Inclusion interaction and effective material properties in a particle-filled composite material system

This work presents a methodology implementing random packing of spheres combined with commercial finite element method (FEM) software to optimize the material properties, such as Young’s modulus, Poisson’s ratio, and coefficient of thermal expansion (CTE) of two-phase materials used in electronic packaging. The methodology includes an implementation of a numerical algorithm of random packing of spheres and a technique for creating conformal FEM mesh of a large aggregate of particles embedded in a medium. We explored the random packing of spheres with different diameters using particle generation algorithms coded in MATLAB. The FEM meshes were generated using software MATLAB and TETGEN. After importing the databases of the nodes and elements into commercial FEM software ANSYS, the composite materials with spherical fillers and the polymer matrix were modeled using ANSYS. The effective Young’s modulus, Poisson’s ratio, and CTE along different axes were calculated using ANSYS by applying proper loading and boundary conditions. It was found that the composite material was virtually isotropic. The Young’s modulus and Poisson’s ratio calculated by FEM models were compared to a number of analytical solutions in the literature. For low volume fraction of filler content, the FEM results and analytical solutions agree well. However, for high volume fraction of filler content, there is some discrepancy between FEM and analytical models and also among the analytical models themselves. The discrepancy is attributed to the multi-body interaction effect of the filler particles when they are getting close.     

Analysis of the elastic buckling of a plywood column

Buckling tests were conducted on specimens of 5-ply lauan plywood for a range of slenderness ratios to measure its buckling stress. Three-dimensional finite element calculations of buckling stress were performed and their validity examined by comparison with experimental results. Both experimental and calculated results revealed that buckling stress is influenced by Young’s modulus values (a measure of stiffness) obtained not only under flexural loading but also under axial loading. When the axial Young’s modulus is larger than the flexural Young’s modulus, the buckling stress is measured as larger than that obtained using the flexural Young’s modulus alone. Inversely, when the axial Young’s modulus is smaller than the flexural Young’s modulus, the buckling stress is measured as smaller than that obtained using the flexural Young’s modulus alone. Therefore, both the Young’s modulus values should be taken into account for determining the buckling stress of a plywood column.     

Effect of UV exposure on the microstructure and mechanical properties of long fiber thermoplastic (LFT) composites

In this work, the effect of ultraviolet (UV) exposure on the microstructure and dynamic Young’s modulus of polypropylene (PP)/21 vol.% E-glass LFT and neat PP was investigated. Microscopic observations revealed that the damage due to UV was confined to the surface region only in the form of surface cracking and exposure of fibers to the surface in the case of long fiber thermoplastic (LFT) and surface cracking in the case of neat PP. Fourier transform infrared spectroscopy showed that the crystallinity of PP in the damaged layer increased, both in neat PP as well as in LFT, with exposure time. This is due to chemicrystallization, which involves rearrangement of amorphous broken polymer chains into crystalline form. Crystallinity of PP in the damaged layer in LFT increased at a higher rate as compared to that in neat PP. Results of nanoindentation showed that the Young’s modulus of the PP in the damaged layer increased, with UV exposure time; the rate of modulus increase being higher in the case of LFT than in neat PP. Although the local Young’s modulus of the degraded layer increased, the dynamic Young’s modulus of the overall composite showed a decrease with UV exposure time.     

Damage model for concrete reinforced with sliding metallic fibers

This contribution presents an effective and practical three dimensional (3D) numerical model to predict the behaviour of concrete matrix reinforced with sliding metallic fibers. Considering fiber-reinforced concrete (FRC) as two-phase composite, constitutive behaviour laws of plain concrete and sliding metallic fibers were described first and then they were combined according to anisotropic damage theory to predict the mechanical behaviour of FRC. The behaviour law used for the plain concrete is based on damage and plasticity theories able to manage localized crack opening in 3D. The constitutive law of the action of sliding metallic fibers in the matrix is based on the effective stress carried by the fibers. This effective stress depends on a damage parameter related to on one hand, on the content and mechanical properties of fibers and on the other hand, on the fiber–matrix bond which itself depends on the localized crack opening. The proposed model for FRC is easy to implement in most of the finite element codes based on displacement formulation; it uses only measurable parameters like Young’s modulus, tensile and compressive strengths, fracture energies and strains at peak stress in tension and compression. A comparison between the experimental data and model results has been also provided in this paper.     

Mechanical properties of alkali treated plant fibres and their potential as reinforcement materials II. Sisal fibres

The tensile strength and Young’s modulus of sisal fibre bundles were determined following alkalisation. The results were then analysed with respect to the diameter and internal structure such as cellulose content, crystallinity index and micro-fibril angle. The tensile strength and stiffness were found to vary with varying concentration of caustic soda, which also had a varying effect on the cell wall morphological structure such as the primary wall and secondary wall. The optimum tensile strength and Young’s modulus were obtained at 0.16% NaOH by weight. The stiffness of the sisal fibre bundles obtained using the cellulose content also referred to as the micro-fibril content was compared with the stiffness determined using the crystallinity index. The stiffness obtained using the crystallinity index was found to be higher than that obtained using the cellulose content however, the difference was insignificant. Alkalisation was found to change the internal structure of sisal fibres that exhibited specific stiffness that was approximately the same as that of steel. These results indicates that the structure of sisal fibre can be chemically modified to attain properties that will make the fibre useful as a replacement for synthetic fibres where high stiffness requirement is not a pre-requisite and that it can be used as a reinforcement for the manufacture of composite materials.     

Young’s modulus of cast HMS 2112-C f composite—prediction and ultrasonic evaluation

Various models for the prediction of strengthening mechanism of metal matrix composites (MMCs) containing either fibres or particulates are analysed. Assuming that the matrix strengthening by dislocations could be treated as equivalent to the effect of different volume fraction of dispersoids, as well as by considering the effect of morphology of reinforcement on the Young’s modulus, an expression for Young’s modulus for MMCs has been derived. The Young’s modulus values thus predicted, using this model, have been validated by ultrasonically-derived values of Young’s modulus of an Al-alloy matrix composite containing 5, 8 and 12 wt% chopped carbon fibre (C _f) dispersoids, in as cast and extruded conditions. Further, the theoretically- and ultrasonically-derived Young’s modulus of cast Al-alloy-C _f composites with 5 and 8 wt%C _f have been found to be comparable with the reported values of Young’s modulus for these weight fractions.     

Bamboo fiber reinforced thermoplastic molding made of steamed wood flour

To improve the mechanical property of moldings made of steamed wood flour, layered wood moldings reinforced with steam-exploded bamboo fiber was prepared. Setting the bamboo fiber weight fractions at 25, 50, and 75%, and number of layers at three-, five-, and seven-layered wood moldings were prepared by compression molding. The results of tensile test showed that the tensile strength as well as Young’s modulus increased along with the increase in the bamboo fiber fractions. Where the bamboo fiber content was 75%, the tensile strength became approximately 3.8 to 5.8 times greater, and the tensile Young’s modulus became approximately 2.5 times greater when compared to moldings of 100% wood flour. This fact shows that bamboo fiber is effective to improve the mechanical property of wood moldings. In addition, the tensile strength also increased as the number of layers increased. This result suggested that interfacial shear stress was produced between the layers of bamboo fiber and wood flour.     

Elastic characteristics of iron-glass materials at low temperatures

We present the results of an investigation of the influence of low temperatures on the elastic characteristics of iron-glass materials with 3, 5, 12, or 20 wt.% of glass at 77–300 K and show that Young’s modulus exponentially decreases as the glass content of the material increases. We suggest a relation for the evaluation of the Young’s modulus of a composite at various temperatures according to its value at room temperature. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 42 – 46, January – February, 1998.     

Weibull modulus of nano-hardness and elastic modulus of hydroxyapatite coating

Here we report the microstructural dependence of nano-hardness (H) and elastic modulus (E) of microplasma sprayed (MIPS) 230 μm thick highly porous, heterogeneous hydroxyapatite (HAP) coating on SS316L. The nano-hardness and Young’s modulus data were measured on polished plan section (PS) of the coating by the nanoindentation technique with a Berkovich indenter. The characteristic values of nano-hardness and Young’s modulus were calculated through the application of Weibull statistics. Both nano-hardness and the Young’s modulus data showed an apparent indentation size effect. In addition, there was an increasing trend of Weibull moduli values for both the nano-hardness and the Young’s modulus data of the MIPS-HAP coating as the indentation load was enhanced from 10 to 1,000 mN. An attempt was made in the present work, to provide a qualitative model that can explain such behavior.     

Tensile strength of windmill palm (Trachycarpus fortunei) fiber bundles and its structural implications

Trachycarpus fortunei (windmill palm) is one of the most widely distributed and widely used palms in East Asia. In order to find further uses for the palm’s fibers, however, more information on their mechanical and anatomical properties is needed. With this in mind, tensile strength and Young’s modulus of windmill palm fiber bundles were investigated and the structural implications considered. The anatomical features in cross-section, the fracture mode, and the microfibril angle (MFA) of natural fiber bundles were determined. The transverse sectional area occupied by fibers in a fiber bundles (S _F) contributes to mechanical strength in practice. It was found that the ratio of S _F to the transverse sectional area of a fiber bundle dramatically increases with a decrease in bundle diameter. Therefore, tensile strength and Young’s modulus of an individual fiber bundle in this species increase in parallel with a decrease in fiber bundle diameter. The observed MFA features might have a relationship with the biomechanical movements of fiber bundles in the windmill palm. The potential uses of windmill palm fibers have been discussed.     

Multiscale homogenization models for the elastic behaviour of metal/ceramic composites with lamellar domains

This study predicts the elastic properties of an innovative metal–ceramic composite with statistically oriented domains of parallel ceramic platelets embedded in a eutectic Al–Si-alloy. For this purpose, a two-step homogenization procedure was employed by finite element- and micromechanical modelling. In a first step, the microstructure of the specimen was divided in domains with the same orientation of lamellae and the elastic properties of single domains were calculated while a precise representation of the shape of the lamellae was attempted. In a second step the elastic constants of a large specimen consisting of many domains were computed both by finite element and micromechanical modelling. The experimental Young’s modulus of such poly-domain specimens was determined by an acoustic resonance method and was lower than predicted. The differences can be explained by microcracks caused by large residual microstresses produced in these materials when they are cooled from the manufacturing temperature.     

Durability analysis of bamboo as concrete reinforcement

Durability is an actual challenge concerning all construction materials. If these materials are natural, the necessity to understand their long term behaviour is extremely important, because they are considered as having a low capacity to maintain their properties with time. Bamboo is a high strength material that can be used, in certain cases, as reinforcement in concrete. As concrete matrix has a high pH, many authors have discussed the decay of vegetal materials when used to reinforce cementitious matrix. This paper presents results of an experimental investigation made to evaluate bamboo durability to be used as concrete reinforcement. The durability was evaluated by changing the tensile strength and Young’s Modulus of bamboo. Five hundred specimens were extracted from a Dencrocalamus giganteus bamboo culms and part of them was set into concrete prisms. A set up was developed to expose the specimens to wetting and drying cycles. Each exposure to wetting and drying lasted 24 h. The specimens without concrete were submitted to a calcium hydroxide solution and the samples with concrete were immersed in tap water. Tensile strength and Young’s Modulus were measured after 7, 15, 30, 45 and 60 cycles. Results did not show any significant variation on these mechanical properties, attesting the durability of bamboo in these aggressive tests.      

Strength of graphenes containing randomly dispersed vacancies

In the present work, the tensile strength of graphenes containing randomly dispersed vacancies is predicted using an atomistic-based continuum progressive fracture model. The concept of the model is based on the assumption that graphene, when loaded, behaves like a plane-frame structure. The finite element method is used to model the structure of graphene and the modified Morse interatomic potential to simulate the nonlinear behavior of the C–C bonds. Randomly dispersed vacancies (1 missing atom) are introduced into graphene using a random numbers algorithm. Graphenes are subjected to incremental uniaxial tension. The model is capable of simulating fracture evolution considering defect interaction. The effects of size, chirality, defect density and defect topology on the Young’s modulus, strength and failure strain of graphenes are examined. Computed results reveal that vacancies may counterbalance the extraordinary mechanical properties of graphene, since 4.4% of missing atoms, corresponding to 13.2% of missing bonds, result in a 50% reduction in Young’s modulus and tensile strength of the material. Also found is a secondary effect of defect topology.     

Scaling functions in conical indentation of elastic-plastic solids

Summary The finite element method was used to simulate the conical indentation of elastic-plastic solids with work hardening. The ratio of the initial yield strength to the Young’s modulus Y/E ranged from 0 to 0.02. Based on the calculation results, two sets of scaling functions for non-dimensional hardness H/K and indenter penetration h are presented in the paper, which have closed simple mathematical form and can be used easily for engineering application. Using the present scaling functions, indentation hardness and indentation loading curves can be easily obtained for a given set of material properties. Meanwhile one can use these scaling functions to obtain material parameters by an instrumented indentation load-displacement curve for loading and unloading if Young’s modulus E and Poisson’s ratio ν are known.     

Probabilistic analysis of a pull-out test

This paper presents a sensitivity analysis of the pull-out strength of reinforcement embedded in concrete. Considering both European and French design codes, this failure strength depends on the variability of uncertain parameters such as Young’s modulus of concrete and yield stresses of materials (concrete and steel); moreover, two failure modes can be observed in the studied experimental test. A methodology allowing the characterization of the sensitivity of the pull-out strength to these uncertain parameters is derived. These parameters are modeled by Lognormal random variables. Results show the evolution of the pull-out strength for different anchorage lengths. Probability density functions of the random variable modeling the failure strength are computed using probabilistic methods. A finite element model is also built to quantify uncertainties concerning failure modes, computing 95% confidence intervals.     

Effect of microstructure on the modulus of PAN-based carbon fibers during high temperature treatment and hot stretching graphitization

The changes of microstructure and Young’s modulus of PAN-based carbon fibers during the high temperature treatment (2400–3000 °C, stretching 0%) and hot stretching graphitization (0–5%, 2400 °C) were compared. It was observed that although the Young’s modulus of the fibers could be increased by the two graphitization techniques, the microstructure parameters determined by X-ray diffraction were different for the same value of modulus. The relationship between microstructure and modulus showed that Young’s modulus not only depended on the preferred orientation, but also related to the crystallite size (L _c and L _a ) and shape (L _a /L _c ). On the other hand, it was found that crystallite size of the fibers was mainly affected by heat treatment temperature and the crystallite shape could be altered by hot stretching graphitization. Further investigation indicated that the fibers were composed of turbostratic carbon structure even after heat treated to 3000 °C, which could be detected from the absence of 101 and 112 peaks in X-ray diffraction pattern, and the interlayer spacing (d₀₀₂) and preferred orientation (Z) were only 0.3430 nm and 14.71°, respectively.     

Ultrasonic evaluation of polyether ether ketone and carbon fiber-reinforced PEEK

Polyether ether ketone (PEEK) and carbon fiber-reinforced (CFR) PEEK are commonly used in medical implants. This study evaluated the mechanical moduli of PEEK and CFR PEEK using nondestructive, ultrasonic tests. The Young’s modulus of CFR PEEK was determined in all the spatial directions. Ultrasonic attenuation has not been studied extensively in PEEK, and not at all in CFR PEEK. The broadband ultrasound attenuations (BUAs) were determined for PEEK and CFR PEEK. The average Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio of PEEK were 4.21, 1.52, 6.25, and 0.388 GPa, respectively. The maximum and minimum Young’s moduli of CFR PEEK were 15.1 and 5.1 GPa measured parallel and perpendicular to the fiber axis respectively. The longitudinal and transverse BUAs of PEEK were 1.33 and 4.37 dB/cm MHz, respectively. The longitudinal BUAs of CFR PEEK parallel and perpendicular to the fiber axis were 2.43 and 1.45 dB/cm MHz, respectively. Characterization of Young’s modulus of CFR PEEK in all the spatial directions is useful for stiffness matching in implant design. The BUA values are useful in modeling the interaction of ultrasound and the PEEK materials and can also be used for developing non-destructive tests to find structural defects in implants made from these materials.     

Mechanical properties and apatite forming ability of TiO<Subscript>2</Subscript> nanoparticles/high density polyethylene composite: Effect of filler content

Composite materials consisting of TiO₂ nanoparticles and high-density polyethylene (HDPE), designated hereafter as TiO₂/HDPE, were prepared by a kneading and forming process. The effect of TiO₂ content on the mechanical properties and apatite forming ability of these materials was studied. Increased TiO₂ content resulted in an increase in bending strength, yield strength, Young’s modulus and compressive strength (bending strength = 68 MPa, yield strength = 54 MPa, Young’s modulus = 7 GPa, and compressive strength = 82 MPa) at 50 vol% TiO₂. The composite with 50 vol% TiO₂ shows a similar strength and Young’s modulus to human cortical bone. The TiO₂/HDPE composites with different TiO₂ contents were soaked at 36.5°C for up to 14 days in a simulated body fluid (SBF) whose ion concentrations were nearly equal to those of human blood plasma. The apatite forming ability, which is indicative of bioactivity, increased with TiO₂ content. Little apatite formation was observed for the TiO₂/HDPE composite with 20 vol% content. However, in the case of 40 vol% TiO₂ content and higher, the apatite layers were formed on the surface of the composites within 7 days. The most potent TiO₂ content for a bone-repairing material was 50 vol%, judging from the mechanical and biological results. This kind of bioactive material with similar mechanical properties to human cortical bone is expected to be useful as a load bearing bone substitute in areas such as the vertebra and cranium.     

Nanomechanical and surface behavior of polydimethylsiloxane-filled nanoporous anodic alumina

In this article, the mechanical and wetting behavior of anodic aluminum oxide (AAO) and nanoporous-filled AAO were investigated using nanoindentation and contact angle measurements. The results showed that the nanoporous AAO was hydrophobic with a contact angle of 105°. The polymer filling affected the surface property and reduced the contact angle to 84°. The effects of the nanoporous filling on the Young’s modulus and the hardness are investigated and discussed. A three-dimensional finite element model was also successfully developed to understand the nanoindentation-induced mechanism. A maximum von Mises stress of 1058 MPa occurred beneath the indenter.