Predictions of young's modulus of inorganic fibrous particulate‐reinforced polymer composites

In this study, the factors affecting the Young's modulus of inorganic fibrous particulate‐reinforced polymer composites were analyzed, and a new expression of the Young's modulus was derived and was based on a simplified mechanical model. This equation was used to estimate the composite Young's modulus. The estimated relative Young's modulus increased nonlinearly with increasing filler volume fraction. Finally, we verified the equation preliminarily by quoting the measured Young's modulus values of poly(butylene terephthalate)/wollastonite, polypropylene/wollastonite, and nylon 6/wollastonite composites reported in the literature. Good agreement was shown between the predictions and the experimental data of the relative Young's modulus values for these three composite systems. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 2957–2961, 2013     

The dependence of the elastic properties of silica/alumina materials on the conditions used for firing

The dependence of the elastic properties of a range of powder compact samples has been measured as a function of firing variables. It was found that both Young's modulus and Poisson's ratio are particularly sensitive to the peak temperature and the time for which the peak temperature is maintained, over a range of these variables for which density is not significantly affected. The material investigated is used industrially for the manufacture of wall tiles. Firing trials conducted in an industrially operated tunnel kiln have indicated that sufficient variation in firing conditions exists, in the cross-section of the tunnel kiln, to cause significant variation in the values of Young's modulus and Poisson's ratio of bodies fired in different positions in the kiln. Microstructural examination of bodies produced to have very similar densities but vastly different values of Young's modulus and Poisson's ratio has indicated that the dependence of Young's modulus and Poisson's ratio on firing conditions can be explained by the extent of sintering within the ceramic matrix.     

The prediction of elastic modulus of the mullite fiber network based on the actual structure architecture

Accurately establishing the relationship between the network architecture characteristics and performance of fibrous porous ceramics is instructive for structural design and performance control. In the present work, fibrous, high porous (82.87–90.02%), low density (0.247–0.512 g/cm³) and low elastic modulus (50.62–188.56 MPa) mullite ceramics were fabricated by freeze casting. The three dimensional network architectures were characterized by X-ray tomography technique and quantitatively analyzed by 3D image analysis software (imorph, www.imorph.fr). The radius (5.04 µm), types, lengths (64.72–96.49 µm) and orientations (0.87–1.45, anisotropy parameter) of fiber segments in the network architecture were investigated. The extracted results were employed to predict the Young's modulus of the mullite fibrous porous ceramics according to a model based on the bending and axial compression of single fiber segment. The predicted Young's modulus agreed well with the experimental results. The differences of Young's modulus and Poisson ratio between the prediction and the model of Markaki and Clyne were compared. The comparison showed that the difference became larger when the aspect ratio of the fiber segment was less than 6 due to the effect of axial compression. The predicted Poisson ratio had a certain dependence on fiber segment aspect ratio and got close to the constant (1/π) reported by Markaki and Clyne with the increase of fiber segment aspect ratio.     

The determination of the axial Young's modulus of honeycomb specimens under bending

For solid specimens, Young's modulus is commonly determined from straightforward uniaxial tension experiments. However, honeycomb specimens are far more challenging to test in tension, and it is therefore desirable to conduct bending experiments to determine Young's modulus. The premise of this work is that the bending response of honeycomb specimens may be significantly different from that of solid specimens, and therefore it is necessary to establish a sound protocol for the determination of the axial Young's modulus of honeycomb specimens under bending. Toward this goal, we present results of a study that combines experimental, finite element simulation, and classical beam theory approaches. These results confirm that accurate measurements of Young's modulus of honeycombs require careful consideration of the specimen geometry and analysis of the data. We demonstrate that the use of conventional Bernoulli‐Euler's beam theory to interpret the data requires very slender specimens. We also show that less slender specimens can be used if the experimental data is interpreted on the basis of three‐dimensional elasticity theory and numerical simulations. A third option is to use a combination of moderately slender specimens and Timoshenko's beam theory.     

Effects of process conditions on Young's modulus and strength of extrudate in short‐fiber‐reinforced polypropylene

We examined the effects of process conditions on Young's modulus and tensile strength of extruded short‐fiber reinforced thermoplastics. With increasing extrusion ratio and decreasing extrusion temperature, the fiber alignment increases, the mean fiber length decreases, and the mechanical properties of the matrix are improved. The orientation parameter, mean fiber length, Young's modulus, and tensile strength of the matrix are described as a function of extrusion ratio and extrusion temperature. The models proposed by Fukuda and Kawata, and Fukuda and Chou are applied to predict Young's modulus and tensile strength of the composites using orientation parameter. By comparing the predicted Young's modulus and tensile strength with experimental results, the validity of the models is examined. The prediction of Young's modulus agreed quit with the experimental results. The tensile strength of composite extruded below the melting point nearly matched that of the neat matrix. There is no the strengthening effect of the fiber since the angle between fracture surface and fiber direction is very small. POLYM. COMPOS. 28:29–35, 2007. © 2007 Society of Plastics Engineers     

Porous biodegradable polyester blends of poly(L‐lactic acid) and poly(ε‐caprolactone): physical properties,morphology, and biodegradation

Poly(L ‐lactic acid) (PLLA), poly(ε‐caprolactone) (PCL), and their films without or blended with 50 wt% poly(ethylene glycol) (PEG) were prepared by solution casting. Porous films were obtained by water‐extraction of PEG from solution‐cast phase‐separated PLLA‐blend‐PCL‐blend‐PEG films. The effects of PLLA/PCL ratio on the morphology of the porous films and the effects of PLLA/PCL ratio and pores on the physical properties and biodegradability of the films were investigated. The pore size of the blend films decreased with increasing PLLA/PCL ratio. Polymer blending and pore formation gave biodegradable PLLA‐blend‐PCL materials with a wide variety of tensile properties with Young's modulus in the range of 0.07–1.4 GPa and elongation at break in the range 3–380%. Pore formation markedly increased the PLLA crystallinity of porous films, except for low PLLA/PCL ratio. Polymer blending as well as pore formation enhanced the enzymatic degradation of biodegradable polyester blends. Copyright © 2006 Society of Chemical Industry     

Intrinsic Mechanical Properties of 20 MAX‐Phase Compounds

The intrinsic mechanical properties of 20 MAX‐phase compounds are calculated using an ab initio method based on density functional theory. A stress versus strain approach is used to obtain the elastic coefficients and thereby obtain the bulk modulus, shear modulus, Young's modulus, and Poisson's ratio based on the Voigt–Reuss–Hill (VRH) approximation for polycrystals. The results are in good agreement with available experimental data. It is shown that there is an inverse correlation between Poisson's ratio and the Pugh ratio of shear modulus to bulk modulus in MAX phases. Our calculations also indicate that two MAX compounds, Ti₂AsC and Ti₂PC, show much higher ductility than the other compounds. It is concluded that the MAX‐phase compounds have a wide range of mechanical properties ranging from very ductile to brittle with the “A” in the MAX phase being the most important controlling element. The measured Vickers hardness in MAX compounds has no apparent correlation with any of the calculated mechanical parameters or their combinations.     

Elastic behaviour of zirconium titanate-zirconia bulk composite materials at room and high temperature

Zirconium titanate-zirconia composites have potential for applications involving variations of temperature. Elastic characterization is necessary to evaluate stresses developed in materials which may be used in these kinds of applications. In this work, Young's and shear modulus and Poisson's ratio of two zirconium titanate-zirconia bulk composites (Z(Y)T70 and Z(Y)T50) have been determined at room temperature by the Impulse Excitation Technique (IET). Furthermore, Young's modulus (E) has been determined at high temperature (up to 1400 °C) for both composites. Young's modulus of Z(Y)T70 composite decreases ≈6% between room temperature and 400 °C due to the presence of zirconia. From 400 to 1400 °C, the decrease of E (≈14%) is due to the presence of zirconium titanate. Young's modulus behaviour at high temperature of Z(Y)T50 composite is determined by the degree of microcrack healing, which depends on the maximum temperature reached.     

Isothermal and adiabatic Young's moduli of alumina and zirconia ceramics at elevated temperatures

The elastic moduli (Young's moduli) of alumina and zirconia ceramics with porosities ranging from almost dense (2–3%) to highly porous (46–52%), the latter prepared with starch as a pore-forming agent, have been measured via impulse excitation and four-point bending tests from room temperature up to more than 1200 °C. It is shown that, independent of the temperature and the material, the porosity dependence of the Young's modulus is well predicted by our exponential relation and that, irrespective of porosity, the temperature dependence follows a master curve that is characteristic of the material (for alumina exhibiting a decrease with a gradually growing tangent slope and for zirconia exhibiting a steep decrease with an inflection point at moderately elevated temperatures below 400 °C). Differences between isothermal (static) and adiabatic (dynamic) values are negligible as long as the materials are purely elastic (i.e. at temperatures below approximately 1000 °C).     

The Influence of Interfacial Adhesion on the Predicted Young's Modulus of Mica-Reinforced Nylon-6

Particle-filled polymer composites have become attractive because of their wide applications and low cost. Various factors influence the mechanical properties of thermoplastic composites. Of these, the aspect ratio of the reinforcement, interfacial adhesion, and binder content are the most important. Other than these, the particle size and particle size distribution of the reinforcement also influence the mechanical properties. In this paper, injection molded mica composites were investigated, using nylon-6 as a binder. Many models are available to predict the Young's modulus of the composites. A theoretical model for Young's modulus by Lewis and Nielsen was used to predict the Young's modulus of the composites. Tetra isopropyl titanate (TYZOR® TPT) was used to modify the adhesion between the reinforcement and the binder by mixing it with the reinforcement prior to compounding. It was found that Young's modulus was greater than the predicted values.     

Fiber orientation control of short‐fiber reinforced thermoplastics by ram extrusion

In this study we examine the fiber orientation distribution, fiber length and Young's modulus of extruded short‐fiber reinforced thermoplastics such as polypropylene. Axial orientation distributions are presented to illustrate the influence of extrusion ratio on the orientation state of the fibrous phase. Fibers are markedly aligned parallel to the extrusion direction with increasing extrusion ratio. The orientation state of extruded fiber‐reinforced thermoplastics (FRTP) is almost uniform throughout the section. The control of fiber orientation can be easily achieved by means of ram extrusion. Experimental results are also presented for Young's modulus of extruded FRTP in the extrusion direction. Young's modulus follows a linear trend with increasing extrusion ratio because the degree of the molecular orientation and the fiber orientation increases. The model proposed by Cox, and Fukuda and Kawada describes the effect of fiber length and orientation on Young's modulus. The value of the orientation coefficient is calculated by assuming a rectangular orientation distribution and calculating the fiber distribution limit angle given by orientation parameters. By comparing the predicted Young's modulus with experimental results, the validity of the model is elucidated. The mean fiber length linearly decreases with increasing extrusion ratio because of fiber breakage due to plastic deformation. There is a small effect on Young's modulus due to fiber breakage by ram extrusion.     

Enhanced mechanical and thermal properties of nanodiamond reinforced low density polyethylene nanocomposites

In this study, the reinforcement effects of low-content hydrophilic nanodiamond (ND) on linear low-density polyethylene (PE) nanocomposites were investigated. ND was incorporated in PE via simple solution blending. The obtained PE/ND nanocomposites were characterized using scanning electron microscopy, ultraviolet–visible spectra, X-ray diffraction, tensile test, thermogravimetry, and differential scanning calorimetry. Generally, PE/ND nanocomposites with poor interfacial interaction cause large agglomerates, resulting in brittle and poor mechanical properties. Owing to the different natures of non-polar PE and polar ND, the higher the ND content, the larger the agglomerates formed in the nanocomposites. However, PE/ND nanocomposites show unique mechanical properties, that is, the Young's modulus, tensile strength, elongation at break, and toughness increased upon the incorporation of ND. The Young's modulus of the PE/ND nanocomposites exceeded the theoretical value calculated using the Halpin–Tsai model. In addition, the toughness increased by 18% at only 0.5 wt% ND loading. Furthermore, there was an increase in the thermal degradation temperature, melting temperature, and crystallization temperature.     

Gel‐spinning of partially saponificated poly(vinyl alcohol)

DMSO/water (80/20 volume ratio) solutions of commercial poly(vinyl alcohol)s (a‐PVA₉₉, a‐PVA₈₈) with degrees of saponification of 99.3 and 88 mol % were gel‐spun into methanol (−20 and −70°C). The dry filaments obtained were drawn at 200°C (a‐PVA₉₉) and 150–180°C (a‐PVA₈₈). The maximum draw ratio and Young's modulus were 26 and 34 GPa for a‐PVA₉₉ and 21 and 24 GPa for a‐PVA₈₈ (drawing temperature: 160°C). So, at first, the dry filaments obtained for a‐PVA₈₈ were drawn at 150–180°C until 10 times their original length. Moreover, the predrawn a‐PVA₈₈ filaments were perfectly saponificated under fixing at the both ends and then the filaments were redrawn at 200°C. The maximum draw ratio and Young's modulus for the filaments (a‐PVA_88→99) predrawn at 150°C were 28 and 39 GPa, respectively. The a‐PVA_88→99 filaments had two melting peaks (228 and 236°C). © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 2872–2876, 2000     

Topological model of alkali germanate glasses and exploration of the germanate anomaly

Germanate glasses are of particular interest for their excellent optical properties as well as their abnormal structural changes that appear with the addition of modifiers, giving rise to the so-called germanate anomaly. This anomaly refers to the nonmonotonic compositional scaling of properties exhibited by alkali germanate glasses and has been studied with various spectroscopy techniques. However, it has been difficult to understand its atomic scale origin, especially since the germanium nucleus is not easily observed by nuclear magnetic resonance. To gain insights into the mechanisms of the germanate anomaly, we have constructed a structural model using statistical mechanics and topological constraint theory to provide an accurate prediction of alkali germanate glass properties. The temperature onsets for the rigid bond constraints are deduced from in situ Brillouin light scattering, and the number of constraints is shown to be accurately calculable using statistical methods. The alkali germanate model accurately captures the effect of the germanate anomaly on glass transition temperature, liquid fragility, and Young's modulus. We also reveal that compositional variations in the glass transition temperature and Young's modulus are governed by the O–Ge–O angular constraints, whereas the variations in fragility are governed by the Ge–O radial constraints.     

Preparation of high-modulus nylon 6 fibers by vibrating hot drawing and zone annealing

To prepare high-modulus fibers, the vibrating hot-drawing and zone-annealing methods have been applied to nylon 6. The vibrating hot drawing was repeated two times, increasing the applied tension; further, the zone annealing was superposed on the vibrating hot-drawn fibers. The superstructure and mechanical properties of each step fiber were investigated. The vibration under a cooperation of heating and tension was very useful for increasing the draw ratio, birefringence, and orientation factor of the amorphous chains. Consequently, the obtained fiber indicated high moduli, namely, Young's modulus of 23 GPa and the dynamic storage modulus at room temperature of 25.3 GPa. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:1993–2000, 1998     

Study of the flexural modulus of natural fiber/polypropylene composites by injection molding

Effect of fiber compression on flexural modulus of the natural fiber composites was examined. The kenaf, bagasse, and polypropylene were mixed into pellets, and composites were fabricated by injection molding. To predict flexural modulus of the composites, the Young's modulus of kenaf and bagasse fiber were measured. Using the obtained Young's modulus, the flexural modulus of the composites was predicted by Cox's model that incorporates the effect of fiber compression. It was found that those fibers with high Young's modulus were more compressed than that with low Young's modulus. Moreover, the distribution of fiber length and orientation in the composites were also investigated. To calculate the orientation factor for the prediction model, the distribution function of fiber orientation was determined to a triangular function. The flexural modulus of the composites increased with increase of volume fraction. The predicted values were in good agreement with the experimental values. Furthermore, it was revealed by SEM that the porous structure of the natural fibers was compressed. The fiber compression ratio (3.6) in bagasse was higher than that in kenaf (1.4) due to the difference in porous structure. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 911–917, 2006     

Theoretical and experimental analyses of Young's modulus and thermal expansion coefficient of the alumina-mullite system

Young's moduli (E) and thermal expansion coefficients (TECs) of the alumina–mullite–pore system (96.4–99.5% relative density) were measured for a wide mullite fraction range from 0 to 100 vol%. Both E and TEC values decreased at high mullite fractions. These properties were theoretically analyzed with four proposed model structures that were constructed by three-phase systems of mullite (or alumina) continuous phase 2–pore dispersed phase 1–alumina (or mullite) dispersed phase 3. The ratios of E(theoretical)/E(experimental) and TEC(theoretical)/TEC(experimental) were very close to unity, depending on the mullite fraction. That is, the measured E and TEC values are closely related to the change in the composite microstructure as a function of mullite fraction.     

Effect of pore clustering on the mechanical properties of ceramics

The reduction in strength and, to a lesser extent, Young's modulus with increased amounts of discrete pores is frequently greater than that predicted by models based on a homogenous pore distribution. The effect of pore distribution has been examined in the present work by producing samples containing a non-homogenous distribution of pores and comparing the results with data reported for samples containing homogenously distributed pores. Young's modulus and, to a greater extent, strength were shown to have stronger dependencies on the porosity content than would be predicted for homogeneous samples. By considering the material as a composite consisting of a pore-rich continuous phase containing a dispersion of pore-free material, various models were used to predict behaviour. It was found that the strength of the material is likely to be governed by the properties of the continuous phase, while the Young's modulus is a function of the properties of the two phases, with the porous phase being described by the Spriggs equation. The implications of the different dependencies of strength and Young's modulus in terms of the resistance to crack propagation following a thermal shock were then considered. Predictions of retained strength were in good agreement with those observed after water quenching.