Effect of Sodium Aluminate on Compressive Strength of Geopolymer at Elevated Temperatures

Geopolymer is an inorganic material synthesized by alkali activation of source materials rich in soluble SiO2 and Al2O3. Many researches have studied the effect of aluminum species on the synthesis of geopolymer. However, it is still unclear about the influence of Al additives on the properties of geopolymer. The current study identified the role of the Al additive on the thermal performance of fly ash based geopolymer and observing the microstructure development of the composite. NaOH pellets were dissolved in water for 14 M (14 moles/L) sodium hydroxide solution which was used as an alkali activator. The weight ratio of alkali activator to fly ash was 0.40. Sodium aluminate powder was employed as an Al additive and added in amounts of 0.5 wt.% to 2 wt.% by the weight of fly ash. The mixture of alkali activator and fly ash was cured in a 75°C dry oven for 24 hours. Then, the hardened geopolymer samples were exposed to 300°C, 600°C and 900°C for 2 hours, respectively. The initial compressive strength after oven curing increased with increasing sodium aluminate content. It was also observed in SEM results that more amounts of geopolymer composite were synthesized as sodium aluminate was added. The compressive strength increased with increasing heating temperature from 300°C to 600°C regardless of sodium aluminate addition. It was consistent with the ATR-FTIR results that the peak position related to asymmetric stretching vibrations of Si-O-T (T: Si or Al) shifted to higher wavenumber as the heating temperature increased, indicating the further geopolymer reaction. In addition, geopolymer sample with higher content of sodium aluminate showed better compressive strength. It was also reflected on the IR results by more shift of the peak position assigned to Si-O-T toward the higher wavenumber. However, the compressive strength decreased after being exposed to 900°C in all samples. The degree of reduction in compressive strength was decreased with increasing sodium aluminate content. The deterioration in compressive strength was most severe in the geopolymer sample without sodium aluminate additive, while the samples with sodium aluminate addition showed better thermal durability at 900°C. This is related to the phase transformation with the occurrence of nepheline phase at 900°C, which was most predominant in the sample without sodium aluminate. In this work, it was concluded that sodium aluminate could be a good additive in the geopolymer synthesis by showing the improved compressive strength at elevated temperatures.

Effect of Particle Size on Alkali-Activation of Slag

In this study grinding experiments were performed in a laboratory ball mill using Polish ferronickel slag in order to study the effect of the particle size on alkali activation and the properties of the produced alkali activated materials (AAMs). In this regard, the particle size distribution and the specific surface area of the grinding products in relation to grinding time were assessed. The experimental results show that products with high compressive strength, e.g. higher than 60 MPa, can be produced when the slag median size decreased from 39.9 μm to 11.9 μm. Also, finer fractions are characterized by higher reactivity and result in the production of AAMs with lower porosity and better mechanical properties.

Educating the Educators: Interdisciplinary Approaches to Enhance Science Teaching

In a rapid-changing world, science teachers face considerable challenges. In addition to the basic curriculum, there must be included several transversal themes, which demand creative and innovative strategies to be arranged and integrated to traditional disciplines. In Brazil, nuclear science is still a controversial theme, and teachers themselves seem to be unaware of the issue, most often perpetuating prejudice, errors and misconceptions. This article presents the authors’ experience in the development of an interdisciplinary pedagogical proposal to include nuclear science in the basic curriculum, in a transversal and integrating way. The methodology applied was based on the analysis of several normative documents that define the requirements of essential learning, competences and skills of basic education for all schools in Brazil. The didactic materials and resources were developed according to the best practices to improve learning processes privileging constructivist educational techniques, with emphasis on active learning process, collaborative learning and learning through research. The material consists of an illustrated book for students, a book for teachers and a manual with activities that can articulate nuclear science to different disciplines: Portuguese, mathematics, science, art, English, history and geography. The content counts on high scientific rigor and articulate nuclear technology with topics of interest to society in the most diverse spheres, such as food supply, public health, food safety and foreign trade. Moreover, this pedagogical proposal takes advantage of the potential value of digital technologies, implementing QR codes that excite and challenge students of all ages, improving interaction and engagement. The expected results include the education of the educators for nuclear science communication in a transversal and integrating way, demystifying nuclear technology in a contextualized and significant approach. It is expected that the interdisciplinary pedagogical proposal contributes to improving attitudes towards knowledge construction, privileging reconstructive questioning, fostering a culture of systematic curiosity and encouraging critical thinking skills.

Residual Modulus of Elasticity of Self-Compacting Concrete Incorporated Unprocessed Waste Fly Ash after Expose to the Elevated Temperature

The present study experimentally investigated the impact of incorporating unprocessed waste fly ash (UWFA) on the residual mechanical properties of self-compacting concrete (SCC) after exposure to elevated temperature. Three mixtures of SCC have been produced by replacing the cement mass by 0%, 15% and 30% of UWFA. Generally, the fire resistance of SCC has been enhanced by replacing the cement up to 15% of UWFA, especially in case of residual modulus of elasticity which considers more sensitive than other mechanical properties at elevated temperature. However, a strong linear relationship has been observed between the residual flexural strength and modulus of elasticity, where both of them affected significantly by the cracks appearance and propagation as a result of elevated temperature. Sustainable products could be produced by incorporating unprocessed waste powder materials in the production of concrete, where the waste materials, CO2 emissions, and the energy needed for processing are reduced.

Measuring the Effect of Ventilation on Cooking in Indoor Air Quality by Low-Cost Air Sensors

The concern of the indoor air quality (IAQ) has been increasing due to its risk to human health. The smoking, sweeping, and stove and stovetop use are the activities that have a major contribution to the indoor air pollution. Outdoor air pollution also affects IAQ. The most important factors over IAQ from cooking activities are the materials, fuels, foods, and ventilation. The low-cost, mobile air quality monitoring (LCMAQM) sensors, is reachable technology to assess the IAQ. This is because of the lower cost of LCMAQM compared to conventional instruments. The IAQ was assessed, using LCMAQM, during cooking activities in a University of Minnesota graduate-housing evaluating different ventilation systems. The gases measured are carbon monoxide (CO) and carbon dioxide (CO2). The particles measured are particle matter (PM) 2.5 micrometer (µm) and lung deposited surface area (LDSA). The measurements are being conducted during April 2019 in Como Student Community Cooperative (CSCC) that is a graduate housing at the University of Minnesota. The measurements are conducted using an electric stove for cooking. The amount and type of food and oil using for cooking are the same for each measurement. There are six measurements: two experiments measure air quality without any ventilation, two using an extractor as mechanical ventilation, and two using the extractor and windows open as mechanical and natural ventilation. 3The results of experiments show that natural ventilation is most efficient system to control particles and CO2. The natural ventilation reduces the concentration in 79% for LDSA and 55% for PM2.5, compared to the no ventilation. In the same way, CO2 reduces its concentration in 35%. A well-mixed vessel model was implemented to assess particle the formation and decay rates. Removal rates by the extractor were significantly higher for LDSA, which is dominated by smaller particles, than for PM2.5, but in both cases much lower compared to the natural ventilation. There was significant day to day variation in particle concentrations under nominally identical conditions. This may be related to the fat content of the food. Further research is needed to assess the impact of the fat in food on particle generations.

Peculiarities of Internal Friction and Shear Modulus in 60Co γ-Rays Irradiated Monocrystalline SiGe Alloys

At present, a number of modern semiconductor devices based on SiGe alloys have been created in which the latest achievements of high technologies are used. These devices might cause significant changes to networking, computing, and space technology. In the nearest future new materials based on SiGe will be able to restrict the A3B5 and Si technologies and firmly establish themselves in medium frequency electronics. Effective realization of these prospects requires the solution of prediction and controlling of structural state and dynamical physical –mechanical properties of new SiGe materials. Based on these circumstances, a complex investigation of structural defects and structural-sensitive dynamic mechanical characteristics of SiGe alloys under different external impacts (deformation, radiation, thermal cycling) acquires great importance. Internal friction (IF) and shear modulus temperature and amplitude dependences of the monocrystalline boron-doped Si1-xGex(x≤0.05) alloys grown by Czochralski technique is studied in initial and 60Co gamma-irradiated states. In the initial samples, a set of dislocation origin relaxation processes and accompanying modulus defects are revealed in a temperature interval of 400-800 ⁰C. It is shown that after gamma-irradiation intensity of relaxation internal friction in the vicinity of 280 ⁰C increases and simultaneously activation parameters of high temperature relaxation processes reveal clear rising. It is proposed that these changes of dynamical mechanical characteristics might be caused by a decrease of the dislocation mobility in the Cottrell atmosphere enriched by the radiation defects.

Modeling Thermo-Photo-Voltaic Selective Emitter Based on a Semi-Transparent Emitter with Integrated Narrow Band-Pass Pre-Filter

This work is a parametric study combining simple and well known optical theories. These simple theories are arranged to form part of one answer to the question: “Can a semi-transparent Thermo-Photo-Voltaic (TPV) emitter have an optical extinction spectrum so much greater than its optical absorption spectrum that it becomes its own band-pass pre-filter, and if so, how well might it be expected to suppress light of undesired wavelengths?” In the report, hypothetical materials and operating temperatures will be used for comparative analyses only. Thermal emission properties of these hypothetical materials were created using two openly available FORTRAN programs. Results indicate that if using highly transparent materials it may be possible to create a thermal emitter that is its own band-pass pre-filter.

Assessment of Ultra-High Cycle Fatigue Behavior of EN-GJL-250 Cast Iron Using Ultrasonic Fatigue Testing Machine

High cycle fatigue comprising up to 107 load cycles has been the subject of many studies, and the behavior of many materials was recorded adequately in this regime. However, many applications involve larger numbers of load cycles during the lifetime of machine components. In this ultra-high cycle regime, other failure mechanisms play, and the concept of a fatigue endurance limit (assumed for materials such as steel) is often an oversimplification of reality. When machine component design demands a high geometrical complexity, cast iron grades become interesting candidate materials. Grey cast iron is known for its low cost, high compressive strength, and good damping properties. However, the ultra-high cycle fatigue behavior of cast iron is poorly documented. The current work focuses on the ultra-high cycle fatigue behavior of EN-GJL-250 (GG25) grey cast iron by developing an ultrasonic (20 kHz) fatigue testing system. Moreover, the testing machine is instrumented to measure the temperature and the displacement of  the specimen, and to control the temperature. The high resonance frequency allowed to assess the  behavior of the cast iron of interest within a matter of days for ultra-high numbers of cycles, and repeat the tests to quantify the natural scatter in fatigue resistance.

Producing and Mechanical Testing of Urea-Formaldehyde Resin Foams Reinforced by Waste Phosphogypsum

Many of thermosetting resins have application only in filled state, reinforced with different mineral fillers. The co-filling of polymers with mineral filler and gases creates a possibility for production of polymer composites materials with low density. This processing leads to forming of new materials – gas-filled plastics (polymer foams). The properties of these materials are determined mainly by the shape and size of internal structural elements (pores). The interactions on the phase boundaries have influence on the materials properties too. In the present work, the gas-filled urea-formaldehyde resins were reinforced by waste phosphogypsum. The waste phosphogypsum (CaSO4.2H2O) is a solid by-product in wet phosphoric acid production processes. The values of the interactions polymer-filler were increased by using two modifying agents: polyvinyl acetate for polymer matrix and sodium metasilicate for filler. Technological methods for gas-filling and recipes of urea-formaldehyde based materials with apparent density 20-120 kg/m3 were developed. The heat conductivity of the samples is between 0.024 and 0.029 W/moK. Tensile analyses were carried out at 10 and 50% deformation and show values 0.01-0.14 MPa and 0.01-0.09 MPa, respectively. The apparent density of obtained materials is between 20 and 92 kg/m3. The changes in the tensile properties and density of these materials according to sodium metasilicate content were studied too. The mechanism of phosphogypsum adsorption modification was studied using methods of FT-IR spectroscopy. The structure of the gas-filled urea-formaldehyde resins was described by results of electron scanning microscopy at three different magnification ratios – x50, x150 and x 500. The aim of present work is to study the possibility of the usage of phosphogypsum as mineral filler for urea-formaldehyde resins and development of a technology for the production of gas-filled reinforced polymer composite materials. The structure and the properties of obtained composite materials are suitable for thermal and sound insulation applications.

Determination of the Thermophysical Characteristics of the Composite Material Clay Cement Paper

In Morocco, the building sector is largely responsible for the evolution of energy consumption. The control of energy in this sector remains a major issue despite the rise of renewable energies. The design of an environmentally friendly building requires mastery and knowledge of energy and bioclimatic aspects. This implies taking into consideration of all the elements making up the building and the way in which energy exchanges take place between these elements. In this context, thermal insulation seems to be an ideal starting point for reducing energy consumption and greenhouse gas emissions. In this context, thermal insulation seems to be an ideal starting point for reducing energy consumption and greenhouse gas emissions. The aim of this work is to provide some solutions to reduce energy consumption while maintaining thermal comfort in the building. The objective of our work is to present an experimental study on the characterization of local materials used in the thermal insulation of buildings. These are paper recycling stabilized with cement and clay. The thermal conductivity of these materials, which were constituted based on sand, clay, cement; water, as well as treated paper, was determined by the guarded-hot-plate method. It involves the design of two materials that will subsequently be subjected to thermal and mechanical tests to determine their thermophysical properties. The results show that the thermal conductivity decreases as well in the case of the paper-cement mixture as that of the paper-clay and seems to stabilize around 40%. Measurements of mechanical properties such as flexural strength have shown that the enrichment of the studied material with paper makes it possible to reduce the flexural strength by 20% while optimizing the conductivity.

Effect of Leachate Presence on Shear Strength Parameters of Bentonite-Amended Zeolite Soil

Over recent years, due to increased population and increased waste production, groundwater protection has become more important, therefore, designing engineered barrier systems such as landfill liners to prevent the entry of leachate into groundwater should be done with greater accuracy. These measures generally involve the application of low permeability soils such as clays. Bentonite is a natural clay with low permeability which makes it a suitable soil for using in liners. Also zeolite with high cation exchange capacity can help to reduce of hazardous materials risk. Bentonite expands when wet, absorbing as much as several times its dry mass in water. This property may effect on some structural properties of soil such as shear strength. In present study, shear strength parameters are determined by both leachates polluted and not polluted bentonite-amended zeolite soil with mixing rates (B/Z) of 5%-10% and 20% with unconfined compression test to obtain the differences. It is shown that leachate presence causes reduction in resistance in general.

Evaluating Mechanical Properties of CoNiCrAlY Coating from Miniature Specimen Testing at Elevated Temperature

CoNiCrAlY alloys have been widely used as bond coats for thermal barrier coating (TBC) systems because of low cost, improved control of composition, and the feasibility to tailor the coatings microstructures. Coatings are in general very thin structures, and therefore it is impossible to characterize the mechanical responses of the materials via conventional mechanical testing methods. Due to this reason, miniature specimen testing methods, such as the small punch test technique, have been developed. This paper presents some of the recent research in evaluating the mechanical properties of the CoNiCrAlY coatings at room and high temperatures, through the use of small punch testing and the developed miniature specimen tensile testing, applicable to a range of temperature, to investigate the elastic-plastic and creep behavior as well as ductile-brittle transition temperature (DBTT) behavior. An inverse procedure was developed to derive the mechanical properties from such tests for the coating materials. A two-layer specimen test method is also described. The key findings include: 1) the temperature-dependent coating properties can be accurately determined by the miniature tensile testing within a wide range of temperature; 2) consistent DBTTs can be identified by both the SPT and miniature tensile tests (~ 650 °C); and 3) the FE SPT modelling has shown good capability of simulating the early local cracking. In general, the temperature-dependent material behaviors of the CoNiCrAlY coating has been effectively characterized using miniature specimen testing and inverse method.

A Hygrothermal Analysis and Structural Performance of Wood-Frame Wall Systems with Low-Permeance Exterior Insulation

Increasing the level of exterior insulation in residential buildings is a popular way for improving the thermal characteristic of building enclosure and reducing heat loss. However, the layout and properties of materials composing the wall have a great effect on moisture accumulation within the wall cavity, long-term durability of a wall as well as the structural performance. A one-dimensional hygrothermal modeling has been performed to investigate moisture condensation risks and the drying capacity of standard 2×4 and 2×6 light wood-frame wall assemblies including exterior low-permeance extruded polystyrene (XPS) insulation. The analysis considered two different wall configurations whereby the rigid insulation board was placed either between Oriented Strand Board (OSB) sheathing and the stud or outboard to the structural sheathing. The thickness of the insulation varied between 0 mm and 50 mm and the analysis has been conducted for eight different locations in Canada, covering climate zone 4 through zone 8. Results show that the wall configuration with low-permeance insulation inserted between the stud and OSB sheathing accumulates more moisture within the stud cavity, compared to the assembly with the same insulation placed exterior to the sheathing. On the other hand, OSB moisture contents of the latter configuration were markedly higher. Consequently, the analysis of hygrothermal performance investigated and compared moisture accumulation in both the OSB and stud cavity. To investigate the structural performance of the wall and the effect of soft insulation layer inserted between the sheathing and framing, forty nail connection specimens were tested. Results have shown that both the connection strength and stiffness experience a significant reduction as the insulation thickness increases. These results will be compared with results from a full-scale shear wall tests in order to investigate if the capacity of shear walls with insulated sheathing would experience a similar reduction in structural capacities.

Eye Tracking: Biometric Evaluations of Instructional Materials for Improved Learning

Eye tracking is a great way to triangulate multiple data sources for deeper, more complete knowledge of how instructional materials are really being used and emotional connections made. Using sensor based biometrics provides a detailed local analysis in real time expanding our ability to collect science based data for a more comprehensive level of understanding, not previously possible, for teaching and learning. The knowledge gained will be used to make future improvements to instructional materials, tools, and interactions. The literature has been examined and a preliminary pilot test was implemented to develop a methodology for research in Instructional Design and Technology. Eye tracking now offers the addition of objective metrics obtained from eye tracking and other biometric data collection with analysis for a fresh perspective.

Effect of Coffee Grounds on Physical and Heating Value Properties of Sugarcane Bagasse Pellets

Objective of this research is to study effect of coffee grounds on physical and heating value properties of sugarcane bagasse pellets. The coffee grounds were tested as an additive for pelletizing process of bagasse pellets. Pelletizing was performed using a Flat–die pellet mill machine. Moisture content of raw materials was controlled at 10-13%. Die temperature range during the process was 75-80 oC. Physical characteristics (bulk density and durability) of the bagasse pellet and pellets with 1-5% coffee ground were determined following the standard assigned by the Pellet Fuel Institute (PFI). The results revealed increasing values of 648±3.4, 659 ± 3.1, 679 ± 3.3 and 685 ± 3.1 kg/m3 (for pellet bulk density); and 98.7 ± 0.11, 99.2 ± 0.26, 99.3 ± 0.19 and 99.4 ± 0.07% (for pellet durability), respectively. In addition, the heating values of the coffee ground supplemented pellets (15.9 ± 1.16, 17.0 ± 1.23 and 18.8 ± 1.34 MJ/kg) were improved comparing to the non-supplemented control (14.9 ± 1.14 MJ/kg), respectively. The results indicated that both the bulk density and durability values of the bagasse pellets were increased with the increasing proportion of the coffee ground additive.

Laboratory Investigation of the Pavement Condition in Lebanon: Implementation of Reclaimed Asphalt Pavement in the Base Course and Asphalt Layer

The road network in the north of Lebanon is a prime example of the lack of pavement design and execution in Lebanon.  These roads show major distresses and hence, should be tested and evaluated. The aim of this research is to investigate and determine the deficiencies in road surface design in Lebanon, and to propose an environmentally friendly asphalt mix design. This paper consists of several parts: (i) evaluating pavement performance and structural behavior, (ii) identifying the distresses using visual examination followed by laboratory tests, (iii) deciding the optimal solution where rehabilitation or reconstruction is required and finally, (iv) identifying a sustainable method, which uses recycled material in the proposed mix. The asphalt formula contains Reclaimed Asphalt Pavement (RAP) in the base course layer and in the asphalt layer. Visual inspection of the roads in Tripoli shows that these roads face a high level of distress severity. Consequently, the pavement should be reconstructed rather than simply rehabilitated. Coring was done to determine the pavement layer thickness. The results were compared to the American Association of State Highway and Transportation Officials (AASHTO) design methodology and showed that the existing asphalt thickness is lower than the required asphalt thickness. Prior to the pavement reconstruction, the road materials were tested according to the American Society for Testing and Materials (ASTM) specification to identify whether the materials are suitable. Accordingly, the ASTM tests that were performed on the base course are Sieve analysis, Atterberg limits, modified proctor, Los Angeles, and California Bearing Ratio (CBR) tests. Results show a CBR value higher than 70%. Hence, these aggregates could be used as a base course layer. The asphalt layer was also tested and the results of the Marshall flow and stability tests meet the ASTM specifications. In the last section, an environmentally friendly mix was proposed. An optimal RAP percentage of 30%, which produced a well graded base course and asphalt mix, was determined through a series of trials.

Reinforcing Effects of Natural Micro-Particles on the Dynamic Impact Behaviour of Hybrid Bio-Composites Made of Short Kevlar Fibers Reinforced Thermoplastic Composite Armor

Hybrid bio-composites are developed for use in protective armor through positive hybridization offered by reinforcement of high-density polyethylene (HDPE) with Kevlar short fibers and palm wood micro-fillers. The manufacturing process involved a combination of extrusion and compression molding techniques. The mechanical behavior of Kevlar fiber reinforced HDPE with and without palm wood filler additions are compared. The effect of the weight fraction of the added palm wood micro-fillers is also determined. The Young modulus was found to increase as the weight fraction of organic micro-particles increased. However, the flexural strength decreased with increasing weight fraction of added micro-fillers. The interfacial interactions between the components were investigated using scanning electron microscopy. The influence of the size, random alignment and distribution of the natural micro-particles was evaluated. Ballistic impact and dynamic shock loading tests were performed to determine the optimum proportion of Kevlar short fibers and organic micro-fillers needed to improve impact strength of the HDPE. These results indicate a positive hybridization by deposition of organic micro-fillers on the surface of short Kevlar fibers used in reinforcing the thermoplastic matrix leading to enhancement of the mechanical strength and dynamic impact behavior of these materials. Therefore, these hybrid bio-composites can be promising materials for different applications against high velocity impacts.

Effect of Temperature on the Water Retention Capacity of Liner Materials

Mixtures of sand and clay are frequently used to serve for specific purposes in several engineering practices. In environmental engineering, liner layers and cover layers are common for controlling waste disposal facilities. These layers are exposed to moisture and temperature fluctuation specially when existing in unsaturated condition. The relationship between soil suction and water content for these materials is essential for understanding their unsaturated behavior and properties such as retention capacity and unsaturated follow (hydraulic conductivity). This study is aimed at investigating retention capacity for two sand-natural expansive clay mixtures (15% (C15) and 30% (C30) expansive clay) at two ambient temperatures within the range of 5 -50 °C. Soil water retention curves (SWRC) for these materials were determined at these two ambient temperatures using different salt solutions for a wide range of suction (up to 200MPa). The results indicate that retention capacity of C15 mixture underwent significant changes due to temperature variations. This effect tends to be less visible when the clay fraction is doubled (C30). In addition, the overall volume change is marginally affected by high temperature within the range considered in this study.

Mechanical and Microstructural Properties of Rotary-Swaged Wire of Commercial-Purity Titanium

Bars made of titanium grade 2 and grade 4 were subjected to rotary forging with up to 2.2 true strain reduction in the cross-section from 10 to 3.81 mm. During progressive deformation, grain refinement in the transverse direction took place. In the longitudinal direction, ultrafine microstructure has not developed. It has been demonstrated that titanium grade 2 strengthens more than grade 4. The ultimate tensile strength increased from 650 MPa to 1040 MPa in titanium grade 4. Hardness profiles on the cross section in both materials show an increase in the centre of the wire.

Assessment of Analytical Equations for the Derivation of Young’s Modulus of Bonded Rubber Materials

The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.