Micromechanics Of Composites Research Articles

Feasibility problems with the differential Mori-Tanaka method and modifications for refining inclusion stress predictions

Prevalent mean-field homogenization techniques excel in approximating effective stiffness, they fall short in predicting the stress states of individual inclusions within the same phase. Differential Mori-Tanaka (DMT) method presents possibilities for estimating stresses/strains in individual inclusions, which can be used for improved micromechanics of short fibre composites. This paper showcases inherent physical admissibility problems associated with DMT and proposes a novel modification to address them. The two schemes viz. DMT and modified-DMT are benchmarked using full-FE results. The modified-DMT effectively circumvents the physical admissibility problems with the DMT and is shown to results in qualitatively superior predictions of stresses in individual inclusions.

Nonlinear elastic general integral equations in micromechanics of random structure composites

We consider static problems for composite materials (CMs) with either locally elastic or peridynamic constitutive properties. The general integral equation (GIE) is the exact integral equationWe consider static problems for composite materials connecting the random fields at the point being considered and the surrounding points. There is a very long and colored history of the development of GIE which goes back to Lord Rayleigh. Owing to the new GIE (forming the second background of micromechanics also called the computational analytical micromechanics, CAM), one proved that local micromechanics (LM) and peridynamic micromechanics (PM) are formally similar to each other for CM of random structures. By now, the GIEs are generalized to CMs (of statistically homogeneous and inhomogeneous structures) with the phases described by local models, strongly nonlocal models (strain type and displacement type, peridynamics), and weakly nonlocal models (strain-gradient theories, stress-gradient theories, and higher-order models). However, a fundamental restriction of all mentioned GIEs is their linearity with respect to a primary unknown variable. The goal of this study is obtaining nonlinear GIEs for PM, and, in a particular case, for LM. For the presentation of PM as a unified theory, we describe PM as the formalized schemes of blocked (or modular) structures so that the experts developing one block need not be experts in the underlying another block (this is a good background for effective collaborations of different teams in so many multidisciplinary areas as PM). The opportunity for the creation of this blocked structure of the PM is supported by a critical generalization of CAM which is extremely flexible, robust, and general.

Damage and failure mechanisms of carbon fiber reinforced composite thin-walled bushings under hygrothermal-mechanical loadings

Numerous thin-walled bushings, injection-molded from AS4 short carbon fiber reinforced polyetherketone (AS4/PEK) composites, are employed in the chains of stenter heat-setting machines. These bushings rapidly deteriorate under the hygrothermal-mechanical loadings prevalent in their service conditions. This necessitates regular replacements, critically limiting machine efficiency. In this paper, considering hygrothermal-mechanical loadings, the macro–micro dual-scale damage model of composite bushings is established. The wet and thermal effects are introduced into constitutive models and damage criteria based on the macro–micro mechanics of composites and their constituents. The micro-damage and macro-destruction phenomena in the bushing are analyzed, and the related measures are proposed to delay its failure. Comparing the simulation results with the test, the macro–micro damage and failure behavior are discussed for the failed bushing. It reveals that stress concentrations near AS4 fibers initiate interfacial damage and microcracks in the PEK matrix, inciting interface debonding and matrix fragmentation, ultimately provoking composites failure. Increasing the interface thickness can delay the onset of damage. Fiber tension failure, matrix tensile, and compressive failure induce destruction at the component extremities. According to the influence of hygrothermal performance, within the glass transition temperature range of 160 °C to 240 °C, selecting composites with higher glass transition temperatures can enhance the failure strength of bushings by 19 %. Conversely, within a moisture absorption range of 0.5 % to 0.8 %, opting for materials with lower moisture absorption decreases the failure strength of bushings by 37 %. Optimal failure strength is achieved with composites having a 0.5 % moisture absorption rate and a 240 °C glass transition temperature.

Studies on effect of failure modes on mechanical properties of staggered composites

Biological materials such as bone, nacre, antler, and teeth are gifted with excellent mechanical properties that have inspired the development of synthetic composites. These superior properties are attributed to the geometrical as well as the material properties of the constituents at a small scale. This paper is focused on the influence of failure modes over the mechanical properties including stiffness, strength, and toughness, after the failure of different interfaces in staggered bio-inspired structures such as regular and stairwise staggered arrangements where stiff platelets are embedded in a pliant matrix. In order to find these properties, this article develops a novel analytical model for stress transfer and effective Young’s modulus of a stairwise staggered composite based on composite micro-mechanics principles. The results indicate that the failure sequence indeed influences mechanical characteristics such as stiffness, strength, and toughness. Also, the results from the present study is capable of quantifying the major contribution of toughness that is obtained from the vertical interface failure, which is ignored in previous studies for estimating the toughness. The results indicate that a toughness contribution as high as 56% from the inclusion of the first failure can be obtained in a stairwise staggered composite. The influence of significant parameters like Young’s moduli ratio between the platelet and matrix ( Ep/Em ) over the strength at different modes of failure showed that the strength at first and second failures increases as the Ep/Em ratio increases. The findings of this study hold significant potential for predicting the failure sequences with their quantified contributions towards the mechanical properties of a bio-inspired staggered composite.

Fast Fourier transform method in peridynamic micromechanics of composites

We consider a static linear bond–based peridynamic (proposed by Silling, see J. Mech. Phys. Solids 2000; 48:175–209) composite materials (CMs) of a periodic structure. In the framework of the second background of micromechanics (also called computational analytical micromechanics), one proved that local micromechanics (LM) and peridynamic micromechanics (PM) are formally analogous to each other for CM of both random and periodic structures. It allows a straightforward generalization of LM methods (including fast Fourier transform, FFT) to their PM counterparts. So, in the PM counterpart of the implicit periodic Lippmann–Schwinger (L-S) equation in LM, we have three convolution kernels corresponding to the properties of the matrix, inclusions, and interactive interface. Eshelby tensor in LM, depending on the inclusion shape, is replaced by PM counterparts depending on the shapes of inclusions, and the interaction interface (although the Eshelby concept of homogeneous eigenfields does not work in PM). The mentioned tensors are estimated once (as in LM) in a frequency domain (also by the FFT method). The possible incorrectness of FFT applications to PM is analyzed and corrected. The polarization schemes of the solution of the L-S equation in the Fourier space have one primary unknown variable (polarization), whereas the PM counterpart contains three primary ones estimated at each step, which are formally similar to the LM case. A description of the generalized basic scheme and the Krylov approach is presented. Computational complexities O(N log2 N) of the FFT methods are the same in both LM and PM.

Raman mapping microspectroscopy of the effects of cryogenic cycling on the interfacial micromechanics of carbon fiber-reinforced polyimide composites

Raman mapping microspectroscopy of the effects of cryogenic cycling on the interfacial micromechanics of carbon fiber-reinforced polyimide composites

Raman mapping microspectroscopy of the effects of cryogenic cycling on the interfacial micromechanics of carbon fiber-reinforced polyimide composites

Raman mapping microspectroscopy was then used to investigate the interfacial stress distributions of the films during different cryogenic-room temperature cycles (-198-25 °C, 0-300 cycles). It was found that the micro stress of CNT-PI films (around 175 MPa) had no significant changes even after 300 cycles. The cryogenic cycling had very little effect on the internal stress, indicating that PI had a good low temperature resistance. For the CF/CNT-PI films, the micro stress distributions of CFs, interface, and matrix regions were successfully obtained. It was found that the CFs bear a greater stress than the matrix, showing that CFs had always been the major stress bearer, confirming the strengthening effect of CFs. When the CF/CNT-PI films were cycled fewer than 250 times, the effect of cryogenic cycling on the micro stress was insignificant. But once the number of cycles reached 300, the compressive stresses on the fiber and interface increased by 21% and 12.9%, respectively, implying a deterioration of the mechanical properties. By Raman mapping, the micro-mechanical distributions of the reinforced material, matrix and interface of the composites under cyclic temperature changes were effectively quantified. This is therefore an effective method for evaluating the safety of composite materials.

“Van Fo Fy Method” in the Micromechanics of Fibrous Composites

“Van Fo Fy Method” in the Micromechanics of Fibrous Composites

Second Moment of Displacement State and Effective Energy-Based Criteria in Peridynamic Micromechanics of Random Structure Composites

Second Moment of Displacement State and Effective Energy-Based Criteria in Peridynamic Micromechanics of Random Structure Composites

Transformation field analysis as a background of clustering discretization methods in micromechanics of composites

A linear composite material (CM) consisting of a homogeneous matrix with either the periodic or random set of heterogeneities is considered. One of the first reduced-order models (ROMs), Transformation Field Analysis (TFA) by Dvorak for the pair strain-eigenstrain (or stress-eigenstress) is modified in terms of the “mixed” pair strain-eigenstress (or stress-eigenstrain) for implementation to clustering-based ROMs initiated by the self-consistent clustering analysis (SCA) by WK Liu. A set of consistency conditions are obtained for both the effective properties and modified eigenfield concentration factors. It is found that modified TFA represents a unified background of all three central clustering-based ROMs: the SCA, virtual clustering analysis (VCA), and finite element analysis–clustering analysis (FCA). One presents the scheme of estimation of inhomogeneous strain concentration factors in some prescribed clusters analyzed by the SCA (nonlinear problem). For statistically homogeneous CMs, a localized version of the modified TFA is proposed for clustering of the matrix (coating) in the vicinity of inclusions. VCA used for the analysis of a finite size inclusion can be modified for the implementation of a combination of both the modified TFA and functional gradient theory.

Linearized ordinary state-based peridynamic micromechanics of composites

Linearized ordinary state-based peridynamic micromechanics of composites

Examining the micromechanics of cementitious composites using In-Situ X-ray measurements

Examining the micromechanics of cementitious composites using In-Situ X-ray measurements

The Influence of Fibre Cross Section Shape and Fibre Surface Roughness on Composite Micromechanics

Many of the carbon and natural fibres used in composite reinforcement have a non-circular cross section. Recently non-circular, or flat, cross section glass fibre products have become commercially available. This paper explores the potential effects that such non-circular fibre cross section shapes may have on the micromechanics of stress transfer at the composite fibre–matrix interface and the resulting changes in composite strength performance. Analytical modelling is used to show how the critical fibre length in composites with non-circular fibres is always less when compared to circular fibres with an equal cross-sectional area. This can result in significant changes to the strength performance of discontinuous fibre reinforced composites. Additionally, it is shown that the surface roughness found on natural and carbon fibres, many of which are also non-circular in cross section, can decrease the critical fibre length still further. These effects have important consequences for the use of single fibre micromechanical tests used for the characterisation of interfacial strength.

Flat glass fibres: The influence of fibre cross section shape on composite micromechanics and composite strength

Many of the fibres used in composite reinforcement have a non-circular cross section and recently non-circular glass fibre products have become commercially available. This paper explores the potential effects that such non-circular fibre shapes may have on the micro-mechanics of stress transfer at the fibre–matrix interface and the resulting changes in composite strength performance. Analytical modelling is used to show how the critical fibre length in composites with non-circular fibres is always less when compared to circular fibres with an equal cross sectional area. This can result in significant changes to the strength performance of discontinuous fibre reinforced composites. Additionally it is shown that non-circularity in fibre cross section can have important consequences for the use of single fibre micromechanical tests in the characterisation of interfacial strength.

Concentration tensors preserving elastic symmetry of multiphase composites

The micromechanics of composites with multiple phases of different shapes embedded into a matrix phase, typically requires symmetrization strategies for their homogenized elasticity tensors, in particular so if the popular Mori–Tanaka estimate is employed. We here explore the implications of such symmetrization techniques, on the concentrations tensors, i.e. on the relations between macroscopic strains imposed onto a representative volume element of microelastic matter, and the microscopic phase strains developing across the materials’ microstructure. Thereby, we adopt the important idea of Mori and Tanaka to approximate the phase strains by the homogeneous strains inside an Eshelbian inhomogeneity embedded into an infinite matrix, together with the phase strains fulfilling the strain average rule; while we refrain from the identification of the strain in the matrix phase as the auxiliary strain imposed remotely at the infinite matrix of Eshelby’s matrix-inhomogeneity problem. Instead of this identification, we allow for a general multilinear relation between auxiliary strains and RVE-related macroscopic strains, and we express the homogenized stiffness as (i) a function of the conversion tensor quantifying the aforementioned multilinear relation, and (ii) as the symmetrized Mori–Tanaka estimate. In this way, the conversion tensor and all phase concentration tensors can be determined in a way which allows the overall elastic stiffness to remain symmetric. This is illustrated by means of two benchmark examples concerning matrix–inclusion composites hosting both spherical and prolate inclusions, with the matrices being isotropic and transversely isotropic, respectively. These examples benefit from analytical expressions for the Hill tensor governing the underlying matrix-inhomogeneity problems.

Prediction of Elastic Properties Using Micromechanics of Polypropylene Composites Mixed with Ultrahigh-Molecular-Weight Polyethylene Fibers.

In this study, we calculated the elastic properties of polypropylene composites mixed with ultrahigh-molecular-weight polyethylene (UHMWPE) fibers. We applied micromechanics models that use numerical analysis, conducted finite element analysis using the homogenization method, and comparatively analyzed the characteristics of polypropylene (PP) containing UHMWPE fibers as reinforcement. The results demonstrate that elastic properties improved as the volume fraction of UHMWPE fiber increased. It was confirmed that the fibers had anisotropic elastic properties due to the shape of the fibers. In addition, it is necessary to compare these findings with future experimental results to obtain data for developing UHMWPE–PP composites.

Numerical study of starch-gluten dough: Deformation and extrusion

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

Research on Micro-Mechanics Modelling of TPU-Modified Asphalt Mastic

To explore the interactions and mechanisms of Thermoplastic polyurethane (TPU)-modified asphalt with different kinds of mineral fillers, a micro-mechanical model for TPU-modified asphalt mastic was established, which considered the interaction between asphalt and mineral powder to effectively analyze the internal mechanisms affecting the rheological properties of TPU-modified asphalt mastic. In this study, according to the micro-mechanics of composites’ principles, the dynamic shear modulus (|G*|) of asphalt mastic with different mass ratios of filler/asphalt (F/A) was calculated by the homogenize morphologically representative pattern (H-MRP) model. The key ratio of F/A, which is close to the test result, can be determined, and a four-phase H-MRP model of the TPU modified asphalt mastic was established after considering the structure of asphalt layer thickness. The results were interpreted based on the known reactions of TPU with asphalt model compounds. The |G*| of TPU-modified asphalt mastic was predicted by using this model. Furthermore, the effects of the complex shear modulus, Poisson’s ratio of TPU-modified asphalt, Poisson’s ratio, particle size of mineral powder, and thickness of the structural asphalt layer in the |G*| of TPU-modified asphalt mastic were analyzed in the whole-model construction, as well as the internal mechanism of the |G*| of TPU modified asphalt mastic. In addition, can also be found the predicted value of |G*| calculated by the four-phase H-MRP model is close to the experimental value after choosing a structural asphalt layer of appropriate thickness.

Micromechanics of composites with interface effects

Micromechanics of composites with interface effects

Analytical model of mechanical properties of carbon fiber magnetic powder film-level magnetic materials for high-speed motors

The speed of high-speed permanent magnet motor has always been restricted by the strength of the rotor. Therefore, this paper proposes a type of magnetic composite rotor suitable for high-speed permanent magnet motors, which can fundamentally solve the problem that it is easy to cause damage for permanent magnets in high speed. In this paper, a combination of theoretical calculation, numerical simulation and experimental verification are used for the magnetic composite material. Based on the theoretical model of the composite micromechanics rule of mixture method, the mechanical properties of the three-phase magnetic composite material are successively deduced. The calculation model of magnetic composite material was compared by using the finite element method and the analytical method, the experimental result was used to verify the correctness of the calculation results. Finally, the influence of carbon fiber thickness and magnetic powder content on the mechanical properties of the material was studied.