Multiscale Composite Materials Research Articles

Hierarchical Composites Patterned via 3D Printed Cellular Fluidics

AbstractAdditive manufacturing of freeform structures containing multiple materials with deterministic spatial arrangement and interactions remains a challenge for most 3D printing processes, due to complex fabrication tool requirements and limitations in printability of some material classes. Here, a versatile method is reported to produce architected composites using the concept of cellular fluidics, in which lattices of unit cells are used as templating scaffolds to guide flowable infill materials in a programmed spatial pattern, upon which they are cured in place to produce a deterministically ordered multimaterial solid. The lattice design relies on the unit cell size, type, strut diameter, surface wetting, and distribution of cellular structures to control liquid flow and retention. Individual unit cells are tuned to achieve reliable infilling and combined into higher‐order architectures to achieve multiscale composite materials with disparate mechanical properties, including those considered non‐printable. Lattice design considerations for leveraging capillary phenomena and demonstrate several methods of patterning polymers in 3D‐printed cellular fluidic structures are presented. The concept of tuning the compressive response of an architected composite using a flexible‐elastomer as the lattice and a stiff‐epoxy as the infill material is illustrated.

Enhancement of the contact behavior of a quasi-isotropic carbon fiber/epoxy matrix laminate with an elastic body by modifying the fiber-matrix interphase using graphene nanoplatelets

This study analyzed the effect of incorporating graphene nanoplatelets in the fiber-matrix interphase on the behavior of a multiscale composite laminate based on carbon fibers and epoxy resin subjected to contact loads. The selected loading mode was the contact between an elastic surface and a cylinder. The multiscale composite material used was a quasi-isotropic laminate with graphene nanoplatelets (GnPs) added at the fiber-matrix interface. The specimens were prepared with 0.0%, 0.1%, and 0.25% by-weight GnPs. Laminate beams were used according to the ASTM D7264 standard, and contact was studied in two configurations, applying the load at the edge of the laminate and in the other, in the plane of the test pieces. The normal strains in the contact region were determined experimentally using the interferometric Moiré technique. These results were compared with estimations using the Hertz contact theory and the finite element method (FEM). The normal strains in the contact area of specimens with fibers modified with 0.1% GnPs were lower than those with 0.25% or fibers without surface modification. Excellent agreement between the experimental results along lines in the contact zone with those estimated with the FEM. The normal strains in a direction perpendicular to the applied load obtained by the Hertz theory for the maximum deformation were slightly higher than those obtained by FEM. Except for those calculated for the normal strain in εy for the load in the direction of the thickness, although the distribution was very similar to those obtained by FEM as well as the experimental one.

Design and optimization of the dual-functional lattice-origami metamaterials

This study proposes a multi-scale composite lattice-origami metamaterial (MCLOM) to achieve excellent bandgap characteristics and energy absorption capacities. The MCLOMs are constructed by considering the high impedance mismatch of lattice structures, the spatial deformability of origami structures, and the tunability of the components in multi-scale composite materials. Firstly, elastic wave propagation characteristics are analyzed in the Bloch wave framework, revealing the realization of complete bandgaps and their generation mechanism by mode shape analysis and transmission spectrum. Subsequently, an optimization framework integrating the particle swarm optimization (PSO) algorithm is developed to maximize the first bandgap’s bandwidth by adjusting various component parameters. Under optimal distribution, the proposed metamaterials achieve remarkable improvements of 289% and 271% in the design objectives of two lattice-origami metamaterials with 90∘ dihedral angle compared to the initial distribution. It can be demonstrated that non-uniform distributions of multi-scale composite materials are dramatically effective for broadband wave attenuation. Additionally, while striving to widen the bandgap, the energy absorption capacities of structures are also crucial. The effect of the distribution of multi-scale composite materials with the optimal bandgap on the energy absorption performance is investigated. The results reveal that the optimal distribution of the lattice-origami metamaterials yields notable improvements of 48.26% and 34.86% under low-velocity impact, and 37.41% and 25.19% under medium-velocity impact. This work presents innovative concepts and approaches for devising and implementing novel dual-functional metamaterials, undoubtedly propelling the continual progress of material science and engineering technology in the times ahead.

Coupling grid nanoindentation and surface chemical analysis to infer the mechanical properties of shale mineral phases

Shale is a low-permeability, multi-phase, and multi-scale composite material with intrinsic heterogeneity in micro-texture and mineralogical composition. In this paper, relationships between the microscale texture and constituent phases of shale were investigated using SEM (scanning electron microscopy)/BSE (backscatter electron imaging)-EDS (energy-dispersive x-ray spectroscopy) methods, together with grid nanoindentation experiments. The mechanical properties of the constituent phases of the carbonate-rich Longmaxi shale samples were extracted based on the spatial distribution of mineral phases and the indentation interaction volume. We analyze the effects of particle size on the interpreted mechanical properties and establish a characteristic length scale based on a probabilistic analysis. The identified characteristic length for extracting the mechanical properties of constituent mineral phases from the grid nanoindentation technique is about 5.8–11.7 μm, i.e., up to 10 times greater than that proposed in prior research. A multi-scale mechanical model was established with considerations of a self-consistent scheme for granular morphology to link the microscopic characteristics with the multi-scale mechanical properties of shales. The modeling results show that the stiffness and the strength of the homogenized nano-porous illite/quartz aggregates in Longmaxi shale can be assessed from the nano-scale mechanical properties of the mineral phases and the nano-scale porosity. This study paves the way to accessing the mechanical properties of the constituent phases of composite materials based on the properties of their building blocks and provides extensive insights into their complex mechanical behavior, representing a major step towards developing reliable multi-scale models for engineering applications.

Assessing the Effect of Cellulose Nanocrystal Content on the Biodegradation Kinetics of Multiscale Polylactic Acid Composites under Controlled Thermophilic Composting Conditions.

This work studied the effect of cellulose nanocrystal (NCC) content on the biodegradation kinetics of PLA-based multiscale cellulosic biocomposites (PLAMCBs). To facilitate biodegradation, the materials were subjected to thermo-oxidation before composting. Biodegradation was carried out for 180 days under controlled thermophilic composting conditions according to the ASTM D 5338 standard. A first-order model based on Monod's kinetics under limiting substrate conditions was used to study the effect of cellulose nanocrystal (NCC) content on the biodegradation kinetics of multiscale composite materials. It was found that thermo-oxidation at 70 °C for 160 h increased the biodegradability of PLA. Also, it was found that the incorporation of cellulosic fibrous reinforcements increased the biodegradability of PLA by promoting hydrolysis during the first stage of composting. Likewise, it was found that partial substitution of micro cellulose (MFC) by cellulose nanocrystals (NCCs) increased the biodegradability of the biocomposite. This increase was more evident as the NCC content increased, which was attributed to the fact that the incorporation of cellulose nanocrystals facilitated the entry of water into the material and therefore promoted the hydrolytic degradation of the most recalcitrant fraction of PLA from the bulk and not only by surface erosion.

Heterogeneous numerical modeling of fatigue damage for asphalt mixtures through complex mechanical impedances

Asphalt mixes, also known as bituminous concrete and asphalt concrete (AC), which are one of the most widely used materials in pavement engineering, are complex, multi-scale composite materials. AC is a heterogeneous material composed of a bituminous matrix and aggregates featuring viscoelastic and elastic behavior, respectively. Fatigue under cyclic loading of this material is one of the main pavement degradation phenomena. Under cyclic loading, the viscoelastic behavior of this material converts part of the energy brought by the loading into dissipated energy due to the viscous effects of the bituminous matrix. It is a heat source that leads to the increase of temperature during phase I of fatigue (self-heating). The second part of the energy is restituted and is the growth driving force of the damage. This work deals with a new thermodynamic approach to describe rheological models applied to viscoelastic materials under mechanical cyclic loading. The dissipation and the energy-released rate are determined based on an electromechanical analogy to simulate damage growth and the temperature increase. Both thermal and mechanical aspects and their coupling are taken into account leading to complete constitutive modeling to simulate the decrease of the AC complex modulus. Using the image processing technique, a heterogeneous microstructure is used to model the AC.

Optimal Design of Multi-Scale Fibre-Reinforced Cement-Matrix Composites Based on an Orthogonal Experimental Design.

Cement-matrix composite are typical multi-scale composite materials, the failure process has the characteristics of gradual, multi-scale and multi-stage damage. In order to delay the multi-stage damage process of cement-matrix composites, the defects of different scales are suppressed by using different scales of fibres and fly ash (FA), and the overall performance of cement-matrix composites is improved, a new multi-scale fibre-reinforced cement-based composite composed of millimetre-scale polyvinyl alcohol fibre (PVA), micron-scale calcium carbonate whisker (CW), and nano-scale carbon nanotubes (CNTs) was designed in this study. The compressive strength, flexural strength, splitting tensile strength, and chloride ion permeability coefficient were used as assessment indices by the orthogonal test design. The impacts of the three fibre scales and fly ash on each individual index were examined, and the overall performance of the multi-scale fibre-reinforced cementitious materials (MSFRCC) was then optimized using grey correlation analysis. The optimized mix ratio for overall performance was PVA: 1.5%, CW: 2%, CNTs: 0.1%, FA: 40%. Compared with the optimal results for each group, the compressive strength of the final optimized MSFRCC group decreased by 8.9%, the flexural strength increased by 28.4%, the splitting tensile strength increased by 10%, and the chloride ion permeability coefficient decreased by 5.7%. The results show that the compressive performance and resistance to chloride ion penetration of the optimized group are slightly worse than those of the optimal group in the orthogonal test, but its flexural performance and splitting tensile performance are significantly improved.

Nonlinear vibrations of multiscale composite beams on a nonlinear softening foundation

This paper describes a new approach to evaluate the instability of beams on a softening elastic foundation. The basis of this approach is solving a nonlinear frequency problem. The beam is made of multiscale composite materials based on carbon nanotubes (CNTs) and long fibers. Homogenization methods are utilized in a sequential process to obtain the effective material properties of these composites. Furthermore, the thermal environment's effect on the beam's response is examined. Reddy's third-order shear deformation theory approximates the induced displacements in the composite beam. Also, the kinetic and strain energies of the beam are calculated based on the von Kármán nonlinear strains and linear thermoelasticity theories. A recently reported Lagrangian nodal weak formulation (LNWF) method is implemented to obtain the linear and nonlinear stiffness and mass matrices governing the beam's vibrations. The modified coefficients for nonlinear stiffness matrices are obtained using the residual Galerkin method across time. Finally, the nonlinear natural frequencies are calculated by employing the iterative displacement control strategy. In the results section, in addition to examining various parameters on nonlinear free vibrations, the effect of these parameters on the displacement required for the loss of stability of the beam placed on the softening foundation is also examined.

Collagen-Based Micro/Nano Fibrous Constructs: Step-By-Step Reverse Biomimetics of Structure and Mechanical Function

Multiscale micro–nano fibrous structures are a cutting-edge research area in material science and have drawn the attention of scientists in recent years. These structures are widely distributed in nature’s materials and hold fascinating and unique properties, such as mechanical behaviors, high surface area to volume ratio, and special multiscale biological functionalities. Herein, we demonstrate step-by-step biomimetics of a multiscale composite material system and the influence of the different structural mechanisms on mechanical behavior. This is done using systematic biomimetics and investigation of the mechanical effect of every constituent. We have fabricated and characterized mechanically and structurally different material systems to get a comprehensive understanding of the structure–function relationship in multiscale biomimetic constructs (MSBCs) and examine the influence of the material selection and structure. We first characterized the electrospun nanofibers made of polyamide 6 (PA6) and gelatin-polyamide 6 (GPA6) and then constructed and characterized the combined constructs. Our micro–nano fibrous structures were constructed from combined unique coral collagen microfibers and PA6 and GPA6 nanofibers. These hierarchical structures demonstrated an entangled network of nanobridges among the micro collagen fibers. However, the GPA6-collagen structures showed better connectivity with the microfibers and were significantly stiffer and stronger than the PA6-collagen structures due to the material compatibility. Furthermore, our structures demonstrated a considerable resemblance with soft tissue structures. We embedded the MSBC in alginate hydrogel to form biocomposites that displayed a hyperelastic nonlinear behavior with significantly improved toughness and a remarkable similarity to the mechanical behavior of native soft tissues. Our results present great potential to be further developed as tailor-designed multiscale next-generation specialized structures for soft tissue repair and replacement.

Preparation of In Situ Growth Multiscale β-Sialon Grain-Reinforced Al2O3-Based Composite Ceramic Tool Materials

A kind of multiscale β-sialon grain-reinforced Al2O3 matrix composite ceramic tool material, named ASN, was prepared and studied. For the ASN, β-sialon (molecular formula: Si4Al2O2N6) was synthesized in situ by a hot-pressing and solid-solution reaction process. A total of six samples were prepared at varying sintering temperatures and holding times under vacuum conditions. The solid solution reaction mechanism of β-sialon, the phase composition, mechanical properties, microstructure, and strengthening and toughening mechanisms of the composite ASN were investigated. As a result, within the experimental parameters, an optimal ASN tool material was obtained under a pressure of 32 MPa and at a temperature of 1550 °C for 20 min. The tested mechanical properties of the optimal sample were as follows: flexural strength 997 ± 59 MPa, fracture toughness 6.4 ± 0.3 MPa·m1/2, Vickers hardness 18.2 ± 0.4 GPa, and relative density 98.1 ± 0.2%. According to crystal defect theory, the solid solution reaction mechanism of in-situ-synthesized β-sialon in an Al2O3 matrix involves a double mechanism of unequivalence (or hetero-valence) and interstitial filling. The multiscale β-sialon grains mainly consisted of four grains, which were elongated β-sialon grains with a diameter of 0.3-0.4 μm and an aspect ratio of 6-9, elongated β-sialon grains with a diameter of 70 nm and an aspect ratio of 10, β-sialon whiskers with a diameter of 0.2 μm and an aspect ratio of 12-15, and intragranular β-sialon whiskers with a diameter of 70 nm. The mechanical properties were improved due to strengthening and toughening mechanisms, such as mixed structure mode (intergranular and transgranular), elongated grain pullout, interface bonding, crack reflection, pinning, and bridging.

A multiscale model for mechanical and fracture behavior of calcium-silicate-hydrate: From molecular dynamics to Peridynamics

Fully understanding the fracture behavior of concrete is a challenging work since concrete is a complex multiscale composite material with a heterogeneous structure at different length scales ranging from nanoscale to macroscale. A new multiscale model framework was proposed in the present study to explore the mechanical properties, including Young's modulus E and ultimate tensile strength UTS, and fracture behavior of calcium-silicate-hydrate (C-S-H) from the nanoscale to mesoscale. The nanoscale C-S-H globule models were built and simulated via molecular dynamics (MD) simulations and then the obtained mechanical properties were employed as the input parameters for the mesoscale Peridynamics (PD) simulations to acquire the E, UTS, and fracture behavior of C-S-H gel. The results reveal that at nanoscale, the mechanical performance of C-S-H is anisotropic: As the size of C-S-H model increases, the E and UTS of C-S-H decrease because the extension of crack in a larger C-S-H model will release more stored energy. At mesoscale as the packing fraction φ increases, the E and UTS of C-S-H gel increase. The resulted E and UTS are in line with former simulations and experimental data implying the effectiveness and accuracy of the proposed multiscale model.

Controlled formation of carbon nanotubes incorporated ceramic composite granules by electrostatic integrated nano-assembly.

Controlled incorporation of carbon nanotubes (CNT) with alumina (Al2O3) and zirconia (ZrO2) nanoparticles using an electrostatic nano-assembly method for the fabrication of homogeneous CNT-incorporated Al2O3-ZrO2 and CNT-incorporated shell-layer Al2O3-ZrO2 composite granules is demonstrated. The spark-plasma-sintered CNT-incorporated shell-layer Al2O3-ZrO2 artifact exhibited approximately 15 times higher electrical conductivity than a homogeneous CNT-incorporating artifact. This novel composite granule fabrication method using an electrostatic integrated assembly of colloidal nanomaterials would be beneficial for the development of multiscale and multicomponent composite materials.

Regularities of Friction of Multiscale Composite Materials Containing Highly Dispersed Particles of Fullerene Soot

Regularities of Friction of Multiscale Composite Materials Containing Highly Dispersed Particles of Fullerene Soot

Mapping-Based Hierarchical Sensitivity Analysis for Multilevel Systems With Multidimensional Correlations

Abstract Hierarchical sensitivity analysis (HSA) of multilevel systems is to assess the effect of system’s input uncertainties on the variations of system’s performance through integrating the sensitivity indices of subsystems. However, it is difficult to deal with the engineering systems with complicated correlations among various variables across levels by using the existing hierarchical sensitivity analysis method based on variance decomposition. To overcome this limitation, a mapping-based hierarchical sensitivity analysis method is proposed to obtain sensitivity indices of multilevel systems with multidimensional correlations. For subsystems with dependent variables, a mapping-based sensitivity analysis, consisting of vine copula theory, Rosenblatt transformation, and polynomial chaos expansion (PCE) technique, is provided for obtaining the marginal sensitivity indices. The marginal sensitivity indices can allow us to distinguish between the mutual depend contribution and the independent contribution of an input to the response variance. Then, extended aggregation formulations for local variables and shared variables are developed to integrate the sensitivity indices of subsystems at each level so as to estimate the global effect of inputs on the response. Finally, this paper presents a computational framework that combines related techniques step by step. The effectiveness of the proposed mapping-based hierarchical sensitivity analysis (MHSA) method is verified by a mathematical example and a multiscale composite material.

Sensitivity-based adaptive sequential sampling for metamodel uncertainty reduction in multilevel systems

Decomposition-based technique is often used in the analysis and design of complex engineering systems for reducing the computational complexity by studying the subsystems decomposed from multilevel systems. Metamodels, as a replacement of original simulation models, can further alleviate the computational burden. However, discrepancy between the simulation models and metamodels, which is defined as metamodel uncertainty, may be introduced in the analysis process of multilevel systems owing to the lack of data. The metamodel uncertainties of sub-models will be further amplified because of the hierarchical uncertainty propagation and interaction between uncertainties, which will have a great impact on the system results. An adaptive sequential sampling strategy based on sensitivity is proposed in this paper so as to improve the prediction accuracy of system response. In this strategy, polynomial-chaos expansion is used to realize the forward propagation of metamodel uncertainty quantified by the Kriging model. The forward propagation is combined with optimization based on maximum variance criterion for searching the input locations that results in the largest variance of system response. Then, the indices of subsystems are obtained to make decisions about which subsystem needs extra samples by combining Karhunen-Loeve expansion and sensitivity analysis. The effectiveness of the proposed sequential sampling strategy method is verified by two mathematical examples and a multiscale composite material.

Homogeneous Model for the Nanoparticle Growth in Polymer Matrices

A promising method of the fabrication of polymer nanocomposite materials relies on the in situ generation of the nanoparticles (NPs) in the matrix due to the thermal or photochemical destruction of some sort of precursor. By means of selective transformation of the clean polymer to the nanocomposite using the direct laser writing or by applying a photomask, one can construct the multiscale structured composite materials for numerous applications, including flexible electronics, photonics, and plasmonics. In this work, we propose a model for the nanoparticle generation and growth in polymers based on Smoluchowski’s equations. Unlike the typical liquids, the diffusion of the particles in polymer matrices does not obey the Stokes–Einstein law. The steep degradation of the NP’s diffusivity with its size results in the self-organization of the particle mass distribution into two fractions. One includes the small clusters that are constantly generated due to the precursor destruction. The other consists of the nearly constant number of relatively large particles that gather the small clusters, acting as heterogeneous growth centers. Such quasi-heterogeneous behavior is possible without any initially existing growth centers, such as impurities and interfaces. The difference of this quasi-heterogeneous behavior from the one suggested by true heterogeneous models is discussed. The possible effects of the nonspherical particle shape and stable configurations of small clusters containing the “magic number” of atoms are studied.

Nonlinear vibrations of variable thickness curved panels made of multi-scale epoxy/fiberglass/CNT material using Jacobi elliptic functions

This article deals with nonlinear vibration study of variable thickness cylindrical panels made of multi-scale composite materials containing epoxy matrix, glass fibers, and carbon nanotubes (CNTs). The elastic properties of multi-scale material have been defined in the context of 3D Mori-Tanaka scheme considering unidirectional aligned macro-fibers and randomly oriented CNTs. It is considered that the panel thickness is varying in axial direction and may have linear and parabolic changes. The governing equations of variable thickness curved panel have been stablished using thin shell theory containing geometric nonlinearity. Then, Jacobi elliptic functions are proposed for solving the governing equations since they leads to exact frequency-amplitude curves of the curved panels. It is reported that frequency-amplitude curves are varying with the changes of CNT weight fraction, fiber orientation, fiber volume, variable thickness parameters, panel curvature radius, and length-to-radius ratio of CNTs.

Numerical study in stochastic homogenization for elliptic partial differential equations: Convergence rate in the size of representative volume elements

SummaryWe describe the numerical scheme for the discretization and solution of 2D elliptic equations with strongly varying piecewise constant coefficients arising in the stochastic homogenization of multiscale composite materials. An efficient stiffness matrix generation scheme based on assembling the local Kronecker product matrices is introduced. The resulting large linear systems of equations are solved by the preconditioned conjugate gradient iteration with a convergence rate that is independent of the grid size and the variation in jumping coefficients (contrast). Using this solver, we numerically investigate the convergence of the representative volume element (RVE) method in stochastic homogenization that extracts the effective behavior of the random coefficient field. Our numerical experiments confirm the asymptotic convergence rate of systematic error and standard deviation in the size of RVE rigorously established in Gloria et al. The asymptotic behavior of covariances of the homogenized matrix in the form of a quartic tensor is also studied numerically. Our approach allows laptop computation of sufficiently large number of stochastic realizations even for large sizes of the RVE.

High grafting strength from chemically bonded 2D layered material onto carbon microfibres for reinforced composites and ultra-long flexible cable electronic devices

Surface modification of carbon microfibres (CF) represents a promising and challenging alternative for creating multiscale and multifunctional hierarchical lightweight high-performance composite materials. In this study, a low-temperature chemical method is developed to graft layered graphene oxide (GO) directly onto CF through covalent bonding, and the grafting is characterised by SEM, FTIR, Raman and XPS spectroscopy. The GO failure stress (FS) measured using in situ nanomechanical pull-out tests is 36.2% higher than the literature values. Since GO fracture is the only breaking mechanism observed, there exists a strong carbon-carbon covalent bonding at the GO-CF interface indicating that the actual grafting strength (GS) is greater than the FS obtained. This elevated GS can substantially increase the interfacial and impact properties necessary in high performance composites. CF and GO-CF are fabricated to current-collector free ultra-long flexible cable-supercapacitors and their electrochemical properties in gel electrolyte are systematically investigated. GO-CF supercapacitor leads to an electrochemical capacitance of 7.8 F cm−3 and an energy density of 6.93 × 10−4 Wh cm−3 at 0.02 A cm−3. Thus, these grafted materials along with advanced composites have substantial promise in ultra-long flexible cable electronics with superior strengths and performances.

Influence of specific mechanical energy during compounding in a co-kneader on electrical and rheological properties of multiscale composite materials

Abstract This paper focuses on the effect of different scales of fillers, from nano to macrometer, on the rheological and electrical behaviour of thermoplastic-based composites. Composites based on poly (etherimide) matrix (PEI) with multiscale reinforcement are processed by melting in a co-kneader to disperse homogeneously carbon nanotubes and glass fibers. We clearly demonstrate the strong link between the liquid-solid transition and the electrical conductivity. We show that the specific mechanical energy is a key parameter. Glass fibers allow to increase the electrical conductivity of blends based on carbon nanotubes and to obtain a lower decreasing of conductivity at the liquid transition which takes place in the same time as rheological and electrical parameters.