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.     

Numerical assessment of an experimental procedure applied to DCB tests

Numerical analysis of the analytic model of an experimental procedure to determine the crack length, the compliance and the energy release rate has been developed. As a first step, bending tests at different spans have been numerically simulated with the purpose of obtaining the flexural and out-of-plane shear moduli of the material. Then the crack length has been determined from the numerical compliance, considering the material properties previously obtained. The critical energy release rate has also been determined analytically and numerically. There is agreement between the numerical results and those obtained from the analytic model of the experimental procedure.     

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.     

Mechanical anisotropy of a monoaxially drawn polypropylene film

The tensile strength values, tensile moduli (measured with an Instron dynamometer) and sonic moduli of a monoaxially oriented polypropylene film were determined. Anisotropy was defined by the ratio between the tensile strength or modulus values in the direction of drawing and in the perpendicular direction. The difference amounting to an order of magnitude between the anisotropy of tensile strength and of the sonic modulus is explained by the existence of cracks between bundles of microfibrils. Anisotropy of the modulus determined with the instron dynamometer is lower than that of tensile strength, but higher than that of the sonic modulus. This is a consequence of the failure of the system which occurs in the transverse direction already at low deformations.     

Theoretical elastic moduli for disordered packings of interconnected spheres

A theoretical model has been developed which provides analytical expressions for the elastic moduli of disordered isotropic ensembles of spheres interconnected by physical bonds. Young's and shear moduli have been derived assuming an ideal random isotropic network and the radial distribution function for disordered packings of spheres. The interparticle interactions are accounted for in terms of surface forces for the two distinct cases of perfectly rigid spheres and spheres deformable at contact. A theoretical expression is also derived in a similar way for the bulk or compressibility modulus. In this case, an atomistic approach has been followed based on the analogy with noble gas solids and colloidal crystals. Also in this case, disordered spatial distribution of the spheres is described statistically. For the case of colloidal aggregates, a total two-body mean-field interaction potential is used which includes the Born repulsion energy. This latter contribution plays an essential role in determining the compression behavior of systems of particles aggregated in the primary minimum of the potential well and, therefore, must not be neglected. Both the expression of the Young's modulus and that of the compressibility modulus derived in this work are found to be consistent with two distinct sets of experimental data which recently appeared in the literature.     

Simulating the effect of surfactant structure on bending moduli of monolayers

We have used dissipative particle dynamics to simulate amphiphilic monolayers on the interface between oil and water. An ultralow interfacial tension is imposed by means of Monte Carlo to resemble the amphiphilic films that separate oil and water regions in microemulsions. We calculate the bending modulus by analyzing the undulation spectrum. By varying the surfactant chain length and topology we investigate the effect of surfactant structure and composition of the monolayer on the bending moduli. We find that increasing the thickness has a larger effect than increasing the density of the layer. This follows from the observations that at a given interfacial tension, the bending modulus increases with chain length and is larger for linear than branched surfactants. The increase with chain length is approximately linear, which is slower than the theoretical predictions at a fixed area. We also investigated a binary mixture of short and long surfactants compared to pure layers of the same average chain length. We find a roughly linear decrease in bending modulus with mole fraction of short surfactants. Furthermore, the mixed film has a lower bending modulus than the corresponding pure film for all mole fractions. Linking the bending moduli to the structure of the surfactants is an important step in predicting the stability of microemulsions.     

Modeling of tensile moduli in polystyrene/ polybutadiene blends

The tensile moduli of polystyrene/polybutadiene blends were studied with reference to the effect of the blend ratio. A comparison between the experimental results and the theoretical predictions of the tensile properties was also made. The models selected were the parallel, series, Halpin–Tsai, Takayanagi, Kerner, and Kunori models. Various theoretical models were applied to predict the location of the phase inversion region in these blends. Different equations were also applied for the prediction of the tensile modulus of cocontinuous structures for comparison. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 755–764, 2002     

Analysis of a reversible five-point bending configuration based on a novel two-sense support

A novel two-sense support for flexural tests has been designed and manufactured in Ikerlan. The aim of this support is to do two-sense bending fatigue tests. In order to reduce the displacement corresponding to a given stress, a novel test configuration, designated as five-point bending, is modelled analytically. Basically, it is a three-point configuration with two supports at the ends that exert forces in the same sense as the applied load. In this way, a partial clamping is obtained that can be modelled by concentrated loads. The model has been checked carrying out quasi-static three-point and five-point bending tests at different spans in unidirectional carbon/epoxy composite specimens. Flexural modulus and the out-of-plane shear modulus have been obtained by linear regression in both cases, after having obtained experimentally the stiffness of the system.     

Elastic moduli of multiblock copolymers in the lamellar phase

We study the linear elastic response of multiblock copolymer melts in the lamellar phase, where the molecules are composed of tethered symmetric AB diblock copolymers. We use a self-consistent field theory method, and introduce a real space approach to calculate the tensile and shear moduli as a function of block number. The former is found to be in qualitative agreement with experiment. We find that the increase in bridging fraction with block number, that follows the increase in modulus, is not responsible for the increase in modulus. It is demonstrated that the change in modulus is due to an increase in mixing of repulsive A and B monomers. Under extension, this increase originates from a widening of the interface, and more molecules pulled free of the interface. Under compression, only the second of these two processes acts to increase the modulus.     

Effect of internal mold release agent on flexural and inter laminar shear properties of carbon and glass fabric reinforced thermoset composites

The study is focused on thermoset composites reinforced with carbon and glass woven fabrics. Two types of thermoset resins, for example, epoxy and vinyl ester were used as the matrix. Varying concentrations of internal mold releasing (IMR) agent was used in the resin. The composites were cured both at room temperature and at 80°C. The flexural properties were studied using 3‐point bending test method. Further theinter‐laminar shear strength (ILSS) was investigated using the short beam shear strength test based on 3‐point bending. The flexural modulus of room temperature cured epoxy resin is higher than that of high temperature cured epoxy resin and cured vinyl ester resin. The flexural modulus is lowest for 1% IMR sample in epoxy system and the modulus for 0% and 2% epoxy are not significantly different. Lowest flexural strength and modulus can be observed for the combination of reinforcement and curing conditions for samples containing 1% IMR for the epoxy systems. Carbon fiber is found to be less compatible with the vinyl ester resin system and the addition of IMR to the resin degraded the properties further. Inter‐laminar shear strength for epoxy‐based composites is not much affected by presence of IMR, but in case of vinyl ester based composites there is a decrease in ILSS on addition of IMR agent. The study explains variation in flexural properties on addition of IMR and change of curing conditions. These results can be used for ascertaining variation in mechanical properties in real use.     

General analysis of the measurements of the lateral crystal lattice moduli of semicrystalline polymers by x-ray diffraction and the application to nylon 6

A mathematical representation based on a linear elastic theory is proposed by which one may investigate the dependences of molecular orientation and crystallinity on the crystal lattice moduli and linear thermal expansion coefficients in the direction perpendicular to the chain axis as commonly measured by x-ray diffraction. In the theoretical calculation, a previously introduced model was employed in which oriented crystalline phase is surrounded by oriented amorphous phase and the strains of the two phases at the boundary are identical. The mathematical analysis indicated that the lateral crystal lattice moduli and linear thermal coefficients as measured by x-ray diffraction may be different from the intrinsic crystal moduli and linear thermal coefficients of a crystal unit cell, depending on the structure of the polymer solid. The numerical calculation was applied to nylon 6. As a result, it may be confirmed that the lateral crystal lattice moduli measured by x-ray diffraction are sensitive to the morphology of the bulk speciments and close to the intrinsic crystal moduli if the morphology of the test specimen can be represented by a parallel model with respect to the original stretching longitudinal direction.     

Aging effect on the mechanical properties of hybrid gels

Sol-gel derived unsupported films and thin rods have been obtained from co-hydrolysis of triethoxysilane and methyldiethoxysilane. The materials are flexible, dense and transparent. Films and rods have been aged for different periods of time in air at room temperature. The elastic modulus has been measured by means of tensile or flexural tests. Measurements showed an increase of elastic modulus with aging time and showed different values for films and rods. The observed evolution of mechanical properties has been related to a corresponding structural modification as highlighted mainly by MAS-NMR studies. Analyses pointed out the crucial role of condensation processes and showed that the stiffness increase arises from the formation of relatively few bonds which link and constrain pre-existing mobile network regions.     

Investigation on Physical and Mechanical Properties of WPC from Corn stalk (Lignocellulosic Fiber) and HDPE

Summary: This study has tried to use HDPE and the coupling agent consistent MAPP and cornstalk fibers, create wood plastic composite material and its physical and mechanical properties such as tensile modulus, flexural modulus and humidity absorption is measured. After determining the percentage of 20, 30 and 40% of corn stalk fibers in the product and the use of two longitudinal mesh levels of 40 and 80 of them and using the 5% MAPP coupling agent testing was done and it was shown that increasing fiber length and percent increase in product humidity is absorbed. This is while the declines by increasing the fiber length changes of samples were during the tensile tests. In the bending test also increased fiber length and flexural modulus was increased.     

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.     

The influence of the mesophase on the transverse and longitudinal moduli and the major poisson ratio in fibrous composites

Expressions for the evaluation of the transverse and longitudinal elastic moduli and the major Poisson ratio of unidirectional fiber composites are derived. The model described is based on the correct version of Kerner's model, which in our case is conveniently modified by introducing a mesophase layer between the fiber and the matrix in the representative volume element surrounding the typical fiber. The expression for the longitudinal elastic modulus derived in this paper, and the law of mixtures already presented in previous papers, give concordant results. Therefore, the law of mixtures, taking the mesophase also into account, and the two-term unfolding model for the mesophase are used for the evaluation of its extent and its properties. The model was applied to a glass filament-epoxy resin composite and its predictions were found to be in good agreement with the experimental data.     

Three-dimensional numerical simulation of viscoelastic phase separation under shear: the roles of bulk and shear relaxation moduli

The morphological, dynamic and rheological characteristics in the viscoelastic phase separation(VPS) of sheared polymer solutions are investigated by three-dimensional(3D) numerical simulations of viscoelastic model. The simulations are accelerated by graphic process unit(GPU) to break through the limitation of computation power. Firstly, the morphological and dynamic characteristics of VPS under shear are presented by comparing with those in classic phase separation(CPS). The results show that the phase inversion and phase shrink take place in VPS under shear. Then, the roles of bulk and shear relaxation moduli in VPS are investigated in details. The bulk relaxation modulus slows down the phase separation process under shear, but not affects the dynamic path of VPS. The dynamic path can be divided into three stages: freezing stage, growth stage and stable stage. The second overshoot phenomenon in the shear stress is observed, and explained by the breakdown and reform of string structures. The shear modulus affects morphology evolution in the late stage of VPS under shear.     

Rheological properties of immiscible polymer blends under parallel superposition shear flow

The small amplitude oscillations can be superimposed parallelly on steady shear flows. The resulting moduli provide information about time‐ and shear‐dependent microstructure. For this purpose, model blends composed of polydimethylsiloxane and polyisobutylene with the viscosity ratio of 7.9 and 0.25 are investigated. The resulting moduli are compared with the results derived from numerical calculation as well as analytical solutions, developed here by introducing the conditions under parallel superposition flow field into MM model. Good agreement is found in the interfacial contribution of the storage moduli for blend with low volume fraction. Moreover, detailed analysis on hydrodynamic interaction between droplets is given to explain the discrepancies. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 431–440, 2008     

Calculating the rigidity of a composite with allowance for flexural deformations of the filler

Models for describing the mechanical properties of inhomogeneous fine-structure polymer systems with marked asymmetry (a large aspect ratio) of one of their components are proposed. Solution of this problem by traditional methods of composite mechanics is limited by two circumstances. The first consists in marked flexural deformations of the fine objects, which are not taken into account in the well-developed analytical techniques based on self-consistency approximations. The second is that the marked structural asymmetry causes significant difficulties in the use of numerical techniques for solving boundary-value problems of composite mechanics because the small thickness of the inclusions (along with their great length) necessitates strong discretization of the continual equations. The backbone deformation model proposed in this study for a composite containing a fine-structure rigid cluster is based on the theory of bending of thin beams. A new numerical technique, which does not require an overly fine partition of the integration domain, is developed as well. An important role of flexural deformations is demonstrated; among other things, they lead to a significant decrease in the elastic moduli of the composites.     

Elastic moduli of ultradrawn polyethylene

The five independent elastic moduli C₁₁, C₁₂, C₁₃, C₃₃, and C₄₄ of oriented high-density polyethylene with draw ratio λ from 1 to 27 have been determined from ?60 to 100°C by an ultrasonic method at 10 MHz. At low temperature the sharp rise in the axial extensional modulus C₃₃ with increasing λ and the slight changes in the other moduli result from chain alignment and the increase in the number of intercrystalline bridges connecting the crystalline blocks. At high temperature (say, 100°C) the transverse extensional modulus C₁₁, as well as the axial (C₄₄) and transverse (C₆₆) shear moduli, also show substantial increases, reflecting the prominent reinforcing effect of stiff crystalline bridges in this temperature region where the amorphous matrix is rubbery. If the crystalline bridges are regarded as the fiber phase, the mechanical behavior can be understood in terms of the Halpin–Tsai equation for aligned short-fiber composites.     

The mechanical moduli of lamellar semicrystalline polymers

Bounds on the elastic constants are derived for semicrystalline polymers whose local morphology is lamellar. Local response matrices (stiffness and compliance) are formulated in three dimensions that simultaneously incorporate uniform in-plane strain and additive forces from layer to layer of crystalline and amorphous phases and uniform stress and additive displacements normal to the lamellar surfaces. Spatial averaging of the stiffness and compliance matrices under the assumption of axially symmetric orientation gives the upper and lower bounds on the longitudinal and transverse tensile moduli and the axial and transverse shear moduli as functions of the separate phase elastic constants, the volume percent crystallinity, and the moments of the orientation 〈cos²θ〉 and 〈cos⁴θ〉. The bounds are much tighter than the Voight upper and Reuss lower bounds that do not recognize phase geometry. Using the known crystal elastic constants of polyethylene, sample calculations on isotropic unoriented materials show that the divergence of bounds at high crystallinity necessitated by the extreme crystal anisotropy shows up only at very high crystallinity. At low temperature the bounds are tight enough to specify G₁, the amorphous modulus, from the measured G and the known crystal elastic constants. At higher temperatures and lower G, the bounds are not tight enough for this purpose but the shear modulus versus crystallinity and temperature data are well fitted by the lamellar lower bound using a temperature-dependent, crystallinity-independent G₁.