Numerical assessment of the analytical models used to determine flexural and shear moduli in I-Beams when the tensile and compressive moduli are different

The different compressive and tensile moduli of fibre reinforced composites have been considered in the analysis of the flexural and shear moduli of I-beams. Firstly, the neutral axis has been determined analytically and then, assuming that location of the neutral axis, the analytical flexural modulus of I-beams has also been obtained. In order to assess the proposed procedure, virtual pure bending and three-point bending tests at different spans have been carried out using the finite element method. The compressive and tensile moduli have been taken into account by defining two parts in the numerical models. The numerical flexural and shear moduli have been determined by reducing the data obtained in the virtual tests. Analytical and numerical results are in good agreement. Therefore, the flexural modulus determined by the proposed analytical approach can be introduced as a material property in the finite element method.     

Measurement of flexural modulus of polymeric foam with improved accuracy using moiré method

The flexural modulus of polymeric foams determined from three-point bending tests is usually inaccurate due to the local deformation undergone by the material during testing. The machine used in the test gives deflection values larger than the actual deflection of the foam specimen due to the deformation of the material at the loading point. This leads to errors in the computation of the modulus value. In this work, the deflection values of a beam made of polymeric foam in a three-point bending test were determined using the moiré method. The change in the moiré pattern at the neutral axis of the foam during loading was recorded and converted into deflection values. The deflection data were used to generate the stress–strain curve from which the flexural modulus of the foam material was determined. The proposed method was verified using aluminum beams, where a high correlation between the deflection data from the machine readings and the moiré method was obtained. The flexural modulus of the foam determined using the moiré method was found to be within 3% of the value published in the material data sheet.     

Investigation of flexural properties and failure behaviour of biaxial braided CFRP

In this research, the experimental tests of quasi-static three-point bending and three-point bending fatigue were carried out for a ±25° biaxial braided carbon fibre reinforced polymer (CFRP) manufactured using vacuum assisted resin transfer moulding (VARTM). A finite element (FE) model was also set up for quasi-static testing and the prediction results revealed that local fibre volume fraction (FVF) is a primary source affecting the mechanical properties of braided CFRP. The fatigue of the braided CFRP was defined as three different stages according to the flexural modulus results. The damage modes of the test specimens were observed via a digital microscope and scanning electron microscope (SEM) and the process-induced defects were summarised. With compiled results and observations, this study provides a better understanding of failure and fatigue behaviour of biaxial braided composites and their flexural properties which offers a good basis for any further research in fibre volume fractions, structure design and manufacturing for braided CFRP.     

Elastic and viscoelastic properties of sugarcane bagasse-filled poly(vinyl chloride) composites

Elastic and viscoelastic properties of sugarcane bagasse-filled poly(vinyl chloride) were determined by means of three-point bending flexural tests and dynamic mechanical and thermal analysis. The elastic modulus, storage modulus, loss modulus, and damping parameter of the composites at fibre contents of 10, 20, 30, and 40% in mass were determined, as well as those of the unfilled matrix. There was a correlation between the elastic modulus and storage modulus of the composites. Moreover, the elastic and viscoelastic properties of the composites were highly influenced by fibre content.     

Determination of compressive strength of unidirectional composites by three-point bending tests

A simple way for obtaining compressive strength of unidirectional composites by three-point bending tests is proposed in the present work. The interpretation of test results includes the stress singularity induced by the applied concentrated load and the determination of the contact zone between loading roller and specimen. Unidirectional carbon/epoxy composite T6T/F593 from Hexcel Composites has been tested by three-point bending with different thicknesses and spans. When failure occurs by compressive stresses, experimental results agree with the strength obtained by compressive tests. The best agreement is obtained in the case of 7 mm nominal thickness and span of 120 mm.     

Determination of longitudinal compressive strength of long fiber composites by three-point bending of [0m/90n/0p] cross-ply laminated strips

A new test method is proposed for measuring longitudinal compressive strength of composite laminates by three-point bending of cross-ply laminates. Optimal cross-ply configuration has been designed in order to get compressive stresses higher than tensile stresses. Thermal and mechanical stresses have been calculated based on the hypothesis of Classical Beam Theory. Cross-ply carbon/epoxy strips with different thicknesses and spans have been tested by three-point bending. Failures on the compressive side have been observed in all cases and no evidence of transverse cracking has been found. Experimental results agree well with compressive strength reference values. The possibility of determination of compressive and tensile strengths by three-point bending from a unique cross-ply lay-up has been also analyzed.     

Fatigue Behavior of Composite Sandwich Panels Under Three Point Bending Load

In this paper, the bending fatigue tests of honeycomb sandwich panels are carried out by using an improved three-point bending test fixture, and the S-N curves at different stress ratios are obtained. Through the records of fatigue damage in the experiment, the failure mode of the honeycomb sandwich panels and the source of fatigue damage are determined. At the same time, through the calculation of the shear stress distribution on the honeycomb wall, the reasons for the difference in the failure morphology of the L-direction and W-direction sandwich panels are clarified. Besides, a life prediction method is proposed and its effectiveness in predicting the fatigue life of sandwich panels has been verified.     

Flexural and tensile moduli of flexible FR4 substrates

A flexible FR4 substrate is not only a core part of current integrated circuit assemblies, but also a promising material for flexible electronics applications. The thin composite sheet typically contains a single-ply of glass fabric which is impregnated with epoxy resin. The single-ply reinforcement leads to large heterogeneity along the through-thickness direction, which causes different behavior in the flexural and tensile moduli. However, no comparative study between the flexural and tensile moduli has been presented for commercialized flexible FR4 substrates. In this study, the flexural and tensile moduli of flexible FR4 substrates were measured using a three-point bending test and a direct tensile test, respectively. Three FR4 substrates were prepared with a different number of glass fabric plies and different types of epoxy resin, with a total thickness ranging from 100 to 150 μm. The effect of the span-to-depth ratio on the flexural modulus was first examined in order to obtain the true flexural modulus from the three-point bending test. For comparison, the strain was accurately measured using a video extensometer to obtain the tensile modulus. In-plane anisotropy and temperature dependence were also investigated for both the flexural and tensile moduli.     

Measurement of the elastic modulus of single bacterial cellulose fibers using atomic force microscopy

The ability of the atomic force microscope to measure forces with subnanonewton sensitivity at nanometer-scale lateral resolutions has led to its use in the mechanical characterization of nanomaterials. Recent studies have shown that the atomic force microscope can be used to measure the elastic moduli of suspended fibers by performing a nanoscale three-point bending test, in which the center of the fiber is deflected by a known force. We extend this technique by modeling the deflection measured at several points along a suspended fiber, allowing us to obtain more accurate data, as well as to justify the mechanical model used. As a demonstration, we have measured a value of 78 +/- 17 GPa for Young's modulus of bacterial cellulose fibers with diameters ranging from 35 to 90 nm. This value is considerably higher than previous estimates, obtained by less direct means, of the mechanical strength of individual cellulose fibers.     

Determination of Activation Energy for Glass Transition of an Epoxy Adhesive Using Dynamic Mechanical Analysis

The activation energy associated with the glass transition relaxation of an epoxy system has been determined by using the three-point bending clamp provided in the recently introduced TA Instruments DMA 2980 dynamic mechanical analyzer. A mathematical expression showing the dependency of modulus measurements on the sample properties and test conditions has also been derived. The experimental results showed that the evaluation of activation energy is affected by the heating rate and test frequency, as well as the criterion by which the glass transition temperature (T _g) is established. It has been found that the activation energy based on the loss tangent (tanδ) peak is more reliable than on the loss modulus (E ₂) peak, as long as the dynamic test conditions do not cause excessive thermal lags. This revised version was published online in August 2006 with corrections to the Cover Date.     

Investigation of bending modulus of fiber-reinforced syntactic foams for sandwich and structural applications

Polymer composite foams or syntactic foams containing 0.9, 1.76, 2.54, 3.54 and 4.5 vol% of E-glass short fibers were processed and subjected to a three-point bending test. The results show that the flexural modulus increased with fiber content, with the exception of 1.76% and 3.5% of fibers. This deviation was due to a higher void content for 1.76% and a non-uniform distribution of fibers in the polymer composite foam system for 3.5%. However, in general, the incorporation of chopped strand fibers improved the flexural behavior of the syntactic foam system without much variation in density, thus making the reinforced syntactic foams act as improved core materials for sandwich and other structural applications. Copyright © 2007 John Wiley & Sons, Ltd.     

Study of the influence of nanoparticles on the behavior of composite materials

The objective of this work is to study the influence of additives of multi-walled carbon nanotubes (MWCNT) and silica nano-powder (SiO₂) on the mechanical behavior of epoxy resin. Different volume fractions of MWCNT and SiO₂were added. Mechanical characterization by tensile, three-point bending and Charpy tests were carried out. The experimental results show an increase in the mechanical performance of the mixtures (MWCNT ​+ ​epoxy), (SiO₂ ​+ ​epoxy) up to 2% of additive. Beyond this value, a degradation of performance was observed. The addition of MWCNT gives better results when compared to the addition of SiO₂. K_IC-K_CV correlations were made using empirical formulas to estimate the critical stress intensity factor K_IC from the impact energy of the Charpy test.Unfortunately, this estimation does not provided a promising results, but other optimization methods were used to fit these empirical models to the behavior of our nanocomposites for which a good estimate was obtained after fitting these empirical models for SiO₂.     

原位沉析法制备壳聚糖棒材的研究

以壳聚糖凝胶膜为模板,将壳聚糖溶液与NaOH凝固液隔离,利用膜渗透原位沉析法制备了高性能的壳聚糖棒材(d=4.5mm),其弯曲强度、弯曲模量和剪切强度分别为92.4MPa,4.1GPa和36.5MPa.扫描电子显微镜(SEM)分析结果表明,原位沉析法制备的壳聚糖棒材具有同心筒状层叠结构,并对其成型机理进行了探讨.     

Polymer nanowire elastic moduli measured with digital pulsed force mode AFM

The mechanical bending behavior of polymer nanowires-polypyrrole and poly(3,4-ethylene dioxythiophene-co-styrene sulfonate)-produced by template molding were measured using a new innovation in atomic force microscopy (AFM). Digital pulsed force mode (DPFM) was used to image and simultaneously perform three-point bend tests along nanowires spanning microchannels in silicon. The bending profiles were analyzed for apparent elastic moduli variations along the suspended length of individually isolated nanowires and compared to classic beam deflection models for various geometric and boundary conditions. The elastic moduli calculated from these AFM data are 2-7 times that expected for bulk polymer values (approximately 1-3 GPa), demonstrating an apparent strengthening of nanostructured polymer even for diameters greater than 100 nm--the accepted boundary for nanoscience. Furthermore, detailed analysis of deflection data versus loading location demonstrates the experimental dependence on test geometry and inherent errors in relying solely on midpoint bending measurements or any single loading configuration for nanomechanical testing as well as the significant contribution of nanoindentation effects.     

Mechanical, thermal, and moisture absorption properties of nano-clay reinforced nano-cellulose biocomposites

In this research, fully environment-friendly, sustainable and biodegradable ‘green’ composites were fabricated. A novel material comprised of microfibrillated cellulose and laponite clay with different inorganic/organic ratios (m/m) was prepared. The composites were characterized by tensile, bending and water absorption tests as well as dynamic mechanical analysis. The morphologies of these nanocomposites were evaluated through scanning electron microscopy. Results showed considerable improvement of mechanical properties; specifically in elastic modulus, tensile strength and flexural modulus with the addition of nanoclay up to 7.5 wt% nano-clay. The modulus of elasticity increased significantly by about 26 % at 5 wt% nanocaly. The flexural modulus increased by about 90 % at 7.5 wt% nanoclay. However, with an increased load of clay in the nanocomposite, the mechanical properties decreased due to the agglomeration of excessive nanoclay. The storage modulus was significantly increased at high temperature with increasing the load of nanoclay.     

Changes in the mechanical properties of tooth-colored direct restorative materials in relation to time

The objective of this study was to determine the flexural strength, flexural modulus, Vickers hardness of a packable composite (Surefil), and an ormocer (Definite) in comparison with a microhybrid composite (Z-100), a microfil composite (Silux Plus) and a polyacid-modified composite resin (Dyract). Flexural strength and flexural modulus were determined using a three-point bending device. Microhardness was measured with a Vickers indentor. The specimens of each material were prepared according to manufacturer's instructions. The specimens were stored in artificial saliva at pH 6, all at 37°C. The groups were tested at the beginning of the test, at 3 months and at 6 months. Flexural strength values of Surefil and Definite showed a progressive increase. The highest MPa values were determined for Surefil (134.4 MPa) and the lowest MPa values were obtained for Dyract (59.6 MPa). The highest flexural modulus values were revealed for Surefil (10.000 GPa). Z-100, Silux Plus and Definite showed a tendency to decline in relation to time for their flexural modulus. GPa values of Silux Plus were stable at 3 and 6 months. Vickers hardness numbers showed that Surefil was the hardest and Dyract was the weakest material. Copyright © 2003 John Wiley & Sons, Ltd.     

Comparison of caustics and the strain gage method for measuring mode I stress intensity factor of PMMA material

Both caustics and strain gage methods are shown to be effective in the determination of mode I stress intensity factor (SIF) at the crack tip. However, there is a lack of investigation with regard to the quantitative comparison of the two methods. In this paper, dynamic three-point bending tests were performed on polymethyl methacrylate (PMMA) specimens using the caustic and the strain gage methods simultaneously. The SIFs calculated by these two methods were analyzed and compared. The results show that the deviations of the SIF values between caustics and the strain gage method are slightly more significant when the orientation of the gage is obtuse rather than acute. Furthermore, this deviation increases with the gage mounted closer to the edge of the specimen when the orientation is acute. In addition, the whole cracking process could be clearly recorded by the caustic method, while the time-evolution of SIF can be roughly obtained with a limited number of strain gages during the crack propagation.     

Pressure effects on bending elasticities of surfactant monolayers in a ternary microemulsion composed of aerosol-OTD2O/decane

Pressure effects on the bending elasticities of surfactant monolayers have been investigated in a microemulsion system composed of aerosol-OT (AOT), D2O, and deuterated decane by means of small angle neutron scattering, neutron spin echo (NSE), and dynamic light scattering (DLS). In this system, a water-in-oil droplet structure, at ambient temperature and pressure, decomposes into two phases, under both increasing temperature and pressure. The authors' previous study showed that the bending modulus kappa of monolayers slightly decreased with increasing temperature, while it increased with increasing pressure. Temperature and pressure dependencies of kappa were explained in terms of a microscopic model, which takes into account the interactions between surfactant molecules. In this paper, the authors present the temperature and pressure dependencies of kappa obtained by the analysis combined with DLS and NSE experiments. The values of the bending modulus and mean displacement of the second-order droplet deformation are reasonable. It was further confirmed that an increase in the attractive interaction between hydrocarbon tails of AOT molecules with increasing pressure could be the origin of the pressure-induced phase transition.     

Thermal,viscoelastic, and mechanical properties of DCPD-containing polymers

The thermal, viscoelastic, and mechanical properties of cured dicyclopentadiene (DCPD)-containing polymers prepared from novel DCPD-modified unsaturated epoxypolyesters and styrene were evaluated. This was accomplished using thermogravimetric analysis, differential scanning calorimetry, dynamic mechanical analysis, three-point bending test, and Brinell’s hardness. The thermal, viscoelastic, and mechanical properties of DCPD-containing polymers were strongly dependent on chemical structure. The cross-linking density (υ _e) of obtained networks increased with increasing content of carbon–carbon double bonds in the poly(ester) structure. In addition, the introduction of DCPD rings into the poly(ester) structure increased the rigidity of the molecular backbone. It resulted in obtaining polymers which showed great improvement in mechanical properties including remarkably higher storage modulus ( E_{20 ^°\textC}^￠ E_{{20\,{}^{\circ}{\text{C}}}}^{'} ), flexural modulus at bending (E _mod), hardness, lower extension at maximum force (ε-F _max), as well as higher thermal stability. These good properties make these materials highly promising as potential candidates for structural applications.     

A proposal for a novel evaluation method of the bending velocities of polymer actuators

This paper proposes a novel evaluation method for three types of velocities of the bending processes of polymer actuators. These velocities are the initial, bending, and backtracking velocities, and the method considers three processes of the bending motion. By calculating the time–width differentiation of the displacement of each process, the initial, bending, and backtracking velocities can be evaluated. Δt of 0.1, 1.0, and 10.0 s were considered to be the differentiations of bending displacement, and the initial, bending, and backtracking velocities were calculated to be 2.15, 0.46, and 0.002 mm/s, respectively. By using the method proposed here, we found that the initial velocity at 75%RH is 2.5 times faster than it was at 45%RH by increasing the adsorption of water. Copyright © 2013 John Wiley & Sons, Ltd.