Interphase Model Research Articles

Probabilistic modeling of surface effects in nano-reinforced materials

This work is concerned with multiscale analysis of nano-reinforced heterogeneous materials. Such materials exhibit surface effects that are typically taken into account through interface models in mean-field homogenization theories. However, both experiments and numerical simulations demonstrate the existence of a perturbed area at the boundary between the inclusion and the matrix phase. This area is modeled as an interphase whose elastic properties randomly fluctuate from point to point and must be characterized from a probabilistic standpoint. In this study, we therefore address (i) the stochastic modeling of the interphase and (ii) the study of the relationship between the random interphase model and a deterministic interface model. The aim of this work is twofold. First of all, we are interested in constructing a probabilistic model for the matrix-valued random field, modeling the elastic properties of the interphase. Then, this model is used to perform a parametric study for the apparent tensor associated with the microstructure. Simulations are specifically used to characterize the influence of both the random interphase and interface models on the material’s overall properties. When the interface model is consistent from a physical point of view, the associated elastic surface properties are computed by solving an optimization problem involving the effective properties of the random medium.

Interphase characterization and modeling of tensile modulus in epoxy/silica nanocomposites

AbstractThe incorporation of second dispersed particulate phases in a polymer matrix enhances its mechanical properties. Because of the high surface to volume ratio of nanoparticles, the molecular structure of the matrix is altered at the nanoparticle/matrix interface and the volume of this perturbed region could be significant. These improved properties are produced by the interfacial interaction of the nanometric domains. In this research, epoxy matrix modified with three different sizes of nanosilica (12, 20, and 40 nm) and the effect of the interphase characteristics on the tensile properties of nanocomposites was investigated. At first, the theoretical values of the elastic modulus using a two‐phase mathematical model compared with the experimental data obtained from the nanocomposite samples and values between 8 and 10 nm were estimated for the interphase thickness. Afterward, considering the three‐phase model, it takes into account that three different regions for interphase volume fraction, including single particles, polymer trapping, and agglomerated nanoparticles, and an equation for evaluation of interphase volume fraction are defined. Also, the interphase tensile modulus was considered continuously changing from the properties of nanoparticle to the polymer matrix properties. Finally, the overall tensile modulus of nanocomposites, which considers different key parameters including nanoparticle size, values for the interphase thickness (h), and interphase tensile modulus (Ei), were calculated. The results were compared with the experimental ones of other studies and a good agreement was found. The smallest value of h as 6 nm for samples containing 12‐nm diameter nanosilica and highest value of h as 8 nm for samples containing 40‐nm diameter nanosilica is reported.

(Invited) Multiscale Modeling of Formation and Properties of Solid-Electrolyte Interphases in Li-Ion Batteries

In this talk we will discuss recent efforts on multiscale modeling of solid-electrolyte interphase (SEI) and cathode-electrolyte interphases(CEI). The complexity and multiscale phenomena operating at electrode/electrolyte interfaces do not allow to access all necessary length and time scales using a single modeling approach. Combining information from high-level ab initio and DFT calculations, polarizable atomistic molecular dynamics simulations, coarse-grained implicit solvent simulations and continuum level modeling, we focus on understanding the mechanisms of formation of SEI/CEI layers, mechanisms of Li-ion transport, and mechanical and failure properties of SEI during charging/discharging processes.

Prediction of bending in SMC using a single parameter damage model that accounts for through thickness microstructural properties

A micromechanics model that utilizes microstructural characteristics for predicting the bending stress-strain response of a SMC composite is presented. The model integrates matrix, interphase and fibre damage models to form a framework that is able to accurately represent the damage response of the SMC using a single parameter damage model that is equivalent to the von mises interfacial stress. This is a valuable capability given the inherent random nature of SMC properties. Before being subjected to three-point bending tests, three SMC samples from different areas of a molded plate were characterized using X-ray computed tomography. The through thickness properties such as fibre orientation and volume fraction were characterized for multiple layers and then used as input data for a finite element model to predict the stress-strain behaviour. It was found that prediction accuracy increased with more layer properties. The model was able to represent the stress strain results within 2% of the experimentally measured response using 12 microstructural layers for a 2.8 mm thick specimen.

Data centric nanocomposites design via mixed-variable Bayesian optimization

Integrating experimental data with computational methods enables multicriteria design of nanocomposites using quantitative and qualitative design variables.

Interphase model for FE prediction of the effective thermal conductivity of the composites with imperfect interfaces

This paper addresses the Finite Element (FE) homogenization of the Effective Thermal Conductivities (ETCs) of the Composites with Imperfect Interfaces (CIIs). To model the imperfect interfaces between the matrix and inclusions in the composites, the thin interphases between the matrix and inclusions are introduced, which are combined with the FE homogenization method to predict the ETCs of the CIIs. The Representative Volume Elements (RVEs) containing the interphases are adopted to characterize the micro-structures of the CIIs and generated by the modified Random Sequential Absorption (RSA) algorithm. Compared with the micro-mechanical models, the proposed interphase model with the FE homogenization method is validated to be able to accurately predict the ETCs of the CIIs. The simulation results demonstrate that the ETCs of the CIIs are size-dependent, and the interphase thickness in the range of 50.0–100.0 nm has few impact on the ETCs of the composites. In addition, the ETCs of the CIIs show an asymptotic behavior so that a transition zone and two plateaus zones can be identified for the curves of the ETCs of the CIIs. This work provides a new and simple approach for predicting the ETCs of the CIIs.

Numerical simulation of the factors affecting the growth of lithium dendrites

Abstract The secondary lithium battery using lithium metal as a negative electrode has attracted more attention due to its extremely high theoretical specific energy. During the charge and discharge cycle, lithium ions are reduced and nonuniformly deposit on the surface of the lithium electrode, which leads to the formation and growth of lithium dendrites. The growth of lithium dendrites can pierce through the separator and causes internal short circuit of the battery as well as battery catastrophes like thermal runaway. The lithium dendrite growth process is complicated and can be affected by various factors. In this paper, a phase field model is developed to simulate the growth process of lithium dendrites, and the effects of anisotropic strength, applied voltage and microstructure of solid electrolyte interphase (SEI) on the growth of lithium dendrites are considered and investigated. The geometric model of solid electrolyte interphase (SEI) is established by numerical reconstruction method. Then, the growth process of lithium dendrites in solid electrolyte interphase (SEI) is investigated, which provides insight on revealing the growth mechanism of lithium dendrites.

A model for predicting critical size for dislocation formation in phase transforming planar particles of energy storage intercalation materials

Defect formation has been widely observed to occur in phase transforming intercalation materials of critical importance to many technological applications. In this work, relying on energy balance argument, we develop a planar particle model to investigate critical conditions for spontaneous dislocation formation in a single-crystalline phase transforming material. Dislocations self-energy is calculated assuming isotropic elasticity, and the work done by the background stress field during dislocation formation is examined based on bilayer and core-shell models of solute distribution. Considering well-known slip systems in cubic crystals, critical sizes are derived, as a function of transformation strain, below which dislocation formation is predicted to remain energetically suppressed throughout complete phase transformation, resulting in completely coherent phase transformation. Effect of the surface flux on the critical size is also examined using a moving interphase model. Minimum dislocation spacing is derived for an array of dislocations which could spontaneously form at the phase boundary when particle size exceeds the critical size. Numerical estimates of the critical size are presented for several materials systems, and the results are discussed with reference to the available experiments. Results of this work could have potentially important implications in terms of designing phase changing materials resistant against cyclic damage.

Achieving the Upper Bound of Piezoelectric Response in Tunable, Wearable 3D Printed Nanocomposites

AbstractThe trade‐off between processability and functional responses presents significant challenges for incorporating piezoelectric materials as potential 3D printable feedstock. Structural compliance and electromechanical coupling sensitivity have been tightly coupled: high piezoelectric responsiveness comes at the cost of low compliance. Here, the formulation and design strategy are presented for a class of a 3D printable, wearable piezoelectric nanocomposite that approaches the upper bound of piezoelectric charge constants while maintaining high compliance. An effective electromechanical interphase model is introduced to elucidate the effects of interfacial functionalization between the highly concentrated perovskite nanoparticulate inclusions (exceeding 74 wt%) and light‐sensitive monomer matrix, shedding light on the significant enhancement of piezoelectric coefficients. It is shown that, through theoretical calculation and experimental validations, maximizing the functionalization level approaches the theoretical upper bound of the piezoelectric constant d33 at any given loading concentration. Based on these findings, their applicability is demonstrated by designing and 3D printing piezoelectric materials that simultaneously achieve high electromechanical sensitivity and structural functionality, as highly sensitive wearables that detect low pressure air (<50 Pa) coming from different directions, as well as wireless, self‐sensing sporting gloves for simultaneous impact absorption and punching force mapping.

A multiscale micromechanical model of adhesive interphase between cement paste and epoxy supported by nanomechanical evidence

Even though epoxy adhesives are used extensively in concrete structures, little fundamental research has been conducted regarding bond formation mechanisms between the adhesive and concrete substrate, which obscures our understanding of degradation mechanisms in the bonded joints. When epoxy adhesive is applied to the concrete substrate, a transition region – termed interphase – is formed between the bulk epoxy and bulk cement paste/aggregate. Properties of interphase are thought to govern the macroscale behavior and durability of epoxy-concrete bonded systems. This work proposes an elastic multiscale model of the interphase region that is based on the existing body of knowledge on the topic. Site-specific statistical nanoindentation was used to experimentally evaluate the interphase region and verify the micromechanical model. Test results indicate that mechanical properties of the interphase region are different from those of bulk epoxy and cement paste. Experimental findings agreed with the postulated multiscale interphase model.

Two-step multiscale homogenization for mechanical behaviour of polymeric nanocomposites with nanoparticulate agglomerations

A multiscale analysis is performed to investigate the effect of nanoparticulate agglomeration on the mechanical properties of polymeric nanocomposites. The percolated interphase model is applied to consider the degradation of the elastic properties of the interphase zone caused by nanoparticulate clusters. Through parametric studies on various agglomeration states, we propose a new index called the ‘clustering density’, which indicates the degree of nanoparticulate agglomeration. As the clustering density increases, a significant degradation in the stiffness of the nanocomposites is observed from 10 to 30%. An efficient two-step homogenization method is proposed in the present study to effectively analyse large size representative volume elements (RVE) containing multi-clusters and free nanoparticles. The proposed computational scheme is based on multiscale homogenization and the clustering density concept. It is concluded that the two-step homogenization approach can provide accurate prediction of the mechanical properties of nanocomposites with heterogeneity from nanoparticle agglomeration with high computational efficiency.

Phase-Field Modeling of Solid Electrolyte Interphase (SEI) Evolution: Considering Cracking and Dissolution during Battery Cycling

Lithium-ion battery (LIB) degrade over time, which compromise its electrochemical performance and mechanical integrity, eventually battery safety. The evolution of solid electrolyte interphase (SEI) layer, which is a passivation layer forming and growing between electrode and electrolyte, is one of the main reasons for the above degradation of LIB. The performance and longevity of LIB highly depend on the stability of the SEI. Unfortunately, it is believed that the SEI layer is not electrochemically and mechanically stable due to the dissolution and cracking of the SEI during the de/lithiation process. Up to date, very few studies have investigated the dissolution and cracking of the SEI layer during the lithium-ion diffusion. In this work, a phase field model is developed to provide insight on the interaction effect of cracking and dissolution of the SEI layer on LIBs performance. We assume that the SEI layer is formed by different solid species precipitated from the electrolyte, which are not stable during the de/lithiation cycling. SEI layer experiences stress concentration and volume change, which lead to the cracking of layer. In the meanwhile, the SEI species may have further reactions with the electrolyte which may lead to the dissolution. The cracking of the SEI layer results in more surfaces to react with electrolyte, and further dissolution, as shown in Figure 1. Moreover, we carry out experiments to focus on imaging the SEI as well as battery performance degradation during SEI formation and evolution. Figure 1

Suspended particle motion close to the surface of rotating cylindrical filtering membrane

The rotational filtration principle is known as an effective approach to slow the plugging of pores in a cylindrical filtering membrane. The existing applications are based on the study of the Taylor-Couette cell with a weak imposed radial inflow through a rotating inner cylinder. They are mostly related to thin filtration with a high transmembrane pressure. We consider a possible flow mode characterized by a high through-flow rate providing the subcritical liquid rotation within the inner cylinder boundary layer. An interphase interaction model is substantiated for the typical conditions considered and equations of a suspended solid particle motion are obtained in a dimensionless form giving similarity criteria of the problem. A number of benefits can be achieved with using this proposed flow mode when the particle size is one order of magnitude less than the boundary layer thickness. The influence of centrifugal force on the phase slip is the most notable when the particles are of the above size. It is possible, in particular, to exclude the contact of such particles with the membrane surface. The results obtained allow extending the application area of the high performance rotational filtration.

Phase-Field Modeling of Solid Electrolyte Interphase (SEI) Evolution: Considering Cracking and Dissolution during Battery Cycling

The Lithium-ion battery (LIB) degrades over time, which compromises its electrochemical performance and mechanical integrity, eventually battery safety. The evolution of solid electrolyte interphase (SEI) layer is one of the main reasons for the above degradation. The performance and longevity of LIB highly depend on the stability of the SEI. Unfortunately, the SEI layer is not electrochemically and mechanically stable due to the dissolution and cracking of the SEI during battery cycling. In this paper, a phase field model is developed to provide insight into the interaction of cracking and dissolution of the SEI layer. SEI layer experiences stress concentration and de/intercalation, which lead to the cracking of layer; meanwhile, the SEI species may have further reactions with the electrolyte which may lead to dissolution. The cracking of the SEI layer can result in more surfaces to react with electrolyte and further dissolution.

Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods

Many interface formulations, e.g. based on asymptotic thin interphase models or material surface theories, involve higher-order differential operators and discontinuous solution fields. In this article, we are taking first steps towards a variationally consistent discretization framework that naturally accommodates these two challenges by synergistically combining recent developments in isogeometric analysis and cut-cell finite element methods. Its basis is the mixed variational formulation of the elastic interface problem that provides access to jumps in displacements and stresses for incorporating general interface conditions. Upon discretization with smooth splines, derivatives of arbitrary order can be consistently evaluated, while cut-cell meshes enable discontinuous solutions at potentially complex interfaces. We demonstrate via numerical tests for three specific nontrivial interfaces (two regimes of the Benveniste–Miloh classification of thin layers and the Gurtin–Murdoch material surface model) that our framework is geometrically flexible and provides optimal higher-order accuracy in the bulk and at the interface.

The effect of vertical ground movement on masonry walls simulated through an elastic–plastic interphase meso-model: a case study

The present paper proposes an interphase model for the simulation of damage propagation in masonry walls in the framework of a mesoscopic approach. The model is thermodynamically consistent, with constitutive relations derived from a Helmholtz free potential energy. With respect to classic interface elements, the internal stress contribute is added to the contact stresses. It is considered that damage, in the form of loss of adhesion or cohesion, can potentially take place at each of the two blocks–mortar physical interfaces. Flow rules are obtained in the framework of the Theory of Plasticity, considering bilinear domains of ‘Coulomb with tension cut-off’ type. The model aims to be a first research step to solve the inverse problem of damage propagation in masonry generated by vertical ground movements, in order to ex-post identify the cause of a visible damage. The constitutive model is written in a discrete form for its implementation in a research-oriented finite element program. The response at the quadrature point is analyzed first. Then, the model is validated through comparisons with experimental results and finally employed to simulate the failure occurred in a wall of an ancient masonry building, where an arched collapse took place due to a lowering of the ground level under part of its foundation.

An investigation of the critical conditions leading to deintercalation induced fracture in two-phase elastic electrode particles using a moving interphase core-shell model

Phase separation has been widely observed in various energy storage systems, and is known to severely impact mechanical integrity and electrochemical performance in lithium intercalation materials. Core-shell type models have been extensively used for modeling diffusion, phase transformation, deformation, and stress generation in phase changing energy storage materials. The purpose of this work is to present a systematic fracture mechanics analysis of two-phase electrode particles with core-shell structure subject to deintercalation using both numerical and analytical models. Mechanical behavior of the host solid is assumed to follow small deformation linear elasticity, and geometry of the particles is considered to be cylindrical/spherical. A moving interphase model accounting for the effect of solution non-ideality is utilized in combination with the weight function method of fracture mechanics to numerically calculate stress intensity factors (SIFs) for pre-existing cracks at the particle surface. Further, an analytical solution in the limit of small surface fluxes and a semi-analytical solution in the presence of large surface fluxes are also developed for the maximum SIF which could arise for a pre-existing surface crack during a complete deintercalation half-cycle. Implication of the results in terms of prediction of a critical particle size to avoid fracture in two-phase electrode particles is also presented. Numerical results along with their comparison with analytical predictions are presented in terms of the concentration and stress profiles, maximum tensile hoop stress, and maximum SIFs for a range of two-phase regular solid solutions and subject to a broad range of surface deintercalation fluxes. We further examine the results of this work by considering a lithium deintercalation system whose thermodynamic behavior is considerably different from that of a regular solution, and the results found using analytical and numerical models are compared.

Modeling the interphase region in carbon nanotube‐reinforced polymer nanocomposites

Carbon nanotubes are regarded as ideal fillers for polymeric materials due to their excellent mechanical properties. Mechanical analysis without consideration of nanotube–matrix interphase, may not give precise predictions. In this work, the impacts of interphase on the behavior of polymer‐based nanocomposites are studied. For this purpose, a closed‐form micromechanical interphase model considering the diameter of nanotube, the thickness of interphase, and mechanical properties of nanotube and polymer is proposed to estimate the overall mechanical properties of nanotube‐reinforced polymer nanocomposites. Furthermore, the effective elastic constants of the nanocomposites for a wide range of diameters and volume fractions of nanotubes, evaluated via the suggested interphase model, are compared with the results of molecular dynamics simulations. Thereafter, the effects of diameter, length and volume fraction of nanotubes on the mechanical properties of nanocomposites are investigated using the suggested model. The results indicate that mechanical properties of nanocomposites are significantly influenced by the interphase. POLYM. COMPOS., 40:E1219–E1234, 2019. © 2018 Society of Plastics Engineers

Effect of interphase zone on the overall elastic properties of nanoparticle-reinforced polymer nanocomposites

In the current work, the effect of interphase region on the mechanical properties of polymer nanocomposites reinforced with nanoparticles is studied. For this purpose, a closed-form interphase model as a function of radial distance based on finite-size representative volume element is suggested to estimate the mechanical properties of particle-reinforced nanocomposites. The effective Young’s and shear moduli of thermoplastic polycarbonate-based nanocomposites for a wide range of sizes and volume fractions of silicon carbide nanoparticles are investigated using the proposed interphase model and molecular dynamics simulations. In order to investigate the effect of particle size, several unit cells of the same volume fraction, but with different particle radii have been considered. The micromechanics-based homogenization results are in good agreement with the results of molecular dynamics simulations for all models. This study demonstrates that the suggested micromechanical interphase model has the capacity to estimate effective mechanical properties of polymer-based nanocomposites reinforced with spherical inclusions.

Multilayer multiferroic composites with imperfect interfaces

We study the macroscopic behaviors of multilayered multiferroic composites with interface imperfections by a direct micromechanical approach. Both generalized interface stress type and generalized linear spring type imperfect interfaces are considered. Concise matrix expressions of the overall behaviors of the layered piezoelectric–piezomagnetic composite with contact imperfection are presented. The key step is to observe that the two types of imperfect interface conditions are equivalent to the perfect ones due to the laminated geometry. Numerical calculations are demonstrated for BaTiO3–CoFe2O4 multilayer media, and are shown in good agreement with the more involved interphase model. Furthermore, it is observed that the interface imperfection would reduce the magnitude of the magnetoelectric voltage coefficients as compared to the corresponding perfect interface case. This feature is opposite to that predicted and observed in the corresponding cylindrical composites.