CHAPTER 4 MODELING OF MECHANICAL PROPERTIES OF POLYMER COMPOSITES
|
|
- Geraldine Little
- 5 years ago
- Views:
Transcription
1 CHAPTER 4 MODELING OF MECHANICAL PROPERTIES OF POLYMER COMPOSITES 4. Introduction Fillers added to polymer matrices as additives are generally intended for decreasing the cost (by increase in bulk) of the in addition to improving some of the physical and mechanical properties of the material. Filler, a chemically inert material can decrease properties like linear expansion coefficient, lubricancy, toughness and elongation percent, while properties like viscosity, thermal conductivity, stiffness, hardness, flame resistance and yield strength increase. Fillers can be organic and inorganic. Non-metallic materials like talc, calcium carbonate, metallic fibers and silica belong to inorganic category while natural fibers (organic origin), wood flour and synthetic fibers are organic fillers. Geometrically, fillers may be spherical, sheet, needle form and fibrous. Filler shape, type and its concentration can influence the mechanical properties of the polymer to which it is added. Particles with non-spherical shape lead to have more viscosity and manifest in several problems during composite shaping (Valavala and Odegard, 2005). Traditionally, composites were reinforced with micronsized inclusions. Recently, processing techniques have been developed to allow the size of inclusions to go down to nanoscale (Jordan, et al., 2005). Although experimental based research can ideally be used to determine structure-property relationships of nanostructured composites, experimental synthesis and characterization of nanostructured composites demands the use of sophisticated processing methods and testing equipment; which could result in exorbitant costs. To this end, computational modeling techniques for the determination of mechanical properties of nanocomposites have proven to be very effective (Liu & Chen, 2003; Sheng, et al., 2004; Chen & Liu, 2004). Computational modeling (CM) for predicting the mechanical properties of composites is highly desirable. Computational modeling of the mechanical properties of polymeric nano-composites for design and development of nanocomposite structures for engineering applications has been suggested by Valavala and Odegard, (2005). The modeling of polymer-based nano-composites has become an 8
2 important topic in recent times because of the need for the development of these materials for engineering applications. It was found that deal with modeling and offering appropriate formulations for the estimation of mechanical properties of polymeric composites. Different modeling theories and equations for describing the reinforcing mechanisms of polymer matrix by additives (like fillers) have been suggested that are discussed in this chapter. 4.2 Overview of the Modeling Method The importance of modeling in understanding of the behavior of matter is illustrated in Figure 4.. The earliest attempt to understanding material behavior is through observation via experiments. Careful measurements of observed data are subsequently used for the development of models that predict the observed behavior under the corresponding conditions. The models are necessary to develop the theory. The theory is then used to compare predicted behavior to experiments via simulation. This comparison serves to either validate the theory, or to provide a feedback loop to improve the theory using modeling data. Therefore, the development of a realistic theory of describing the structure and behavior of materials is highly dependent on accurate modeling and simulation techniques. Valavala and Odegard (2005) have presented a review of modeling techniques for predicting the mechanical behavior of polymeric nano-composites. It is proposed that mechanical properties of nano-structured materials can be determined by a select set of computational methods. Details Computational Chemistry and Computational Mechanics modeling are presented. Computational Chemistry techniques are primarily used to predict atomic structure using first-principles theory, while Computational Mechanics is used to predict the mechanical behavior of materials and engineering structures. To facilitate the development of nano-structured polyamide composite materials for this purpose, constitutive relationships must be developed that predict the bulk mechanical properties of the materials as a function of the molecular structure of the polyamide and reinforcement. These constitutive relationships can be used to influence the design of these materials before they are synthesized. Even though it has been shown that these materials have the potential to have excellent mechanical properties, the relatively 9
3 high costs of development and manufacturing of nano-polymer composites has been prohibitive. A lower cost approach is the use of particles in the polymer. Figure 4. The schematic of developing theory and validation of experimental data through simulation. Vollenberg and Heikens (989) explained that if there is a strong interaction between the polymer and the particle, the polymer layer in the immediate proximity of the particle will have a higher density. For most systems, density is proportional to elastic modulus, so the region directly surrounding the inclusions will be a region of high modulus. The polymer right outside this high modulus region will have a lower density due to the polymer chains that are moved towards the particle. For large particles, the size of the low density region will be relatively large, and the contribution of the high modulus filler will be diminished. For nano-particles, the number of particles for a given volume fraction is much larger, thus the particles will be much closer to one another. If the particles are densely packed, the boundary layer of polymer at the interface will comprise a large percentage of the matrix and can create a system where there is no space for a low modulus region to form. This results in the elastic moduli of composites with smaller particle (nano) size being greater than the moduli of composites with larger inclusions (Jordan, et al., 2005). The small inter-particle distance in nano-composites was used as another parameter to explain the changes in the elastic modulus and strength of these materials compared to the composites with micron-sized particles. 20
4 The same parameter also plays a role in the glass transition temperature changes observed in nano-composites versus composites with micron-sized reinforcement. Ash, et al. (2002) found that for their system the glass transition temperature was constant until around 0.5% weight fraction of particles, and then had a sharp drop, and then it remained constant for weight fractions above %. When there is little or no interfacial interaction between the filler and matrix and the inter-particle distance is small enough, the polymer between two particles acts as a thin film, and for thin films, the glass transition temperature decreases with the drop of film thickness. The distance between particles in a composite with the filler weight fraction below 0.5% is relatively large, and in such case the polymer between each particle is not considered to belong to the thin film regime. As the filler concentration increases, the inter-particle distance and the resulting thickness of the film decrease. This theory, however, does not explain why the glass transition temperature levels off rather than continues to drop as a function of increasing weight fraction of the filler. The behavior of polymeric nano-composite systems are shown in the Table 4.. From the viewpoint of fundamental laws, reinforcing effect of nano-particles is dependent on Aspect Ratio and also on the interactions between fillers particles and polymeric matrix (Jordan, et al., 2005). Figure 4.2 shows typical tensile stress displacement curves for PVC and its nano-composites. Pure PVC is brittle, however, when CaCO 3 nano-particles are added in the PVC matrix, the composites show ductile behaviors, such as stress whitening and necking. Their Young s modulus, tensile yield strength and elongation at break are calculated and plotted in Figures 4.3 to 4.5. In Figure 4.3, Young s modulus of the PVC/CaCO 3 nano-composites is observed to increase with the loading of CaCO 3 nano-particles up to 5 wt% and then decrease marginally at 7.5 wt%. These results confirm that the CaCO 2 nano-particles do stiffen PVC. The yield strength of the nano-composites is plotted in Figure 4.5 and is broadly independent of nano-particle loading (Xie, et al., 2004). 2
5 Table 4. Behavior of polymer nano-composite (Jordan, et al., 2005). Attribute Crystalline State Amorphus State Elastic modulus Increase w/volume fraction Increase or no change with decrease of size Increase w/volume fraction Increase w/decrease size Greater increase than for good interaction Yield stress/strain Ultimate stress/strain Density/volume Strain-to failure T g Crystallinity Viscoalasticity Increase w/volume fraction Increase w/decrease size Decrease with addition of particles Increase w/ decrease size No unfilled result for change in V f Lower than pure for small volume fraction Increased volume as size decreases N/A Decrease with addition of particles Decrease with addition of particles Decrease with addition of particles N/A No major effect No major effect Increase w/volume fraction Increase w/decrease size N/A Increase w/volume fraction Increase w/decrease size Increase w/volume fraction Increase w/decrease size N/A Decrease with addition of particles Nano>micro after 20% weight Decrease with addition of particles Increased volume as size decreases N/A increase with addition of particles increase with addition of particles Increase w/decrease size Level until 0%, drops off level -0 N/A N/A Increase w/volume fraction nano less Decrease with addition of particles Figure 4.2 Tensile stress - displacement curves for PVC and nano-composites 22
6 Figure 4.3 Variation of Young s modulus of nano-composite with nano-particle loading. Figure 4.4 Variation of tensile yield strength of nano-composite with nano-particle loading. 4.3 Theoretical Developments 4.3. Guth s Equation and Nicolais-Narkis Theory The modulus and yield strength of particle-filled composites can be predicted by Guth s equation (Equation 4.) and Nicolais-Narkis theory (Equation 4.2), respectively (Bliznakov, et al., 2000): E C = E m φ f + 4. φ f 2 (4.) 23
7 σ yc = σ ym.2 φ f 2/3 (4.2) Where, E and σ y are Young s modulus and yield strength, respectively; subscripts m, f, and c denote matrix, filler and composite, and Φ f is volume fraction of particles. It is quite obvious, that the experimental modulus (except at 7.5 wt% loading) and yield strength values are larger than the predicted values, as shown in Figures 4.3 and 4.4. These results indicate the limitations of the theories when applied to nano-composites. The strong interaction between CaCO 3 nano-particles and PVC matrix caused by the large interfacial areas has led to much higher elongations-at-break, with a maximum at 5 wt% nanoparticles, as shown in Figure 4.5 (Xie, et al., 2004). Figure 4.5 Variation of Charpy notched impact energy of nano-composites with nanoparticle loading (Xie, et al., 2004). The specific surface area of filler gives important information about the filler reinforcement properties. In his review paper on filler-elastomeric interactions, Wang (998) notes that the specific surface area of carbon black directly affects dynamic mechanical properties. When the surface area for silica increases, there is a higher compound viscosity which requires more energy (torque) for mixing and also contributes to the buildup of heat in the mixture. If too much heat is generated the compound will cure prematurely. At the 24
8 same time, as the filler surface areas increases the tensile and tear strength of the rubber increases. Much is still unknown concerning the mechanisms of how these properties directly relate to reinforcement and what the exact mechanisms of reinforcement are (Jordan, et al., 2005) The Mixture Rule The field of composite material behavior can be studied from two perspectives: micromechanics and macromechanics. The goal of most micromechanics approaches is to determine the elastic moduli or stiffness of a composite material in terms of the elastic properties of the constituent materials. Most of the analytical models presented presume the idealization that there is perfect adhesion between the phases and that the particles are spherical and evenly dispersed. Some of the earlier attempts in modeling composites were performed by Einstein and Guth. Guth and Smallwood extended Einstein s theory to explain rubber reinforcement. Both of these attempts have proved to be applicable, but only at low concentrations of particulate. Thus, the focus will be on the newer works, separated into two approaches, defined as either a mechanics of materials or an elasticity approach. In the mechanics of materials approach some simplifying assumptions are made, the most significant of which is that the strain in the matrix is equal to the strain in the particulate. With this assumption the most simplistic of all methods of predicting the moduli of a composite, known as the rule of mixtures, can be obtained (Haghighat, et al., 2005): E c = E f φ f + E p φ p (4.3) E c, E f, and E p, are the elastic modulus of compound, filler and polymer matrix, respectively. φ f is the volume fraction of filler and φ p is the volume fraction of polymer matrix. The mixing law represents the linear relationship of elastic modulus in which the effects of size, shape and particle distribution has been neglected. Generally, the law of mixtures has been considered as the upper limit of elastic modulus. The absolute lower bound on elastic modulus can be obtained, assuming equal stress in the matrix and particulate (Haghighat, et al., 2005; Zhang, et al., 2003): 25
9 E c = φ f + φ (4.4) p E f E p The upper and lower limits on elastic moduli represent the most widely used relationships derived through material mechanics approach. Although other expressions have also been proposed using various assumptions, the elasticity approach has received maximum attention (Haghighat, et al., 2005). Two of the most important models which are now applied for the nano-composites are proposed by Hashin and Halpin-Tsai model (Haghighat, et al., 2005). Although, the calculated values resulting from these models do not accurately predict the mechanical properties, these may be considered as an estimation of elastic modulus for nanocomposite samples. In the following, the related equations for these models have been discussed Hashin-Shtrikman Model The composite spheres model, introduced by Hashin, consists of a graduation of sizes of spherical particles fixed in a continuous matrix phase. In line with this model, Hashin and Shtrikman developed the bounds for the shear and bulk modulus (Hashin, 962; Wang and Pyrz, 2004; Haghighat, et al., 2005). The resulting bounds on the Young s modulus are as follows: Lower bound for the Bulk moduli, K l : K l = K + φ 2 (4.5) 3φ + K 2 K 3K + 4G The upper bound on K u is, K u = K 2 + φ (4.6) 3φ + 2 K K 2 3K 2 + 4G 2 Similarly, the lower bound of the Shear moduli, G l : G l = G + φ 2 G 2 G + 6(K + 2G )φ 5G (3K + 4G ) (4.7) 26
10 and the corresponding upper bound: G u = G 2 + φ G G 2 + 6(K 2 + 2G 2 )φ 2 5G 2 (3K 2 + 4G 2 ) (4.8) The resulting bounds on the Young s modulus are following equations: Lower bound: E l = 9Kl G l 3K l + G l = 9 k + 3 k + φ 2 k 2 k + k 2 k + φ 2 3φ G + 3k + 4G 3φ + G + 3k + 4G φ 2 G 2 G + 6(k + 2G )φ 5G (3k + 4G ) φ 2 G 2 G + 6(k + 2G )φ 5G (3k + 4G ) (4.9) Upper bound: E u = 9Ku G u 3K u + G u = 9 k k 2 + k k 2 + k k 2 + φ φ 3φ G k 2 + 4G 2 3φ + G k 2 + 4G 2 φ G G 2 + 6(k + 2G )φ 5G 2 (3k 2 + 4G 2 ) φ G G 2 + 6(k + 2G )φ 5G 2 (3k 2 + 4G 2 ) (4.0) In the above equation, subscripts and 2 refer to the polymer and the filler respectively. It may be worth mentioning that the above equations are applicable when K <K 2 and G <G 2 (Wang and Pyrz, 2004; Haghighat, et al., 2005). 27
11 4.3.4 Halpin-Tsai Model The semi-empirical equations suggested by Halpin-Tsai are yet another way for predicting the composite properties, equations 4. and 4.2: Where E = E ( + ζηφ 2 ) ηφ 2 (4.) η = E 2 E E 2 E + ζ (4.2) These equations result from simplification and approximation of micromechanical complex models. The importance of this method lies in its simplicity and its ability for generalization. The only problem in this method is related to the parameter of ζ, which is best determined experimentally. Generally, this parameter for particulate composites has been approximated to have a value of 2 for matter properties (Haghighat, et al., 2005). Some other mechanical relationships for the Young s modulus and Poisson s ratio of composites have been given by Budiansky (965) as follows: E = υ = 9KG 3K + G 3K 2G 6K + 2G (4.3) (4.4) and for each constituent K n = E n 3 6υ n (4.5) G n = E n 2 + 2υ n (4.6) Where, n = or 2 (denoting continuous and filler phases respectively). 28
12 4.3.5 Micro-mechanics Models It is well known that most composite materials are anisotropic/transversely isotropic. Many composite analyses are performed using a macroscopic approach where the properties of the composites are homogenized to produce an anisotropic, yet homogeneous continuum before the analysis is conducted. However, the micromechanical approach to analyzing composites considers the filler and the matrix separately and applies the loading and the boundary conditions at the individual filler and matrix level. The overall properties of the composite are developed by relating the average stresses and strains. Thus the micro-mechanical approach is expected to provide much more detail into the true interactions between the filler and matrix, potentially leading to a more accurate model of the composite behavior (Gardner, 994). Two continuum-based micro-mechanic models are briefly described in the following sub-sections Mori-Tanaka Model The Mori-Tanaka approach, which is based on the Eshelby Tensor, can be used to predict the elastic properties of two-phase composites (matrix and effective particle phases) as a function of the effective particle volume fraction and geometry and they may be perfectly bonded to each other (Mori & Tanaka, 973; Benveniste, 987). The Mori- Tanaka approach has been used to accurately predict overall properties of composites when the reinforcements are on the micrometer-scale level, or higher (Odegard, et al., 2005). At these higher length scales, the assumption of the existence of two phases is apparently acceptable. However, for nanometer-sized reinforcement, it has been shown that the molecular structure of the polymer matrix is significantly perturbed at the reinforcement/polymer interface, and this perturbed region is on a length scale that is the same at that of the nanometer-sized reinforcement. Therefore, at the nanometer level, the reinforcement and adjacent polymer region is not accurately described as consisting of just two phases, thus the Mori-Tanaka model is not expected to perform well for nanostructured reinforcements Effective Interface Model Because of the aforementioned drawbacks to the Mori-Tanaka approach, another modeling approach was developed. The effective interface model can be used to predict 29
13 the elastic properties of a composite with effective particles that have an interface of the same spherical shape as the effective particle. The effective interface has a finite size and models the region immediately surrounding the spherical reinforcement, which is commonly referred to as an interphase or an interaction zone (Dunn & Ledbetter, 995). Odegard, et al. (2005) reported that unlike the Mori-Tanaka model, the effective interface model should be applicable to both nanometer-sized and larger-sized reinforcement. 4.4 Final Remarks on Models A critical analysis of the brief literature on the modeling of the mechanical properties of polymer composites presented above suggests that there is no general appropriate and correct model applicable for all nano-composites for estimating their properties. The conclusions from these researches and studies may be summarized as follows:. Considering the dimensions of polymer chains and their crystalline assemblies, it can be said that all polymers have structure on the nanometer size scale and, further, that the mechanical properties of polymers are governed by the interactions of these nanostructures with one another. Therefore, to influence the interactions that govern the mechanical properties of polymers, specific nano-scale reinforcement is efficient and beneficial. 2. Where the particle/matrix interface has a high energy, a very stiff network can be formed. In such situations, the stiffness of the matrix is much lower than the network stiffness and the mechanical behavior of the composite material can be rather well predicted on the basis of a structural modeling. 3. From a very general point of view, the elastic modulus of a filled polymer is affected by (i) the elastic properties of its constitutive phases (i.e., modulus and Poisson s ratio), (ii) the volume fraction of filler (iii) the morphology (i.e., shape, aspect ratio, and distribution of the filler into the polymeric matrix), and (iv) the interactions between fillers. Various models are proposed in the literature to understand the complex interplay between these parameters and to predict of the elastic modulus of polymer composites. 4. The available theoretical models may be used to predict elastic modulus as a first approximation or initial estimation. 30
14 5. Micromechanical approach to analyzing composites considers the filler and the matrix separately and applies the loading and the boundary conditions at the individual filler and matrix level. 4.5 Summary To facilitate the development of nano-structured composites, constitutive relationships are developed that predict the bulk mechanical properties of the materials as a function of the molecular structure of the polyamide and reinforcement. These constitutive relationships can be used to influence the design of these materials before they are synthesized. In this study the following theoretical models obtained from literature were used to predict Young s modulus of micro and nano-composite samples synthesized.. The Rule of Mixtures 2. Nicolais-Narkis Theory and the Guth s equation 3. The composite sphere model of Hashin-Shtrikman. 4. The semi-empirical micromechanical model of Halpin-Tsai. Results obtained from these computations and their predictive capability is discussed later in Chapter-6. 3
Continuum Modeling Techniques to Determine Mechanical Properties of Nanocomposites
International OPEN ACCESS Journal Of Modern Engineering Research (IJMER) Continuum Modeling Techniques to Determine Mechanical Properties of Nanocomposites Sonali Gholap 1, Dr. Dhananjay R. Panchagade
More informationModule 7: Micromechanics Lecture 34: Self Consistent, Mori -Tanaka and Halpin -Tsai Models. Introduction. The Lecture Contains. Self Consistent Method
Introduction In this lecture we will introduce some more micromechanical methods to predict the effective properties of the composite. Here we will introduce expressions for the effective properties without
More informationMODELLING INTERACTION EFFECT OF NANOSILICA PARTICLES ON NANOSILICA/EPOXY COMPOSITE STIFFNESS
MODELLING INTERACTION EFFECT OF NANOSILICA PARTICLES ON NANOSILICA/EPOXY COMPOSITE STIFFNESS Mulyadi a*, I. Gitman a, C. Pinna a, C. Soutis b a Department of Mechanical Engineering, The University of Sheffield,
More informationAM11: Diagnostics for Measuring and Modelling Dispersion in Nanoparticulate Reinforced Polymers. Polymers: Multiscale Properties.
AM11: Diagnostics for Measuring and Modelling Dispersion in Nanoparticulate Reinforced Polymers Polymers: Multiscale Properties 8 November 2007 Aims Provide diagnostic tools for quantitative measurement
More informationTABLE OF CONTENTS. Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA
Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA TABLE OF CONTENTS 1. INTRODUCTION TO COMPOSITE MATERIALS 1.1 Introduction... 1.2 Classification... 1.2.1
More informationModule 7: Micromechanics Lecture 29: Background of Concentric Cylinder Assemblage Model. Introduction. The Lecture Contains
Introduction In this lecture we are going to introduce a new micromechanics model to determine the fibrous composite effective properties in terms of properties of its individual phases. In this model
More informationMechanical and Thermal Properties of Coir Fiber Reinforced Epoxy Composites Using a Micromechanical Approach
Mechanical and Thermal Properties of Coir Fiber Reinforced Epoxy Composites Using a Micromechanical Approach Sandhyarani Biswas Department of Mechanical Engineering, N.I.T Rourkela, INDIA Abstract: Now-a-days,
More informationCHEM-C2410: Materials Science from Microstructures to Properties Composites: basic principles
CHEM-C2410: Materials Science from Microstructures to Properties Composites: basic principles Mark Hughes 14 th March 2017 Today s learning outcomes To understand the role of reinforcement, matrix and
More informationMechanical Behavior of Fullerene Reinforced Fiber Composites with Interface Defects through Homogenization Approach and Finite Element Method
, pp.67-82 http://dx.doi.org/1.14257/ijast.215.78.6 Mechanical Behavior of Fullerene Reinforced Fiber Composites with Interface Defects through Homogenization Approach and Finite Element Method P. Prasanthi
More informationChapter 6: Mechanical Properties of Metals. Dr. Feras Fraige
Chapter 6: Mechanical Properties of Metals Dr. Feras Fraige Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility Toughness
More informationThermal-Mechanical Decoupling by a Thermal Interface Material
Thermal-Mechanical Decoupling by a Thermal Interface Material Haibing Zhang, Ph.D. Research and Development Chemist Andy Cloud Product Development Manager Abstract Thermal-mechanical decoupling by a silicone
More informationNITRILE RUBBER (NBR) NANOCOMPOSITES BASED ON DIFFERENT FILLER GEOMETRIES (Nanocalcium carbonate, Carbon nanotube and Nanoclay)
CHAPTER 5 NITRILE RUBBER (NBR) NANOCOMPOSITES BASED ON DIFFERENT FILLER GEOMETRIES (Nanocalcium carbonate, Carbon nanotube and Nanoclay) 5.1 Introduction Nanocalcium carbonate (NCC) is a particulate nanofiller
More informationMicromechanics modeling for the stiffness and strength properties of glass fibers/cnts/epoxy composites
High Performance Structures and Materials V 279 Micromechanics modeling for the stiffness and strength properties of glass fibers/cnts/epoxy composites M. Kim, F. A. Mirza & J. I. Song School of Mechatronics
More informationPredicting Elastic Properties of Unidirectional SU8/ZnO Nanocomposites using COMSOL Multiphysics
Predicting Elastic Properties of Unidirectional SU8/ZnO Nanocomposites using COMSOL Multiphysics Neelam Mishra 1, and Kaushik Das *1 1 School of Minerals Metallurgical and Materials Engineering, Indian
More informationDIGIMAT for NANO-COMPOSITES
DIGIMAT for NANO-COMPOSITES Document Version 2.0.1, February 2010 info@e-xstream.com www.e-xstream.com Materials: Engineering Plastics, Reinforced Plastics, Mineral and Clay fillers. e-xstream Technology:
More informationFig. 1. Circular fiber and interphase between the fiber and the matrix.
Finite element unit cell model based on ABAQUS for fiber reinforced composites Tian Tang Composites Manufacturing & Simulation Center, Purdue University West Lafayette, IN 47906 1. Problem Statement In
More informationUNIT I SIMPLE STRESSES AND STRAINS
Subject with Code : SM-1(15A01303) Year & Sem: II-B.Tech & I-Sem SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) UNIT I SIMPLE STRESSES
More informationModeling of the Mechanical Properties of Nanoparticle/Polymer Composites
Polymer, Vol. 46, no. 2, pp. 553-562 (2005) Modeling of the Mechanical Properties of Nanoparticle/Polymer Composites G.M. Odegard 1*, T.C. Clancy 2, T.S. Gates 3 1 Michigan Technological University, Department
More informationComputational Analysis for Composites
Computational Analysis for Composites Professor Johann Sienz and Dr. Tony Murmu Swansea University July, 011 The topics covered include: OUTLINE Overview of composites and their applications Micromechanics
More information3D Compression Molding
Autodesk Simulation Moldflow Insight 2014 3D Compression Molding Executive summary In this work, the simulation results from a program developed for the three-dimensional analysis of compression molding
More informationA micromechanical model for effective elastic properties of particulate composites with imperfect interfacial bonds
International Journal of Solids and Structures 42 (2005) 4179 4191 www.elsevier.com/locate/ijsolstr A micromechanical model for effective elastic properties of particulate composites with imperfect interfacial
More informationMECHANICS OF CARBON NANOTUBE BASED COMPOSITES WITH MOLECULAR DYNAMICS AND MORI TANAKA METHODS. Vinu Unnithan and J. N. Reddy
MECHANICS OF CARBON NANOTUBE BASED COMPOSITES WITH MOLECULAR DYNAMICS AND MORI TANAKA METHODS Vinu Unnithan and J. N. Reddy US-South American Workshop: Mechanics and Advanced Materials Research and Education
More informationSize Effect of Clay Filler Particles on Mechanical Properties of Pultruded Polymer Composites Under Shear Loading
Minnesota State University, Mankato Cornerstone: A Collection of Scholarly and Creative Works for Minnesota State University, Mankato All Theses, Dissertations, and Other Capstone Projects Theses, Dissertations,
More informationEffect of different crosslink densities on the thermomechanical properties of polymer nanocomposites
Effect of different crosslink densities on the thermomechanical properties of polymer nanocomposites *Byungjo Kim 1), Joonmyung Choi 2), Suyoung Yu 3), Seunghwa Yang 4) and Maenghyo Cho 5) 1), 2), 3),
More informationModule 4: Behaviour of a Laminae-II. Learning Unit 1: M1. M4.1 Mechanics of Composites. M4.1.1 Introduction to Mechanics of Composites
Module 4: Behaviour of a Laminae-II Learning Unit 1: M1 M4.1 Mechanics of Composites M4.1.1 Introduction to Mechanics of Composites The relation between ply uniaxial strengths and constituent properties
More informationModule-4. Mechanical Properties of Metals
Module-4 Mechanical Properties of Metals Contents ) Elastic deformation and Plastic deformation ) Interpretation of tensile stress-strain curves 3) Yielding under multi-axial stress, Yield criteria, Macroscopic
More informationHow materials work. Compression Tension Bending Torsion
Materials How materials work Compression Tension Bending Torsion Elemental material atoms: A. Composition a) Nucleus: protons (+), neutrons (0) b) Electrons (-) B. Neutral charge, i.e., # electrons = #
More informationIMPACT PROPERTIES OF POLYMERIC NANOCOMPOSITES WITH DIFFERENT SHAPE OF NANOPARTICLES. Robert VALEK a, Jaroslav HELL a
IMPACT PROPERTIES OF POLYMERIC NANOCOMPOSITES WITH DIFFERENT SHAPE OF NANOPARTICLES Robert VALEK a, Jaroslav HELL a a SVUM, a. s., Podnikatelska 565, 19 11 Prague, Czech Republic, valek@svum.cz Abstract
More informationMechanical Properties of Polypropylene/Calcium Carbonate Nanocomposites
Materials Research, Vol. 12, No. 4, 517-522, 2009 2009 Mechanical Properties of Polypropylene/Calcium Carbonate Nanocomposites Daniel Eiras a, *, Luiz Antonio Pessan b a PPG-CEM/DEMa, Universidade Federal
More informationMechanical Properties of Polymers. Scope. MSE 383, Unit 3-1. Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept.
Mechanical Properties of Polymers Scope MSE 383, Unit 3-1 Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept. Structure - mechanical properties relations Time-dependent mechanical
More informationMICROMECHANICAL DEFORMATIONS IN PARTICULATE FILLED POLYMERS: THE EFFECT OF ADHESION
MICROMECHANICAL DEFORMATIONS IN PARTICULATE FILLED POLYMERS: THE EFFECT OF ADHESION K. Renner, J. Móczó, B. Pukánszky Laboratory of Plastics and Rubber Technology, Department of Physical Chemistry and
More informationTensile stress strain curves for different materials. Shows in figure below
Tensile stress strain curves for different materials. Shows in figure below Furthermore, the modulus of elasticity of several materials effected by increasing temperature, as is shown in Figure Asst. Lecturer
More informationComposite models 30 and 131: Ply types 0 and 8 calibration
Model calibration Composite Bi-Phase models 30 and 3 for elastic, damage and failure PAM-CRASH material model 30 is for solid and 3 for multi-layered shell elements. Within these models different ply types
More informationME 582 Advanced Materials Science. Chapter 2 Macromechanical Analysis of a Lamina (Part 2)
ME 582 Advanced Materials Science Chapter 2 Macromechanical Analysis of a Lamina (Part 2) Laboratory for Composite Materials Research Department of Mechanical Engineering University of South Alabama, Mobile,
More informationEvaluation of Effective Elastic Moduli Using Micromechanics
IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Evaluation of Effective Elastic Moduli Using Micromechanics To cite this article: Misba Mehdi Mrs. et al 2018 IOP Conf. Ser.:
More informationAn integrated approach to the design of high performance carbon fibre reinforced risers - from micro to macro - scale
An integrated approach to the design of high performance carbon fibre reinforced risers - from micro to macro - scale Angelos Mintzas 1, Steve Hatton 1, Sarinova Simandjuntak 2, Andrew Little 2, Zhongyi
More informationOutline. Tensile-Test Specimen and Machine. Stress-Strain Curve. Review of Mechanical Properties. Mechanical Behaviour
Tensile-Test Specimen and Machine Review of Mechanical Properties Outline Tensile test True stress - true strain (flow curve) mechanical properties: - Resilience - Ductility - Toughness - Hardness A standard
More informationComposite Materials. Fibre-Matrix Interfaces. There is nothing there really except the two of you (or the fiber and matrix).
Composite Materials Fibre-Matrix Interfaces There is nothing there really except the two of you (or the fiber and matrix). Composite Parameters Fibre properties Composite Interfaces Matrix properties Fibre
More informationComposite Structures. Indian Institute of Technology Kanpur
Mechanics of Laminated Composite Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 21 Behavior of Ribbon Fiber Composites Ribbon Reinforced Composites: Introduction Quite often,
More informationMATERIALS. Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle?
MATERIALS Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: A. Composition
More informationPolymer Nanocomposites: Introduction
Chapter 1 Polymer Nanocomposites: Introduction Downloaded via 148.251.232.83 on April 5, 2019 at 22:23:00 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published
More informationEXPERIMENTAL STUDY ON YOUNG S MODULUS E OF A POLYMER COMPOSITE REINFORCED BY NANO TITANIUM DIOXIDE PARTICLES
Vietnam Journal of Mechanics, VAST, Vol. 34, No. (202), pp. 9 25 EXPERIMENTAL STUDY ON YOUNG S MODULUS E OF A POLYMER COMPOSITE REINFORCED BY NANO TITANIUM DIOXIDE PARTICLES Nguyen Dinh Duc, Dinh Khac
More informationAspect Ratio Requirements for Nanotube-Reinforced, Polymer-Matrix Composites
Aspect Ratio Requirements for Nanotube-Reinforced, Polymer-Matrix Composites J.A.Nairn Wood Science and Engineering, Oregon State University, Corvallis, OR 97330, USA Abstract A fiber s efficiency in a
More informationStiffness Predictions for Unidirectional Short-Fiber Composites: Review and Evaluation
Stiffness Predictions for Unidirectional Short-Fiber Composites: Review and Evaluation Charles L. Tucker III Department of Mechanical and Industrial Engineering University of Illinois at Urbana-Champaign
More informationAnalysis of high loss viscoelastic composites
Analysis of high loss viscoelastic composites by C. P. Chen, Ph.D. and R. S. Lakes, Ph.D. Department of Engineering Physics Engineering Mechanics Program; Biomedical Engineering Department Materials Science
More informationSTEEL FIBER CURVATURE IN CONCRETE COMPOSITES: MODULUS PREDICTIONS USING EFFECTIVE STEEL FIBER PROPERTIES
American Journal of Applied Sciences 11 (1): 145-151, 2014 ISSN: 1546-9239 2014 Science Publication doi:10.3844/ajassp.2014.145.151 Published Online 11 (1) 2014 (http://www.thescipub.com/ajas.toc) STEEL
More informationEffect of Interlayers on Mechanical Properties and Interfacial Stress Transfer of 2D Layered Graphene- Polymer Nanocompsites
University of Kentucky UKnowledge Theses and Dissertations--Mechanical Engineering Mechanical Engineering 2017 Effect of Interlayers on Mechanical Properties and Interfacial Stress Transfer of 2D Layered
More informationIntroduction to Engineering Materials ENGR2000. Dr. Coates
Introduction to Engineering Materials ENGR2 Chapter 6: Mechanical Properties of Metals Dr. Coates 6.2 Concepts of Stress and Strain tension compression shear torsion Tension Tests The specimen is deformed
More informationJohns Hopkins University What is Engineering? M. Karweit MATERIALS
Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: MATERIALS A. Composition
More informationME 7502 Lecture 2 Effective Properties of Particulate and Unidirectional Composites
ME 75 Lecture Effective Properties of Particulate and Unidirectional Composites Concepts from Elasticit Theor Statistical Homogeneit, Representative Volume Element, Composite Material Effective Stress-
More informationDEVELOPMENT OF SOPHISTICATED MATERIALS USING THE COMPUTER SIMULATION
7 th INTERNATIONAL MULTIDISCIPLINARY CONFERENCE Baia Mare, Romania, May 17-18, 2007 ISSN-1224-3264 DEVELOPMENT OF SOPHISTICATED MATERIALS USING THE COMPUTER SIMULATION Zuzana MURČINKOVÁ Ing. Zuzana MURČINKOVÁ,
More informationBuckling Behavior of 3D Randomly Oriented CNT Reinforced Nanocomposite Plate
Buckling Behavior of 3D Randomly Oriented CNT Reinforced Nanocomposite Plate Outline Introduction Representative Volume Element (RVE) Periodic Boundary Conditions on RVE Homogenization Method Analytical
More informationDepartment of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela , India
Composites, Article ID 629175, 12 pages http://dx.doi.org/10.1155/2014/629175 Research Article Effect of Fiber Geometry and Representative Volume Element on Elastic and Thermal Properties of Unidirectional
More informationFinite element modelling of mechanical properties of polymer composites
Loughborough University Institutional Repository Finite element modelling of mechanical properties of polymer composites This item was submitted to Loughborough University's Institutional Repository by
More informationHOSSEINMAMANPUSH a, HOSSEIN GOLESTANIAN b,c1
ISSN : 2250-0138 (Online) ISSN: 0976-2876(Print) VALUATION OF FFCTIV MATRIAL PROPRTIS OF RANDOMLY DISTRIBUTD CARBON NANOTUB COMPOSITS CONSIDRING INTRFAC FFCT HOSSINMAMANPUSH a, HOSSIN GOLSTANIAN b,c1 a
More informationMechanical Properties of Fiber Reinforced Composites Using Buckminster Fullerene Reinforcement
IJRMET Vo l. 4, Is s u e Sp l - 1, No v 2013- Ap r i l 2014 ISSN : 2249-5762 (Online ISSN : 2249-5770 (Print Mechanical Properties of Fiber Reinforced Composites Using Buckminster Fullerene Reinforcement
More informationPolymer engineering syllabus (BSc)
Polymer engineering syllabus (BSc) First semester Math 1 Physics 1 Physics 1 lab General chemistry General chemistry lab workshop Second semester Math 2 Physics 2 Organic chemistry 1 Organic chemistry
More informationInternational Journal of Engineering Science
International Journal of Engineering Science 63 (2013) 1 9 Contents lists available at SciVerse ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci
More informationA CRITERION OF TENSILE FAILURE FOR HYPERELASTIC MATERIALS AND ITS APPLICATION TO VISCOELASTIC-VISCOPLASTIC MATERIALS
MTS ADHESIVES PROGRAMME 1996-1999 PERFORMANCE OF ADHESIVE JOINTS Project: PAJ1; Failure Criteria and their Application to Visco-Elastic/Visco-Plastic Materials Report 2 A CRITERION OF TENSILE FAILURE FOR
More informationEVALUATION OF EFFECTIVE MECHANICAL PROPERTIES OF COMPLEX MULTIPHASE MATERIALS WITH FINITE ELEMENT METHOD
U.P.B. Sci. Bull., Series D, Vol. 79, Iss. 3, 2017 ISSN 1454-2358 EVALUATION OF EFFECTIVE MECHANICAL PROPERTIES OF COMPLEX MULTIPHASE MATERIALS WITH FINITE ELEMENT METHOD Mohamed said BOUTAANI 1, Salah
More informationHygrothermal stresses in laminates
Hygrothermal stresses in laminates Changing environment conditions (temperature and moisture) have an important effect on the properties which are matrix dominated. Change in temperaturet and moisture
More informationMechanical Properties
Mechanical Properties Elastic deformation Plastic deformation Fracture I. Elastic Deformation S s u s y e u e T I II III e For a typical ductile metal: I. Elastic deformation II. Stable plastic deformation
More informationAn Elasto-Visco-Plastic Multiscale Model for Fibrous Unidirectional Composite Materials
An Elasto-Visco-Plastic Multiscale Model for Fibrous Unidirectional Composite Materials by Shari Lynn King A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for
More informationTwo-step multiscale homogenization of polymer nanocomposites for large size RVEs embodying many nanoparticles
Two-step multiscale homogenization of polymer nanocomposites for large size RVEs embodying many nanoparticles *Kyungmin Baek 1), Hyunseong Shin 2), Jin-Gyu Han 3) and Maenghyo Cho 4) 1), 2), 3), 4) Department
More informationThe effect of interfacial bonding on the damping behavior of nanocomposites
The effect of interfacial bonding on the damping behavior of nanocomposites Literature review The rapid and continuous growth in aerospace, automotive, and military applications requires special materials
More informationDepartment of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
5 th Australasian Congress on Applied Mechanics, ACAM 2007 10-12 December 2007, Brisbane, Australia Toughening mechanisms in novel nano-silica epoxy polymers A.J. Kinloch 1, B.B. Johnsen 1, R.D. Mohammed
More informationMicromechanical analysis of FRP hybrid composite lamina for in-plane transverse loading
Indian Journal of Engineering & Materials Sciences Vol. 15, October 2008, pp. 382-390 Micromechanical analysis of FRP hybrid composite lamina for in-plane transverse loading K Sivaji Babu a *, K Mohana
More information, to obtain a way to calculate stress from the energy function U(r).
BIOEN 36 014 LECTURE : MOLECULAR BASIS OF ELASTICITY Estimating Young s Modulus from Bond Energies and Structures First we consider solids, which include mostly nonbiological materials, such as metals,
More informationViscoelastic Damping Characteristics of Indium-Tin/SiC Particulate Composites
Viscoelastic Damping Characteristics of Indium-Tin/SiC Particulate Composites HyungJoo Kim, Colby C. Swan Ctr. for Computer-Aided Design, Univ. of Iowa Roderic Lakes Engineering Physics, Univ. of Wisconsin
More informationfive Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS
More informationA Constitutive Framework for the Numerical Analysis of Organic Soils and Directionally Dependent Materials
Dublin, October 2010 A Constitutive Framework for the Numerical Analysis of Organic Soils and Directionally Dependent Materials FracMan Technology Group Dr Mark Cottrell Presentation Outline Some Physical
More informationArchetype-Blending Multiscale Continuum Method
Archetype-Blending Multiscale Continuum Method John A. Moore Professor Wing Kam Liu Northwestern University Mechanical Engineering 3/27/2014 1 1 Outline Background and Motivation Archetype-Blending Continuum
More informationMODELLING THE THERMOELASTIC PROPERTIES OF SHORT FIBRE COMPOSITES WITH ANISOTROPIC PHASES
MODELLING THE THERMOELASTIC PROPERTIES OF SHORT FIBRE COMPOSITES WITH ANISOTROPIC PHASES P.J.Hine*, C.D.Price*, B.Whiteside $, A.M.Cunha # and I.M.Ward* * - IRC in Polymer Science and Technology, University
More informationMechanical Properties of Epoxy/Al 2 O 3 Nanocomposites
Mechanical Properties of Epoxy/Al 2 O 3 Nanocomposites M. J. Kadhim*, A. K. Abdullah, I. A. Al-Ajaj, and A. S. Khalil Department of Physics, College of Science, Baghdad University, Baghdad, Iraq. Abstract
More informationMICROMECHANICAL ANALYSIS OF FRP COMPOSITES SUBJECTED TO LONGITUDINAL LOADING
MICROMECHANICAL ANALYSIS OF FRP COMPOSITES SUBJECTED TO LONGITUDINAL LOADING N. Krishna Vihari 1, P. Phani Prasanthi 1, V. Bala Krishna Murthy 2* and A. Srihari Prasad 3 1 Mech. Engg. Dept., P. V. P. Siddhartha
More informationAuthors: Correspondence: ABSTRACT:
Multi-Scale Modeling of the Impact and Failure of Fiber Reinforced Polymer Structures using DIGIMAT to LS-DYNA Interface Authors: L. Adam, R. Assaker & R. Ramaya e-xstream engineering S.A. 7, Rue du Bosquet.
More informationIJSER 1. INTRODUCTION. M.Elhadary
1591 A new failure criterion for GRP composite materials subjected to in-phase and out-of-phase biaxial fatigue loading under different stress ratios M.Elhadary Abstract this studying the fatigue behavior
More informationRVE Analysis of Light Weight Carbon Nanotubes Embedded Piezoelectric Fibre Composites
Nanoscience and Nanotechnology 2016, 6(1): 11-16 DOI: 10.5923/j.nn.20160601.03 RVE Analysis of Light Weight Carbon Nanotubes Embedded Piezoelectric Fibre Composites V. K. Srivastava 1,*, H. Berger 2, U.
More informationPrediction of Micromechanical Behaviour of Elliptical Frp Composites
Prediction of Micromechanical Behaviour of Elliptical Frp Composites Kiranmayee.Nerusu Dept. of Mechanical Engg. P. V. P. Siddhartha Institute of Technology, Vijayawada 520 007, A.P, India. P. Phani Prasanthi
More informationPharmaceutical compounding I Colloidal and Surface-Chemical Aspects of Dosage Forms Dr. rer. nat. Rebaz H. Ali
University of Sulaimani School of Pharmacy Dept. of Pharmaceutics Pharmaceutical Compounding Pharmaceutical compounding I Colloidal and Surface-Chemical Aspects of Dosage Forms Dr. rer. nat. Rebaz H. Ali
More informationMaterials and Structures. Indian Institute of Technology Kanpur
Introduction to Composite Materials and Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 16 Behavior of Unidirectional Composites Lecture Overview Mt Material ilaxes in unidirectional
More informationStrength of Materials and Elasticity Approach to Stiffness of Fibrous Composites Using the Concept of Interphase
Strength of Materials and Elasticity Approach to Stiffness of Fibrous Composites Using the Concept of Interphase E. Sideridis, G. A. Papadopoulos, E. Kyriazi Department of Mechanics, National Technical
More informationExercise: concepts from chapter 8
Reading: Fundamentals of Structural Geology, Ch 8 1) The following exercises explore elementary concepts associated with a linear elastic material that is isotropic and homogeneous with respect to elastic
More informationMicromechanics of Colloidal Suspensions: Dynamics of shear-induced aggregation
: Dynamics of shear-induced aggregation G. Frungieri, J. Debona, M. Vanni Politecnico di Torino Dept. of Applied Science and Technology Lagrangian transport: from complex flows to complex fluids Lecce,
More informationMatteo Basso *, Ahmed Elmarakbi. d Arco, Italy
International Conference on Automotive Composites ICAutoC 2016 A. Elmarakbi and A.L. Araújo (Editors) IDMEC 2016 Multiscale Analysis of the Mechanical Performance improvement of composites CFRP laminates,
More informationConclusion and Future Work
Chapter 7 7. Chapter 7 and Future Work Chapter 7 Abstract This chapter gives the details of correlations of the spectroscopic investigation results with those available from other studies and also summarizes
More informationChapter 2: Elasticity
OHP 1 Mechanical Properties of Materials Chapter 2: lasticity Prof. Wenjea J. Tseng ( 曾文甲 ) Department of Materials ngineering National Chung Hsing University wenjea@dragon.nchu.edu.tw Reference: W.F.
More informationMechanical properties 1 Elastic behaviour of materials
MME131: Lecture 13 Mechanical properties 1 Elastic behaviour of materials A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Deformation of material under the action of a mechanical
More informationTHE INFLUENCE OF IN-PLANE DENSITY VARIATION ON ENGINEERING PROPERTIES OF ORIENTED STRANDBOARD: A FINITE ELEMENT SIMULATION
Proceedings of McMat5: 5 Joint ASME/ASCE/SES Conference on Mechanics and Materials June 1-3, 5, Baton Rouge, Louisiana, USA 255 THE INFLUENCE OF IN-PLANE DENSITY VARIATION ON ENGINEERING PROPERTIES OF
More informationINTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011
Interlaminar failure analysis of FRP cross ply laminate with elliptical cutout Venkateswara Rao.S 1, Sd. Abdul Kalam 1, Srilakshmi.S 1, Bala Krishna Murthy.V 2 1 Mechanical Engineering Department, P. V.
More informationResearch Article Multiscale Validation of the Applicability of Micromechanical Models for Asphalt Mixture
Advances in Materials Science and Engineering Volume 2015, Article ID 937126, 8 pages http://dx.doi.org/10.1155/2015/937126 Research Article Multiscale Validation of the Applicability of Micromechanical
More informationSoufiane Belhouideg. Keywords Composite materials, homogenization method, Eshelby s inclusion problem.
Prediction of effective mechanical properties of composite materials using homogenization approach: Application to tungsten fiber reinforced bulk metallic glass matrix composite Soufiane Belhouideg Abstract
More informationMechanical properties of polymers: an overview. Suryasarathi Bose Dept. of Materials Engineering, IISc, Bangalore
Mechanical properties of polymers: an overview Suryasarathi Bose Dept. of Materials Engineering, IISc, Bangalore UGC-NRCM Summer School on Mechanical Property Characterization- June 2012 Overview of polymer
More informationTensile Properties of Thermoplastic-Laminated Composites Based on a Polypropylene Matrix Reinforced with Continuous Twaron Fibers
Tensile Properties of Thermoplastic-Laminated Composites Based on a Polypropylene Matrix Reinforced with Continuous Twaron Fibers J. L. MENA-TUN, P. I. GONZALEZ-CHI Centro de Investigación Científica de
More informationContinuum Mechanics. Continuum Mechanics and Constitutive Equations
Continuum Mechanics Continuum Mechanics and Constitutive Equations Continuum mechanics pertains to the description of mechanical behavior of materials under the assumption that the material is a uniform
More informationRHEOLOGICAL AND MORPHOLOGICAL PROPERTIES OF NANOCOMPOSITES BASED ON PA66/PA6/MULTI-WALLED CARBON NANOTUBE PREPARED BY MELT MIXING
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS RHEOLOGICAL AND MORPHOLOGICAL PROPERTIES OF NANOCOMPOSITES BASED ON PA66/PA6/MULTI-WALLED CARBON NANOTUBE PREPARED BY MELT MIXING A. M. Hadizadeh 1,
More informationInteraction of Two Parallel Short Fibers in the Matrix at Loss of Stability
Copyright c 2006 Tech Science Press CMES, vol.13, no.3, pp.165-169, 2006 Interaction of Two Parallel Short Fibers in the Matrix at Loss of Stability A.N.Guz and V.A.Dekret 1 Abstract: Stability problem
More informationChange in physico-mechanical and thermal properties of polyamide / silica nanocomposite film
International Journal of Engineering Research and Development e-issn: 2278-067X, p-issn: 2278-800X, www.ijerd.com Volume 7, Issue 6 (June 2013), PP. 01-05 Change in physico-mechanical and thermal properties
More informationNORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.
NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric
More informationStructural and Mechanical Properties of Nanostructures
Master s in nanoscience Nanostructural properties Mechanical properties Structural and Mechanical Properties of Nanostructures Prof. Angel Rubio Dr. Letizia Chiodo Dpto. Fisica de Materiales, Facultad
More information