Micromechanical Approach Research Articles

Modeling the interfacial failure and resulting mechanical properties of z-pinned additively manufactured composites

The mechanical properties of Fused Filament Fabrication (FFF) parts are limited in the build direction, albeit advantages such as design flexibility and in-house customization. In this paper, a novel z-pinning approach that enhances mechanical properties in the build direction by depositing material across multiple layers within the part was investigated through numerical simulations and validated experimentally. A finite element model for z-pinned composite structures was developed by assigning fiber-orientation dependent material properties obtained using a micromechanics approach to beads and pins. The bead-to-bead and pin-to-pin adhesions within the z-pinned structures were modeled using a cohesive traction separation law. The properties of cohesive elements for carbon fiber-reinforced polylactic acid (CF-PLA) z-pinned composites were calibrated using tensile experiments. The elastic modulus and tensile strength of CF-PLA z-pinned composites in the build direction were predicted with the developed numerical model. The numerical investigation on various geometrical parameters revealed that the largest pin volume increases the stiffness and tensile strength by 40% and thus, has the greatest influence on the mechanical properties of the z-pinned composites. The effect of z-pin geometrical parameters on the mechanical properties was summarized to aid in the design of z-pinned additively manufactured composite structures.

Micromechanical controls on the brittle-plastic transition in rocks

SUMMARYThe rheology of rocks transitions from a cataclastic brittle behaviour to plastic flow with increasing pressure and temperature. This brittle-plastic transition is empirically observed to occur when the material strength becomes lower than the confining stress, which is termed Goetze’s criterion. Such a criterion works well for most silicates but is not universal for all materials. We aim to determine the microphysical controls and stress–strain behaviour of rocks in the brittle-plastic transition. We use a micromechanical approach due to Horii and Nemat-Nasser, and consider representative volume elements containing sliding wing-cracks and plastic zones. We find solutions for frictional slip, plastic deformation and crack opening at constant confining pressure, and obtain stress–strain evolution. We show that the brittle-plastic transition depends on the confining stress, fracture toughness and plastic yield stress but also critically on the friction coefficient on pre-existing defects. Materials with low friction are expected to be more brittle, and experience transition to fully plastic flow at higher pressure than anticipated from Goetze’s criterion. The overall success of Goetze’s criterion for the brittle-plastic transition in rocks is likely arising from the low toughness, high strength and medium friction coefficient character of most rock forming minerals.

Nonlinear static and dynamic (deflection/stress) responses of porous functionally graded shell panel and experimental validation

The static and dynamic characteristics of functionally graded (FG) structures have been investigated in this article, considering full geometrical nonlinearity. The finite element (FE) solutions are obtained for the graded panel by modelling through higher-order kinematics (HSDT) and Green-Lagrange strain-displacement relations (GLNST). The desired graded panel properties are obtained through Voigt’s micromechanical approach, considering different grading patterns (exponential, EPL; sigmoid, SGM and power law, POL). Additionally, to maintain the generality of the graded structure, different porosity distribution types (even and uneven, EVP and UEP) are incorporated into the proposed mathematical model. Further, the numerical solutions are obtained using Newmark’s method’s direct iterative technique and constant integration steps. The solution sensitivities are verified for the developed algorithm via adequate convergence and comparison tests. In addition, the experimental validation is performed using the layerwise fabricated luffa-fibre reinforced FG plates to validate the proposed theoretical model’s accuracy. Lastly, the responses are computed using the newly derived model for the variable design-dependent parameters associated with the FG structural geometry and properties. The final deliverables, that is the nonlinear deflection responses (NDFR)/stress values, are discussed under mechanical loadings (static and dynamic).

A cuboidal open cell model for constitutive modeling of surface effects in fluid-saturated porous materials

Fluid-saturated porous elastic materials, made up of connected networks of solid ligaments and characteristically having open pores, are commonly found in geological, biological and engineering materials. Surface effects can affect significantly the mechanical performance of such porous materials at macro scale, especially when the solid ligaments and the pores have micro or nano scale sizes. In the present study, in order to explicitly link pore-level geometrical parameters and surface effects with effective poroelastic properties as well as constitutive equations governing poroelastic deformation, we combine the top-down homogenization approach presented a previous study (Chen et al., 2021) with the bottom-up micromechanics approach. Inspired by the Gibson-Ashby cubic cell model for open-cell foams and the cellular networks typically found in fluid-saturated porous materials, we propose a cuboidal open cell model, with surface effects and fluid compressibility accounted for. For two limiting cases, i.e., the undrained state and the drained state, we demonstrate that both the surface moduli and residual surface stress (i.e., surface tension) prevent the deformation of solid ligaments, thus stiffening the porous material with enlarged effective Young's moduli. Further, we reveal that the two surface effect parameters (i.e., residual surface stress versus surface moduli) exhibit a coupling effect on effective moduli: when one parameter is large enough, the variation of the other affects significantly the effective moduli. As applications of the proposed model, we characterize mechanical behaviors of the porous material under typical loadings (e.g., uniaxial and non-proportional multiaxial tension) in both undrained and drained states; we also describe, for the first time, the stress concentration of a compressible liquid inclusion (e.g., a cell) with surface tension embedded in a fluid-saturated porous material with surface effects. Results of this study are beneficial for understanding and investigating how surface effects influence the poroelastic parameters of fluid-saturated porous materials having sufficiently small open pores.

Experimental and theoretical studies of effective piezoelectric coefficients of 2-2 connectivity AlN/AlScN composite piezoelectric films

Aluminum nitride (AlN) and Sc-doped AlN have become the most popular piezoelectric thin-film materials in the fields of RF and smart sensing. AlN/AlScN composite films based on 2-2 connectivity exhibit stronger interaction and better lattice matching between AlN and AlScN, resulting in improved nucleation, growth kinetics, crystal quality, piezoelectric response, and surface morphology. In this work, a method for predicting the effective coefficients of AlN/AlScN composite piezoelectric thin films is proposed and validated. This prediction method is based on first-principles calculations, the Reuss model theory, and the Mori-Tanaka (MT) method. It also conforms to the mean strain and stress theory of the micromechanical approach. The precise compliance, dielectric and piezoelectric properties (Sij, ε, dij) of AlN/Al0.8Sc0.2N composite film with different thickness ratios are calculated. Through the deflection measurement of piezoelectric cantilever with proof mass based on AlN/Al0.8Sc0.2N composite film, the experimental piezoelectric stress coefficient (d31) is calculated. The correctness of the prediction method is verified by comparing the theoretical calculation (d31* = −3.1pC/N) and experimental data (d31 = −3.4pC/N), showing excellent agreement within experimental error. Meanwhile, the voltage sensitivity of the accelerometer is significantly enhanced by the AlN/AlScN composite piezoelectric film. It is believed that this work will broaden the theoretical study and application of the AlN/AlScN composite piezoelectric film.

Mechanical Homogenization of Transversely Isotropic CNT/GNP Reinforced Biocomposite for Wind Turbine Blades: Numerical and Analytical Study

One of the biggest problems facing the use of carbon nanotubes in reinforced composites is agglomeration within the matrix phase. This phenomenon—caused by Van der Waals forces—leads to dispersion problems and weakens the properties of the composites. This research presents a multi-stage homogenization approach used to investigate the influence of the aspect ratio, volume fraction, and agglomeration of the nanofillers on the effective mechanical properties of a polymer biocomposite containing randomly dispersed carbon nanotubes and graphene nanoplatelets. The first stage consisted in evaluating the properties of the reinforced polymers by the CNT/GNP. The second step consisted in combining the reinforced polymers with different natural and synthetic unidirectionally oriented fibers. It was found that agglomeration has a huge influence on the mechanical properties of the composite. The novelty of this work consisted of the consideration of the parameters influencing the elastic properties using different micromechanics approaches and numerical techniques.

Wave Dispersion Behaviors of Multi-Scale CNT/Glass Fiber/Polymer Nanocomposite Laminated Plates.

In this paper, wave propagation in multi-scale hybrid glass fiber (GF)/carbon nanotube (CNT)/polymer nanocomposite plates is studied for the first time by means of refined higher-order plate theory. The hybrid nanocomposite consists of CNTs and glass fibers (GF) as reinforcing components distributed within a polymeric matrix. A hierarchical micromechanical approach is used to predict the effective mechanical properties of the hybrid nanocomposite, including the three-dimensional (3D) Mori-Tanaka method and the rule of mixture. Moreover, a refined-type higher-order shear deformation theory (HSDT) is implemented to take into account the influence of the shear deformation on the motion equations of the system. Then, the governing equations are achieved on the basis of the energy-based Hamilton's principle. Finally, the derived equations will be solved analytically for the purpose of extracting the natural frequency of the continuous system. A set of numerical examples are provided to cover the effects of various parameters on the wave dispersion characteristics of the plate. It can be declared that the hybrid nanocomposite system can achieve higher wave frequencies compared with other types of composite structures. Additionally, it is found that the selection of the lay-ups and length-to-diameter ratio plays a significant role in the determination of the sandwich plate's acoustic response.

Exact solution of Eshelby's inhomogeneity problem in strain gradient theory of elasticity and its applications in composite materials

A new micromechanical approach to deal with the problem of Eshelby's inhomogeneity is developed for the prediction of the effective properties of composite materials according to the strain gradient elasticity theory. The method is based on the Green's function technique leading to an integral equation of the heterogeneous elastic problem. Within the simplified strain gradient elasticity theory, the integral equation for an infinite heterogeneous medium subjected to non-homogeneous boundary conditions is acquired. Thanks to this integral equation, the exact solution of Eshelby's inhomogeneity problem is detailed for spherical inhomogeneity and isotropic elastic behavior. From the expression of strain localization relations, the effective elastic properties of a two-phase composite material are then predicted through Mori Tanaka's homogenization scheme. To test the relevance of the suggested approach, its predictions are compared with results issued from some reference models and experimental data.

Computer Simulation of Composite Materials Behavior under Pressing.

Composite materials have a wide range of functional properties, which is ensured by using various technological methods of obtaining both the matrix or fillers and the composition as a whole. A special place belongs to the composition formation technology, which ensures the necessary structure and properties of the composite. In this work, a computer simulation was carried out to identify the main dependencies of the behavior of composite materials in the process of the main technological operations of their production: pressing and subsequent sintering. A polymer matrix randomly reinforced with two types of fillers: spherical and short cylindrical inclusions, was used to construct the finite element models of the structure of composites. The ANSYS Workbench package was used as a calculation simulation platform. The true stress-strain curves for tension, Poisson's ratios, and ultimate stresses for composite materials were obtained using the finite element method based on the micromechanical approach at the first stage. These values were calculated based on the stretching diagrams of the matrix and fillers and the condition of the ideality of their joint operation. At the second stage, the processes of mechanical pressing of composite materials were modelled based on their elastic-plastic characteristics from the first stage. The result is an assessment of the accumulation of residual strains at the stage before sintering. The degree of increase in total strain capability of composite materials after sintering was shown.

Micromechanical Approach to Predict Mechanical Properties of Particulate-Dispersed Composites with Dissimilar Interfacial Phases

The mechanical properties of composites are affected by their constituents. For the development of high-performance composites, it is expected that a technique will be developed which can predict the mechanical properties of composites based on the mechanical properties of their constituents. This study developed a technique based on a micromechanical approach to predict the mechanical properties of composites with interfacial phases between reinforcements and matrix. A double-inclusion model (Hori and Nemat-Nasser, 1993) is effective for the solution of such problems, of which the validity remains unclear. Problems with a particle surrounded by an interfacial phase embedded in an infinite body were calculated via the model and finite element analysis to verify the model. It was found that the macroscopic average stress of the double inclusion could be accurately solved by the model, although the microscopic stress of each phase could not be calculated with high accuracy. Therefore, a micromechanical approach based on the model was formulated and applied to particulate-dispersed composites consisting of zirconia and titanium, and fabricated by spark plasma sintering, in which Ti oxides were created along the interface between zirconia and titanium. As a result, the elastic-plastic stress–strain curves of the composites could be predicted. The approach can investigate the mechanical properties of composites with various shapes of reinforcement surrounded by dissimilar materials in a matrix. It can be concluded that the approach is promising for the development of composites with an excellent mechanical performance.

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.

Modelling of 3D-printed bio-inspired Bouligand cementitious structures reinforced with steel fibres

Latencies and limitations exist in the simulation of bio-inspired structures or highly complex geometries manufactured by digital concrete fabrication. This study develops a computational framework to portray the anisotropic material attributes and predict the crack patterns of hardened 3D printed fiber-reinforced concrete beams. Bio-inspired Bouligand structures printed with four pitch angles of 0˚, 15˚, 30˚, and 45˚ are adopted to validate the numerical model. Extensive experiments, including uniaxial compressive tests, splitting tensile tests, and three-point bending tests, are conducted. The material model is attained from the samples extracted from the printed concrete blocks with and without steel fibres after a 28-day curing age for an accurate representation of the design and process. The micromechanical modelling approach is employed to obtain the homogeneous materials for the macro-scale model. The finite element (FE) analysis provides sound agreement with the experiment results of both stress–strain curves and crack patterns. In addition, under bending loading, the 3D printed beams with a unidirectional printing pattern or a small pitch angle perform better than those with larger pitch angles.

Creep-fatigue properties of austenitic cast iron D5S with tension and compression dwell: A dislocation density-based crystal plasticity study

To predict and better understand the creep-fatigue behaviour of austenitic cast iron D5S under tension and compression dwell at 800∘C, a physics-based crystal plasticity model that describes the complex rate- and temperature-dependent deformation of the material as a function of the dislocation density is implemented. In addition to the tension and compression dwell direction, the effect of three different dwell times (30, 180 and 600 s) on the creep-fatigue properties is investigated. The dislocation density-based crystal plasticity simulations are compared to experimental tests from a prior work. While relaxation tests and low-cycle fatigue (LCF) tests without dwell assist in systematically identifying the material parameters, creep-fatigue (CF) data is used to validate the predictions. The virtual testing is performed on a large-scale representation of the actual test specimen with a polycrystalline structure. To analyse the fatigue damage mechanism, small-scale predictions are also conducted using a micromechanical unit cell approach. Here, a single graphite nodule frequently found in the material is embedded into the austenitic matrix. In the present work, a close agreement is achieved between the predicted CF behaviour and the experimental results. Consistent with the experimental findings, the simulation results show that the addition of compression dwell leads to an uplift of the overall tensile stress level, which significantly reduces the fatigue life of the material. The unit cell studies demonstrate that during this uplift, a strong localisation of stresses and strains arises at the graphite/matrix interface, triggering the nucleation and growth of cavities and/or debonding.

Elastic Properties of Jute Fiber Reinforced Polymer Composites with Different Hierarchical Structures.

A two-stage micromechanics technique is used to predict the elastic modulus, as well as the major and minor Poisson’s ratio of unidirectional natural fiber (NF) reinforced composites. The actual NF microstructure consists of cellulose, hemicellulose, lignin, lumen, etc., and these constituents and their contributions are neglected in classical models while quantifying their mechanical properties. The present paper addresses the effect of the real microstructure of the natural jute fiber (JF) by applying a micromechanics approach with the Finite Element Method. Six different hierarchically micro-structured JFs are considered to quantify the JF elastic properties in the first level of homogenization. Later, the JF reinforced polypropylene matrix properties are investigated in the second stage by adopting a homogenization approach. Taking into account the different hierarchical structures (HS), the fiber direction modulus (E1), transverse modulus (E2 and E3), in-plane and out-of-plane shear modulus (G12 and G23), and major (ν12, ν13) and minor (ν23, ν21) Poisson’s ratios are estimated for JF and JF reinforced polypropylene composites. The predicted elastic modulus from micromechanics models is validated against the analytical results and experimental predictions. From the present work, it is observed that the HS of NF needs to be considered while addressing the elastic properties of the NF-reinforced composite for their effective design, particularly at a higher volume fraction of NF.

A combinatorial approach to the elastic response of electrospun mats: Architectural framework and single fiber properties

Electrospun is a unique class of porous and heterogeneous materials with multi-length-scales constituents that offer a rich variety of surface functionalities to serve a host of applications. Upscaling the electrospun materials from the laboratory to the industry is often limited by the lack of understanding of their mechanical properties. Herein, we developed a theoretical framework to predict the elastic constants of the electrospun mats that hinges on the concept of elastic properties of constituent fibers, three-dimensional (3D) alignment of fibers, and local fiber curvature. Enabled by continuum-based micromechanical approaches, this framework successfully predicted the elastic moduli regardless of bead-string morphology and local architectural heterogeneities present within the electrospun mats. The 3D fiber orientation distribution obtained using X-ray nano-computed tomography (nanoCT) analysis served as a key input for the validation of the analytical model. In general, the predicted elastic moduli are in reasonably good agreement with the experimental data of randomly oriented and preferentially aligned polylactic acid (PLA)-based electrospun mats. To demonstrate our analytical model's versatility and reliability, another set of PA6(3)-based electrospun mats has been chosen from the literature for validation purposes. The parametric analysis has been performed to provide a roadmap to improve the elastic moduli of electrospun mats and justify the assumed values of some of the key attributes.

Exact second moments of strain for composites with isotropic phases

In micromechanical approaches to failure prediction of inhomogeneous microstructures or homogenization of inelastic materials, local field fluctuations beyond the mean field are relevant, but not easily accessible except for resorting to full-field simulations. However, any analytical estimate of the effective strain energy density combined with the Hill–Mandel condition implies some information about the probability distributions of local fields such as stresses and strains. In this paper, analytical equations for the second moments of local fields are derived for particulate composites with isotropic phases. Explicit expressions are provided using the Mori–Tanaka approach, the Hashin–Shtrikman bounds and the singular approximation. The results are compared to full-field simulations of a random sphere assemblage. As the Hashin–Shtrikman covariance is isotropic, it is not well-suited for predicting the behavior under deviatoric loadings. The singular approximation and Mori–Tanaka methods yield sensible approximations for the second moment of matrix strain.

Integrated multi-scale modeling of variant selection during stress-induced martensite formation in metastable β Ti-alloys

Stress-induced martensite formation is the predominant mechanism during the deformation of various functional and structural Ti- alloys. To predict the performance of these alloys, stress-induced martensite formation was modeled as a function of crystal orientation and stress state. We present an integrated micromechanical modeling approach using finite element (FE) analysis and an elastic spectral solver based on Fast Fourier Transforms (EFFT), which allows direct correlation of the available work from martensite formation under complex stress-states in an in-situ characterized microstructure. The model is applied as a virtual analogue of an experimental 3-point bending test of a metastable β Ti–10V–2Fe–3Al alloy containing 5% α. The FE model incorporates the experimental β microstructure from electron backscattering diffraction (EBSD) with anisotropic elastic behavior. The EFFT solver uses strain fields in two local regions from the FE model to predict local stresses in experimental microstructures containing β and α phases. The stress and orientation data are used to predict the available work from stress-induced α″ martensite formation of the six different α″ variants. It was found that stress and available work concentrated around the tips of lamellar α, making these regions preferred nucleation sites for α″ formation, which is in excellent agreement with the in-situ experimental observations. This suggests that the local stress conditions in the β phase play a more important role in triggering α″ formation than the compositional inhomogeneity in the β phase at α-β interfaces. Using the integrated model, the first variants forming at low levels of deformation could be confidently predicted. However, the transformation behavior at elevated levels of deformation could not be properly captured. This indicates the need of further model improvement, including Dirichlet boundary conditions for the EFFT solver and accounting for the role of plasticity induced by phase transformation.

Numerical study of starch-gluten dough: Deformation and extrusion

Numerical investigation of starch-gluten model was conducted using composite micromechanics approach, which considered starch as circular filler embedded/surrounded by gluten matrix. The model developed was then compared with different starch-gluten models reported in literatures. The starch-gluten circular filler model simulations with different starch-filler diameters showed consistent results with the dough microstructure model, which suggested that the model can be used for dough process simulation, such as extrusion-based printing. Using similar approach, the extrusion model was then developed using billet representing starch-gluten dough being forced through the barrel with dies at different entry angles and ram extrusion speeds. Reducing the entry angles increased the extrusion force due to viscoelastic behaviour of dough. Likewise, a similar increased force results were obtained when the extrusion speeds were increased. • Starch-gluten model results is consistent with the dough microstructure model. • Extrusion speed and nozzle entry angle are important in dough 3D printing process. • The shape of different starch influenced the stress-strain behaviour of dough.

Multiscale Recursive Micromechanics of Three-Dimensional Woven Composite Thermal Protection Materials Thermal Conductivities

Multiscale micromechanics predictions have been made for effective thermal conductivities and local thermal fields for a novel three-dimensional woven composite thermal protection system material. The multiscale recursive micromechanics approach, which enables micromechanics models to call other micromechanics models (or themselves recursively) to consider finer and finer length scales, has been employed. The multiscale model uses a recently developed version of the high-fidelity generalized method of cells micromechanics theory at each of three length scales. The results focus on the impact of the microstructural geometry representation at each length scale on the material’s effective thermal conductivity, along with the local thermal flux and temperature fields induced in the microstructures.

A micromechanical approach to elastic modulus of long-term aged chicken feather fibre/poly(lactic acid) biocomposites

Abstract The modulus of elasticity is a critical parameter for the performance design and analysis of biofibre-based biocomposite materials. As a result of criteria such as internal heterogeneity, the random distribution of fibres and the success of interfacial adhesion between the fibre and the matrix, it becomes difficult to predict the modulus of elasticity in practical ways. Therefore, one of the aims of this study is to determine the modulus of elasticity of biocomposite material reinforced with discontinuous and random fibres by means of micromechanical models and experimentally. In addition, it is also aimed to reveal which micromechanical model can be used reliably in predicting the modulus of elasticity of both aged and non-aged biocomposite materials due to the relationship between the analytical and experimental results. In order to achieve these objectives, initially, chicken feather fibre/poly (lactic acid) biocomposite specimens having 2, 5 and 10 % chicken feather fibre mass fractions were mixed and manufactured by extruding, and subsequently, tensile test specimens according to the appropriate standard were formed by the injection-moulding method. An agreement between the moduli of elasticity obtained from 6 micromechanical models and experimentally from the slope of the stress–strain curves resulting from tensile tests was determined.