Micromechanics-based Method Research Articles

Analytical simulation of the effects of local mechanisms and microstructure on the creep response of unidirectional ceramic matrix composites

A micromechanics-based method has been developed to analyze the creep response of uncoated ceramic matrix minicomposites. Although the global stress level at which the creep response is analyzed is lower than the composite proportional limit, local stresses are assumed to be high enough that localized damage is present in the composite in the form of matrix microcracks. To model the composite creep response including the effects of matrix cracking, a fiber shear lag-based methodology is employed. In this approach, stresses are assumed to vary in the fiber as a function of time and distance from the crack plane. The varying stresses are then used to compute the overall creep strain for the composite. Various assumptions regarding the level of matrix microcracking in the composite, and the level of creep in the fiber and matrix in various portions of the composite unit cell, are also examined. The creep response of the fiber is modeled using a linear Burgers model. The model is applied to a SiCf/SiC unidirectional minicomposite system. The computed creep results are compared to experimentally obtained values. The effects of the local fiber volume fraction on the overall creep response of the composite are also studied. This work will allow increased understanding of the key material damage mechanisms and load sharing that take place during creep conditions and can be expanded to provide improved analysis methods for full macrocomposites.

Analytical simulation of effects of local mechanisms on tensile response of ceramic matrix minicomposites

A micromechanics-based method based on a fiber shear lag analysis was developed to analyze the fast-fracture response of uncoated ceramic matrix minicomposites. The model was applied to two SiCf/SiC fiber minicomposite systems that were fabricated by Rolls-Royce High Temperature Composites, Inc., and the University of Connecticut. The analysis approach accounts for the fact that on average, the cracks in an actual minicomposite often have an irregular geometry. The effects of local variations in the fiber volume ratio on the composite response were also investigated. Parametric studies were performed to investigate the effects of the interfacial shear stress, global fiber volume fraction, and percentage of the composite that remains uncracked on the proportional limit stress and the composite secondary modulus. This work will facilitate an increased understanding of the key material mechanisms that take place during fast-fracture loading.

A Two-Level Homogenization Approach for Polymer Nanocomposites with Coated Inclusions

In polymer nanocomposites, other than the matrix and inclusion, a third phase so-called interphase, is commonly observed. Inter-phase properties affect the overall macroscopic mechanical behavior. It is crucial to model the interphase and obtain the effective composite properties accordingly. Homogenization theory is very useful and powerful; however, many of the homogenization-based techniques have deficiencies. The goal of the study is to combine two very well-known homogenization techniques to model the polymer nanocomposites with coated inclusions. One of the goals of the study is to demonstrate the deficiency that originated from the interphase modeling and overcome this problem by the proposed two-level homogenization method. This method aims to model load transfer between the matrix and the reinforcement element through the interphase in a correctly. For this purpose, first, an effective inclusion is formed using finite element homogenization, then the effective inclusion and the matrix are homogenized using micromechanics-based Double Inclusion method. The proposed method provides a remarkable improvement compared to the micromechanics-based method for the soft interphase case.

A simplified continuous–discontinuous approach to fracture based on decoupled localizing gradient damage method

In this work, two fracture modelling methods i.e., extended FEM (XFEM) and localizing gradient damage method (LGDM), are combined to get the advantages of both methods while eliminating their limitations. The LGDM is a micromechanics-based method that avoids spurious damage growth and incorrect damage initiation observed in conventional gradient damage method (CGDM). However, in the LGDM, a cracked/discontinuous domain is not fully realized due to its continuous nature, even at high damage. This leads to numerous non-physical effects in LGDM like high strains, severe stress oscillations and incorrect representation of secondary variables. These shortcomings are rectified in the combined continuous–discontinuous (XFEM + LGDM) approach by introducing XFEM at the end of damage evolution to impose a discontinuous crack in the domain. To simplify the implementation, a fully coupled LGDM is converted to a decoupled LGDM using an operator-split (staggered) methodology. It is observed from numerical examples that the decoupling of LGDM leads to a reduction in the computational effort without compromising accuracy. Besides, the XFEM+LGDM approach avoids use of cohesive zone modelling necessary in existing XFEM+CGDM approaches. Moreover, the proposed method (combined XFEM + LGDM) is also investigated in the multi-physical framework of thermoelasticity. The numerical results reveal that the shortcomings mentioned earlier are rectified in a physically consistent manner under mode I and mixed-mode conditions.

A micromechanics model to predict effective thermal conductivity of rGO/MMT/polymer composites

In recent years, enhanced thermal conductive properties of polymer composites filled with reduced graphene oxide (rGO) have been studied for diverse applications. However, rGO fillers tend to form aggregates, making it difficult to reach the maximum enhancement through the use of rGO. Experiments have shown that the hydrogen bond between rGO and montmorillonite (MMT) can lead to a stable dispersion of rGO with the result of improving the effective thermal conductivity (ETC) of the composite. However, the mechanisms of this phenomenon are not yet well known. In this work, a micromechanics-based method is proposed to provide an analytical expression of the ETC of rGO/MMT/polymer composites. The predictions are in good agreement with the experimental data, demonstrating the effectiveness of the proposed framework. Also, the effect of the orientation of the fillers is investigated, which useful to determine the optimal orientation and filling ratio to meet various requirements in the material performance design and preparation of rGO/MMT/polymer composites.

Efficient numerical evaluation of transmission loss in homogenized acoustic metamaterials for aeronautical application

This work wants to investigate the soundproofing level of passive acoustic metamaterials made of Melamine Foam and cylindrical Aluminum inclusions. Latest research shows promising acoustical possibilities on controlling certain frequencies, varying their geometry or material configuration. Typically, acoustic metamaterials are plates with inclusions that resonate in low frequencies and block basses. Investigation is carried to use them for the improvement of aircraft cabin quietness. An homogenization method is adopted to study the metamaterial: this is modelled as viscoelastic material with inclusions, using a frequency-dependent approach, and the effective properties of the homogenized metamaterial are derived using a micromechanics-based method that allow us to prescribe the simplest mesh for periodical geometries (in this case, cylindrical) by reducing drastically the computation time. MSC Actran is used for vibro-acoustic simulations, in particular for the evaluation of Sound Transmission Loss in metamaterial panels with different volume fractions and in a sandwich panel with metamaterial core. This last has been compared with a classical sandwich panel used in aeronautics and it has been demonstrated that metamaterial gets higher transmission loss over all the frequency range.

Effective elastoplastic properties of carbon nanotube-reinforced aluminum nanocomposites considering the residual stresses

The residual stresses (RSs) can be generated by the thermal mismatch between the carbon nanotubes (CNTs) and aluminum (Al) matrix during the manufacturing process of this type of nanocomposite materials. It may play a significant role in the strengthening capability of the CNT/Al nanocomposites. In this work, a micromechanics-based method is developed to a comprehensive analyze the effect of thermal RSs on the overall elastoplastic behavior of the CNT/Al nanocomposites. Also, the micromechanical model includes an agglomerated state for the CNTs within the Al nanocomposites. Generally, a good agreement is observed between the results of the present model and available experiment. The results clearly emphasize that for a more realistic prediction in the case of the overall elastoplastic behavior of CNT/Al nanocomposites, the consideration of thermal RSs in the micromechanical analysis is essential. It is found that the thermal RSs can seriously reduce both the yield strength and ultimate tensile strength of the nanocomposites. Moreover, the proposed model is employed to investigate the influences of several important parameters such as volume fraction, aspect ratio and directional behavior of CNTs, degree of CNT agglomeration within the matrix on the elastic modulus, thermal expansion behavior and overall elastoplastic response of CNT-reinforced Al nanocomposites. The herein reported results could be actually useful to guide an accurate modeling and the design of a wide range of metal matrix nanocomposites reinforced by CNTs.

A comprehensive study on thermal conductivities of wavy carbon nanotube-reinforced cementitious nanocomposites

The thermal conductivities of cementitious nanocomposites reinforced by wavy carbon nanotubes (CNTs) are determined by the effective medium (EM) micromechanics-based method. The nanocomposite is composed of sinusoidally wavy CNTs as reinforcement and cement paste as matrix. The interfacial region between the CNTs and cementitious material is considered in the analysis. The effects of volume fraction and waviness parameters of CNTs, interfacial thermal resistance, type of CNTs placement within the matrix including aligned or randomly oriented CNTs, cement paste properties on the thermal conductivity coefficients of the nanocomposite are studied. The estimated values of the model are in very good agreement with available experimental data. Two parameters of CNT waviness and interfacial region contributions should be included in the modeling to predict realistic results for both aligned and randomly oriented CNT-reinforced nanocomposites. The results reveal that thermal conductivities K22 (transverse in-plane thermal conductivity) and K33 (longitudinal in-plane thermal conductivity) of the nanocomposites are remarkably dependent on the CNT waviness. Also, it is found that the CNT waviness moderately affects the thermal conductivity of a cementitious nanocomposite containing randomly oriented CNTs. However, the non-straight shape of CNTs does not influence the value of thermal conductivity K11 (transverse out of plane thermal conductivity). The achieved results can be useful to guide the design of cementitious nanocomposites with optimal thermal conductivity properties.

Impact of grain shape on the micromechanics-based extraction of single-crystalline elastic constants from polycrystalline samples with crystallographic texture

A micromechanics-based method (“inverse self-consistent approximation”) that can extract all the independent elastic constants of single crystals from those of polycrystals with crystallographic texture was newly developed. In the developed method, all the elastic constants in an anisotropic polycrystal were measured by resonant ultrasound spectroscopy, and the crystallographic orientations and shapes of the grains were analyzed. Then, the elastic constants of a single crystal, which reproduce those of the polycrystal, were determined on the basis of Eshelby's inclusion theory and the effective-medium approximation, taking into account the elastic interaction between the grains, which reflects their shapes and orientations. The developed method determined the elastic constants of pure Cu and pure Mg single crystals from those of polycrystals quite precisely. The differences between the elastic constants obtained using our method and the values measured using single crystals were only ∼ 1%. In contrast, the application of an inverse Voigt–Reuss–Hill approximation, which cannot consider the effect of the grain shape on the elastic interaction, resulted in a relatively poor evaluation for pure single-crystalline Cu which exhibits strong elastic anisotropy. This indicates that the grain shape clearly affects the elastic interaction between the grains exhibiting high elastic anisotropy and influences the extracted single-crystalline elastic constants. In terms of the actual application of the inverse self-consistent approximation, the single-crystalline elastic constants of AZ31 Mg alloy, whose single crystals cannot be prepared easily, were clarified.

Iterative Method to Predict Effective Elastic Moduli of Multiphase Particulate Composites

AbstractIn multiphase particulate composites, the deviation and mismatch of the elastic moduli of different particles may significantly affect the overall mechanical performance of the composites. This study investigates the effects of such deviations on the macroscopic properties of multiphase composites via an iterative micromechanics-based method. The elastic properties of the particles are assumed to obey certain statistical distributions. In the proposed iterative method, the composites are divided into multiple two-phase composites and their strain concentration tensors are derived by means of the inclusion matrix–reference medium model, which is a modification of the generalized self-consistent method. Iterative solutions are established that take into account the effects of the variation in the elastic properties of the particles in terms of the effective shear and bulk moduli. The findings show that the proposed iterative method converges quickly and that the results agree well with the experimen...

Effect of residual interface stresses on effective specific heats of multiphase thermoelastic nanocomposites

The interface energy theory developed by Huang et al. is further extended to incorporate the effect of the residual interface stresses on the effective specific heats of multiphase thermoelastic nanocomposites. First, a micromechanics-based method is employed to derive the expressions of the effective specific heats at constant-strain and constant-stress of the composites. Second, in order to take into account the influence of the interface stresses on the overall properties of the nanocomposites, a thermoelastic interface constitutive relation expressed in terms of the first Piola–Kirchhoff interface stresses and the Lagrangian description of the generalized Young–Laplace equations are presented. Finally, by means of the Helmholtz free energy of the “equivalent inclusion” (the inclusion together with its interface), analytical expressions of the size-dependent effective specific heats of the nanocomposites are obtained. The model is illustrated by an example of a “three-phase thermoelastic composite” showing that the overall properties of the nanocomposites are influenced by the “residual interface stresses,” which was sometimes ignored in the literature.

A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

This study aimed to develop a method to build a ‘bridge’ between the macro fracture mechanics model and stochastic micromechanics-based properties so that the macro fracture mechanics model can be expanded to the fracture mechanics problem of functionally graded materials (FGMs) with stochastic mechanical properties. An analytical fracture mechanics model is developed to predict the stress intensity factors (SIFs) in FGMs with stochastic uncertainties in phase volume fractions. Considering the stochastic description of the phase volume fractions, a micromechanics-based method is developed to derive the explicit probabilistic characteristics of the effective properties of the FGMs so that the stochastic mechanical properties can be combined with the macro fracture mechanics model. A thought for choosing the samples efficiently is proposed so that the stable probabilistic characteristic of SIFs can be obtained with a very small sample size. The probability density function of SIFs can be determined by developing a histogram from the generated samples. The present method may provide a thought to establish an analytical model for the crack problems of FGMs with stochastic properties.

Subject-Specific p-FE Analysis of the Proximal Femur Utilizing Micromechanics-Based Material Properties

Novel subject-specific high-order finite element models of the human femur based on computer tomographic (CT) data are discussed with material properties determined by two different methods, empirically based and micromechanics based, both being determined from CT scans. The finite element (FE) results are validated through strain measurements on a femur harvested from a 54-year-old female. To the best of our knowledge, this work is the first to consider an inhomogeneous Poisson ratio and the first to compare results obtained by micromechanics-based material properties to experimental observations on a whole organ. We demonstrate that the FE models with the micromechanics-based material properties yield results which closely match the experimental observations and are in accordance with the empirically based FE models. Because the p-FE micromechanics-based results match independent experimental observations and may provide access to patient-specific distribution of the full elasticity tensor components, it is recommended to use a micromechanics-based method for subject-specific structural mechanics analyses of a human femur.

The performance of 1–3 piezoelectric composites with a porous non-piezoelectric matrix

A micromechanics-based method is developed to evaluate the performance of 1–3 piezoelectric composites with a porous non-piezoelectric matrix. The classical Mori–Tanaka method is first used to analyze the porous polymer matrix, then the Mori–Tanaka method for piezoelectric composites is used to analyze the porous polymer matrix with embedded piezoceramic fibers. A parametric study is conducted to investigate the influence of the volume fraction, shape and orientation of the pores on the mechanical properties of the polymer matrix and the performance of the 1–3 piezoelectric composites. The results of the study show that the performance of the piezoelectric composites is significantly enhanced by the presence of pores in the matrix, particularly by cylindrical pores perpendicular to the piezoceramic fibers.

ジルコニア粒子強化ニッケル基複合材料のディスク曲げ試験による破壊強度評価

In an effort to obtain a reasonable fracture criterion necessary for a micromechanics-based approach to the design of ceramic-metal “functionally graded materials,” disk-bending tests have been carried out for a series of zirconia (PSZ: ZrO2-2 mol%Y2O3) particle-reinforced nickel (Ni) matrix composites fabricated by hot-press consolidation of PSZ-Ni powder mixtures with several different compositions (0, 20, 40, 60, 80 and 100 vol% PSZ). Disk-shaped samples of typical dimensions 20 mm dia.×1 mm are radially “four-point” bent at room temperature; it is thereby found that the samples containing PSZ over 40 vol% fracture by radial cracking under equibiaxial loading. The convex-face tensile strains at fracture of these samples are determined by assuming a simple geometry of spherical bending; the corresponding fracture stresses in PSZ particles are calculated with a micromechanics-based method which takes account of the plasticity of the Ni matrix. The results are analyzed on the basis of a fracture-mechanics criterion in terms of the energy release rate for a penny-shaped crack under multiaxial loading. An equivalent normal stress σneq is then defined as σneq=\sqrtσn2+τ2⁄(1−0.5ν)2, where σn and τ are the normal and shear stresses acting on the crack surface and ν is Poission’s ratio. It is found that fracture occurs when the maximum value of σneq in PSZ particles reaches a constant level. Scanning electron microscopic observations give evidence of this particle cracking-controlled fracture.