Analytical Micromechanical Model Research Articles

Mechanical properties of porous Si3N4–SiC composites fabricated at 1200 °C

Porous Si3N4–SiC composites are potentially very attractive for various advanced applications such as aerospace and solar thermal power plants. However, processing of these porous composites is difficult and expensive due to the requirement of very high temperatures. In the present work, porous Si3N4–SiC composites were fabricated at only 1200 °C using phosphoric acid both as a pore former and binder. Porous composites with a constant SiC content were fabricated using various H3PO4 content and the morphology and mechanical properties of the porous composites were systematically investigated. The addition of SiC particles resulted in significant improvement of stiffness, compressive strength, and flexural strength over monolithic porous Si3N4, and porous composites fabricated using 40 vol% H3PO4 yielded the best properties of longitudinal elastic constant >50 GPa, flexural strength >80 MPa, and compressive strength >180 MPa. The achieved mechanical properties have been discussed in light of the analytical micromechanical models for Young's modulus and minimum solid area theory. Finally, the influence of processing temperature on the evolution of porosity and crystalline phases has been systematically studied and the dependence of porous composites' stiffness on these parameters has been investigated in detail.

Progressive damage analysis for fatigue life prediction in plain weave composites: A multi-scale approach

This study introduces an analytical micromechanical model considering progressive damage designed to predict the elastic and strength properties of plain weave composites subjected to fatigue loading. The presented model is composed of a multi-scale micromechanical model, wherein a progressive damage mechanism has been incorporated. During the development of this multi-scale micromechanical model, a representative volume element was chosen and homogenized, utilizing assumptions pertaining to identical out-of-plane stresses and in-plane strains. These assumptions satisfy the conditions of equilibrium and displacement continuity in the representative volume element and, through a three-step process, enhance the model’s accuracy in applying the damage model and predicting the elastic properties of plain weave composites under static loading. Subsequently, the damage mechanism was progressively developed by accounting for the crucial role of matrix crack growth. This was achieved by employing the kinetic theory of fracture for polymers and integrating it with the multi-scale micromechanical model. Ultimately, the elastic and strength properties of plain weave composites under fatigue loading were predicted. A comparison of the results derived from the present model with those available in the literature demonstrated a high degree of agreement.

Non-destructive evaluation of the curing of a polybenzoxazine nanocomposite blend for space applications using fluorescence spectroscopy and predictive mechanical modelling

In this study, we employ fluorescence spectroscopy to monitor the curing process of a novel polybenzoxazine (PBZ) resin blend containing a polyhedral oligomeric silsesquioxane (POSS) reagent in a non-destructive way and compare it with the differential scanning calorimetry data. Our resin blend has been carefully selected for study on the International Space Station in 2024 as part of the Euro Materials Ageing 1 Programme (AO-2020-EMA) supported by the European Space Agency (ESA) and the French Space Agency (CNES). Computational simulations of PBZ-POSS blend composites are investigated to determine their effective mechanical responses based on constituent micro-stresses with periodic boundary conditions and continuum-based analytical micromechanical models. Further investigations are focused on the development of different representative volume element models, including periodic, non-periodic, and overlap inclusions, and the comparison with experimental data. Fluorescence spectroscopy and computational and analytical methods can offer a non-destructive approach to gaining insights into polymerisation processes and effective mechanical responses.

Fiber orientation and crimp level might control the auxetic effect of biological tissues

We propose an analytical micromechanical model for studying the lamellar-composite-like structure of fibrous soft tissue. The tissue under consideration is made up of several lamellae, and is designed to resemble the annulus fibrosus (AF) tissue or media layer of arterial tissue, for example. The collagen fibers are arranged in parallel in each lamella and the fiber orientation differs from one lamella to its neighbors. The parallel fibers in each lamella of AF tissue, for example, have been observed to have a crimped microstructure. The proposed model incorporates this quality, considering fiber waviness as a sinusoidal shape and taking into account the fiber dispersion in different layers, where both fiber and matrix are considered as solid phases. We find that collagen-fiber waviness and layer orientation have a significant influence on Poisson’s ratio. The effective Poisson’s ratio predicted by the proposed model demonstrates that the crimped collagen fiber microstructure might weaken the auxetic effect of fibrous soft tissue, which might explain why, as the literature suggests, the auxetic behavior is more difficult to observe than large Poisson’s ratios. As opposed to the many studies that use the well-known hyperelastic fiber-based constitutive model, in which out-of-plane expansion is often observed, the present work explains the auxetic response found in modeling and in experimental data from the perspective of collagen fiber microstructure.

A computational micromechanical approach to predicting Young’s modulus of continuous banana and palmyra fiber-reinforced epoxy composites

The prediction of Young’s modulus properties of a hybrid composite using micromechanical models based on the geometrical characteristics and individual constituent properties of materials is a challenging task for the researchers. In this work, the micromechanical and experimental approaches are used to evaluate the hybrid effect on the Young’s modulus properties of continuous banana and palmyra fiber-reinforced epoxy composites. In computational modeling, a square unit cell is employed by using ANSYS to study the effect of the fiber weight percentage and weight ratio over Young’s modulus properties along the longitudinal and transverse direction. The effectiveness of the numerical predictions is evaluated by comparing with the experimental results and analytical micromechanical models (Rule of hybrid Mixture, Halpin–Tsai (HT), and Lewis and Nielsen). In the experimental approach, the hybrid composites were fabricated with the continuous banana and palmyra fibers reinforced with epoxy by varying the fiber percentages (10%, 20%, 30% and 40%) and weight ratios (1:1, 1:3, and 3:1). The micromechanical approaches show that Young’s modulus of the hybrid composites is consistently increased with the fiber percentages. The longitudinal Young’s modulus obtained by the Lewis and Nielsen equation gave good agreement with numerical and experimental results. On the other hand, the experimental transverse Young’s modulus gave a better fit with the inverse rule of hybrid mixture as compared with other analytical model predictions.

Prediction of mechanical behavior of rocks with strong strain-softening effects by a deep-learning approach

Rock materials exhibit various mechanical characteristics, and it is difficult to describe the strain–stress relation with strong strain-softening behavior by a single constitutive law. In the present study, a long short term memory (LSTM) deep learning method is proposed to predict the material’s deformation under different loading conditions. Unlike the traditional analysis method focusing on the determination of effective tangent stiffness tensor, the constructed LSTM-based procedure requires only the strain–stress values in certain cases to predict the future mechanical behaviors, even for rock materials with strong strain-softening, indicating that the loading history can be taken into account as time sequence data. In order to validate the accuracy, two applications are provided with the established LSTM model: predicting the deformation of granite and sandstone in conventional triaxial compression tests without introducing any elastoplastic parameters or constitutive laws, where the dataset for training the LSTM model is collected alternatively from an analytical micromechanical damage model and from laboratory experiments by considering a wide range of confining pressure. Comparisons of accuracy and convergence rate with different neural network structures are also carried out to check the best performance of the procedure. Implementation method of the trained LSTM model in Finite Element program as a constitutive relation is also provided and applied to the simulation of sandstone. Comparisons show that the LSTM-FEM method provides a good capacity to predict the mechanical behavior of rocks.

Ultrasonic study of the elastic properties of functionally graded and equivalent monolithic composites

• Stiffness comparison between an FGM and equivalent monolithic composite was done. • Elastic constants were measured using ultrasound phase spectroscopy. • Despite the gradient structure, the FGM displays quasi-isotropic elastic properties. • Stiffness depends only on the ceramic content, gradient structure has no influence. • Hashin Shtrikman lower bound provides the best fit for the stiffness of the FGM. The aim of this work is to compare the stiffness of a graded composite and equivalent monolithic particulate reinforced composite experimentally. Hybrid Al-SiC-graphite composites were fabricated using spark plasma sintering. Longitudinal elastic constants were measured using non-destructive ultrasound phase spectroscopy. It is seen that for the graded composites, the stiffness depends solely on the reinforcement content, while the gradient structure has no influence. Comparison with analytical micromechanical models show that the Hashin Shtrikman lower bound predicts the elastic constants most accurately.

Eshelby tensors and overall properties of nano-composites considering both interface stretching and bending effects

In this study, analytical micromechanical models are developed for nanocomposites with both interface stretching and bending effects. First, the interior and exterior Eshelby tensors for a spherical nano-inclusion, with an interface defined by the Steigmann–Ogden (S–O) model, subjected to an arbitrary uniform eigenstrain are derived. Correspondingly, the stress/strain concentration tensors for a spherical nano-inhomogeneity subjected to arbitrary uniform far-field stress/strain loadings are also derived. Using the obtained concentration tensors, the effective bulk and shear moduli are derived by employing the dilute approximation and the Mori–Tanaka method, respectively, which can be used for both nano-composites and nano-porous materials. An equivalent interface curvature parameter reflecting the influence of the interface bending resistance is found, which can significantly simplify the complex expressions of the effective properties. In addition to size-dependency, the closed form expressions show that the effective bulk modulus is invariant to interface bending resistance parameters, in contrast to the effective shear modulus. We also put forward a characteristic interface curvature parameter, near which the effective shear modulus is affected significantly. Numerical results show that the effective shear moduli of nano-composites and nano-porous materials can be greatly improved by an appropriate surface modification. Finally, the derived effective modulus with the S–O interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.

Prediction of the Basic Creep of Normal and High-strength Concretes based on an Analytical Micromechanical Model

Prediction of the Basic Creep of Normal and High-strength Concretes based on an Analytical Micromechanical Model

FEM micromechanical modeling of nanocomposites with carbon nanotubes

Abstract Mechanical properties of carbon nanotube (CNT)-based nanocomposites are broadly discussed in the literature. The influence of CNT arrangements on the elastic properties of nanocomposites based on the finite-element method (FEM) and representative volume element (RVE) approach is presented here. This study is an application of RVE modeling in the characterization of elastic behavior of CNT polymer nanocomposites. Our main contribution is the analysis of the impact of a nanotube arrangement on the elastic properties of nanocomposite to comprehensively determine the material constants. While most of the articles are focused on one distribution, not all material constants are determined. Our FEM analysis is compared with micromechanical models and other results from the literature. The current work shows that nanotube arrangements lead to different results of elastic properties. The analytical micromechanical models are consistent with the numerical results only for axial Young’s modulus and Poisson’s ratio, whereas other elastic constants are lower than the numerical predictions. The results of these studies indicate that FEM can predict nanocomposite mechanical properties with good accuracy. This article is helpful and useful to comprehensively understand the influence of CNT arrangements on the elastic properties of nanocomposites.

Understanding the Stiffness of Porous Asphalt Mixture through Micromechanics

Micromechanics, which can be used to relate the properties of a composite to the properties of individual constituents, is considered a good approach to understanding the fundamental mechanisms behind the behavior of asphalt materials. Compared with the semi-empirical and numerical micromechanical models, analytical micromechanical models do not need calibration factors. In addition, they can provide analytical solutions on the basis of a series of assumptions. Using these models, researchers have separated the effects of different stiffening mechanisms (i.e., the volume-filling reinforcement, the physicochemical reinforcement, and the particle-contact reinforcement) for mastic. However, similar research work has not been conducted for asphalt mixtures and, moreover, the characteristics of the particle-contact reinforcement have not been deeply analyzed by researchers. Therefore, this paper aims to understand the stiffness of asphalt mixture through micromechanics. The focus of this study was on porous asphalt mixture where particle-contact reinforcement plays an important role in its behavior. The stiffening effects of different mechanisms were separated using analytical micromechanical models. The effects of temperature/frequency and the properties of the matrix phase on the stiffening effect of the particle-contact reinforcement were analyzed.

Numerical modelling of the elastic properties of 3D-printed specimens of thermoplastic matrix reinforced with continuous fibres

Numerical modelling of 3D-printed Fused Filament Fabrication (FFF) specimens with thermoplastic matrices reinforced with continuous fibres is still in its infancy. The existing numerical work is mostly related to the adhesion between printed filaments and not to the mechanical properties. However, the latter are one of the most important parameters that define the structural behaviour of the material.A numerical three-step multi-scale model is introduced in the present study, concentrating on the fundamental aspect of the elastic properties. The most encountered reinforced Nylon FFF structures with continuous fibres of glass, carbon and, Kevlar, are examined. The concept of Representative Volume Element (RVE) is utilized for the combination of matrix and fibres at the micro-scale and the addition of voids at the meso-scale. Finally, at the macro-scale, tension simulations are performed for specimens with various lay-ups.The results of the numerical model are validated using analytical models and experimental data. A new analytical micro-mechanical model is developed as an alternative to the more cumbersome Mori–Tanaka model. A series of experimental testing is performed for Kevlar-reinforced Nylon specimens to accompany the limited existing data and aid the validation process. The comparison reveals a good correlation with the analytical models for the micro- and meso-scale and to the experimental data for the macro-scale, leading to a robust conclusion for its validity and efficiency.

Predicting the mechanical properties of unidirectional fiber reinforced plastics from fiber and resin properties using data mining

Accurate prediction of unidirectional (UD) fiber reinforced plastics' (FRP) mechanical properties can significantly shorten the time from material design to structural application. Data mining, as a promising alternative approach to the traditional analytical micromechanics model and finite element model, can overcome their limitations of lack of certain constituent parameters and failure to differentiate processings. In order to establish a reliable predictive model for UD FRP properties based on fiber and resin properties by means of data mining, this paper created a mechanical property database of 203 kinds of FRPs and their constituents. Statistical tools were then applied to build and test structure-property correlation models. Results suggest that only longitudinal tensile modulus and longitudinal tensile strength can be credibly predicted, whereas the prediction of other six properties was quite unreliable or even infeasible. Overall, the study revealed that data mining, limited by incompleteness of data and complicated failure mechanisms, can only partially replace the actual testing of UD FRP properties.

An analytical micromechanics‐based multiscale model for the analysis of functionally graded nanocomposites

AbstractAn analytical multiscale model is presented in this article for the analysis of functionally graded nanocomposites. The multiscale scheme is composed of a microscale problem whose solution provides the constitutive model for the macroscale problem. For nanoparticle‐reinforced composites, the microscale problem consists of three phases, namely the nanoparticle, the matrix, and an interphase layer between the matrix and the nanoparticle. An analytical micromechanical model based on Green's function is employed to solve the triple‐phase microscale problem. The homogenized properties of the FG nanocomposite are determined by the micromechanical problem and used in the macroscale level, at every macroscopic material point in which the constitutive model is required. As an example, a nanocomposite beam under bending is considered as the macroscale problem which is investigated by classical, first‐order, and third‐order shear deformation theories. The results obtained from the presented method are compared with the relevant data for similar problems using various higher‐order elasticity theories. By comparing the results of higher‐order theories and those obtained by the presented multiscale method, the internal length parameter of the higher‐order theories is correlated to the volume fraction of the interphase layer between the nanoparticle and the matrix.

Correlation between grain boundary evolution and mechanical properties of ultrafine-grained metals

We put stiffness and strength of ultrafine-grained metals under scrutiny by means of experimental and analytical mechanics. Samples of Al 1050 were processed by Accumulative Roll Bonding (ARB) at different cycles to give ultrafine-grained microstructures. The microstructure, strength, and stiffness of the processed Al were analyzed by XRD and SEM. An analytical micromechanical model was developed to explain the predicted changes in the mechanical properties of the ultrafine-grained Al. It was revealed that an ultrafine-grained pure metal (e.g., Al) possesses a heterogeneous microstructure with the grain boundary stiffness lower than the grain/subgrain stiffness. This heterogeneous microstructure gave a decrease-after-increase behavior of the overall stiffness of Al during ARB. The grain boundary fraction of the microstructure increased from 1.9% after 2 cycles to 13.4% after 9 cycles of ARB. The stiffness decreased to 0.73 of its maximum value obtained after 2 cycles.With the aim of changing the stiffness and strength of the grain boundary, other samples were processed such that 4% SiC particles were added to Al sheets during the 1st-ARB cycle. The addition of SiC particles gave stiffer and stronger grain boundaries, which enhanced the overall stiffness and strength during ARB. Both the stiffness and strength were observed continuously increasing during ARB up to 484% and 793% after 9 cycles compared to the unprocessed Al, respectively.

Experimental and numerical investigation of reduction in shape distortion for angled composite parts

Controlling the fabrication process induced shape distortion in composite parts is a concern of composite industry and relevant researchers in the recent year. This study focused on the numerical as well as experimental investigation of the effect of addition of silica microparticles on the mechanical properties and the cured shape of glass/vinyl ester angled composite parts. UD glass fabric/ vinyl ester laminated composite parts were fabricated without and with the addition of silica microparticles. The thermal and mechanical properties of resin samples containing silica particles were characterised using Dilatometer and Universal Testing Machine. It was found that the addition of silica microparticles has reduced the thermal expansion coefficients (CTE) and increased the modulus of resin. These thermal and mechanical properties were then used as matrix properties for three-phase composite laminated parts. The analytical micromechanical model was used to determine the thermomechanical properties of composite lamina. The numerical investigations of spring-in in angled composite parts were performed on commercial FEA software, COMSOL Multiphysics® (v5.4). The experimental results showed that the angled part without any fillers had a higher spring-in value of 1.807°, while the other part having 5% fillers exhibited a lower spring-in value of 0.632° only. The numerical results were found to be in close agreement with the experimental results.

Multiscale analysis of the low-velocity impact behavior of ceramic nanoparticle-reinforced metal matrix nanocomposite beams by micromechanics and finite element approaches

An efficient multiscale analysis is proposed to investigate the dynamic behavior of metal matrix nanocomposite beams reinforced by SiC nanoparticles under low-velocity impact loads. First, an analytical micromechanics model is developed to obtain the effective elastic properties of ceramic nanoparticle-reinforced metal matrix nanocomposite, and then the finite element method is used to predict the dynamic response of beams made of this nanocomposite material. Two important microstructural features, including size effect and agglomeration of nanoscale particles, are incorporated into the micromechanical analysis. The present simulation results for the elastic modulus and low-velocity impact response show good agreement with previously published results. The effects of volume percent, diameter and dispersion type of ceramic nanoparticles, geometrical features and boundary conditions of nanostructure, velocity and size of projectile on the contact force, and center deflection time histories of metal matrix nanocomposite beams are extensively examined. Analysis shows that homogenously distributed SiC nanoparticles into the metal matrix nanocomposites can obviously increase the nanostructure/projectile contact force and decrease both the beam center deflection and impact duration which is due to the enhancement of elastic properties. However, the ceramic nanoparticle agglomeration has an effect on the decrease of contact force and the increase of both the center deflection and impact duration. Also, it is concluded that decreasing nanoparticle size can increase the contact force and decrease the beam center deflection.

Effects of nano-sized ceramic particles on the coefficients of thermal expansion of short SiC fiber-aluminum hybrid composites

Coefficients of thermal expansion (CTE) for short SiC fiber-reinforced aluminum matrix hybrid composites (AMHCs) containing nano-sized SiC particles are predicted through a novel multi-step micromechanics approach. The thermo-mechanical properties of aluminum matrix filled with SiC nanoparticles are extracted utilizing an analytical micromechanics model as a first step. These effective properties are then used in the Mori-Tanaka method to obtain the effective CTEs of AMHCs. The modeling of nanoparticle agglomeration often formed in real engineering situations, is accomplished using a nested method. The predictions of the developed micromechanical model are compared to experimental measurements available in the literature, and an acceptable agreement is observed between them. The effects of the volume fraction, diameter and agglomerated degree of SiC nanoparticles, and also the volume fraction and aspect ratio of SiC short fibers on the AMHC CTEs are investigated. In addition to randomly oriented fiber-reinforced AMHCs, modeling of the effective CTEs of aligned short fiber-reinforced AMHCs is performed. The results reveal that addition of nano-sized SiC particles reduces the CTE of short SiC-fiber-reinforced AMHCs. The decrease of particle size and increase of fiber aspect ratio also assist in improving the overall thermo-elastic properties of AMHCs. However, the presence of the ceramic nanoparticle agglomeration leads to increase the AMHC CTEs. According to the micromechanical analysis, it is found that the alignment of short fibers is an efficient method to reduce the AMHC CTEs.

Effect of carbon nanotube on cured shape of cross-ply polymer matrix nanocomposite laminates: analytical and experimental study

Cured shape of cross-ply [02/902]T fiber-reinforced composite laminates and the effect of multi-wall carbon nanotubes (MWCNTs) on the mechanical and thermal properties of laminates have been investigated. The nanocomposite laminate used in this study is composed of three phases: carbon fiber, polymer matrix and MWCNT. The volume fractions of 0%, 1%, 2% and 3% MWCNT were used to prepare nanocomposites. The mechanical and thermal properties of nanocomposites and fiber-reinforced nanocomposite laminates have been calculated by using analytical micromechanical models. Analytical micromechanical models were applied to determine the mechanical and thermal properties for two-phase nanocomposite composed of MWCNT and polymer matrix. The obtained mechanical and thermal data were considered as matrix properties and used in properties calculation of three-phase fiber-reinforced nanocomposite laminates. A developed model was used to determine curvature and the effect of MWCNT on the curvature in different specimens. Nonlinear relations have been considered for non-mid-plane strain equations. The addition of 1% volume fraction of MWCNT led to decreasing curvature and increasing critical size almost 14% and 9%, respectively, in different directions. The results were used to develop model and to compare with those calculated by Hyer model. Finally, unsymmetrical cross-ply [02/902]T laminates with different weight fractions of 0, 0.1%, 0.25% and 0.5% MWCNT were fabricated. The curvature of cured composite laminates, obtained by experimental study, was compared with that developed as Hyer models and good agreements were observed between the predicted model and experimental data. The experimentally predicted and developed model for the curvature of cross-ply [02/902]T fiber-reinforced nanocomposite laminates is better than the Hyer model.

Damage analysis of unidirectional Ti hybrid nanocomposites containing nanoparticles

In the present work, a nested micromechanical model is presented to analyze the biaxial initial damage envelopes of unidirectional silicon carbide (SiC) fiber-reinforced titanium (Ti) matrix hybrid nanocomposites containing SiC nanoparticles. Firstly, an effort is made to obtain the elastic modulus, yield strength and coefficient of thermal expansion (CTE) of the nanoparticle-reinforced metal matrix nanocomposites by developing an analytical micromechanical model. Size factor and agglomerated state for the nanoparticles into the metal matrix, generation of dislocations by nanoparticle/matrix thermal mismatch and Orowan strengthening mechanism are considered at the nanoscale. Then, a unit cell-based micromechanical model is proposed to extract the biaxial initial damage envelopes of the SiC nanoparticle/SiC fiber-reinforced metal matrix hybrid nanocomposites. The Fiber/matrix interfacial debonding and matrix yielding are included as the dominant damage modes. Also, thermal residual stress (RS) arisen from the fiber/matrix thermal mismatch during the MMC manufacturing process are considered in the analysis. A reasonable agreement is observed between the results of the present model and available experiments for both of the nanocomposite and hybrid nanocomposite thermomechanical properties. It is shown that the SiC nanoparticles are indeed a very effective strengthening agent for the MMCs which can postpone the deterioration initiation due to the interfacial debonding under transverse tension. The presented model is applied to examine the effects of several parameters, including the nanoparticles volume fraction, diameter, size factor and dispersion type and also the thermal mismatch and fiber/matrix interfacial conditions on the biaxial initial damage behavior of the metal matrix hybrid nanocomposites.