Computational Micromechanics Model Research Articles

Electrical conductivity of multifunctional cementitious composites reinforced by graphene derivatives: A finite element-based computational micromechanics model

Graphene derivatives (GDs) are known for their considerable conductivity and electron mobility, making them promising candidates for developing electrically conductive cementitious composites (CCs). Consequently, CCs reinforced with GDs (CRGDs) can serve a variety of applications in the construction industry. Despite several experimental studies on the conductivity of CRGDs, finite element (FE) models have rarely been developed to investigate the conductivity of CRGDs. Previous FE models primarily focused on one-dimensional fillers like carbon nanotubes within polymeric matrices, overlooking the distinctive anisotropic behaviour of GDs in cementitious matrices. This study introduces a computational micromechanics model (CMM), integrating the representative elementary volume (REV) concept with FE analysis, to investigate the electrical conductivity of CRGDs. This model is particularly noted for its computational efficiency, as it converts the problem dimensions from 3D to 2D while ensuring an acceptable degree of accuracy. The CMM captures the anisotropic conductivity of GDs and includes critical conductivity mechanisms such as conductive pathways, the tunnelling effect, and field emission. Subsequently, REV size sensitivity analysis is performed to ensure the statistical relevance of the REV, followed by the model's validation against experimental data from the literature. Afterwards, the model's sensitivity analysis clarifies how different parameters, including the constituent properties, influence prediction results. The sensitivity analysis results suggest that the aspect ratio of GDs has considerable impacts on the electrical conductivity and the percolation threshold of CRGDs. Ultimately, this study aims to provide insights into the optimization and design of electrically conductive CRGDs and lay the foundation for future research in this area.

Thermal conductivity of cementitious composites reinforced with graphene-based materials: An integrated approach combining machine learning with computational micromechanics

Graphene-based materials (GMs) have significant potential for enhancing the thermal conductivity of cementitious composites. This study uses both machine learning (ML) and computational micromechanics models (CMMs) through a hybrid modelling approach to investigate the thermal conductivity of GM-reinforced cementitious composites (GRCCs). Accordingly, validated CMMs were used to train the ML models, which were then employed to predict the thermal conductivity of GRCCs. The results show that, among the parameters investigated, the volume fraction of GMs is the most influential factor in predicting the thermal conductivity of GRCCs, followed by their aspect ratio.

A novel experimental method and computational micromechanical model for in-situ damage detection and prediction of stiffness degradation in cross-ply FML

A novel experimental method for in-situ damage detection in symmetrical and balanced glass/epoxy laminates composed of unidirectional layers is introduced in this paper. A 3D finite-element micromechanical model accompanies this method to predict stiffness degradation in a cross-ply fiber-metal laminate caused by transverse cracks and metal damage. The model is developed in Abaqus. Two user-defined subroutines, UMAT and UHARD, are coded in FORTRAN and linked to the model. Using a Python script, periodic boundary conditions are applied to the model. The predictions are validated against conventional loading-unloading experimental tests. Validation shows excellent agreement between the proposed model and the experiment.

Piezoelectric performance of lead-free PDMS/CNT/BaTiO3 piezocomposites with imperfect interphases and CNT agglomerations

Three-dimensional (3D) printable lead-free piezocomposites offer scalable and environmentally friendly solutions in many engineering applications. Typically, the composite system consists of polymeric matrices reinforced with active polycrystalline particles, and possibly nanoadditives. The presence of interfacial inclusion/matrix damage could not only compromise the structural integrity of the component but also significantly alter its ability to act as functional smart materials. In addition, both the agglomeration of the nanoadditives, such as carbon nanotubes (CNTs), and the degree of polarization could also affect the electromechanical behavior of the composite. In this paper, we develop a computational micromechanical model for the study of the influence of three types of internal defects on the piezoelectric performance of such composites. We investigate the influence of (a) the texture of the active phase, which is linked to the degree of polarization; (b) the effect of agglomerations of the CNTs; and (c) the presence of damage in the inclusion/matrix interphase region. Performance is assessed through the macroscopic response in various figures of merit. This work provides numerical evidence that the effective piezoelectric constants related to normal strain modes are strongly affected by the presence of damage in the interphase. Instead, the piezoelectric constant related to the shear strain remains unchanged by interfacial damage. Near the percolation threshold of the CNTs, piezocomposites exhibit a notable improvement in the piezoelectric response compared to the composite without nanomodification, as noted in previous works. Interestingly, this trend also applies in the presence of interfacial damage, and it is described in this work. The piezoelectric performance also depends on the texture of the active particles. We find, under some simplifications, the optimal orientation for the crystallites, and we find how the texture changes the performance in the presence of damage. Regarding energy harvesting applications, optimal energy conversion efficiency has been observed for polycrystalline inclusions that resembles a highly oriented single crystal and CNT volume fraction of 60 of percolation threshold. This is a quite surprising result since the optimal is usually expected for volume fractions very close to percolation and active inclusions with some orientational dispersion. The optimal CNT volume fraction depends on the presence of interfacial damage. Under perfect interface conditions, the energy conversion efficiency is improved with the presence of CNT agglomerations. Under imperfect interface conditions, there is no enhancement due to the addition of CNT.

A computational micromechanics model to predict mechanical properties of porous silica aerogels

Porous silica aerogel is an ultra-low-density material with nanostructures that leads to its excellent physio-chemical properties. Considering the characteristics of the material, a micromechanical model to assess the microstructure–property relations is highly demanded. In this study, a cuboctahedron unit cell is proposed as a representative volume element of the silica aerogel to correlate with its density and compressive stress–strain curves. The backbone lattice-structure combined with the dead ends is established to represent the periodic configuration of the aerogel. It is implemented in both the numerical scheme with the finite element method and the analytical model by modifying the Gibson–Ashby model. Furthermore, the crushing behaviors of the material under large deformation are discussed in the numerical study. Due to the features of load-bearing skeletons and non-load-bearing short pillars, the compression process of the silica aerogel exhibits strong nonlinear behaviors. Overall, this computational micromechanics model is capable of accurately simulating the stress–strain curves of silica aerogels with different densities under different loading levels. This work provides a general framework to quantify the microstructure–property relations of porous silica aerogels and also other porous materials.

Micromechanical assessment of local failure mechanisms and early-stage ply crack formation in cross-ply laminates

Three-dimensional computational micromechanical models are developed to study local failure mechanisms and early-stage ply crack formation in a carbon fiber/epoxy [0/90/0] cross-ply laminate under tensile loading. Pressure-dependent inelastic deformation of the epoxy is captured by a user-defined material model, where brittle cavitation and ductile failure are considered local failure mechanisms. Manufacturing-induced defects, including nonuniform fiber spatial dispersion and resin pockets, are represented in the 90° ply. The effects of ply constraints on the local distortional and dilatational energy densities in the matrix are evaluated. Brittle cavitation is found to be the first and dominating failure mechanism, while local inelastic deformation indirectly influences the number and location of cavitation sites. Inelastic deformation is deemed necessary for predicting the linkage of the microcracks that are induced by brittle cavitation. The study provides important insight into the early-stage formation of ply cracks, which is essential for analyzing the subsequent ply crack formation.

3D spatial reconstruction of macroscopic austenite–martensite transition zones in NiTi wires induced by tension and twisting using diffraction/scattering computed tomography

Macroscopic austenite–martensite transition zones in thin superelastic NiTi wires subjected to stretching, twisting and their combination were reconstructed via diffraction/scattering computed tomography. The method allows to visualize spatial distributions of both phases from a series of X-ray diffraction scans. A cone-shaped, radially symmetric transformation front was observed in stretched wire both with and without applied pre-twist. Twisting of a pre-stretched wire (with a cone-shaped transformation band front already developed) led to the formation of a multi-prong localization morphology recognizable on the surface. Transition zones in these cases are highly heterogeneous complex 3D objects exhibiting distinct phase gradients; the longitudinal size of the zones is comparable with the wire diameter. In contrast, localized martensitic strips parallel with wire axis and with a wedge-like cross-section appeared on the surface of the wire which was twisted only. We discuss the observed localization patterns with respect to current computational simulations and micromechanical models.

Computational micromechanics model based failure criteria for chopped carbon fiber sheet molding compound composites

Chopped carbon fiber sheet molding compound has a great potential in lightweight automotive, marine, and aerospace applications. One of the most challenging tasks is to predict the failure strength of the material due to its anisotropy and heterogeneity, as well as complex stress states in real-world working conditions. In this paper, a novel constitutive model of carbon fiber chip is proposed to capture the pre- and post-failure behaviors under different loading modes. On this basis, we propose a new computational micromechanics model, which is calibrated and validated by uniaxial tensile, compressive, and in-plane shear experiments. Furthermore, a set of microstructures representative volume element (RVE) models under complex loading conditions are reconstructed to understand the relationship between the microstructure characteristics and the failure envelopes. Finally, several modified versions of classical failure criteria are proposed for anisotropic materials with consideration of the fiber orientation tensor. The modified Tsai-Wu failure criterion, which shows the best accuracy among all failure criteria, is highlighted in the comparative study.

Micromechanical modeling of compressive behavior in freeze‐casted ceramic

AbstractIn this study, a novel computational micromechanical framework is proposed to predict the effective mechanical properties of the ice‐templated ceramics under off‐axis compressive loading. The mechanical behavior is simulated by a computational micromechanical model and validated against experimental results. Smeared cracking approach was used to describe failure in ice‐templated alumina. The representative volume element (RVE) was developed based on the honeycomb analogy of lamellar walls considering the morphology of the material. The periodic boundary conditions were applied in RVE to simulate bulk behavior of the material. The compression testing was conducted on the ice‐templated alumina samples to obtain the effective compressive moduli and strength with different loading angles. Digital image correlation method was used to measure strain field during the experiment and quantify the effective misalignment angle corresponding to porous material. The effective stiffness and strength obtained from RVE analysis compared well with experimental results. The proposed micro‐mechanical RVE model allows for determining the properties of the ice‐templated porous ceramic for various off‐axis angles.

Notch insensitivity in fatigue failure of chopped carbon fiber chip-reinforced composites using experimental and computational analysis

This study focuses on the notch effect on the fatigue failure of chopped carbon fiber chip-reinforced sheet molding compound (SMC) composites by using both experimental and numerical methods. The S-N diagrams of notched specimens are first obtained experimentally, which exhibit large scatter and are shown to depend on the spatial distribution of local fiber orientations. After considering the effect of this spatial distribution by adopting a new fatigue damage parameter to normalize the results, we achieve a much better correlation in the normalized S-N diagram for all the notched specimens with different hole diameters. Next, compared with the fatigue results of smooth specimens without notches, we find that SMC composites under tension-tension fatigue loading exhibit notch-insensitivity, which renders this type of composites a better candidate in joints or similar applications. Meanwhile, the fatigue failure mechanisms of notched SMC composites are explored through a microstructure characterization procedure. On this basis, a computational micromechanics model considering the notch effect and an improved multi-scale progressive damage fatigue law, calibrated by coupon-level fatigue tests of smooth SMC composites under different loading conditions, are employed to predict the fatigue behavior of notched SMC composites. We show that detailed failure processes and fatigue life of notched SMC composites can be efficiently and adequately predicted by this computational framework.

Micromechanical simulation and experimental investigation of aluminum-based nanocomposites

Ceramic reinforced metal matrix nanocomposites are widely used in aerospace and auto industries due to their enhanced mechanical and physical properties. In this research, we investigate the mechanical properties of aluminum/Nano-silica composites through experiments and simulations. Aluminum/Nano-silica composite samples with different weight percentages of silica nanoparticles are prepared via powder metallurgy. In this method, Nano-silica and aluminum powders are mixed and compressed in a mold, followed by sintering at high temperatures. Uniaxial tensile testing of the nanocomposite samples shows that adding one percent of Nano-silica causes a considerable increase in mechanical properties of nanocomposite compared to pure aluminum. A computational micromechanical model, based on a representative volume element of aluminum/silica nanocomposite, is developed in a commercial finite element software. The model employs an elastoplastic material model along with a ductile damage model for aluminum matrix and linear elastic model for nano-silica particles. Via careful determination of model parameters from the experimental results of pure aluminum samples prepared by powder metallurgy, the proposed computational model has shown satisfactory agreement with experiments. The validated computational model can be used to perform a parametric study to optimize the microstructure of nanocomposite for enhanced mechanical properties.

Computational micromechanical modeling of transverse tensile damage behavior in unidirectional glass fiber-reinforced plastic composite plies: Ductile versus brittle fracture mechanics approach

A detailed micromechanical finite element analysis methodology is presented to predict the transverse tensile (fiber perpendicular) failure behavior of a unidirectional (UD) glass fiber-reinforced plastic composite ply. In order to understand the constituent-level stress–strain and damage behavior, finite element analysis is accomplished using representative volume element (RVE) that consists of random fiber distribution as observed in the microscopic image of an actual composite ply. For modeling the fiber/matrix interface failure behavior, cohesive zone module (cohesive surface/cohesive element) of Abaqus® is used. In order to capture the epoxy matrix stiffness and strength degradation, the following two different approaches are used: (i) initially, the linear Drucker–Prager plasticity model in combination with a ductile fracture criterion is used; (ii) later, a brittle failure approach such as the quadratic normal stress criterion within the framework of eXtended finite element method is used. From the detailed micromechanical analysis of the RVE, it is observed that the initial damage in the RVE occurs in the form of fiber/matrix interface decohesion. With increasing tensile load, interface crack propagates and creates a stress concentration region in the matrix material, adjacent to the crack tip. Further load application causes both interface crack tip and matrix stress concentration to move away from the load application direction. As soon as the interface crack tip reaches approximately 60° to 70° away from the load application direction, the conjunction of the matrix damage with the interface crack leads to the RVE final failure. The predicted average stress–strain curves from the above-mentioned two different epoxy matrix failure criterions (ductile and brittle) correlate very well with the experimental results, indicating that the brittle failure behavior of a UD fiber-reinforced plastic composite ply under transverse tensile load is mainly controlled by the fiber/matrix interface properties.

Computational micromechanics model for the analysis of fiber kinking in unidirectional fiber-reinforced polymers

A computational micromechanics (CMM) model is developed to analyze fiber kinking, which is a failure mechanism that takes place in fiber-reinforced composites when they are loaded under longitudinal compression. The CMM model consists of a single AS4 carbon fiber with an initial misalignment embedded in an 8552 polymer matrix. The deformation of the model is governed by periodic boundary conditions (PBC). The relatively simple CMM model enables the evaluation of the role played by initial misalignment of the fiber, shear yielding of the matrix and fiber-matrix debonding. A novel microscale experimental technique devoted to the characterization of the longitudinal compressive strength of the fibers, Xcf, is developed. By exercising the model and comparing it with several models in the literature, the nonlinear shear response of the composite lamina is shown to play a fundamental role not only in the prediction of the compressive strength Xc, but also during the post-peak regime in terms of residual stress σr and fiber rotation φ. Finally, the influence of the fiber-matrix interface damage (not considered in most other fiber kinking models) on the fiber kinking phenomenon is assessed through a parametric study.

Micromechanisms of leading edge erosion of wind turbine blades: X‐ray tomography analysis and computational studies

AbstractMicromechanisms of leading edge erosion of wind turbine blades are studied with the use of X‐ray tomography and computational micromechanics simulations. Computational unit cell micromechanical models of the coatings taking into account their microscale and nanoscale structures have been developed and compared with microscopy studies. It was observed that the heterogeneities, particles, and voids in the protective coatings have critical effect on the crack initiation in the coatings under multiple liquid impact. The damage criterion for the formation of initial defects in the top coating is determined, and it is maximum principal stress criterion. Porosity or stiff particles in the coatings change the damage initiation sites, moving it from the contact surface to the pores or particles closest to the surface. Increasing the thickness of the polymer coatings allows reducing the stress amplitude, thus delaying the damage.

Failure criteria of unidirectional carbon fiber reinforced polymer composites informed by a computational micromechanics model

Failure prediction for carbon fiber reinforced polymer (CFRP) composites has been a longstanding challenge. In this study, we address this challenge by first applying a well-established computational micromechanics model based on representative volume element to predict the failure envelopes of unidirectional (UD) CFRP composites. Then, these failure envelopes are compared with the classical failure criteria. We have evaluated the performances of these failure criteria and identified the aspects for further improvement in their accuracies for the UD CFRP composites studied herein. Based on the failure mechanisms from computational analyses and the comparisons between predicted failure envelopes and classical failure criteria, a new set of homogenized failure criteria is proposed. The newly proposed failure criteria show significant improvement according to our computational and experimental results. Furthermore, we have compared the proposed failure criteria with existing experimental data and computational results available in the literature for different types of composites. Good agreements are generally observed.

Microstructure and Property-Based Statistically Equivalent Representative Volume Elements for Polycrystalline Ni-Based Superalloys Containing Annealing Twins

This paper has three major objectives related to the development of computational micromechanics models of Ni-based superalloys, containing a large number of annealing twins. The first is the development of a robust methodology for generating 3D statistically equivalent virtual polycrystalline microstructures (3D-SEVPM) of Ni-based superalloys. Starting from electron backscattered diffraction (EBSD) images of sections, the method develops distributions and correlation functions of various morphological and crystallographic parameters. To incorporate twins in the parent grain microstructure, the joint probability of the number of twins and parent grain size, and the conditional probability distributions of twin thickness and twin distance are determined. Subsequently, a method is devised for inserting twins following the distribution functions. The overall methodology is validated by successfully comparing various statistics of the virtual microstructures with 3D EBSD data. The second objective is to establish the microstructure-based statistically equivalent representative volume element or M-SERVE that corresponds to the minimum SERVE size at which the statistics of any morphological or crystallographic feature converge to that of the experimental data. The Kolmogorov–Smirnov (KS) test is conducted to assess the convergence of the M-SERVE size. The final objective is to estimate the property-based statistically equivalent RVE or P-SERVE, defined as the smallest SERVE, which should be analyzed to predict effective material properties. The crystal plasticity finite-element model is used to simulate SERVEs, from which the overall material response is computed. Convergence plots of material properties including the yield strength and hardening rate are used to assess the P-SERVE. A smaller P-SERVE compared to the M-SERVE indicates that the characteristic features of twins implemented in determining the M-SERVE are more stringent than those for determining material properties.

Experimental and computational analysis of failure mechanisms in unidirectional carbon fiber reinforced polymer laminates under longitudinal compression loading

This study investigates the failure mechanisms of notched unidirectional (UD) carbon fiber reinforced polymer (CFRP) laminates subjected to longitudinal compressive loading. A sequence of failure initiation and propagation is observed based on optical microscopy images of specimens during failure. The micrographs reveal that the main failure mechanism in UD laminates is fiber kinking failure. The influence of manufacturing defects and voids on fiber kinking mechanisms is also analyzed. The results show that the voids in the resin-rich area lead to kink-band splitting, while in some cases the voids cause the kink-band to deflect in a new direction depending on the location of the voids. The next focus of this study is to propose a computational micromechanics model considering local fiber waviness to study the fiber kinking failure mechanism. The computational results on kink-band formation and stress-strain response show good consistency with our experimental analysis. Finally, the failure envelopes of σ11-σ22 and σ11-τ12 subjected to combined loading conditions are obtained from the computational model, which provide essential inputs for future theoretical failure criteria.

Micromechanical models for the stiffness and strength of UHMWPE macrofibrils

Ultrahigh molecular weight polyethylene (UHMWPE) fibers have a complex hierarchical structure that at the micron-scale is composed of oriented chain crystals, lamellar crystals, and amorphous domains organized into macrofibrils. We developed a computational micromechanical modeling study of the effects of the morphological structure and constituent material properties on the deformation mechanisms, stiffness and strength of the UHMWPE macrofibrils. Specifically, we developed four representative volume elements, which differed in the arrangement and orientation of the lamellar crystals, to describe the various macrofibrillar microstructures observed in recent experiments. The stiffness and strength of the crystals were determined from molecular dynamic simulations of a pure PE crystal. A finite deformation crystal plasticity model was used to describe the crystals and an isotropic viscoplastic model was used for the amorphous phase. The results show that yielding in UHMWPE macrofibrils under axial tension is dominated by the slip in the oriented crystals, while yielding under transverse compression and shear is dominated by slips in both the oriented and lamellar crystals. The results also show that the axial modulus and strength are mainly determined by the volume fraction of the oriented crystals and are insensitive to the arrangements of the lamellar crystals when the modulus of the amorphous phase is significantly smaller than that of the crystals. In contrast, the arrangement and size of the lamellar crystals have a significant effect on the stiffness and strength under transverse compression and shear. These findings can provide a guide for new materials and processing design to improve the properties of UHMWPE fibers by controlling the macrofibrillar morphologies.

Computational Study of the Effects of Processing Parameters on the Nonlinear Elastoplastic Behavior of Polymer Nanoclay Composites

Processing parameters (e.g., exfoliation extent and volume fraction) of clay particles in polymeric resins play a crucial role in the mechanical properties of polymer nanoclay composites (PNCs). This paper is aimed to investigate the effects of clay aspect ratio and volume fraction on the global mechanical properties (e.g., effective stiffness, yield strength, and ultimate tensile strength) of PNCs. During the process, computational micromechanics models are adopted to simulate the nonlinear elastoplastic behavior of the PNCs of varying clay particle volume fractions and aspect ratios subjected to uniaxial tension. A representative volume element (RVE) of the PNCs is employed for the finite-element-method (FEM) based computational simulations. The polymeric matrix is treated as an idealized elastoplastic solid with isotropic hardening behavior, and the clay particles are treated as stiff elastic platelets distributed evenly in the stack and stagger configurations in the matrix. Seven volume fractions (Vf = 0.5%, 1%, 2%, 5%, 7.5%, 10%, and 15%) and seven aspect ratios (the ratio of platelet length over thickness ρ = 1, 2, 5, 10, 20, 50 and 100) of the reinforcing clay particles are utilized. Numerical experiments show that the effective modulus of the PNCs at small strains increases with the increase of either the clay volume fraction or the platelet aspect ratio largely following those predicted by classic micromechanics models. However, at the low particle aspect ratios (e.g., ρ = 1, 2, 5 and 10), the ultimate tensile strength of the clay composite is nearly independent of the clay volume fraction up to 5% in the present study, i.e., the polymeric matrix governs the PNC strength; at the large particle aspect ratios (e.g., ρ = 20 and 50), the ultimate tensile strength is significantly enhanced with growing clay volume fraction higher than 5% and reaches ~150% of that of the polymeric matrix at ρ = 50 and Vf = 10%. A comparative study is conducted for stack and stagger models for the prediction of the mechanical properties of PNCs. It shows that the stack model predicts slightly larger values of the effective stiffness and tensile strength than the stagger model. The numerical study shows that a large platelet aspect ratio through full exfoliation of the clay particles in matrix is crucial to achieving the preferable mechanical properties of PNCs as evidenced in experiments. The present results can be utilized to quantitatively explain the mechanical properties of clay particle-reinforced composites and PNCs within the framework of classic micromechanics, and provide guidelines for computer-aided nanocomposites design for processing property-tailorable PNCs.

A simple procedure to evaluate Cauchy stress tensor at the macro level based on computational micromechanics under general finite strain states

This paper presents a new methodology to evaluate the Cauchy stress tensor at the macro level in computational micromechanics models. The use of control nodes to specify boundary conditions of a Representative Volume Element (RVE) allows deriving equations for the Cauchy stress components, with the consequence that numerical integration in the RVE is not performed. The proposed method allows use of computational micromechanics in commercial Finite Element software for a RVE subjected to general infinitesimal or finite strains. Because this methodology is obtained from the equivalence of power in the microscopic and macroscopic scales (Hill–Mandel principle) in a quasi-static problem, it is capable of dealing with micro-constituents under several constitutive laws. Numerical examples presented include simulations of elastic, hyper-elastic, and elasto-plastic fiber composite materials and a honeycomb microstructure. The present methodology can be used in multi-scale models to analyze non-linear structures made of heterogeneous materials.