Micromechanical Approach Research Articles

Micro-mechano-morphology-informed continuum damage modeling with intrinsic 2nd gradient (pantographic) grain–grain interactions

In a previous work, we have shown that a granular micromechanics approach can lead to load path dependent continuum models. In the present work, we generalize such a micromechanical approach introducing an intrinsic 2nd gradient energy storage mechanism (resembling pantographic micromechanism), in the grain–grain interaction. Such a mechanism, represents long-range effects but could also be thought as deriving from the utilization of an actual pantographic connection between two grains in a granular metamaterial. Taking advantage of the homogenization approach developed in previous works, we determine the mechanical behavior of the macro-scale continuum and carry out parametric analyses with respect to the averaged intergranular distance and with respect to the stiffness associated to the pantographic term. We show that with the inclusion of the pantographic term mentioned above, the desired thickness of the localization zone can be modeled and finely tuned successfully. We also show that the complex mechanics of load-path dependency can be predicated by the micromechanical effects and the introduced pantographic term.

Free vibration analysis of three-phase CNT/polymer/fiber laminated tow-steered quadrilateral plates considering agglomeration effects

This paper introduces a numerical model for predicting the properties of the tow-steered three-phase CNT/polymer/fiber composition. The free vibration of laminated quadrilateral plates is addressed. The behavior of the matrix reinforced with the carbon-nanotube (CNT) additive is calculated based on the Eshelby–Mori–Tanaka micromechanics approach. The approach considers the probable agglomerated CNT phases in the mixture. Every lamina of the laminate is assumed to be constructed by the curvilinear fiber arrangement dipped in the nanocomposite matrix. The fiber placement paths follow smooth orientation angle changing routes. Several homogenization techniques are presented in detail to evaluate the overall properties of the tow-steered three-phase CNT/polymer/fiber laminate. The principle of virtual work based on the first-order shear deformation plate theory is implemented through the NURBS isogeometric analysis method. Some representative results are obtained and compared with those available in the literature to demonstrate the quality of the proposed formulation. The effects of problem variables including the layup, mixture quality, boundary condition, and micromechanical model on the free vibration behavior are investigated by performing parametric studies.

Multiscale viscoplastic modeling of recycled glass fiber-reinforced thermoplastic composites: Experimental and numerical investigations

One of the main challenges facing fiber-reinforced polymer composites is the lack of options for end-of-life recycling. The environmental impact of waste materials disposed of at landfill sites, by incineration, or by erratic dispersion in the environment is accelerating the need to find innovative solutions to increase the value of recycled materials. This research aims to investigate the relationship between microstructural parameters and the mechanical properties of a recycled thermoplastic composite material. The latter is processed by thermocompression molding of a polyamide (PA66) matrix reinforced with chopped glass strands. An innovative approach is proposed to link the local microstructure of the composite to the mechanical behavior of the recycled material. It exploits an experimental characterization of the material microstructure using optical microscopy and X-ray micro-computed tomography (mCT). The experimental findings are implemented into a numerical modeling strategy to mimic the flexural behavior, based on a micromechanical approach coupling mean and full-field analysis. The region of interest is reconstructed from detailed 3D images using a modified random sequential adsorption (MRSA) algorithm, while other regions are modeled as homogenized macro-scale continua. Furthermore, the abilities of the proposed approach are proven by incorporating the viscoplastic behavior of the random heterogeneous material induced by the polymer matrix. The originality of the present research consists of the multi-scale FE analysis and the experimental validation for the viscoplastic behavior of the recycled composite material, taking into account influences from the microstructure.

An Experimentally Based Micromechanical Framework Exploring Effects of Void Shape on Macromechanical Properties.

A micromechanical simulation approach in a Multi-Scale Modeling (MSM) framework with the ability to consider manufacturing defects is proposed. The study includes a case study where the framework is implemented exploring a cross-ply laminate. The proposed framework highlights the importance of correct input regarding micromechanical geometry and void characteristics. A Representative Volume Element (RVE) model is developed utilizing true micromechanical geometry extracted from micrographs. Voids, based on statistical experimental data, are implemented in the RVE model, and the effects on the fiber distribution and effective macromechanical properties are evaluated. The RVE algorithm is robust and maintains a good surrounding fiber distribution around the implemented void. The local void fraction, void size, and void shape affect the effective micromechanical properties, and it is important to consider the phenomena of the effective mechanical properties with regard to the overall void fraction of an RVE and the actual laminate. The proposed framework has a good prediction of the macromechanical properties and shows great potential to be used in an industrial implementation. For an industrial implementation, weak spots and critical areas for a laminate on a macro-level are found through combining local RVEs.

Multi-scale in situ mechanical investigation of the superelastic behavior of a Cu–Al–Be polycrystalline shape memory alloy

The superelastic behavior of a Cu–Al–Be alloy was studied in situ during tensile tests combining two high-energy synchrotron techniques. The initial microstructure was reconstructed using diffraction contrast tomography; the elastic strain and stress tensors of each individual grain were then determined using a 3D X-ray diffraction microscopy technique. The alloy was heat-treated until coarse grains formed, and the probed volume fraction was limited to ∼ 200 grains. The mean grain size, as estimated from both techniques, agreed well with that determined by optical microscopy, i.e., approximately 130 µm. During the early stage of the martensitic transformation (MT), 187 grains with strong stress heterogeneities were detected in the elastic domain; in particular, the stress values along the tensile direction varied by a factor of three between different grains. The reconstructed 3D microstructure served as input data for finite element modeling, wherein a micromechanical approach factoring in the martensitic transformation was used to simulate the in situ tensile tests. The coupled numerical and experimental tensors of the 187 grains confirmed strong stress heterogeneities between them. The influence of the position and crystallographic orientation of the neighboring grains were also examined.

Impact of Micromechanical Approaches on Wave Propagation of FG Plates via Indeterminate Integral Variables with a Hyperbolic Secant Shear Model

The aim of this paper is to analyze the impacts of micromechanical approaches on the wave propagation of a functionally graded (FG) plate via indeterminate integral variables with hyperbolic secant shear displacement models. This model is established based on a high-order theory and a new displacement field with four unknowns introducing indeterminate integral variables with a secant hyperbolic shear function. Six micromechanical approaches are applied to approximate the effective material properties of an FG plate, namely Voigt’s model, Reuss’ model, Hashin–Shtrikman’s lower, and upper bound models, Tamura’s model, and the LRVE model. The volume fractions are supposed to change corresponding to the power-law and sigmoid. By applying Hamilton’s principle, general formulae of the wave propagation were obtained to get the wave modes and phase velocity curves of wave propagation in FG plates, with the impact of Voigt’s, Reuss’, Hashin–Shtrikman’s bounds, Tamura’s, and LRVE explicit micromechanical models.

Adaptable Optical Microwaveguides From Mechanically Flexible Crystalline Materials.

Flexible organic crystals (elastic and plastic) are important materials for optical waveguides, tunable optoelectronic devices, and photonic integrated circuits. Here, we present highly elastic organic crystals of a Schiff base, 1-((E)-(2,5-dichlorophenylimino)methyl)naphthalen-2-ol (1), and an azine molecule, 2,4-dibromo-6-((E)-((E)-(2,6-dichlorobenzylidene)hydrazono)methyl)phenol (2). These microcrystals are highly flexible under external mechanical force, both in the macroscopic and the microscopic regimes. The mechanical flexibility of these crystals arises as a result of weak and dispersive C-H⋅⋅⋅Cl, Cl⋅⋅⋅Cl, Br⋅⋅⋅Br, and π⋅⋅⋅π stacking interactions. Singly and doubly-bent geometries were achieved from their straight shape by a micromechanical approach using the AFM cantilever tip. Crystals of molecules 1 and 2 display a bright-green and red fluorescence (FL), respectively, and selective reabsorption of a part of their FL band. Crystals 1 and 2 exhibit optical-path-dependent low loss emissions at the termini of crystal in their straight and even in extremely bent geometries. Interestingly, the excitation position-dependent optical modes appear in both linear and bent waveguides of crystals 1 and 2, confirming their light-trapping ability.

Stiffness and stress fluctuations in dental cement paste: a continuum micromechanics approach

Calcite-reinforced hydrates provide the superior mechanical properties of Biodentine, a cementitious material used in dentistry. Herein, a self-consistent micromechanics model links two nanoindentation-probed, lognormally distributed microstiffness distributions of infinitely many hydrate phases, to the material’s macrostiffness, quantified from longitudinal and transverse ultrasonic wave transmission experiments. Thereby, the model provides values for the Poisson’s ratio of the hydrates and for a microcrack density reflecting grain boundary defects. Moreover, the model-predicted hydrate microstresses turn out as beta-distributed, while the overall stiffness can be equally well upscaled from only two, piecewise uniform, hydrate phases exhibiting median microstiffness values. Highlights Grid nanoindentation provides lognormal distributions of hydrate stiffness They enter a microelastic model for dental cement paste This model considers grain boundary defects as isotropically-oriented closed cracks It provides micro-stress fluctuations resulting from hydrate stiffness distributions Median values of hydrate stiffness govern the overall paste stiffness

Elastic modulus and Poisson’s ratio of graphene nanoplatelet/glass fiber-reinforced polymer hybrid composites subjected to off-axis loading

Effective elastic properties of the graphene nanoplatelet (GNP)/unidirectional glass fiber (GF)-reinforced polyimide composites subjected to off-axis loading are predicted using a closed-form hierarchical micromechanical approach. The effects of volume fraction, agglomeration and non-flat structure of GNPs, graphene/polymer interfacial region, and fiber volume fraction on the off-axis elastic modulus and off-axis Poisson’s ratio are investigated. In order to verify the accuracy of the present micromechanical method, predictions are compared with the experimental data. Adding GNPs into the polymeric resin increases the elastic modulus of all off-axis coupons. When flat GNPs are uniformly dispersed in the polyimide resin, much more improvement in the off-axis elastic properties is achieved. The results indicate that agglomeration and non-flat structure of the GNP can drastically decrease the off-axis elastic modulus. It is observed that the off-axis elastic response of hybrid composites may be sensitive to the material property and thickness of the interfacial region.

Time-dependent creep fatigue damage evolution in C/SiC composite: Theory and analytical prediction

In this paper, the time-dependent damage evolution in carbon fiber-reinforced silicon carbide ceramic-matrix composites (C/SiC CMCs) under creep fatigue loading at elevated temperature was analyzed using a micromechanical approach. Synergistic effects of creep fatigue peak stress level and damage in the matrix and the interface on time-dependent damage evolution in C/SiC composites were analyzed. Next, relationships of time-dependent creep fatigue damage mechanisms, damage parameters, environmental temperature and duration were determined. Then, the effects of composite constituent properties, creep fatigue damage state, environmental temperature, and duration on time-dependent damage evolution in C/SiC composites were analyzed. Furthermore, time-dependent composite strain response and interface debonding and oxidation state in C/SiC composite under different creep fatigue peak stress levels were predicted. Under creep fatigue loading, the composite internal damage evolution contributed to the increased time/temperature-dependent composite peak strain. Hysteresis-based damage parameters were developed and utilized to monitor C/SiC composite internal damage evolution. Under creep fatigue loading, the hysteresis area and width increased with oxidation duration to a peak value and remained constant, and the hysteresis modulus decreased with oxidation duration.

Investigations of fatigue crack propagation in ER8 railway wheel steel with varying microstructures

In this study, fatigue crack occurrences and propagations of high-speed railway wheel steel grade ER8 were investigated through both experiments and FE simulations. Three varying microstructures of the wheel steel including as-received, ferrite- and bainite-containing microstructures, which were obtained by specific heat treatment routes, were characterized. Stress-controlled fatigue tests were carried out for determining relationships between crack propagation rate and stress intensity factor of the steels. In addition, FE simulations of fatigue crack developments on both macro- and micro-scale using representative volume element (RVE) 2D models were conducted with consideration of microstructural features. The extended finite element method (XFEM) coupled with the Paris law was applied in the cyclic simulations for predicting crack propagation. For the microstructure level, flow stress-strain curves based on micromechanics approach and corresponding fatigue damage parameters of different phases in steels were identified and afterwards calibrated with experimental results. Finally, influences of ferrite, pearlite and bainite on fatigue crack resistance in the wheel steel were precisely examined by the RVE model. It was found that fatigue micro-cracks mostly initiated close to interface regions between soft and hard phases. The bainitic phase could obviously retard fatigue crack propagation of steel, whereas the ferritic phase contrarily exhibited deteriorated crack resistance. Moreover, the proposed framework could be acceptably employed for predicting fatigue crack propagation behavior and its rate in railway wheel subjected to microstructure changes occurred.

A combined experimental and micromechanical approach to investigating PTC and NTC effects in CNT-polypropylene composites under a self-heating condition

The present study proposed a combined experimental and micromechanical approach to investigating positive temperature coefficient (PTC) and negative temperature coefficient (NTC) effects in carbon nanotube (CNT)-polypropylene composites under a self-heating condition. The electrical and heating performance of the composites were investigated by electrical conductivity measurements and self-heating tests with various input voltages. The test results showed that composites with a CNT content of 5.0 wt.% exhibited excessive heat generation, showing a transition of the PTC effect to the NTC effect. Moreover, a micromechanical modeling was proposed to predict the occurrence of the PTC and NTC effects in the composites, considering various distances between CNTs and wavinesses of CNT. The change of the distance between CNTs under a heating condition was estimated, using the molecular dynamics software Material studio. Comparisons between the predictions and the experimental results were made to show the applicability of the proposed modeling scheme.

Stochastic fatigue life prediction in C/SiC composites at elevated temperature by micromechanics-based damage model

In this paper, a micromechanical approach is developed to predict the fatigue life and fracture process in different C/SiC composites subjected to different stochastic fatigue loading spectrums at elevated temperatures. Three types of stochastic fatigue load spectrums are considered in the fatigue life prediction at elevated temperature, that is, constant, increasing, and decreasing stochastic stress with cycles. Stress distribution between intact and broken fibers and the broken fibers fraction under stochastic fatigue loading spectrum are determined using the Global Load Sharing criterion considering multiple fatigue damage mechanisms at elevated temperatures. A new damage parameter of fatigue life degradation rate is developed to characterize the effect of stochastic loading on fatigue damage and fracture in C/SiC composites. Relationships between stochastic fatigue loading spectrum, broken fibers fraction, fatigue life, and fatigue life degradation rate in different C/SiC composite are established. Effects of stochastic fatigue loading spectrum type, stress level, and testing temperature on fatigue life degradation rate are discussed. The fatigue life degradation rate is very sensitive to the fiber preform, loading sequence, and testing temperature.

Genetic programming-assisted micromechanical models of graphene origami-enabled metal metamaterials

Graphene origami (GOri) enabled metallic metamaterials are novel nanomaterials simultaneously possessing negative Poisson's ratio (NPR) and enhanced mechanical properties that are independent of the topology/architecture of the structure. Predicting their material properties via existing micromechanical models, however, is a great challenge. In this paper, a highly efficient micromechanical modeling approach based on molecular dynamics (MD) simulation and genetic programming (GP) algorithm is developed to address this key issue. The GP-based Halpin-Tsai model is extensively trained from MD simulation data to accurately predict the Young's modulus of GOri/Cu metamaterials with various GOri folding degrees, graphene contents and temperatures with a high coefficient of determination (R2) of ∼0.95. Meanwhile, the well-trained GP-based rule of mixture can accurately predict the coefficient of thermal expansion (CTE), Poisson's ratio and density of metamaterials with R2 of ∼0.95, ∼0.93 and ∼0.99, respectively. The excellent agreement between our estimated results and experimental data shows that the models developed herein are highly efficient and accurate in predicting mechanical properties that are essential for the analysis and design of functionally graded metal metamaterial composite structures. The theoretical results demonstrate that the proposed functionally graded metamaterial beam achieves significantly improved bending performance.

Multiscale failure analysis of a 3D woven composite containing manufacturing induced voids and disbonds

Multiscale failure simulations of a three-dimensional woven composite repeating unit cell considering six scales, spanning the woven composite mesoscale to the sub-microscale voids, have been performed. The multiscale recursive micromechanics approach, which enables recursive integration of general micromechanics theories over an arbitrary number of length scales, has been employed within the NASA Multiscale Analysis Tool. The multiscale model uses both the generalized method of cells and Mori-Tanaka micromechanics theories and considers failure in the constituent materials using a simple damage model. Baseline results, from a model of a composite containing distributed voids, are compared to uniaxial experimental data for an AS4 carbon fiber/ RTM6 epoxy matrix orthogonal three-dimensional woven composite with good agreement in terms of global stiffness and global failure stress. The multiscale model is then used to examine the nonlinear response of the material to other loading conditions. Case studies, motivated by X-ray computed tomography data, are presented on the effects of manufacturing induced voids and cracks.

Micromechanics Approach for the Overall Elastic Properties of Ceramic Matrix Composites Incorporating Defect Structures

Abstract The initial mechanical response of ceramic matrix composites (CMCs) is linear until the proportional limit. This initial response is characterized by linear elastic properties, which are anisotropic due to the orientation and arrangement of fibers in the matrix. The linear elastic properties are needed during various phases of analysis and design of CMC components. CMCs are typically made with ceramic unidirectional (UD) or woven fiber preforms embedded in a ceramic matrix formed via various processing routes. The matrix processing of interest in this work is the polymer impregnation and pyrolysis (PIP) process. As this process involves pyrolysis to convert a preceramic polymer into ceramic, considerable volume shrinkage occurs in the material. This volume shrinkage can lead to significant defects in the final material in the form of porosity of various size, shape, and volume fraction. These defect structures can have a significant impact on the elastic and damage response of the material. In this paper, a multiscale micromechanics modeling framework is developed to study the effects of processing-induced defects on the linear elastic response of a PIP-derived CMC. A combination of analytical and computational micromechanics approaches is used to derive the overall elastic tensor of the CMC as a function of the underlying constituents and/or defect structures. It is shown that the volume fraction and aspect ratio of porosity at various length scales play an important role in accurate prediction of the elastic tensor. Specifically, it is shown that the through-thickness elastic tensor components cannot be predicted accurately using the micromechanics models unless the effects of defects are considered.

Thermal conductivity of Cu-matrix composites reinforced with coated SiC particles: Numerical modeling and experimental verification

Copper-matrix composites reinforced with silicon carbide (SiC) particles are heat sink materials with potential application in the electronic industry. A major challenge in the manufacturing of these materials, involving sintering process, is to prevent the decomposition of SiC and the subsequent dissolution of silicon in the copper matrix. This is overcome by coating SiC particles with metallic layers. In this study, a combined experimental and computational micromechanics approach was used to investigate thermal conductivity of Cu-matrix composites reinforced with silicon carbide particles coated with chromium, titanium, or tungsten layers. Plasma Vapor Deposition (PVD) was used to produce the metallic layers on SiC particles, while Spark Plasma Sintering (SPS) to consolidate the powder mixtures of copper and coated silicon carbide. Thermal conductivities of the fabricated three-phase composites Cu/SiC/Cr, Cu/SiC/Ti and Cu/SiC/W were evaluated using the Laser Flash technique. Finite Element Method (FEM) and Variational Asymptotic Method (VAM) based homogenization techniques were used for computational modeling of thermal conductivity. In the numerical models complex material microstructures were accounted for using micro-CT images of the sintered compacts. Comparison of the experimental results with simulations highlighted the importance of including the effect of imperfect interfaces to accurately model thermal conductivity of the investigated composites.

Finite element method based micromechanical methodology for homogenizing fiber/fabrics-reinforced composites and their progressive failure

The complex microstructure of fabrics makes it challenging to homogenize them using an analytical/semi-analytical micro-mechanics approach like the Mori-Tanaka and the method of cells. Analytical approaches developed for fabrics estimate their elastic constants and do not easily accommodate material nonlinearities. Numerical schemes such as the finite element method (FEM) have been developed to analyze failure in fabrics and not necessarily find moduli of the homogenized material. Here we use the FEM based micro-mechanics approach to both homogenize fiber-reinforced and plain/twill/satin weave, as well as braids/fabrics-reinforced composites using simplified unit cells. The homogenization is based on Hill’s averaging theorem and employs tie constraints to impose periodic displacements and anti-periodic tractions on boundaries of the unit cell. A continuum damage mechanics approach is used to study damage initiation and progression, and degradation of material properties. The predicted elastic constants, failure modes and ultimate strengths of fabrics are found to compare well with their either experimental or computed values available in the literature. We have also analyzed delamination and damage propagation in a laminate with an open hole at the centroid and uniform tensile tractions at its end faces to estimate its ultimate strength that is found to agree well with the experimental value.

Study of boundary layer effects at ply interfaces of laminated composites using homogenization theory

A conventional analysis of unidirectional composite laminates is based on the use of average (or homogenized) properties, of the heterogeneous media, at the ply level. Plies with different orientations are stacked up to create the laminate. At free edges of the laminate, strong interfacial boundary layers are created, giving rise to large transverse normal and shear stresses. Away from free edges, and on other boundaries, these boundary layers are not present. In this work, possibly for the first time, the interface between the plies is studied in interior regions, away from the free edge. This is important because the effective media creates a fictitious interface, and true local stress states may be very different from that obtained from the conventional analysis, due to a breakdown of inherent asymptotic assumptions. This study proposes a new micromechanical approach to resolve inter-ply interfaces. Using this method, it is shown that interfacial boundary layer plays a significant role in the local stress state. This is demonstrated through the specific example of a cross-ply laminate.

Micromechanical approach to determine the effects of surface and interfacial roughness in materials and structure under cosinusoidal normal pressure

Contact mechanics is a topic that performs the investigation of the deformation of solids that touch each other at one or more points. A principal distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies' surfaces and stresses acting tangentially between the surfaces. This study focuses mainly on the normal stresses that are caused by applied forces. As a case study, the present work aims at investigating the bi-dimensional contact mechanics of wavy cosinusoidal anisotropic finite planes. To achieve this objective, results on the displacement and stress component are first calculated with the help of the Lekhnitskii formalism. Then, with the application of normal pressure at plane surface and by applying boundary conditions at depth h of solid we obtain solution for the contact pressure in closed form. In case of infinite anisotropic plane where the depth h tends to infinite, by using results obtained with finite h we derive the analytical solution for vertical displacement at the surface. As an illustration, behaviour of a monoclinic material under consinusoidal pressure is analyzed