Search results for: modulus of elasticity
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 936

Search results for: modulus of elasticity

186 Analysis of High Resolution Seismic Reflection Data to Identify Different Regional Lithologies of the Zaria Batholith Located in the Basement Complex of North Central Nigeria

Authors: Collins C. Chiemeke, A. Onugba, P. Sule

Abstract:

High resolution seismic reflection has recently been carried out on Zaria batholith, with the aim of characterizing the granitic Zaria batholiths in terms of its lithology. The geology of the area has revealed that the older granite outcrops in the vicinity of Zaria are exposures of a syntectonics to late-tectonic granite batholiths which intruded a crystalline gneissic basement during the Pan-African Orogeny. During the data acquisition the geophone were placed at interval of 1 m, variable offset of 1 and 10 m was used. The common midpoint (CMP) method with 12 fold coverage was employed for the survey. Analysis of the generated 3D surface of the p wave velocities from different profiles for densities and bulk modulus revealed that the rock material is more consolidated in South East part of the batholith and less consolidated in the North Western part. This was in conformity with earlier identified geology of the area, with the South Eastern part majorly of granitic outcrop, while the North Western part is characterized with the exposure of gneisses and thick overburden cover. The difference in lithology was also confirmed by the difference in seismic sections and Arial satellite photograph. Hence two major lithologies were identified, the granitic and gneisses complex which are characterized by gradational boundaries.

Keywords: basement complex, batholith, high resolution, lithologies, seismic reflection

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185 Refinement of Thermal and Mechanical Properties of Poly (Lactic Acid)/Poly (Ethylene-Co-Glycidyle Methacrylate)/ Hexagonal Boron Nitride Blend-Composites through Electron-Beam Irradiation

Authors: Ashish Kumar, T. Venkatappa Rao, Subhendu Ray Chowdhury, S. V. S. Ramana Reddy

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The main objective of this work is to determine the influence of electron beam irradiation on thermal and mechanical properties of Poly (lactic acid) (PLA)/Poly (ethylene-co-glycidyle methacrylate) (PEGM)/Hexagonal boron nitride (HBN) blend-composites. To reduce the brittleness and improve the toughness of PLA, the PLA/PEGM blend is prepared by using twin-screw Micro compounder. However, the heat deflection temperature (HDT) and other tensile properties were reduced. The HBN has been incorporated into the PLA/PEGM blend as part per hundred i.e. 5 phr and 10phr to improve the HDT. The prepared specimens of blend and blend-composites were irradiated to high energy (4.5 MeV) electron beam (E-beam) at different radiation doses to introduce the cross linking among the polymer chains and uniform dispersion of HBN particles in the PLA/PEGM/HBN blend-composites. The further improvement in the notched impact strength and HDT have been achieved in the case of PLA/PEGM/HBN blend-composites. The irradiated PLA/PEGM/HBN 5phr blend composite shows high notched impact strength and HDT as compared to other unirradiated and E-beam irradiated blend and blend-composites. The improvements in the yield strength and tensile modulus have also been noticed in the case of E-beam irradiated PLA/PEGM/HBN blend-composites as compared to unirradiated blend-composites.

Keywords: blend-composite, e-beam, HDT, PEGM, PLA

Procedia PDF Downloads 185
184 Increasing Toughness of Oriented Polyvinyl Alcohol (PVA)/Fe3O4 Nanocomposite

Authors: Mozhgan Chaichi, Farhad Sharif, Saeede Mazinani

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Polymer nanocomposites are a new class of materials for fabricating future multifunctional and lightweight structures. To obtain good mechanical, thermal and electrical properties, it is essential to achieve uniform dispersion of nanoparticles in polymer matrix. Alignment of nanoparticles in matrix can enhance mechanical, thermal, electrical and barrier properties of nanocomposites in oriented direction. Fe3O4 nanoparticles have generated huge activity in many areas of science and engineering due to its magnetic properties. Magnetic nanoparticles have been investigated for a wide range of applications in sensors, magnetic energy storage, environmental remediation, heterogeneous catalysts and drug delivery. The magnetic response from the Fe3O4 nanoparticles can facilitate with the alignment of nanofillers in a polymer matrix under magnetic field, aiming at fabricating composites with directional properties and functions. Here we report oriented nanocomposites based on Fe3O4 nanoparticles and poly (vinyl alcohol) (PVA), which prepared via a facile aqueous solution by applying a low external magnetic field (750 G). A significant enhancement of mechanical properties, and especially toughness of nanofilms, of oriented PVA/ Fe3O4 nanocomposites is obtained at low nanoparticles loading. Orientation of nanoparticles can align polymer chains and enhance mechanical properties. For example, orientation of 0.1 wt. % Fe3O4 nanoparticles increase 31% toughness and 23% modulus of oriented nanocomposite in compare of pure films, which indicate good dispersion of nanoparticles and efficient load transfer between nanoparticles and matrix.

Keywords: magnetic nanoparticles, nanocomposites, toughness, orientation

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183 Assessing Influence of End-Boundary Conditions on Stability and Second-Order Lateral Stiffness of Beam-Column Elements Embedded in Non-Homogeneous Soil

Authors: Carlos A. Vega-Posada, Jeisson Alejandro Higuita-Villa, Julio C. Saldarriaga-Molina

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This paper presents a simplified analytical approach to conduct elastic stability and second-order lateral stiffness analyses of beam-column elements (i.e., piles) with generalized end-boundary conditions embedded on a homogeneous or non-homogeneous Pasternak foundation. The solution is derived using the well-known Differential Transformation Method (DTM), and it consists simply of solving a system of two linear algebraic equations. Using other conventional approaches to solve the governing differential equation of the proposed element can be cumbersome and the solution challenging to implement, especially when the non-homogeneity of the soil is considered. The proposed formulation includes the effects of i) any rotational or lateral transverse spring at the ends of the pile, ii) any external transverse load acting along the pile, iii) soil non-homogeneity, and iv) the second-parameter of the elastic foundation (i.e., shear layer connecting the springs at the top). A parametric study is conducted to investigate the effects of different modulus of subgrade reactions, degrees of non-homogeneities, and intermediate end-boundary conditions on the pile response. The same set of equations can be used to conduct both elastic stability and static analyses. Comprehensive examples are presented to show the simplicity and practicability of the proposed method.

Keywords: elastic stability, second-order lateral stiffness, soil-non-homogeneity, pile analysis

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182 Quantification of Dowel-Concrete Interaction in Jointed Plain Concrete Pavements Using 3D Numerical Simulation

Authors: Lakshmana Ravi Raj Gali, K. Sridhar Reddy, M. Amaranatha Reddy

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Load transfer between adjacent slabs of the jointed plain concrete pavement (JPCP) system is inevitable for long-lasting performance. Dowel bars are generally used to ensure sufficient degree of load transfer, in addition to the load transferred by aggregate interlock mechanism at the joints. Joint efficiency is the measure of joint quality, a major concern and therefore the dowel bar system should be designed and constructed well. The interaction between dowel bars and concrete that includes various parameters of dowel bar and concrete will explain the degree of joint efficiency. The present study focuses on the methodology of selecting contact stiffness, which quantifies dowel-concrete interaction. In addition, a parametric study which focuses on the effect of dowel diameter, dowel shape, the spacing between dowel bars, joint opening, the thickness of the slab, the elastic modulus of concrete, and concrete cover on contact stiffness was also performed. The results indicated that the thickness of the slab is most critical among various parameters to explain the joint efficiency. Further displacement equivalency method was proposed to find out the contact stiffness. The proposed methodology was validated with the available field surface deflection data collected by falling weight deflectometer (FWD).

Keywords: contact stiffness, displacement equivalency method, Dowel-concrete interaction, joint behavior, 3D numerical simulation

Procedia PDF Downloads 146
181 Composite Materials from Epoxidized Linseed Oil and Lignin

Authors: R. S. Komartin, B. Balanuca, R. Stan

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the last decades, studies about the use of polymeric materials of plant origin, considering environmental concerns, have captured the interest of researchers because these represent an alternative to petroleum-derived materials. Vegetable oils are one of the preferred alternatives for petroleum-based raw materials having long aliphatic chains similar to hydrocarbons which means that can be processed using conventional chemistry. Epoxidized vegetable oils (EVO) are among the most interesting products derived from oil both for their high reactivity (epoxy group) and for the potential to react with compounds from various classes. As in the case of epoxy resins starting from petrochemical raw materials, those obtained from EVO can be crosslinked with different agents to build polymeric networks and can also be reinforced with various additives to improve their thermal and mechanical performances. Among the multitude of known EVO, the most common in industrial practice are epoxidized linseed oils (ELO) and epoxidized soybean oils (ESO), the first with an iodine index over 180, the second having a lower iodine index but being cheaper. On the other hand, lignin (Ln) is the second natural organic material as a spread, whose use has long been hampered because of the high costs associated with its isolation and purification. In this context, our goal was to obtain new composite materials with satisfactory intermediate properties in terms of stiffness and elasticity using the characteristics of ELO and Ln and choosing the proper curing procedure. In the present study linseed oil (LO) epoxidation was performed using peracetic acid generated in situ. The obtained bio-based epoxy resin derived from linseed oil was used further to produce the new composites byloading Ln in various mass ratios. The resulted ELO-Ln blends were subjected to a dual-curing protocol, namely photochemical and thermal. The new ELO-Ln composites were investigated by FTIR spectrometry, thermal stability, water affinity, and morphology. The positive effect of lignin regarding the thermal stability of the composites could be proved. The results highlight again the still largely unexplored potential of lignin in industrial applications.

Keywords: composite materials, dual curing, epoxidized linseed oil, lignin

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180 Nanoscale Mapping of the Mechanical Modifications Occurring in the Brain Tumour Microenvironment by Atomic Force Microscopy: The Case of the Highly Aggressive Glioblastoma and the Slowly Growing Meningioma

Authors: Gabriele Ciasca, Tanya E. Sassun, Eleonora Minelli, Manila Antonelli, Massimiliano Papi, Antonio Santoro, Felice Giangaspero, Roberto Delfini, Marco De Spirito

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Glioblastoma multiforme (GBM) is an extremely aggressive brain tumor, characterized by a diffuse infiltration of neoplastic cells into the brain parenchyma. Although rarely considered, mechanical cues play a key role in the infiltration process that is extensively mediated by the tumor microenvironment stiffness and, more in general, by the occurrence of aberrant interactions between neoplastic cells and the extracellular matrix (ECM). Here we provide a nano-mechanical characterization of the viscoelastic response of human GBM tissues by indentation-type atomic force microscopy. High-resolution elasticity maps show a large difference between the biomechanics of GBM tissues and the healthy peritumoral regions, opening possibilities to optimize the tumor resection area. Moreover, we unveil the nanomechanical signature of necrotic regions and anomalous vasculature, that are two major hallmarks useful for glioma staging. Actually, the morphological grading of GBM relies mainly on histopathological findings that make extensive use of qualitative parameters. Our findings have the potential to positively impact on the development of novel quantitative methods to assess the tumor grade, which can be used in combination with conventional histopathological examinations. In order to provide a more in-depth description of the role of mechanical cues in tumor progression, we compared the nano-mechanical fingerprint of GBM tissues with that of grade-I (WHO) meningioma, a benign lesion characterized by a completely different growth pathway with the respect to GBM, that, in turn hints at a completely different role of the biomechanical interactions.

Keywords: AFM, nano-mechanics, nanomedicine, brain tumors, glioblastoma

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179 Assessment of the Remains in Historic Urban Area Based on Spatial Prototype: Case Study on Jingmen City, China

Authors: Guangtong Xu, Yi He

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Like most historic and cultural cities in China, the historic urban area of Jingmen city is facing a typical spatial problem of fragmentation and fuzzification. This study focuses on exploring a method for evaluating the existing values of historic urban area based on spatial prototype, a concept introduced into urban morphology from 'Archetype' in architectural typology. As the spatial elements and built-up relationship of historic city, spatial prototype has habitual structural characteristics and formal modulus. It is the inherent logic and order rules behind the scattered historic environment, providing a clue to understand the spatial characteristics and a basis for guiding the construction and conservation in historic urban areas. Three criteria, the resolution of historical elements, the completeness of historical structure and the renewal potential of associated land, were selected to construct the integrated assessment system. These three dimensions are linked to the spatial prototype and its constituent elements, as well as the transformation relationship in ancient and present day. The results showed that historic urban areas have changed from a holistic city to different existing types dominated by their historic structure elements. It is necessary to improve the pertinence of planning strategies and develop diversified management measures in the conservation scope of historic urban area. Moreover, a constructive-conservation strategy should be put forward to enhance the integrity of historic urban area based on the trace of spatial prototype and evaluation results.

Keywords: constructive conservation, existing value, historic urban area, spatial prototype

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178 Effects of Hierarchy on Poisson’s Ratio and Phononic Bandgaps of Two-Dimensional Honeycomb Structures

Authors: Davood Mousanezhad, Ashkan Vaziri

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As a traditional cellular structure, hexagonal honeycombs are known for their high strength-to-weight ratio. Here, we introduce a class of fractal-appearing hierarchical metamaterials by replacing the vertices of the original non-hierarchical hexagonal grid with smaller hexagons and iterating this process to achieve higher levels of hierarchy. It has been recently shown that the isotropic in-plane Young's modulus of this hierarchical structure at small deformations becomes 25 times greater than its regular counterpart with the same mass. At large deformations, we find that hierarchy-dependent elastic buckling introduced at relatively early stages of deformation decreases the value of Poisson's ratio as the structure is compressed uniaxially leading to auxeticity (i.e., negative Poisson's ratio) in subsequent stages of deformation. We also show that the topological hierarchical architecture and instability-induced pattern transformations of the structure under compression can be effectively used to tune the propagation of elastic waves within the structure. We find that the hierarchy tends to shift the existing phononic bandgaps (defined as frequency ranges of strong wave attenuation) to lower frequencies while opening up new bandgaps. Deformation is also demonstrated as another mechanism for opening more bandgaps in hierarchical structures. The results provide new insights into the role of structural organization and hierarchy in regulating mechanical properties of materials at both the static and dynamic regimes.

Keywords: cellular structures, honeycombs, hierarchical structures, metamaterials, multifunctional structures, phononic crystals, auxetic structures

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177 Apatite-Forming Ability of Doped-Ceria Coatings for Orthopedic Implants

Authors: Ayda Khosravanihaghighi, Pramod Koshy, Bill Walsh, Vedran Lovric, Charles Christopher Sorrell

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There is an increasing demand for orthopedic implants owing to the increasing numbers of the aging population. Titanium alloy (Ti6Al4V) is a common material used for orthopedic implants owing to its advantageous properties in terms of good corrosion resistance, minimal elastic modulus mismatch with bone, bio-inertness, and high mechanical strength. However, it is important to improve the bioactivity and osseointegration of the titanium alloy and this can be achieved by coating the implant surface with suitable ceramic materials. In the present work, pure and doped-ceria (CeO₂) coatings were deposited by spin coating on the titanium alloy surface in order to enhance the biological interactions between the surface of the implant and the surrounding tissue. In order to examine the bone-binding ability of an implant, simulated body fluid (SBF) tests were conducted in order to assess the capability of apatite layer formation on the surface and thus predict in vivo bone bioactivity. Characterization was done using scanning electron microscopy (SEM) and X-ray diffraction (XRD) analyses to determine the extent of apatite formation. Preliminary tests showed that the CeO₂ coatings were biocompatible and that the extent of apatite formation and its characteristics can be enhanced by doping with suitable metal ions.

Keywords: apatite layer, biocompatibility, ceria, orthopaedic implant, SBF, spin coater, Ti-implant

Procedia PDF Downloads 155
176 Economic Development Impacts of Connected and Automated Vehicles (CAV)

Authors: Rimon Rafiah

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This paper will present a combination of two seemingly unrelated models, which are the one for estimating economic development impacts as a result of transportation investment and the other for increasing CAV penetration in order to reduce congestion. Measuring economic development impacts resulting from transportation investments is becoming more recognized around the world. Examples include the UK’s Wider Economic Benefits (WEB) model, Economic Impact Assessments in the USA, various input-output models, and additional models around the world. The economic impact model is based on WEB and is based on the following premise: investments in transportation will reduce the cost of personal travel, enabling firms to be more competitive, creating additional throughput (the same road allows more people to travel), and reducing the cost of travel of workers to a new workplace. This reduction in travel costs was estimated in out-of-pocket terms in a given localized area and was then translated into additional employment based on regional labor supply elasticity. This additional employment was conservatively assumed to be at minimum wage levels, translated into GDP terms, and from there into direct taxation (i.e., an increase in tax taken by the government). The CAV model is based on economic principles such as CAV usage, supply, and demand. Usage of CAVs can increase capacity using a variety of means – increased automation (known as Level I thru Level IV) and also by increased penetration and usage, which has been predicted to go up to 50% by 2030 according to several forecasts, with possible full conversion by 2045-2050. Several countries have passed policies and/or legislation on sales of gasoline-powered vehicles (none) starting in 2030 and later. Supply was measured via increased capacity on given infrastructure as a function of both CAV penetration and implemented technologies. The CAV model, as implemented in the USA, has shown significant savings in travel time and also in vehicle operating costs, which can be translated into economic development impacts in terms of job creation, GDP growth and salaries as well. The models have policy implications as well and can be adapted for use in Japan as well.

Keywords: CAV, economic development, WEB, transport economics

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175 Studies on Toxicity and Mechanical Properties of Nonmetallic Printed Circuit Boards Waste in Recycled HDPE Composites

Authors: Shantha Kumari Muniyandi, Johan Sohaili, Siti Suhaila Mohamad

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The aim of this study was to investigate the suitability of reusing nonmetallic printed circuit boards (PCBs) waste in recycled HDPE (rHDPE) in terms of toxicity and mechanical properties. A series of X-ray Fluorescence Spectrometry (XRF) analysis tests have been conducted on raw nonmetallic PCBs waste to determine the chemical compositions. It can be seen that the nonmetallic PCBs approximately 72% of glass fiber reinforced epoxy resin materials such as SiO2, Al2O3, CaO, MgO, BaO, Na2O, and SrO, 9.4% of metallic materials such as CuO, SnO2, and Fe2O3, and 6.53% of Br. Total Threshold Limit Concentration (TTLC) and Toxicity Characteristic Leaching Procedure (TCLP) tests also have been done to study the toxicity characteristics of raw nonmetallic PCB powders, rHDPE/PCB and virgin HDPE for comparison purposes. For both of the testing, Cu was identified as the highest metal element contained in raw PCBs with the concentration of 905 mg/kg and 59.09 mg/L for TTLC and TCLP, respectively. However, once the nonmetallic PCB was filled in rHDPE composites, the concentrations of Cu were reduced to 134 mg/kg for TTLC and to 3 mg/L for TCLP testing. For mechanical properties testing, incorporation of 40 wt% nonmetallic PCB into rHDPE has increased the flexural modulus and flexural strength by 140% and 36%, respectively. While, Izod Impact strength decreased steadily with incorporation of 10 – 40 wt% nonmetallic PCBs.

Keywords: nonmetallic printed circuit board, recycled HDPE, composites, mechanical properties, total threshold limit concentration, toxicity characteristic leaching procedure

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174 An Investigation on the Pulse Electrodeposition of Ni-TiO2/TiO2 Multilayer Structures

Authors: S. Mohajeri

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Electrocodeposition of Ni-TiO2 nanocomposite single layers and Ni-TiO2/TiO2 multilayers from Watts bath containing TiO2 sol was carried out on copper substrate. Pulse plating and pulse reverse plating techniques were applied to facilitate higher incorporations of TiO2 nanoparticles in Ni-TiO2 nanocomposite single layers, and the results revealed that by prolongation of the current-off durations and the anodic cycles, deposits containing 11.58 wt.% and 13.16 wt.% TiO2 were produced, respectively. Multilayer coatings which consisted of Ni-TiO2 and TiO2-rich layers were deposited by pulse potential deposition through limiting the nickel deposition by diffusion control mechanism. The TiO2-rich layers thickness and accordingly, the content of TiO2 reinforcement reached 104 nm and 18.47 wt.%, respectively in the optimum condition. The phase structure and surface morphology of the nanocomposite coatings were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The cross sectional morphology and line scans of the layers were studied by field emission scanning electron microscopy (FESEM). It was confirmed that the preferred orientations and the crystallite sizes of nickel matrix were influenced by the deposition technique parameters, and higher contents of codeposited TiO2 nanoparticles refined the microstructure. The corrosion behavior of the coatings in 1M NaCl and 0.5M H2SO4 electrolytes were compared by means of potentiodynamic polarization and electrochemical impedance spectroscopy (EIS) techniques. Increase of corrosion resistance and the passivation tendency were favored by TiO2 incorporation, while the degree of passivation declined as embedded particles disturbed the continuity of passive layer. The role of TiO2 incorporation on the improvement of mechanical properties including hardness, elasticity, scratch resistance and friction coefficient was investigated by the means of atomic force microscopy (AFM). Hydrophilicity and wettability of the composite coatings were investigated under UV illumination, and the water contact angle of the multilayer was reduced to 7.23° after 1 hour of UV irradiation.

Keywords: electrodeposition, hydrophilicity, multilayer, pulse-plating

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173 Production of Biocomposites Using Chars Obtained by Co-Pyrolysis of Olive Pomace with Plastic Wastes

Authors: Esra Yel, Tabriz Aslanov, Merve Sogancioglu, Suheyla Kocaman, Gulnare Ahmetli

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The disposal of waste plastics has become a major worldwide environmental problem. Pyrolysis of waste plastics is one of the routes to waste minimization and recycling that has been gaining interest. In pyrolysis, the pyrolysed material is separated into gas, liquid (both are fuel) and solid (char) products. All fractions have utilities and economical value depending upon their characteristics. The first objective of this study is to determine the co-pyrolysis product fractions of waste HDPE- (high density polyethylene) and LDPE (low density polyethylene)-olive pomace (OP) and to determine the qualities of the solid product char. Chars obtained at 700 °C pyrolysis were used in biocomposite preparation as additive. As the second objective, the effects of char on biocomposite quality were investigated. Pyrolysis runs were performed at temperature 700 °C with heating rates of 5 °C/min. Biocomposites were prepared by mixing of chars with bisphenol-F type epoxy resin in various wt%. Biocomposite properties were determined by measuring electrical conductivity, surface hardness, Young’s modulus and tensile strength of the composites. The best electrical conductivity results were obtained with HDPE-OP char. For HDPE-OP char and LDPE-OP char, compared to neat epoxy, the tensile strength values of the composites increased by 102% and 78%, respectively, at 10% char dose. The hardness measurements showed similar results to the tensile tests, since there is a correlation between the hardness and the tensile strength.

Keywords: biocomposite, char, olive pomace, pyrolysis

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172 Low-Temperature Fabrication of Reaction Bonded Composites, Based on Sic and (Sic+B4C) Mixture, Infiltrated with Si-Al Alloy

Authors: Helen Dilman, Eyal Oz, Shmuel Hayun, Nahum Frage

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The conventional approach for manufacturing silicon carbide and boron carbide reaction bonded composites is based on infiltrating a ceramic porous preform with molten silicon. The relatively high melting temperature of the silicon infiltrating medium is a drawback of the process. The present contribution is concerned with an approach that allows obtaining reaction bonded composites by pressure-less infiltration at a significantly lower (850-1000oC) temperature range. This approach was applied for the fabrication of fully dense SiC/(Si-Al) and (SiC+B4C)/(Si-Al) composites. The key feature of the approach is based on using Si alloys with low melting temperature and the Mg-vapor atmosphere, under which an adequate wetting between ceramics and liquid alloys for the infiltration process is achieved. In the first set of the experiments ceramic performs compacted from multimodal SiC powders (with the green density of about 27 vol. %) without free carbon addition were infiltrated by Si-20%Al alloy at 950oC. In the second set, 19 vol. % of a fine boron carbide powder was added to SiC powders as a source of carbon. The green density of the SiC-B4C preforms was about 23-25 vol. %. In both cases, successful infiltration was achieved and the composites were fully dense. The density of the composites was about 3g/cm3. For the SiC based composites the hardness value was 750±150HV, Young modulus-280GPa and bending strength-240±30MPa. These values for (SiC-B4C)/(Si-Al) composites (1460±200HV, 317GPa and 360±20MPa) were significantly higher due to the formation of novel ceramics phases. Microstructural characteristics of the composites and their phase composition will be discussed.

Keywords: boron carbide, composites, infiltration, low temperatures, silicon carbide

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171 Probabilistic Models to Evaluate Seismic Liquefaction In Gravelly Soil Using Dynamic Penetration Test and Shear Wave Velocity

Authors: Nima Pirhadi, Shao Yong Bo, Xusheng Wan, Jianguo Lu, Jilei Hu

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Although gravels and gravelly soils are assumed to be non-liquefiable because of high conductivity and small modulus; however, the occurrence of this phenomenon in some historical earthquakes, especially recently earthquakes during 2008 Wenchuan, Mw= 7.9, 2014 Cephalonia, Greece, Mw= 6.1 and 2016, Kaikoura, New Zealand, Mw = 7.8, has been promoted the essential consideration to evaluate risk assessment and hazard analysis of seismic gravelly soil liquefaction. Due to the limitation in sampling and laboratory testing of this type of soil, in situ tests and site exploration of case histories are the most accepted procedures. Of all in situ tests, dynamic penetration test (DPT), Which is well known as the Chinese dynamic penetration test, and shear wave velocity (Vs) test, have been demonstrated high performance to evaluate seismic gravelly soil liquefaction. However, the lack of a sufficient number of case histories provides an essential limitation for developing new models. This study at first investigates recent earthquakes that caused liquefaction in gravelly soils to collect new data. Then, it adds these data to the available literature’s dataset to extend them and finally develops new models to assess seismic gravelly soil liquefaction. To validate the presented models, their results are compared to extra available models. The results show the reasonable performance of the proposed models and the critical effect of gravel content (GC)% on the assessment.

Keywords: liquefaction, gravel, dynamic penetration test, shear wave velocity

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170 Bulk Electrical Resistivity of Geopolymer Mortars: The Effect of Binder Composition and Alkali Concentration

Authors: Mahdi Babaee, Arnaud Castel

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One of the main hurdles for commercial adaptation of geopolymer concrete (GPC) as a low-embodied-carbon alternative for Portland cement concrete (PCC) is the durability aspects and its long-term performance in aggressive/corrosive environments. GPC is comparatively a new engineering material and in the absence of a track record of successful durability performance, proper experimental studies to investigate different durability-related characteristics of GPC seem inevitable. In this context, this paper aims to study the bulk electrical resistivity of geopolymer mortars fabricated of blends of low-calcium fly ash (FA) and ground granulated blast-furnace slag (GGBS). Bulk electrical resistivity is recognized as one of the most important parameters influencing the rate of corrosion of reinforcing bars during the propagation phase of corrosion. To investigate the effect of alkali concentration on the resistivity of the samples, 100x200 mm mortar cylinders were cast at different alkali concentration levels, whereas the modulus ratio (the molar ratio of SiO2/Na2O) was fixed for the mixes, and the bulk electrical resistivity was then measured. Also, the effect of the binder composition was assessed with respect to the ratio of FA to GGBS used. Results show a superior performance of samples with higher GGBS content. Lower concentration of the solution has increased the resistivity by reducing the amount of mobile alkali ions in the pore solution. Moreover, GGBS-based samples showed a much sharper increase in the electrical resistivity with decreasing the moisture content.

Keywords: bulk resistivity, corrosion, durability, geopolymer concrete

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169 (De)Criminalising Sex Toys in Thailand: A Law and Economics Approach

Authors: Piyanee Khumpao

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Under the Thai Penal Code and Customs Act, sex toys are criminalized and completely prohibited through the legal interpretation as obscene objects by law enforcement, despite there is no explicit legal sanction against them. The purpose of preventing people from accessing sex toys is to preserve public morals. However, sex toys are still available, exposed, and sold publicly in main cities throughout Thailand. They are easily observed by people of any age. This paper argues that sexuality is human nature and human right. Human deserves sexual pleasure as long as getting sexual pleasure does not inflict any harm on others. Using sex toys in private (individually and/or as a couple with mutual consent) does not constitute any harm nor degrade public moral. Therefore, the complete ban of sex toys shall be lifted and decriminalized. Nevertheless, the economic analysis illustrates that criminalization and prohibition of sex toys would lead to its black market – higher price and lower quantity. Although it is socially desirable to have fewer sex toys in the market, there will usually be high demand for them because sexual pleasure is natural and, hence, people have a lower price elasticity of demand for such things, including pornography. Thus, its deterrent effect is not very effective. Moreover, sex toys vendors still always exist because higher price incentivizes them to act illegally and may gain benefits from selling low-quality sex toys. Consequently, consumers do not have a choice to select high-quality sex toys at a reasonable price. Then, they are forced to purchase low quality sex toys at a higher price. They also may suffer from health issues as well as other harms from its dangerous/toxic substances since lower quality products are manufactured poorly to save costs. A law and economics approach supports the decriminalization of sex toys in Thailand. Other measures to control its availability shall be adopted to protect the vulnerable, such as children. Options are i) zoning or regulation on-premises selling sex toys as in Singapore, Japan, and China, ii) regulations of sex toys as medical apparatus like in the state of Alabama, and iii) the prevention of sex toys exposure in the real (physical) appearance (i.e., allowing virtual exposure of sex toys) like in India.

Keywords: human nature, law and economics approach, sex toys, sexual pleasure

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168 Preparation of Fe3Si/Ferrite Micro-and Nano-Powder Composite

Authors: Radovan Bures, Madgalena Streckova, Maria Faberova, Pavel Kurek

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Composite material based on Fe3Si micro-particles and Mn-Zn nano-ferrite was prepared using powder metallurgy technology. The sol-gel followed by autocombustion process was used for synthesis of Mn0.8Zn0.2Fe2O4 ferrite. 3 wt.% of mechanically milled ferrite was mixed with Fe3Si powder alloy. Mixed micro-nano powder system was homogenized by the Resonant Acoustic Mixing using ResodynLabRAM Mixer. This non-invasive homogenization technique was used to preserve spherical morphology of Fe3Si powder particles. Uniaxial cold pressing in the closed die at pressure 600 MPa was applied to obtain a compact sample. Microwave sintering of green compact was realized at 800°C, 20 minutes, in air. Density of the powders and composite was measured by Hepycnometry. Impulse excitation method was used to measure elastic properties of sintered composite. Mechanical properties were evaluated by measurement of transverse rupture strength (TRS) and Vickers hardness (HV). Resistivity was measured by 4 point probe method. Ferrite phase distribution in volume of the composite was documented by metallographic analysis. It has been found that nano-ferrite particle distributed among micro- particles of Fe3Si powder alloy led to high relative density (~93%) and suitable mechanical properties (TRS >100 MPa, HV ~1GPa, E-modulus ~140 GPa) of the composite. High electric resistivity (R~6.7 ohm.cm) of prepared composite indicate their potential application as soft magnetic material at medium and high frequencies.

Keywords: micro- and nano-composite, soft magnetic materials, microwave sintering, mechanical and electric properties

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167 Investigation of Mechanical Properties and Positron Annihilation Lifetime Spectroscopy of Acrylonitrile Butadiene Styrene/Polycarbonate Blends

Authors: Ayman M. M. Abdelhaleem, Mustafa Gamal Sadek, Kamal Reyad, Montasser M. Dewidar

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The main objective of this research is to study the effect of adding polycarbonate (PC) to pure Acrylonitrile Butadiene Styrene (ABS) using the injection moulding process. The PC was mixed mechanically with ABS in 10%, 20%, 30%, 40%, and 50% by weight. The mechanical properties of pure ABS reinforced with PC were investigated using tensile, impact, hardness, and wear tests. The results showed that, by adding 10%, 20%, 30%, 40%, and 50% wt. of PC to the pure ABS, the ultimate tensile strength increased from 55 N/mm2 for neat ABS to 57 N/mm2 (i.e. 3.63%), 60 N/mm2 (i.e. 9.09%), 63 N/mm2 (i.e. 14.54%), 66 N/mm2 (i.e. 20%), 69 N/mm2 (i.e. 25.45%) respectively. Test results also revealed nearly 5.72% improvement in young's modulus by adding 10% of PC to ABS, 16.74% improvement by adding 20%, 23.34% improvement by adding 30%, 27.75% improvement by adding 40%, and no other increase in case of 50%. The impact test results showed that with the increase of the PC content, first, the impact strength decreased and then increased gradually. The impact strength decreased rapidly when the content of PC was 0% to 10% range. As well as, in the case of 20%, 30%, 40%, and 50% PC, the impact strength is increased. The hardness test results, using the Shore D tester, showed that, as the PC particles contents increased, the hardness increased from 76 for the ABS to 80 for 10% PC, and decreased to 79 for 20% PC, and then increased to 80 in case of 30%, 40%, and 50% PC. Wear test results showed that PC improves the wear resistance of ABS/PC blends. Positron annihilation lifetime spectroscopy showed that with an increase of PC in ABS/PC blends, a slight decrease in free volume size and an increase in the tensile strength due to good adhesion between PC and ABS matrix, which acted as an advantage in the polymer matrix.

Keywords: ABS, PC, injection molding process, mechanical properties, lifetime spectroscopy

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166 Investigating the Minimum RVE Size to Simulate Poly (Propylene carbonate) Composites Reinforced with Cellulose Nanocrystals as a Bio-Nanocomposite

Authors: Hamed Nazeri, Pierre Mertiny, Yongsheng Ma, Kajsa Duke

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The background of the present study is the use of environment-friendly biopolymer and biocomposite materials. Among the recently introduced biopolymers, poly (propylene carbonate) (PPC) has been gaining attention. This study focuses on the size of representative volume elements (RVE) in order to simulate PPC composites reinforced by cellulose nanocrystals (CNCs) as a bio-nanocomposite. Before manufacturing nanocomposites, numerical modeling should be implemented to explore and predict mechanical properties, which may be accomplished by creating and studying a suitable RVE. In other studies, modeling of composites with rod shaped fillers has been reported assuming that fillers are unidirectionally aligned. But, modeling of non-aligned filler dispersions is considerably more difficult. This study investigates the minimum RVE size to enable subsequent FEA modeling. The matrix and nano-fillers were modeled using the finite element software ABAQUS, assuming randomly dispersed fillers with a filler mass fraction of 1.5%. To simulate filler dispersion, a Monte Carlo technique was employed. The numerical simulation was implemented to find composite elastic moduli. After commencing the simulation with a single filler particle, the number of particles was increased to assess the minimum number of filler particles that satisfies the requirements for an RVE, providing the composite elastic modulus in a reliable fashion.

Keywords: biocomposite, Monte Carlo method, nanocomposite, representative volume element

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165 Evaluation of Duncan-Chang Deformation Parameters of Granular Fill Materials Using Non-Invasive Seismic Wave Methods

Authors: Ehsan Pegah, Huabei Liu

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Characterizing the deformation properties of fill materials in a wide stress range always has been an important issue in geotechnical engineering. The hyperbolic Duncan-Chang model is a very popular model of stress-strain relationship that captures the nonlinear deformation of granular geomaterials in a very tractable manner. It consists of a particular set of the model parameters, which are generally measured from an extensive series of laboratory triaxial tests. This practice is both time-consuming and costly, especially in large projects. In addition, undesired effects caused by soil disturbance during the sampling procedure also may yield a large degree of uncertainty in the results. Accordingly, non-invasive geophysical seismic approaches may be utilized as the appropriate alternative surveys for measuring the model parameters based on the seismic wave velocities. To this end, the conventional seismic refraction profiles were carried out in the test sites with the granular fill materials to collect the seismic waves information. The acquired shot gathers are processed, from which the P- and S-wave velocities can be derived. The P-wave velocities are extracted from the Seismic Refraction Tomography (SRT) technique while S-wave velocities are obtained by the Multichannel Analysis of Surface Waves (MASW) method. The velocity values were then utilized with the equations resulting from the rigorous theories of elasticity and soil mechanics to evaluate the Duncan-Chang model parameters. The derived parameters were finally compared with those from laboratory tests to validate the reliability of the results. The findings of this study may confidently serve as the useful references for determination of nonlinear deformation parameters of granular fill geomaterials. Those are environmentally friendly and quite economic, which can yield accurate results under the actual in-situ conditions using the surface seismic methods.

Keywords: Duncan-Chang deformation parameters, granular fill materials, seismic waves velocity, multichannel analysis of surface waves, seismic refraction tomography

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164 Robust Design of a Ball Joint Considering Uncertainties

Authors: Bong-Su Sin, Jong-Kyu Kim, Se-Il Song, Kwon-Hee Lee

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An automobile ball joint is a pivoting element used to allow rotational motion between the parts of the steering and suspension system. And it plays a role in smooth transmission of steering movement, also reduction in impact from the road surface. A ball joint is under various repeated loadings that may cause cracks and abrasion. This damages lead to safety problems of a car, as well as reducing the comfort of the driver's ride, and raise questions about the ball joint procedure and the whole durability of the suspension system. Accordingly, it is necessary to ensure the high durability and reliability of a ball joint. The structural responses of stiffness and pull-out strength were then calculated to check if the design satisfies the related requirements. The analysis was sequentially performed, following the caulking process. In this process, the deformation and stress results obtained from the analysis were saved. Sequential analysis has a strong advantage, in that it can be analyzed by considering the deformed shape and residual stress. The pull-out strength means the required force to pull the ball stud out from the ball joint assembly. The low pull-out strength can deteriorate the structural stability and safety performances. In this study, two design variables and two noise factors were set up. Two design variables were the diameter of a stud and the angle of a socket. And two noise factors were defined as the uncertainties of Young's modulus and yield stress of a seat. The DOE comprises 81 cases using these conditions. Robust design of a ball joint was performed using the DOE. The pull-out strength was generated from the uncertainties in the design variables and the design parameters. The purpose of robust design is to find the design with target response and smallest variation.

Keywords: ball joint, pull-out strength, robust design, design of experiments

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163 Finite Element Analysis of Shape Memory Alloy Stents in Coronary Arteries

Authors: Amatulraheem Al-Abassi, K. Khanafer, Ibrahim Deiab

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The coronary artery stent is a promising technology that can treat various coronary diseases. Materials used for manufacturing medical stents should have high biocompatible properties. Stent alloys, in particular, are remarkably promising good clinical outcomes, however, there is threaten of restenosis (reoccurring of artery narrowing due to fatty plaque), stent recoiling, or in long-term the occurrence of stent fracture. However, stents that are made of Nickel-titanium (Nitinol) can bare extensive plastic deformation and resist restenosis. This shape memory alloy has outstanding mechanical properties. Nitinol is a unique shape memory alloy as it has unique mechanical properties such as; biocompatibility, super-elasticity, and recovery to original shape under certain loads. Stent failure may cause complications in vascular diseases and possibly blockage of blood flow. Thus, studying the behaviors of the stent under different medical conditions will help the doctors and cardiologists to predict when it is necessary to change the stent in order to prevent any severe morbidity outcomes. To the best of our knowledge, there are limited published papers that analyze the stent behavior with regards to the contact surfaces of plaque layer and blood vessel. Thus, stent material properties will be discussed in this investigation to highlight the mechanical and clinical differences between various stents. This research analyzes the performance of Nitinol stent in well-known stent design to determine its bearing with stress and its dislocation in blood vessels, in comparison to stents made of different biocompatible materials. In addition, a study of its performance will be represented in the system. Finite Element Analysis is the core of this study. Thus, a physical representative model will be discussed to show the distribution of stress and strain along the interaction surface between the stent and the artery. The reaction of vascular tissue to the stent will be evaluated to predict the possibility of restenosis within the treated area.

Keywords: shape memory alloy, stent, coronary artery, finite element analysis

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162 Enhanced Mechanical Properties and Corrosion Resistance of Fe-Based Thin Film Metallic Glasses via Pulsed Laser Deposition

Authors: Ali Obeydavi, Majid Rahimi

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This study explores the synthesis and characterization of Fe-Cr-Mo-Co-C-B-Si thin film metallic glasses fabricated using the pulsed laser deposition (PLD) technique on silicon wafer and 304 stainless steel substrates. it systematically varied the laser pulse numbers (20,000; 30,000; 40,000) and energies (130, 165, 190 mJ) to investigate their effects on the microstructural, mechanical, and corrosion properties of the deposited films. Comprehensive characterization techniques, including grazing incidence X-ray diffraction, field emission scanning electron microscopy, atomic force microscopy, and transmission electron microscopy with selected area electron diffraction, were utilized to assess the amorphous structure and surface morphology. Results indicated that increased pulse numbers and laser energies led to enhanced deposition rates and film thicknesses. Nanoindentation tests demonstrated that the hardness and elastic modulus of the amorphous thin films significantly surpassed those of the 304 stainless steel substrate. Additionally, electrochemical polarization and impedance spectroscopy revealed that the Fe-based metallic glass coatings exhibited superior corrosion resistance compared to the stainless steel substrate. The observed improvements in mechanical and corrosion properties are attributed to the unique amorphous structure achieved through the PLD process, highlighting the potential of these materials for protective coatings in aggressive environments.

Keywords: thin film metallic glasses, pulsed laser deposition, mechanical properties, corrosion resistance

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161 Parameters Identification of Granular Soils around PMT Test by Inverse Analysis

Authors: Younes Abed

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The successful application of in-situ testing of soils heavily depends on development of interpretation methods of tests. The pressuremeter test simulates the expansion of a cylindrical cavity and because it has well defined boundary conditions, it is more unable to rigorous theoretical analysis (i. e. cavity expansion theory) then most other in-situ tests. In this article, and in order to make the identification process more convenient, we propose a relatively simple procedure which involves the numerical identification of some mechanical parameters of a granular soil, especially, the elastic modulus and the friction angle from a pressuremeter curve. The procedure, applied here to identify the parameters of generalised prager model associated to the Drucker & Prager criterion from a pressuremeter curve, is based on an inverse analysis approach, which consists of minimizing the function representing the difference between the experimental curve and the curve obtained by integrating the model along the loading path in in-situ testing. The numerical process implemented here is based on the established finite element program. We present a validation of the proposed approach by a database of tests on expansion of cylindrical cavity. This database consists of four types of tests; thick cylinder tests carried out on the Hostun RF sand, pressuremeter tests carried out on the Hostun sand, in-situ pressuremeter tests carried out at the site of Fos with marine self-boring pressuremeter and in-situ pressuremeter tests realized on the site of Labenne with Menard pressuremeter.

Keywords: granular soils, cavity expansion, pressuremeter test, finite element method, identification procedure

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160 Asset Liability Modelling for Pension Funds by Introducing Leslie Model for Population Dynamics

Authors: Kristina Sutiene, Lina Dapkute

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The paper investigates the current demographic trends that exert the sustainability of pension systems in most EU regions. Several drivers usually compose the demographic challenge, coming from the structure and trends of population in the country. As the case of research, three main variables of demographic risk in Lithuania have been singled out and have been used in making up the analysis. Over the last two decades, the country has presented a peculiar demographic situation characterized by pessimistic fertility trends, negative net migration rate and rising life expectancy that make the significant changes in labor-age population. This study, therefore, sets out to assess the relative impact of these risk factors both individually and in aggregate, while assuming economic trends to evolve historically. The evidence is presented using data of pension funds that operate in Lithuania and are financed by defined-contribution plans. To achieve this goal, the discrete-time pension fund’s value model is developed that reflects main operational modalities: contribution income from current participants and new entrants, pension disbursement and administrative expenses; it also fluctuates based on returns from investment activity. Age-structured Leslie population dynamics model has been integrated into the main model to describe the dynamics of fertility, migration and mortality rates upon age. Validation has concluded that Leslie model adequately fits the current population trends in Lithuania. The elasticity of pension system is examined using Loimaranta efficiency as a measure for comparison of plausible long-term developments of demographic risks. With respect to the research question, it was found that demographic risks have different levels of influence on future value of aggregated pension funds: The fertility rates have the highest importance, while mortality rates give only a minor impact. Further studies regarding the role of trying out different economic scenarios in the integrated model would be worthwhile.

Keywords: asset liability modelling, Leslie model, pension funds, population dynamics

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159 Characterization of Erodibility Using Soil Strength and Stress-Strain Indices for Soils in Some Selected Sites in Enugu State

Authors: C. C. Egwuonwu, N. A. A. Okereke, K. O. Chilakpu, S. O. Ohanyere

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In this study, initial soil strength indices (qu) and stress-strain characteristics, namely failure strain (ϵf), area under the stress-strain curve up to failure (Is) and stress-strain modulus between no load and failure (Es) were investigated as potential indicators for characterizing the erosion resistance of two compacted soils, namely sandy clay loam (SCL) and clay loam (CL) in some selected sites in Enugu State, Nigeria. The unconfined compressive strength (used in obtaining strength indices) and stress-strain measurements were obtained as a function of moisture content in percentage (mc %) and dry density (γd). Test were conducted over a range of 8% to 30% moisture content and 1.0 g/cm3 to 2.0 g/cm3 dry density at applied loads of 20, 40, 80, 160 and 320 kPa. Based on the results, it was found out that initial soil strength alone was not a good indicator of erosion resistance. For instance, in the comparison of exponents of mc% and γd for jet index or erosion resistance index (Ji) and the strength measurements, qu and Es agree in signs for mc%, but are opposite in signs for γd. Therefore, there is an inconsistency in exponents making it difficult to develop a relationship between the strength parameters and Ji for this data set. In contrast, the exponents of mc% and γd for Ji and ϵf and Is are opposite in signs, there is potential for an inverse relationship. The measured stress-strain characteristics, however, appeared to have potential in providing useful information on erosion resistance. The models developed for the prediction of the extent or the susceptibility of soils to erosion and subjected to sensitivity test on some selected sites achieved over 90% efficiency in their functions.

Keywords: characterization of erodibility, selected sites in Enugu state, soil strength, stress-strain indices

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158 Copolymers of Epsilon-Caprolactam Received via Anionic Polymerization in the Presence of Polypropylene Glycol Based Polymeric Activators

Authors: Krasimira N. Zhilkova, Mariya K. Kyulavska, Roza P. Mateva

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The anionic polymerization of -caprolactam (CL) with bifunctional activators has been extensively studied as an effective and beneficial method of improving chemical and impact resistances, elasticity and other mechanical properties of polyamide (PA6). In presence of activators or macroactivators (MAs) also called polymeric activators (PACs) the anionic polymerization of lactams proceeds rapidly at a temperature range of 130-180C, well below the melting point of PA-6 (220C) permitting thus the direct manufacturing of copolymer product together with desired modifications of polyamide properties. Copolymers of PA6 with an elastic polypropylene glycol (PPG) middle block into main chain were successfully synthesized via activated anionic ring opening polymerization (ROP) of CL. Using novel PACs based on PPG polyols (with differ molecular weight) the anionic ROP of CL was realized and investigated in the presence of a basic initiator sodium salt of CL (NaCL). The PACs were synthesized as N-carbamoyllactam derivatives of hydroxyl terminated PPG functionalized with isophorone diisocyanate [IPh, 5-Isocyanato-1-(isocyanatomethyl)-1,3,3-trimethylcyclohexane] and blocked then with CL units via an addition reaction. The block copolymers were analyzed and proved with 1H-NMR and FT-IR spectroscopy. The influence of the CL/PACs ratio in feed, the length of the PPG segments and polymerization conditions on the kinetics of anionic ROP, on average molecular weight, and on the structure of the obtained block copolymers were investigated. The structure and phase behaviour of the copolymers were explored with differential scanning calorimetry, wide-angle X-ray diffraction, thermogravimetric analysis and dynamic mechanical thermal analysis. The crystallinity dependence of PPG content incorporated into copolymers main backbone was estimate. Additionally, the mechanical properties of the obtained copolymers were studied by notched impact test. From the performed investigation in this study could be concluded that using PPG based PACs at the chosen ROP conditions leads to obtaining well-defined PA6-b-PPG-b-PA6 copolymers with improved impact resistance.

Keywords: anionic ring opening polymerization, caprolactam, polyamide copolymers, polypropylene glycol

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157 Convergence Results of Two-Dimensional Homogeneous Elastic Plates from Truncation of Potential Energy

Authors: Erick Pruchnicki, Nikhil Padhye

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Plates are important engineering structures which have attracted extensive research since the 19th century. The subject of this work is statical analysis of a linearly elastic homogenous plate under small deformations. A 'thin plate' is a three-dimensional structure comprising of a small transverse dimension with respect to a flat mid-surface. The general aim of any plate theory is to deduce a two-dimensional model, in terms of mid-surface quantities, to approximately and accurately describe the plate's deformation in terms of mid-surface quantities. In recent decades, a common starting point for this purpose is to utilize series expansion of a displacement field across the thickness dimension in terms of the thickness parameter (h). These attempts are mathematically consistent in deriving leading-order plate theories based on certain a priori scaling between the thickness and the applied loads; for example, asymptotic methods which are aimed at generating leading-order two-dimensional variational problems by postulating formal asymptotic expansion of the displacement fields. Such methods rigorously generate a hierarchy of two-dimensional models depending on the order of magnitude of the applied load with respect to the plate-thickness. However, in practice, applied loads are external and thus not directly linked or dependent on the geometry/thickness of the plate; thus, rendering any such model (based on a priori scaling) of limited practical utility. In other words, the main limitation of these approaches is that they do not furnish a single plate model for all orders of applied loads. Following analogy of recent efforts of deploying Fourier-series expansion to study convergence of reduced models, we propose two-dimensional model(s) resulting from truncation of the potential energy and rigorously prove the convergence of these two-dimensional plate models to the parent three-dimensional linear elasticity with increasing truncation order of the potential energy.

Keywords: plate theory, Fourier-series expansion, convergence result, Legendre polynomials

Procedia PDF Downloads 108