Society35, no. 16 (2015): 4411-4422.

[77] Krishnan, Saravanan Vanal, Muthumanickam Muthukaruppan Ambalam, Ragavendran Venkatesan, Jeyanthinath Mayandi, and Vishnukanthan Venkatachalapathy. "Technical review: Improvement of mechanical properties and suitability towards armor applications–Alumina composites."Ceramics International47, no. 17 (2021): 23693-23701.

[78] Huang, Chin-Yu, and Yu-Liang Chen. "Effect of mechanical properties on the ballistic resistance capability of Al2O3-ZrO2 functionally graded materials."Ceramics International42, no. 11 (2016): 12946-12955.

[79] Venkatesan, J., Mohammad Ashraf Iqbal, and V. Madhu. "Experimental and numerical study of the dynamic response of B4C ceramic under uniaxial compression."Thin-Walled Structures154 (2020): 106785.

[80] Islam, Md Rushdie Ibne, J. Q. Zheng, and Romesh C. Batra. "Ballistic performance of ceramic and ceramic-metal composite plates with JH1, JH2 and JHB material models."International Journal of Impact Engineering137 (2020): 103469.

[81] Dresch, Alexander B., Janio Venturini, and Carlos P. Bergmann. "Improving the flexural-strength-to-density ratio in alumina ceramics with the addition of silicon nitride."Ceramics International47, no. 3 (2021): 3964-3971.

[82] Zhang, Xueqin, Qiaoyu Meng, Keqiang Zhang, Rongqi Zhu, Zhaoliang Qu, Ying Li, and Rujie He. "3D-printed bioinspired Al2O3/polyurea dual-phase architecture with high robustness, energy absorption, and cyclic life."Chemical Engineering Journal463 (2023): 142378.

[83] Billotte, Catherine, Edith Roland Fotsing, and Edu Ruiz. "Optimization of alumina slurry for oxide-oxide ceramic composites manufactured by injection molding."Advances in Materials Science and Engineering2017 (2017).

[84] Lakhdar, Y., C. Tuck, J. Binner, A. Terry, and R. Goodridge. "Additive manufacturing of advanced ceramic materials."Progress in Materials Science116 (2021): 100736.

[85] Lee, Jihyun, Sujin Park, Bong Ki Ryu, and Chang-Jun Bae. "Facilitation mechanisms of ceramic additive manufacturing: Acceleration and phase transition."Journal of the European Ceramic Society42, no. 6 (2022): 3044-3048.

[86]Liu, Zhiwen, Changbao Ma, Zhengxu Chang, Ping Yan, and Fazhi Li. "Research progress on crack formation mechanism and inhibition strategy for ceramic additive manufacturing."Journal of the European Ceramic Society(2023).

[87] Li, Suwen, Gang Wang, Keqiang Zhang, Xueqin Zhang, Lu Zhang, Wenqing Wang, and Rujie He. "Mechanical properties of Al2O3 and Al2O3/Al interpenetrated functional gradient structures by 3D printing and melt infiltration."Journal of Alloys and Compounds950 (2023): 169948.

[88] ISO/ASTM52900-15, “Standard terminology for additive manufacturing–general principles terminology,” International Organization for Standardization: Geneva, Switzerland, 2015.

[89] Najmon, Joel C., Sajjad Raeisi, and Andres Tovar. "Review of additive manufacturing technologies and applications in the aerospace industry."Additive manufacturing for the aerospace industry(2019): 7-31.

[90] Chen, Zhe, Xiaohong Sun, Yunpeng Shang, Kunzhou Xiong, Zhongkai Xu, Ruisong Guo, Shu Cai, and Chunming Zheng. "Dense ceramics with complex shape fabricated by 3D printing: A review."Journal of Advanced Ceramics10 (2021): 195-218.

[91] Shahrubudin, Nurhalida, Te Chuan Lee, and R. J. P. M. Ramlan. "An overview on 3D printing technology: Technological, materials, and applications."Procedia Manufacturing35 (2019): 1286-1296.

[92] Zhang, Feng, Zongan Li, Mengjia Xu, Shiyan Wang, Na Li, and Jiquan Yang. "A review of 3D printed porous ceramics."Journal of the European Ceramic Society42, no. 8 (2022): 3351-3373.

[93] Li, Zhi, Qianyi Chen, Bing Jiao, Qi Wang, Haijun Zhang, Quanli Jia, Shaowei Zhang, and Jianghao Liu. "Direct laser powder-bed fusion additive manufacturing of complex-shaped TiB2-B4C composite with ultra-fine eutectic microstructure and outstanding mechanical performances."Journal of the European Ceramic Society43, no. 3 (2023): 1230-1236.

[94] Rueschhoff, Lisa, William Costakis, Matthew Michie, Jeffrey Youngblood, and Rodney Trice. "Additive manufacturing of dense ceramic parts via direct ink writing of aqueous alumina suspensions."International Journal of Applied Ceramic Technology13, no. 5 (2016): 821-830.

[95] Zhang, Xueqin, Keqiang Zhang, Bin Zhang, Ying Li, and Rujie He. "Mechanical properties of additively-manufactured cellular ceramic structures: A comprehensive study."Journal of Advanced Ceramics11, no. 12 (2022): 1918-1931.

[96] Hostaša, Jan, Martin Schwentenwein, Guido Toci, Laura Esposito, Dominik Brouczek, Andreana Piancastelli, Angela Pirri, Barbara Patrizi, Matteo Vannini, and Valentina Biasini. "Transparent laser ceramics by stereolithography."Scripta Materialia187 (2020): 194-196.

[97] Zaiemyekeh, Zahra, Gholamhossein Liaghat, and Muhammad K. Khan. "Effect of Al2O3 nanoparticles on the mechanical behaviour of aluminium-based metal matrix composite synthesized via powder metallurgy."Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications235, no. 10 (2021): 2340-2355.

[98] Lo, Calvin, Tomoko Sano, and James D. Hogan. "Microstructural and mechanical characterization of variability in porous advanced ceramics using X-ray computed tomography and digital image correlation."Materials Characterization158 (2019): 109929.

[99] Wang, Zhiyong, and Peifeng Li. "Dynamic failure and fracture mechanism in alumina ceramics: Experimental observations and finite element modelling."Ceramics International41, no. 10 (2015): 12763-12772.

[100] Zhang, Bin, Xueqin Zhang, Wenqing Wang, Keqiang Zhang, Suwen Li, Ying Li, Gang Wang, and Rujie He. "Mechanical properties of additively manufactured Al2O3 ceramic plate-lattice structures: Experiments & Simulations."Composite Structures311 (2023): 116792.

[101] DeVries, Matthew, Ghatu Subhash, Alexander Mcghee, Peter Ifju, Tyrone Jones, James Zheng, and Virginia Halls. "Quasi-static and dynamic response of 3D-printed alumina."Journal of the European Ceramic Society38, no. 9 (2018): 3305-3316.

[102]张Xueqin,李克强张,本张,阴g Li, and Rujie He. "Quasi-static and dynamic mechanical properties of additively manufactured Al2O3 ceramic lattice structures: effects of structural configuration."Virtual and Physical Prototyping17, no. 3 (2022): 528-542.

[103] Mariani, Marco, Ruben Beltrami, Paolo Brusa, Carmen Galassi, Raffaele Ardito, and Nora Lecis. "3D printing of fine alumina powders by binder jetting."Journal of the European Ceramic Society41, no. 10 (2021): 5307-5315.

[104] Zhou, Fenghua, and Jean-Francois Molinari. "Stochastic fracture of ceramics under dynamic tensile loading."International journal of solids and structures41, no. 22-23 (2004): 6573-6596.

[105] Zhang, Hongjia, Antoine Jérusalem, Enrico Salvati, Chrysanthi Papadaki, Kai Soon Fong, Xu Song, and Alexander M. Korsunsky. "Multi-scale mechanisms of twinning-detwinning in magnesium alloy AZ31B simulated by crystal plasticity modeling and validated via in situ synchrotron XRD and in situ SEM-EBSD."International Journal of Plasticity119 2019): 43-56.

[106] Statnik, Eugene S., Codrutza Dragu, Cyril Besnard, Alexander JG Lunt, Alexey I. Salimon, Aleksey Maksimkin, and Alexander M. Korsunsky. "Multi-scale digital image correlation analysis of in situ deformation of open-cell porous ultra-high molecular weight polyethylene foam."Polymers12, no. 11 (2020): 2607.

[107],加威,陈京,安安王晓东Zhou, and Zhenglong Yang. "Applying multi-scale silica-like three-dimensional networks in a PEO matrix via in situ crosslinking for high-performance solid composite electrolytes."Materials Chemistry Frontiers5, no. 21 (2021): 7767-7777.

[108] Simons, E. C., J. Weerheijm, and Lambertus J. Sluys. "Simulating brittle and ductile response of alumina ceramics under dynamic loading."Engineering Fracture Mechanics216 (2019): 106481.

[109] Falco, S., N. Fogell, S. Kasinos, and L. Iannucci. "Homogenisation of micromechanical modelling results for the evaluation of macroscopic material properties of brittle ceramics."International Journal of Mechanical Sciences220 (2022): 107071.

[110] Schwarzer, Eric, Stefan Holtzhausen, Uwe Scheithauer, Claudia Ortmann, Thomas Oberbach, Tassilo Moritz, and Alexander Michaelis. "Process development for additive manufacturing of functionally graded alumina toughened zirconia components intended for medical implant application."Journal of the European Ceramic Society39, no. 2-3 (2019): 522-530.

[111] Han, Taihao, Jie Huang, Gaurav Sant, Narayanan Neithalath, and Aditya Kumar. "Predicting mechanical properties of ultrahigh temperature ceramics using machine learning."Journal of the American Ceramic Society105, no. 11 (2022): 6851-6863.

[112] Ramesh, K. T., James D. Hogan, Jamie Kimberley, and Angela Stickle. "A review of mechanisms and models for dynamic failure, strength, and fragmentation."Planetary and Space Science107 (2015): 10-23.

[113]Akrami, Saeid, Parisa Edalati, Masayoshi Fuji, and Kaveh Edalati. "High-entropy ceramics: Review of principles, production and applications."Materials Science and Engineering: R: Reports146 (2021): 100644.

[114]Cantor, Brain, I. T. H. Chang, Peter Knight, and A. J. B. Vincent. "Microstructural development in equiatomic multicomponent alloys."Materials Science and Engineering: A375 (2004): 213-218.

[115]Yeh, J‐W., S‐K. Chen, S‐J. Lin, J‐Y. Gan, T‐S. Chin, T‐T. Shun, C‐H. Tsau, and S‐Y. Chang. "Nanostructured high‐entropy alloys with multiple principal elements: novel alloy design concepts and outcomes."Advanced engineering materials6, no. 5 (2004): 299-303.

[116]Jones, Eppie R., Gloria Gonzalez-Fortes, Sarah Connell, Veronika Siska, Anders Eriksson, Rui Martiniano, Russell L. McLaughlin et al. "Upper Palaeolithic genomes reveal deep roots of modern Eurasians."Nature communications6, no. 1 (2015): 8912.

[117]Zhu, Jiatong, Xuanyu Meng, Jie Xu, Ping Zhang, Zhihao Lou, Michael J. Reece, and Feng Gao. "Ultra-low thermal conductivity and enhanced mechanical properties of high-entropy rare earth niobates (RE3NbO7, RE= Dy, Y, Ho, Er, Yb)."Journal of the European Ceramic Society41, no. 1 (2021): 1052-1057.

[118]Liu, Debao, Baolu Shi, Liyan Geng, Yiguang Wang, Baosheng Xu, and Yanfei Chen. "High-entropy rare-earth zirconate ceramics with low thermal conductivity for advanced thermal-barrier coatings."Journal of Advanced Ceramics11, no. 6 (2022): 961-973.

[119]Teng, Zhen, Yongqiang Tan, and Haibin Zhang. "High-entropy pyrochlore A2B2O7 with both heavy and light rare-earth elements at the A site."Materials15, no. 1 (2021): 129.

[120]Luo, Xuewei, Lirong Luo, Xiaofeng Zhao, Huangyue Cai, Shuaishuai Duan, Chunhui Xu, Shuo Huang, Hongyun Jin, and Shuen Hou. "Single-phase rare-earth high-entropy zirconates with superior thermal and mechanical properties."Journal of the European Ceramic Society42, no. 5 (2022): 2391-2399.

[121]Zhao, Weijun, Fan Yang, Zhaoli Liu, Heng Chen, Zhiheng Shao, Xuesong Zhang, Kaixian Wang, and Liyan Xue. "A novel (La0. 2Sm0. 2Eu0. 2Gd0. 2Tm0. 2) 2Zr2O7 high-entropy ceramic nanofiber with excellent thermal stability."Ceramics International47, no. 20 (2021): 29379-29385.

[122]Witte, Ralf, Abhishek Sarkar, Leonardo Velasco, Robert Kruk, Richard A. Brand, Benedikt Eggert, Katharina Ollefs, Eugen Weschke, Heiko Wende, and Horst Hahn. "Magnetic properties of rare-earth and transition metal based perovskite type high entropy oxides."Journal of Applied Physics127, no. 18 (2020).

[123]Chen, Heng, Huimin Xiang, Fu-Zhi Dai, Jiachen Liu, and Yanchun Zhou. "High entropy (Yb0. 25Y0. 25Lu0. 25Er0. 25) 2SiO5 with strong anisotropy in thermal expansion."Journal of Materials Science & Technology36 (2020): 134-139.

[124]Wang, Yuhao, Yu-Jun Jin, Zhao-Ying Ding, Gui Cao, Zhan-Guo Liu, Tao Wei, Jia-Hu Ouyang, Ya-Ming Wang, and Yu-Jin Wang. "Microstructure and electrical properties of new high-entropy rare-earth zirconates."Journal of Alloys and Compounds906 (2022): 164331.

[125]Zhang, L. J., M. D. Zhang, Z. Zhou, J. T. Fan, P. Cui, P. F. Yu, Q. Jing et al. "Effects of rare-earth element, Y, additions on the microstructure and mechanical properties of CoCrFeNi high entropy alloy."Materials Science and Engineering: A725 (2018): 437-446.

[126]Li, G. R., M. Liu, H. M. Wang, D. Zhang, F. Tang, C. W. Wang, Y. T. Zhao, G. Chen, and X. Z. Kai. "Effect of the rare earth element yttrium on the structure and properties of boron-containing high-entropy alloy."Jom72 (2020): 2332-2339.

[127]Zhang, Xiang, Nan Li, Xin Chen, Mark Stroup, Yongfeng Lu, and Bai Cui. "Direct selective laser sintering of high-entropy carbide ceramics."Journal of Materials Research38, no. 1 (2023): 187-197.