Micromechanics Of Composites Research Articles

A continuum damage model for fatigue life prediction of 2.5D woven composites

Abstract A new model based on continuum damage mechanics is proposed to predict the fatigue life of 2.5D woven composites. First, a full-cell model reflecting the real microstructure of 2.5D woven composites is established in ANSYS. Subsequently, three independent damage variables are defined in the framework of the composite micromechanics to establish the component constitutive relations associated with damage. The strain energy density release rate and damage evolution equations for the matrix, fiber in yarns, and matrix in yarns are derived. Finally, the proposed model is implemented for fatigue life prediction and damage evolution analysis of 2.5D woven composites at 20 and 180°C. The results show that the numerical results are in good agreement with the relevant experimental results.

The effects of plasticity mechanisms on micromechanics of composites with fiber waviness defects under compression

Micromechanics simulations of fiber-reinforced polymer-matrix composites with waviness defects are conducted to investigate the effect of constitutive model selection on the nucleation, evolution, and interaction of damage modes under in-plane compression. A 2D finite element model with fibers, matrix and fiber-matrix interfaces is used, considering damage modes at the constituent level (i.e., fiber-matrix interface damage, matrix plasticity, void nucleation and growth). Results show that the pressure-dependency of the polymer matrix is key for accurate predictions of strain localization in the fiber kinking mode and fiber-matrix interface crack behavior and extent at regions of waviness imperfections.

Experience nature as a basis for building strong composite structures

Introduction. The article is devoted an analytical overview of the methods of applying the Nature solutions for designing structures made of plastics reinforced with fibers, in particular, using rational curved fiber trajectories. The first section provides an overview of different structural models and some approaches to the micromechanics of composites.
 Materials and methods. Sections 2-7 discuss: analysis of rational elastic-strength properties of wood and composites for crack arrest by weak interface; methods for constructing curved paths of fibers of “flowing holes”; analyzes the applied and promising technologies for manufacturing attachment points, in which holes are formed using curvilinear fiber paths; “nature-inspired” principles of optimal design of pipe composite structures similar in structure to ladder of bamboo stalk; examples of the effective use of fibrous composites in elastic elements such as leaf springs; developing additive technologies for 3D printing of fiber composite parts with fiber laying along calculated trajectories.
 Results. Each section of the article presents conclusions related to the peculiarities of composites structures calculation and design: calculations show that in order to increase the crack resistance of fibrous composites, it is necessary to significantly increase the shear characteristics of the binder and strive for rational properties created by Nature in wood; as a result of the calculation, it turns out that the maximum stress per fiber at the optimal reinforcement structure becomes about 3–4 times less than with a uniform rectilinear laying; rational reinforcement leads to a significant reduction in local stresses per fiber, elimination of splits and damages of fibers and an increase in the carrying capacity of the assembly; it has been shown that the bamboo rings are arranged to prevent the barrel from splitting from bending compressive stresses and tangential stresses when the barrel is twisted by wind load; analyzed the relationship of equal-strength profiling with Leonardo’s rule for tree crown branching. The works on creation of bio-similar shape and structure of curvilinear reinforcement of specimens for correct determination of unidirectional composites strength at tension along fibres were discussed; analyzed the role of composite technologies in modern mechanical engineering, in particular, in the creation of composite structures in open space.
 Conclusions. The article is devoted to the analysis of the tasks of fibrous composites macromechanics, therefore, in the opinion of the authors, the three most promising and related areas in macromechanics of composites that require further research are biomechanics of strength, computer modeling of optimal structures and technological mechanics of composites.

Porosity-based representative elementary volume for geomaterials and its fractal theory-based approximate criterion

<p indent=0mm>The representative volume element (RVE) and/or the representative elementary volume (REV) and their existence and determination are a basic scientific issue in the research field of size effect. The similarities and differences between the RVE and REV are analyzed from the fields of composite micromechanics and geotechnical engineering. A three-level classification of the REV research on geomaterials is then proposed based on these fields, especially REV research in geotechnical engineering. The pore size distribution and the corresponding fractal dimension are introduced and selected as the constrained parameters for describing the complex pore structure of geomaterials. Accordingly, an approximate criterion is first presented via theoretical deduction and comparison with previous research results, through which the size of a P-REV of mesoscale porous geomaterials can be determined using their pore size distributions (i.e., the edge length of the cubic P-REV is approximately equal to five times of the maximum pore diameter). Finally, some statistical methods, such as low-order probability functions, are utilized to validate the performance of the proposed criterion. The verification results using two types of geomaterials, namely, sandstone and foamed concrete, reveal that both are in a reasonable agreement, indicating that the P-REV determined according to this approximate criterion can provide representative statistical results and find a balance between characterization accuracy and calculation efficiency.

In-plane compression modulus and strength of Nomex honeycomb cores

The stress-strain response and deformation mechanism of a range of Nomex honeycomb cores tested under in-plane compression has been examined experimentally. The cores with a thin wall displayed extensive bending deformation of the cell walls inclined to the horizontal (loading is vertical) and failed in bending. The cores with thicker walls failed by a shear-type instability of the cells indicated by tilting of vertical cell wall segments. The failure strain decreased with increasing core density. The modulus and compressive strength of the core were compared to micromechanical predictions. Normalized modulus and strength values varied between the various cores. The average modulus and strength results allow backing out of the modulus and bending strength of the Nomex paper. The results were in reasonable agreement with published tensile test results and composite micromechanics.

Multiscale analysis of elastic waves in soft materials: From molecular chain networks to fiber composites

We provide a multiscale analysis of elastic waves in soft microstructured materials including the underlying molecular chain network mechanisms and micromechanics of hyperelastic fiber composites. First, we examine the interplay between the crosslinked and entangled polymer chains and elastic wave characteristics in finitely deformed materials. Next, we study the shear wave propagation in a class of heterogeneous hyperelastic composites. In particular, we consider the transversely isotropic fiber composites with phases characterized by the stiffening behavior stemming from the non-Gaussian statistics of polymer chains. By employing a micromechanics-based approach, we derive explicit expressions for phase velocities in terms of material properties and volume fraction of the phases. Our results indicate the significant influence of the variety of length-scales mechanisms on the elastic wave characteristics. We provide examples to illustrate the influence of the mechanisms under different loading conditions, wave propagation directionality, and material microstructure parameters.

Biomimetic design of fibrous composite structures

The paper is devoted to the analysis of the use of Nature’s methods in the design of composite structures, in particular, with the use of optimal curvilinear paths for laying fibers. In the first part models of different structural levels in macro-, mini-, micro-mechanics of composites are noted. The second part includes analysis of the optimal elastic-strength properties of wood and composites for crack stopping by weak interfaces. The third part is devoted to methods for modeling curvilinear fibers trajectories “flowing around the holes”. In the fourth part the technologies for manufacturing joints are analyzed in which holes are formed using curved fiber trajectories. The fifth part describes the “bio-inspired” principles for the optimal design of composite pipe structures which are similar to multilink bamboo stems. In the sixth part examples of the effective use of fiber composites in elastic elements are considered. The seventh part is devoted to the intensively developing additive technologies of three-dimensional printing of parts made from fiber composites with laying the fibers along the calculated trajectories. The role of composite technologies in creating structures in open space is analyzed.

EFFICIENT MULTISCALE RECURSIVE MICROMECHANICS OF COMPOSITES FOR ENGINEERING APPLICATIONS

EFFICIENT MULTISCALE RECURSIVE MICROMECHANICS OF COMPOSITES FOR ENGINEERING APPLICATIONS

Generalized effective fields method in peridynamic micromechanics of random structure composites

We consider a static problem for statistically homogeneous matrix linear bond-based peridynamic composite materials (CMs). For the media subjected to remote homogeneous volumetric boundary loading, one proved that the effective behavior of this media is governed by conventional effective constitutive equation as in the local elasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional elasticity of composite materials (CMs) with their adaptation to peridynamics. This is extraction from the material properties a constituent of the matrix properties. Effective moduli are expressed through the introduced new notion of the average local polarization tensor. The average is performed over the surface of the extended inclusion phase rather than over an entire space. Any spatial derivatives of displacement fields are not required. The basic hypotheses of locally elastic micromechanics are generalized to their peridynamic counterparts. In particular, in the generalized effective field method (EFM) proposed, the effective field is evaluated from self-consistent estimations by the use of closing of a corresponding integral equation in the framework of the quasi-crystalline approximation. In so doing, the classical effective field hypothesis is relaxed, and the hypothesis of the ellipsoidal symmetry of the random structure of CMs is not used. One demonstrates some similarity and difference with respect to other methods (the dilute approximation and Mori-Tanaka approach) proposed before in micromechanics of peridynamic CMs. Comparative numerical analyses of these methods are performed for 1D case.

A framework for three-dimensional finite element analysis of unidirectional and cross-ply composite layups through localized microstructures under hygromechanical conditions

Fiber-reinforced polymers (FRPs) are sensitive to moisture diffusion. Deterioration caused by moisture can limit their service lives considerably. In this work, a three-dimensional finite element modeling and analysis framework is presented to investigate the moisture diffusion kinetics inside fiber-reinforced inside polymer matrix composites by considering different angle and cross-ply orientations. A small localized representative volume element considering a few fibers in the neighborhood of three-layer stacks has been analyzed. The emphasis is on the effect of different fiber orientations over moisture saturation time and diffusion-induced stresses. Stresses induced due to moisture diffusion in FRPs are evaluated on the free fiber ends. The numerical results from finite element approximations are compared with theories of composite micromechanics such as rule of mixtures, Halpin–Tsai model and concentric cylinder assemblage framework. It is observed that the orientation of fiber layers can greatly influence the moisture ingress inside the matrix and resulting stresses. At intermediate time durations of moisture progression, the cross-ply orientation had ~ 25% lower weight gain in comparison with the unidirectional ply orientations. The overall von Mises stresses at the fiber matrix interface were also lower in cross-ply orientations by ~ 40% in comparison with the other orientations with similar fiber volume fraction. The three-layered cross-ply, 90/90/90 orientation took almost 50% more time to fully saturate with moisture in comparison with the unidirectional, 0/0/0 orientation. The interpretations from the smaller local microstructural models presented in this work can be extended to study and design the structure scale composite layups for the improved moisture durability.

The Effects of Geometry and Chemical Composition of Nanoparticles on The Fracture Toughness of iPP Nanocomposites

This research deals with possible hybrid effects in the fracture energy of hybrid nanocomposites while taking a critical approach toward the currently-prevailing engineering practice of applying classical composite micromechanics to nanocomposites. For this purpose, different nanoparticles were embedded in an isotactic polypropylene matrix. The particles had different geometries (fibrous and platelets) and different chemical structures (organic vapor grown carbon nanofibers (VGCF); graphene nanoplatelets (GNP); and inorganic nanoclays, SiO2 nanofibers, and ZrO2 nanofibers). Almost all the composite systems presented improvements in the fracture energy, whereas the iPP/VGCF/GNP presented a positive hybrid effect. The main conclusion was that each nanocomposite system should be analyzed individually according to the constituent properties; the quality of the dispersion; and, primarily, by the type of interaction between the particles and the matrix.

Generalized Mori–Tanaka Approach in Micromechanics of Peristatic Random Structure Composites

A statistically homogeneous random matrix medium with the bond-based peridynamic properties (see Silling, J Mech Phys Solids 48:175–209, 2000) of constituents is considered. For the media subjected to remote homogeneous volumetric boundary loading, one proved that the effective behavior of this media is described by conventional effective constitutive equation which is intrinsic to the local elasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional elasticity of CMs and adapted to peristatics. This is extraction from the material properties a constituent of the matrix properties. Effective properties moduli are expressed through the introduced local stress polarization tensor averaged over the extended inclusion phase rather than in an entire space. One proposes a generalization of a dilute approximation method to their peristatic counterpart in the sense that the volume fraction of the particles is small and their mutual interaction can be neglected. As in a classical approach, the essential assumption in the generalized Mori–Tanaka method (MTM) states that each extended inclusion behaves as an isolated one in the infinite matrix and subject to some effective strain field coinciding with the average strain in the truncated matrix. Comparative numerical analyses of both the dilute approximation and MTM method are performed for 1D case.

Translation of segment scale stiffening into macroscale reinforcement in polymer nanocomposites

Structuring of polymer nanocomposites (PNCs) with an aid of relatively weak external magnetic fields has been studied as a method for control of the nano‐ and microstructure. Magnetic nanoparticles (NPs) were assembled into high aspect ratio one‐dimensional strings and unidirectionally oriented with the magnetic field (B = 0–50 mT) within the photopolymer matrix. The effect of the anisotropic MNPs assemblies on the mechanical properties was studied over a wide temperature range for the first time. The impact of various reinforcing mechanisms was distinguished with respect to the position of the glass transition temperature (Tg). The reinforcing effect exhibits temperature dependency with a maximum ~65°C above the glass transition and only negligible effect below the Tg. In addition, significant directional anisotropy of stiffness was observed. Composite micromechanics was applied to interpret the orientation and size‐dependent reinforcement of PNCs, and temperature‐dependent stiffness of the polymer‐MNP structures was quantified. The presence of polymer chains with altered dynamics surrounding the MNPs inside the anisotropic assemblies was proposed to be an essential nanoscale mechanism mediating the stress transfer and contributing to mechanical robustness of the hybrid structures and PNCs. POLYM. ENG. SCI., 60:587–596, 2020. © 2019 Society of Plastics Engineers

Biobased Composites from Biobased-Polyethylene and Barley Thermomechanical Fibers: Micromechanics of Composites.

The cultivation of cereals like rye, barley, oats, or wheat generates large quantities of agroforestry residues, which reaches values of around 2066 million metric tons/year. Barley straw alone represents 53%. In this work, barley straw is recommended for the production of composite materials in order to add value to this agricultural waste. First of all, thermomechanical (TMP) fibers from barley straw are produced and later used to reinforce bio-polyethylene (BioPE) matrix. TMP barley fibers were chemically and morphologically characterized. Later, composites with optimal amounts of coupling agent and fiber content ranging from 15 to 45 wt % were prepared. The mechanical results showed the strengthening and stiffening capacity of the TMP barley fibers. Finally, a micromechanical analysis is applied to evaluate the quality of the interface and to distinguish how the interface and the fiber morphology contributes to the final properties of these composite materials.

Variational principles and generalized Hill’s bounds in micromechanics of linear peridynamic random structure composites

We consider a static problem for statistically homogeneous matrix linear peridynamic composite materials (CMs). The basic feature of the peridynamic model considered is a continuum description of a material behavior as the integrated non-local force interactions between infinitesimal particles. In contrast to these classical local and non-local theories, the peridynamic equation of motion introduced by Silling (J Mech Phys Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. Estimation of effective moduli of peridynamic CMs is performed by generalization of some methods used in locally elastic micromechanics. Namely, the admissible displacement and force fields are defined. The theorem of work and energy, Betti’s reciprocal theorem, and the theorem of virtual work are proved. Principles of minimum of both potential energy and complimentary energy are generalized. The strain energy bounds are estimated for both the displacement and force homogeneous volumetric boundary conditions. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CM are generalized to the case of peridynamics, and the energetic definition of effective elastic moduli is proposed. Generalized Hill’s bounds on the effective elastic moduli of peridynamic random structure composites are obtained. In contrast to the classical Hill’s bounds, in the new bounds, comparable scales of the inclusion size and horizon are taken into account that lead to dependance of the bounds on both the size and shape of the inclusions. The numerical examples are considered for the 1D case.

Experimental Study of the Mechanical Properties and Microstructures of Lightweight Toughness Cement-Based Composites.

The effects of cenospheres, an industrial waste residue, on the compressive strength, flexural strength, toughness, ductility, chemical component, microstructures, and micromechanics of lightweight toughness cement-based composites (LTCCs) by comprehensive experimental tests are explored in this paper. The results indicate that an increase in the amount of cenospheres leads to a decrease in the compressive and flexural strength of LTCCs. However, the specific strength of LTCCs increases with increasing cenosphere content. LTCCs containing 20% cenospheres and 1% fiber volume have the best toughness and ductility. Significant strain hardening occurs during the four-point bending and uniaxial tensile process. Furthermore, the incorporation of cenospheres promotes the hydration reaction of LTCCs due to its high pozzolanic activity. The LTCC cement paste has a low bonding strength to the fiber, which helps the fiber to be pulled out to produce greater bending deformation and tensile strain. The elastic modulus and hardness of the LTCC cement paste decrease linearly with increasing cenosphere content, which also causes the LTCC microstructure to become loose and more ettringite to generate. The weak interfacial transition zone between the cenospheres and the cement matrix is the important reason for the decreasing compressive strength of the LTCC. In conclusion, LTCC incorporating cenospheres is suitable for long-span steel deck pavements due to its light weight and excellent toughness. The successful application of cenospheres in engineering construction can save natural resources and contribute to sustainable development.

Micromechanics modeling and validation of thermal-mechanical damage in DER353 epoxy/borosilicate glass composite subject to high strain rate deformation

With advances in the design and manufacturing of composite materials, the number of their defense and civil applications has grown significantly. This calls for detailed experiments and modeling of composite materials for their characterization and performance analysis. Experiments show that adiabatic heating becomes more noticeable at high-strain-rate deformation, causing the stress-strain slopes to become negative. However, most rate-dependent micromechanics models, e.g. in a previous work by the authors [1], lack an interpretation of the relation between energy dissipation and adiabatic temperature rise. In this study, a continuum damage model (CDM) with adiabatic heating is established to enhance the accuracy of the micromechanics model under high-strain-rate impacts. The model predicts the behavior of a heterogeneous material and punch shear strength tests are used for validation. The model is calibrated using results from experiments conducted in a split-Hopkinson pressure bar (SHPB). A constitutive law for the DER353 epoxy in the finite rotation framework is presented first, focusing on the connection between the energy dissipation and local temperature rise. Next, the model is implemented in a finite element framework and calibrated using a SHPB experiment. Lastly, the DER353 epoxy model is applied to a unidirectional fiber composite micromechanics model as a predictive tool. Results show that damage initiates at the material interface and diffuses into individual phases. In addition, the punch shear experiment results are compared with results from the single-fiber RVE model. The comparison shows that the micromechanical model can be used as a multiscale analysis tool. The findings in this work can be used to explore the performance of more complicated microstructures, e.g. woven composites.

Elastic Behavior of Coarse-Grained SnAgCu (SAC) Solder Joints Based on an Anisotropic Multi-scale Predictive Modeling Approach

Lead-free electronic interconnections made of Sn-rich solder alloys usually contain only a few highly anisotropic grains, rendering their overall thermo-mechanical behavior highly dependent on each crystal’s morphology and orientation. Miniaturization and heterogeneous integration will further reduce the length-scale of interconnections and exacerbate this piece-to-piece variation among different solder joints. The objective of this paper is to predict the elastic response and intergranular stresses in coarse-grained SAC (SnAgCu) solder joints, starting with orientation sensitive anisotropic predictive models of the elastic behavior of single crystals. The properties of the single crystal are, in turn, predicted by a multi-scale method, where each grain is modeled as a collection of Sn dendrites embedded in a eutectic Sn-Ag matrix. The eutectic phase, in turn, is modeled as an effective homogenized composite material consisting of nano-scale Ag3Sn particles embedded in a highly anisotropic tin matrix. All homogenization for prediction of single-crystal elastic properties is based on composite micromechanics, using Eshelby’s method and Mori–Tanaka homogenization. Elastic response of a few-grained solder joints is then numerically predicted from the anisotropic behavior of the single crystal, by explicitly modeling the grain morphology in finite element analysis (FEA). Stress distributions along grain boundaries are simulated and analyzed in terms of the misorientation angle between neighboring grains. The mismatch in von Mises stress along the boundaries varies up to 55% for grain structures considered here. This multi-scale predictive modeling approach is explicitly sensitive to microstructural features such as the morphology of: (1) the intermetallic compound (IMC) reinforcements in the eutectic phase; (2) dendrites; and (3) grains. Thus, this modeling approach is ideally suited for: (1) parametric studies of the effect of microstructural tailoring on solder joint thermo-mechanical behavior and (2) examining the effects of microstructural evolution caused by static and cyclic thermo-mechanical aging. This work forms the starting point for future development of microstructurally based anisotropic models of crystal-scale inelastic behavior.

Optimization of digital volume correlation computation in SR-microCT images of trabecular bone and bone-biomaterial systems.

A micromechanical characterization of biomaterials for bone tissue engineering is essential to understand the quality of the newly regenerated bone, enabling the improvement of tissue regeneration strategies. A combination of microcomputed tomography in conjunction with in situ mechanical testing and digital volume correlation (DVC) has become a powerful technique to investigate the internal deformation of bone structure at a range of dimensional scales. However, in order to obtain accurate three-dimensional strain measurement at tissue level, high-resolution images must be acquired, and displacement/strain measurement uncertainties evaluated. The aim of this study was to optimize imaging parameters, image postprocessing and DVC settings to enhance computation based on 'zero-strain' repeated high-resolution synchrotron microCT scans of trabecular bone and bone-biomaterial systems. Low exposures to SR X-ray radiation were required to minimize irradiation-induced tissue damage, resulting in the need of advanced three-dimensional filters on the reconstructed images to reduce DVC-measured strain errors. Furthermore, the computation of strain values only in the hard phase (i.e. bone, biomaterial) allowed the exclusion of large artefacts localized in the bone marrow. This study demonstrated the suitability of a local DVC approach based on synchrotron microCT images to investigate the micromechanics of trabecular bone and bone-biomaterial composites at tissue level with a standard deviation of the errors in the region of 100 microstrain after a thorough optimization of DVC computation. LAY DESCRIPTION: Understanding the quality of newly regenerated bone after implantation of novel biomaterials is essential to improve bone tissue engineering strategies and formulation of biomaterials. The relationship between microstructure and mechanics of bone has been previously addressed combining microcomputed tomography with in situ mechanical testing. The addition of an image-based experimental technique such as digital volume correlation (DVC) allows to characterize the deformation of materials in a three-dimensional manner. However, in order to obtain accurate information at the micro-scale, high-resolution images, obtained for example by using synchrotron radiation microcomputed tomography, as well as optimization of the DVC computation are needed. This study presents the effect of different imaging parameters, image postprocessing and DVC settings for as accurate investigation of trabecular bone structure and bone-biomaterial interfaces. The results showed that when appropriate image postprocessing and DVC settings are used DVC computation results in very low strain errors. This is of vital importance for a correct understanding of the deformation in bone-biomaterial systems and the ability of such biomaterials in producing new bone comparable with the native tissue they are meant to replace.

Comparison of probabilistic models for stress rupture failure in continuous unidirectional fiber composite structures

Stress rupture is an important failure phenomenon in composite overwrapped pressure vessels, which is highly unpredictable other than on a statistical basis. Even then, there are several statistical models, with varying bases in composite micromechanics and molecular failure mechanisms. Choosing among these models is not trivial, even when micromechanical details of the failure process are reasonably well appreciated, and one has available a reasonably large database of strength and lifetime data. As a result, there is little in the way of guidance to choose the most appropriate model. One important issue is that accurate predictions are desired at relatively low service loads compared to the strength, and low probabilities of failure that are far less, e.g., 10−6, than can be directly confirmed using the data itself. In essence, one needs a robust and accurate statistical model free of inconsistencies associated with such low stress levels and probabilities of failure. This paper performs an in-depth comparison of several current models, which have varying physical bases. The models compared differ in the number of parameters to be estimated from data. The results of this study, however, show that over a broad range of parameter values these models give surprisingly similar failure probability predictions. While practitioners may have a preference for one model over another, the basis for such a choice is not easily established, given the fidelity of typical data.