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Melvin Sweeney Practical Thermoforming: Principles and Applications, John florian Injection and Compression Molding Fundamentals, edited by Avraam 1. Cheremisinoff Anagnostis E. Zachariades and Roger S. Porter Mallinson Bhowmick and Howard L. Stephens Barlow Lutz, Jr. Emulsion Polymer Technology, Robert D. Athey, Jr. Mixing in Polymer Processing, edited by Chris Rauwendaal Kricheldorf Computational Modeling of Polymers, edited by Jozef Bicerano Chanda and Salil K.
Prediction of Polymer Properties, Jozef Bicerano Christine Albertsson and Samuel J. Huang Polymer Toughening, edited by Charles B. Arends Cheremisinoff and Paul N. Diffusion in Polymers, edited by P. Neogi Polymer Devolatilization, edited by Ramon J. Hsieh and Roderic P. Thermoplastic Melt Rheology and Processing, A. Shenoy and 0. Saini Expanded, John Florian Kitayama, and Otto Vogl Handbook of Thermoplastics, edited by Olagoke Olabisi Expanded, Charles P.
MacDermott and Aroon V. Shenoy Metallized Plastics, edited by K. Mittal Oligomer Technology and Applications, Constantin V. Uglea Wise, Gary E. Wnek, Debra J. Trantolo, Thomas M. Cooper, and Joseph 0. Karian Polymer Blends and Alloys, edited by Gabriel 0. Shonaike and George P. Simon Star and Hyperbranched Polymers, edited by Munmaya K.
Mishra and Shiro Kobayashi Belcher Diaz-Calleja, Margarita G. Prolongo, Rosa M. Masegosa, and Catalina Salom LeGrand and John T. Bendler Cornelia Vasile Bhowmick and Howard 1.
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Polymer Modifiers and Additives, edited by John T. Grossman Practical Injection Molding, Bernie A. Olmsted and Madin E. Davis Williams It has thus resulted in much greater efficiency.
Various studies have compared the results obtained from such techniques with the results obtained from the traditional tensile tests especially for the elastic modulus calculation 19 - The instrumented indentation techniques have been long used for materials quality control in industrialised environments. It is anticipated in the near future these techniques to be attractive also in the nanocomposites industry due to the simplicity and practicality of the experiments involved.
Such techniques apart from the local characterization of the material might be also crucial in the study of the bulk material elastic properties if their results are manipulated through computational methods. In this study in particular, specimens with highly dispersed nanosilica particles in the epoxy resin were fabricated. The mechanical performance of the nanocomposites was characterized by uniaxial compression tests and an instrumented ball indentation at room temperature. The results obtained from the experimental tests and more specifically the elastic modulus was compared the Halpin-Tsai and Lewis-Nielsen models as well as with a developed finite element model simulating the ball indentation experiment.
The silica SiO 2 nanoparticles were supplied as a colloidal silica-sol at a concentration of 40 wt. The modulus of silica can be found in the literature as 69 GPa The silica nanoparticles for the Nanopox F are synthesised from an aqueous sodium silicate solution. The mixture was degassed for 15 min in a vacuum oven to remove the entrapped air, which then was blended with the appropriate stoichiometric amounts of SP Hardener based on the amount of DGEBA and the masterbatch for 10 min.
The nanomodified resin was afterwards degassed in the vacuum oven before curing to remove any air entrapped in the mixture and then poured into silicon moulds.
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The measurements followed the EN ISO testing standard using dumbbell shaped specimens for the pure resin samples and for those reinforced with nanosilica at a strain rate of 0. E-moduli were calculated within the linear section of the stress-strain curves. Indentations were carried out using a cemented carbide ball diamond indenter of 0.
The samples were fabricated as discussed in section 2. These were subsequently machined on a lathe and polished to an accuracy of 0. After machining and polishing, a delay of at least 3 hours was steadily applied in order to let the samples cool down to ambient temperature. A weak preload was applied first in order to detect the surface contact and to establish a zero datum.
Then a load controlled loading step to a maximum of N was applied as shown in the schematic in Figure 1 , which was followed by a dwell time of 5s and then unloading down to 0mN at the same rate as the loading stage. On a given specimen, various points were selected which were purposely scattered on the surface. At least 10 measurements were conducted on each specimen.
The ball indentation experimental results were simulated with the aid of FEA-based procedure. The ball indentation results are the input data to the introduced FEM continuous simulation algorithm of the ball indentation test in order to calculate the whole stress-strain curve of the materials under study. In order to advance with the calculation an axisymmetric FEA model of the semi-infinite layered half-space was built in relation to other work Figure 2 shows the axisymmetric FEA model where the boundary conditions and the finite element discretization network are clearly represented.
In order to describe the interface between the indentor and the surface of the epoxy nanocomposite samples contact elements were used. Preliminary results have shown that the contact element stiffness and friction coefficient in a large range of their values do not affect the evaluation results. The ball indentation test has been simulated by considering effectively two load steps. The first load step simulated the loading stage of the indenter into the epoxy nanocomposites. The second step, which can be called as the relaxation stage the ball indentor was removed leading to the material elastic-plastic recovery.
In three-dimensional stress-strain problems, the material status is oriented by the position of the principal stress vector relative to the yield surface. In general, the two available hardening rules are the isotropic and the kinematic one. In the first case the yield surface remains centered on its initial center and expands in size as the plastic strain develops. On the other hand, the kinematic hardening assumes that the yield surface remains constant in size and the surface translates in stress space with progressive yielding, whereas the Besseling model is used 23 - 25 , also called sub-layer or overlay model, to characterize the material behavior.
Considering that the kinematic hardening rule leads to a rapid convergence in the corresponding FEM calculations, this feature was applied in the developed procedure. In Figure 3 typical stress-strain curves under tension loading are illustrated where the silica nanocomposites show higher tensile strengths and moduli than the neat epoxy without reducing significantly its failure strain even at high nanosilica content.
Fracture of all specimens occurred soon after yielding and prior the full occurrence of plastic strain softening as observed from the stress-strain curves. The increase in the modulus of the nanocomposites was expected since the modulus of silica is about 69 GPa. In addition, the homogeneous dispersion of these high stiffness nanofillers in the matrix enhanced the fracture toughness of the system as indicated by the larger area under stress-strain curve of the nanocomposite system.
As the tensile load increases, the matrix tries to elongate however, the nanofillers resist deformation. This result in slightly smaller deformation compared to the neat polymer. Therefore, nanocomposites sustain more loads compared to the pure epoxy system and contribute to a higher tensile modulus and strength.
The modulus for the pure epoxy resin was measured to be 3. The fracture surfaces of specimens having neat epoxy resin samples showed characteristic river lines and a smooth surface as shown in Figure 4 a. The silica nanocomposites revealed in contrary a fracture surface with severely distracted patterns as illustrated in Figure 4 b. It should be noted that the SEM used in the current work is incapable of revealing the details in a nano level. It is believed though that for the silica nanoparticle specimens the particle-matrix interfacial adhesion is indeed strong.
This is probably because the silica nanoparticles were beforehand surface-modified with silane coupling agent, which can react with both inorganic particles and epoxy resin and yield strong interfacial adhesion, which results in the increase in moduli as monitored from the tensile tests. Both surface profiles show that they have a specific repeatable pattern that has characteristic large wavelengths and some arbitrary imperfections.
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As expected it is apparent from the surface profiles that the modified epoxy with nanosilica particles produced deeper valleys with large fluctuations than the neat epoxy resin on which this effect was on a lesser scale. A more multifaceted rapid crack propagation have been occurred through the silica nanoparticles. The arithmetic average surface roughness, R a , and the mean Roughness depth R z develop similar tendency, as shown in Figure 6.
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The redline arrows in the optical microscope photos show the position of the line scans where the profiles where measured. Figure 7 illustrates typical depth-load curves of indentations made at a peak indentation load of N on the pure epoxy resins and the two types of nanocomposites. The creep under constant load is clearly visible. No cracks were formed during indentation as no steps or discontinuities were found on the loading curves. The results portray clearly the stiffening effect that the nanosilica introduces to the epoxy resin.
Figure 8 shows a typical diagram of both the loading and the relaxation stage during the indentation procedure describing the penetration depth d vs. During the loading stage the curve is digitized in a number of F i - d i pairs as the corresponding table that is superimposed in the Figure 8 explains so to create the input data to the developed FEA. The first pair of the applied force F 1 and the consequent penetration depth d 1 are read initially. Assuming an initial value for the first tangent modulus E 1 of the nanocomposites' stress-strain curve, corresponding to its elasticity modulus, the indentation FEA model, considering the depth d 1 , a penetration force F FEA1 is determined, which is compared to the measured real one F 1.