Determination Of Elastic Modulus Research Articles

Micromechanical properties characterization of 4H–SiC single crystal by indentation and scratch methods

Growth and micromachining of single crystal silicon carbide (SiC) have drawn extensive attention in wide bandgap semiconductors and remained challenging. The micromechanical properties (i.e., hardness, elastic modulus, fracture toughness), which are the key to machinability and machining quality (and therefore the yield of the grown SiC), of 4H–SiC were assessed by nanoindentation, microhardness, and microscratch tests. Consistent values of true indentation hardness of 4H–SiC can be obtained by different approaches without the need for the area function of the indenter. Accurate determination of elastic modulus (i.e., 583.5 GPa) and indentation hardness (i.e., 38 GPa) of 4H–SiC by the instrumented indentation technique requires low loads with slight indentation-induced damage. Consistent values of fracture toughness Kc of 4H–SiC were obtained by different methods such as the Vickers/Berkovich indenter-induced cracking method (2.1 MPa·m1/2), energy-based nanoindentation approaches (the critical void volume fraction of 0.062 should be used for 4H–SiC when the deterioration of indentation hardness is used), and linear elastic fracture mechanics (LEFM)-based scratch approach with a spherical indenter (2.6 MPa·m1/2). This work provides the guidance for the mechanical machining of 4H–SiC wafers and the paradigm of micromechanical characterization of brittle solids by indentation and scratch technologies.

Determination of elastic moduli and Poisson’s ratios of bi-modulus materials based on the results of four-point bending test

Determination of elastic moduli and Poisson’s ratios of bi-modulus materials based on the results of four-point bending test

Determination of the Dynamic Modulus of Elasticity of Pine Based on the PZT Transducer

A new method for the determination of the dynamic modulus of elasticity (Ed) of pine wood, based on the transverse vibration excitation and electromechanical impedance (EMI) response of the lead zirconate titanate (PZT) transducer is proposed. The influence of the length to thickness ratio of the pine specimen on the measurement accuracy was studied through modal simulation analysis. Based on the results of the modal simulation, the size of the pine specimen was optimized, and the scanning frequency range of the EMI response was determined. On this basis, the EMI simulation and test of the pine specimen coupled with a PZT patch were carried out to verify the effectiveness of the novel method. The impedance simulation results of three kinds of pine specimens show that a unique and significant formant appears in the real part of each EMI response curve, and the maximum relative errors of the rectangular PZT patch and circular PZT patch are 1.34% and 1.81%, respectively. The impedance test results of three kinds of pine specimens indicate that the maximum relative errors of the rectangular PZT patch and circular PZT patch are 1.41% and 1.68%, respectively, compared with the corresponding results obtained by the traditional transverse vibration method. Simulation and experimental results verify the validity of the proposed method for the elastic modulus determination of pine wood.

Inline Determination of the Gel Elastic Modulus During Milk Coagulation Using a Multifiber Optical Probe

AbstractFrom a state-of-the-art point of view, it is currently possible to optically monitor the enzymatic coagulation of milk for real time estimation of the elastic modulus to cut the gel at optimum gel firmness. However, European cheese industry produces a wide variety of cheeses, many of them artisanal, and has a very fragmented productive structure with many small-, medium-sized companies. Therefore, if the technology is to be successfully uptake, it must be not only accurate but very low-cost. The objective of this work was to evaluate a low-cost commercial multifiber probe, for inline optical determination of curd firmness during cheese making. Preliminary tests were carried out to select the most appropriate fiber core size and wavelength and after that coagulation trials were performed following a fully randomized factorial design with two factors, i.e., concentration of protein (3.2, 3.6 and 4.0%) and added calcium (150, 200 and 250 mg L−1), with three replicates. The observed linear increase of the least square means of the initial voltage with the protein content (V0 = 0.15[P, %] + 0.88; R2 = 0.999), will be likely synergistic with the elastic modulus prediction if the model needs to be corrected for protein. Finally, the multifiber probe allowed predicting curd firmness using the proposed model with SEP values < 7 Pa. The present work has proven that a low-cost multifiber probe is suitable for accurate, real-time prediction of curd firmness during cheese manufacture.

Determination of local stiffness for the joint of tunnel lining in the simulation

In the numerical simulation of shield tunnel, the treatment of joints will greatly affect the accuracy of numerical analysis. Because the stiffness of the joint is lower than the stiffness of segments, the local weakening method is adopted in this paper , which can simulate the stiffness heterogeneity in the transverse and longitudinal directions of the tunnel lining. In the method, lower local stiffness is used for the joint which is the connection between segments and rings of lining, while the stiffness of segments keeps to be unchanged. The local stiffness of the joint, which is represented by the elastic modulus of the joint in the simulation, is the key point. To verify the validity of the method, multiple full-scale experiment [11-14] objects are analyzed and the simulation results are compared to the experiment data. Then the empirical formula of elastic modulus of the weakening joint is proposed by analyzing the three-ring lining in a full-scale experiment under different assemblages. Further, the empirical formula of elastic modulus for the joint is expanded to the large-diameter tunnel and super-large-diameter tunnel. It provides a good reference for the determination of elastic modulus of the joint in the simulation of shield tunnel.

Asymmetric indentation: problem and solution

Vickers and Knoop testers are the most common tools used to measure the hardness of materials. However, a very small tilt in the sample surface even in the order of a fraction of a degree produces a noticeable asymmetry, which affects the accuracy of the measured hardness. In this investigation, a mathematical approach has been used to correct asymmetry in the Vickers and Knoop indentations in both metallic and ceramic materials. Measurements were taken for metals such as aluminium 6061(Al-6061), 304 stainless steel as well as various zirconia toughened ceramic materials including tetragonal zirconia doped with: 2.5 mol% Y2O3 (TZ2.5Y), 3 mol% Y2O3 (TZ3Y) and the composite containing 20 wt% alumina (TZ3Y20A), all prepared from commercial powders. A hardness tester equipped with Vickers and Knoop indenters was used for hardness and elastic modulus determination. Optical and scanning electron microscopes have been used to get the indentation micrographs. The method enabled accurate determination of both hardness and elastic modulus from corrected Vickers and Knoop indentations. The hardness and elastic modulus values obtained in this study are in good agreement with reported data for similar materials. The results obtained in this study have been successfully validated using the Zwick reference block. The developed method is readily applicable for the most widely used Vickers hardness machines for the correction of asymmetric indentations if existing, consequently leading to accurate determination of the hardness.

Nanoscale identification and characterization of the shear strength of minerals and organic matter in shale

Shales are composed of minerals and organic matter, whose individual properties are essential to determining the rock’s macroscopical deformation and strength. Scanning electron microscopy combined with electron energy dispersive spectroscopy (EDS) has been extensively used to evaluate composition, while peak-force atomic force microscopy (AFM) has been used on the determination of elastic modulus with nanometric resolution. Still, there is a need for tools to conduct an in-depth study of the minerals’ tribomechanical properties. Atomic force microscopy is a tool that can contribute to these studies, as it can simultaneously measure the tribomechanical properties and identify the phases. In this work, we propose using atomic force microscopy and energy dispersive spectroscopy to identify the shale components and to measure the in situ tribomechanical properties from the different phases. Friction images between the atomic force microscopy tip and the surface were acquired as a function of load. Minerals and organic matter were later identified by colocalized energy dispersive spectroscopy mapping. Then, the frictional characteristics of the major shale constituents were obtained by adjusting the Derjaguin-Muller-Toporov model to the selected components. Moreover, the identification of the different phases was performed. The results show that friction at the nanometer scale was observed to be higher for organic matter than for any other shale constituent, while shear strength was observed to be higher for quartz and lower for organic matter. These characteristics were used to differentiate shale constituents. It is shown that a careful comparison of friction can be used to differentiate the sulfite pyrite, tectosilicates (quartz, andesine, and albite), phyllosilicate biotite, and organic matter. The presented methodology gives novel information on friction properties in the nanoscale that are comparable to available centimetric characterization techniques contributing to the understanding of rock strength.

On determination of elastic modulus and indentation hardness by instrumented spherical indentation: influence of surface roughness and correction method

Although, surface roughness can influence the determination of elastic moduli and indentation hardness to some extent by instrumented spherical indentation test, limited work has been done to quantitatively reveal and minimize these influences. In the present work, through a large number of finite element (FE) simulations and analyses, we clarified the evolution trend of determined elastic moduli and indentation hardness corresponding to different normalized indentation depths (h/R) and normalized roughness (S q/R). On this basis, an area correction method was proposed to improve the measurement accuracy in the elastic moduli and indentation hardness. The FE results show that, with the newly proposed correction method, the maximum relative error in determined elastic moduli is reduced from about ±7% to ±2%, and that in the determined indentation hardness is reduced from about ±13% to ±5%, when S q/R ≤ 2.2 × 10−3 and h/R = 5%. Applications were then illustrated on four typical metallic materials (i.e., AA 7075, AA 2014, steel 316 L, and copper T2). The experimental results demonstrate that the proposed correction method is able to mitigate the effects of surface roughness on the determination of elastic moduli and indentation hardness to obtain more correct results.

A committee machine-based estimation of shear velocity log by combining intelligent systems and rock-physics model using metaheuristic algorithms

Estimation of reservoir parameters such as porosity, lithology and determination of elastic moduli is based on well-logging data and seismic velocity information. However, the lack of shear velocity log in many wells, and the high costs of its acquisition have led to developing different approaches for shear velocity estimation. Currently, shear velocity estimation is accomplished by common industrial methods such as empirical equations, regression analysis, intelligent methods and rock-physics models (RPMs). The current study proposes that robust, accurate and cost-effective intelligent methods coupled with suitable RPM provide reasonable estimations of the shear velocity in an optimal processing time. Hybridizing intelligent models with RPMs in the framework of a committee machine is an optimal solution for shear velocity estimation of carbonate reservoirs. The intelligent methods used in this study include neural network (NN), fuzzy logic (FL) and an adaptive-neuro fuzzy inference system (ANFIS). In this research, for each individual intelligent model and a developed RPM, the optimal weights were allocated by Metaheuristic optimization algorithms including genetic algorithm (GA), ant colony optimization routing (ACOR) and simulated annealing (SA)). To obtain the best results with the lowest mean squared error (MSE), a total of 9408, 10801 and 12288 models were created and tested in MATLAB to optimally parametrize the GA, ACOR and SA, respectively. The results showed that the combination of the applied intelligent models with the developed RPMs leads to a higher correlation coefficient with reference to the measured Shear velocity in test dataset. The use of a combination of intelligent methods in the form of committee-machine instead of individual methods has led to a reduction in error and improved the results by up to 2% Considering the high sensitivity of shear wave velocity in geomechanical and reservoir characterization studies, even small improvements in its estimation can significantly reduce error in the characterization of hydrocarbon reservoirs.

New Correlations for the Determination of Undrained Shear, Elastic Modulus, and Bulk Density Based on Dilatometer Tests (DMT) for Organic Soils in the South of Quito, Ecuador

The Marchetti Dilatometer test is a non-destructive in situ test that can be used to determine the geotechnical properties of soils. This paper presents the results of a study that investigated the correlations between the parameters obtained from the Marchetti Dilatometer test and geomechanical parameters for soft soils, mainly organic soils, obtained in the laboratory. The study was conducted in the El Garrochal sector in Southern Quito, Ecuador. The results of the study showed that there are significant correlations between the Marchetti Dilatometer test and the undrained shear strength, modulus of elasticity, and density of soil. The equations that were developed in this study can be used to estimate these geomechanical parameters from the results of the Marchetti Dilatometer test for the South Quito sector, which are valuable for geotechnical engineers to design structures in these types of soils. The equations that were developed in this study can be used to improve the accuracy of the design of these structures.

Micromechanical characterization of microwave dielectric ceramic BaO–Sm 2O 3–5TiO 2 by indentation and scratch methods

Mechanical characterization of dielectric ceramics, which have drawn extensive attention in wireless communication, remains challenging. Micromechanical properties with microstructures of dielectric ceramic BaO-Sm₂O₃-5TiO₂ (BST) were assessed by nanoindentation, microhardness, and microscratch tests under different indenters, along with X-ray diffraction, scanning electron microscopy, and Raman spectroscopy. Accurate determination of elastic modulus (i.e., 260 GPa) and indentation hardness (i.e., 16.2 GPa) of brittle BST ceramic by instrumented indentation technique requires low loads with little indentation-induced damage. Elastic modulus and indentation hardness were analyzed by different methodologies such as energy-based and displacement-based approaches, and elastic recovery of Knoop imprint. Consistent values (about 3.1 MPa·m^1/2) of fracture toughness of BST ceramic were obtained by different methods such as Vickers indenter-induced cracking method, energy-based nanoindentation approaches, and linear elastic fracture mechanics-based scratch approach with a spherical indenter, demonstrating successful applications of indentation and scratch methods in characterizing fracture properties of brittle solids. The deterioration of elastic modulus or indentation hardness with the increase in indentation load is caused by indentation-induced damage, and can be used to determine fracture toughness of material by energy-based nanoindentation approaches, and the critical void volume fraction is 0.27 (or 0.18) if elastic modulus (or indentation hardness) of the brittle BST ceramic is used. The fracture work at the critical load corresponding to the initial decrease in elastic modulus or indentation hardness can also be used to assess fracture toughness of brittle solids, opening new venues of application of nanoindentation test as a means to characterize fracture toughness of brittle ceramics.

Interfacial Nanoblisters Formed in Water Serving as Freestanding Platforms for Measuring Elastic Moduli of Polymeric Nanofilms.

Polymeric nanofilms have been widely utilized in diverse cutting-edge technologies, yet accurately determining their elastic moduli remains challenging. Here we demonstrate that interfacial nanoblisters, which are produced by simply immersing substrate-supported nanofilms in water, represent natural platforms for assessing the mechanical properties of polymeric nanofilms using the sophisticated nanoindentation method. Nevertheless, high-resolution, quantitative force spectroscopy studies reveal that the indentation test must be performed on an effective freestanding region around the nanoblister apex and meanwhile under an appropriate loading force, to obtain load-independent, linear elastic deformations. The nanoblister stiffness increases with either decreasing its size or increasing its covering film thickness, and such size effects can be adequately rationalized by an energy-based theoretical model. The proposed model also enables an exceptional determination of the film elastic modulus. Given that interfacial blistering is a frequently occurring phenomenon for polymeric nanofilms, we envision that the presented methodology would stimulate broad applications in relevant fields.

Assessment of the Rock Elasticity Modulus Using Four Hybrid RF Models: A Combination of Data-Driven and Soft Techniques

The determination of the rock elasticity modulus (EM) is an indispensable key step for the design of rock engineering problems. Traditional experimental analysis can accurately measure the rock EM, but it requires manpower and material resources, and it is time consuming. The EM estimation of new rocks using former published empirical formulas is also a possibility but can be attached of high uncertainties. In this paper, four types of metaheuristic optimization algorithms (MOA), named the backtracking search optimization algorithm (BSA), multi-verse optimizer (MVO), golden eagle optimizer (GEO) and poor and rich optimization algorithm (PRO), were utilized to optimize the random forest (RF) model for predicting the rock EM. A data-driven technology was used to generate an integrated database consisting of 120 rock samples from the literature. To verify the predictive performance of the proposed models, five common machine-learning models and one empirical formula were also developed to predict the rock EM. Four popular performance indices, including the root-mean-square error (RMSE), mean absolute error (MAE), the coefficient of determination (R2) and Willmott’s index (WI), were adopted to evaluate all models. The results showed that the PRO-RF model has obtained the most satisfactory prediction accuracy. The porosity (Pn) is the most important variable for predicting the rock EM based on the sensitive analysis. This paper compares the performance of the RF models optimized by using four MOA for the rock EM prediction. It provides a good example for the subsequent application of soft techniques on the EM and other important rock parameter estimations.

Determination of Elastic Modulus, Stress Relaxation Time and Thermal Softening Index in ZWT Constitutive Model for Reinforced Al/PTFE.

Al/PTFE has the advantages of high impact-responsive energy release, appropriate sensitivity, a fast energy release rate, and high energy density, and it is increasingly widely being used in the field of ammunition. In this paper, based on the traditional formula Al/PTFE (26.5%/73.5%), the reinforced Al/PTFE active materials are prepared by the process of cold pressing, sintering, and rapid cooling. Quasi static and dynamic compression experiments were carried out under different compression pressures (200~800 MPa), strain rates (0.002 s-1, 0.02 s-1, 1400~3300 s-1), and temperatures (23 °C, -20 °C, -30 °C, -40 °C). The effects of pressure, strain rate, and temperature on the quasi-static and dynamic compression properties of Al/PTFE materials are analyzed. The results show that the reinforced Al/PTFE specimens show a significant correlation between temperature and strain rate. Based on the classical Zhu-Wang-Tang (ZWT) constitutive model, the ZWT constitutive model parameters of the reinforced Al/PTFE active materials under different pressing pressures at room temperature and the ZWT constitutive model parameters of the reinforced Al/PTFE active materials at low temperature are obtained by fitting, respectively. The accuracy of the constitutive model parameters (elastic modulus, stress relaxation time, and thermal softening index) is verified. In this paper, a constitutive model considering both temperature and strain rate effects is established in order to provide reference for the study of mechanical properties of active materials.

Low cycle fatigue properties assessment and damage influence on DP 500/800 steel sheet

A dual phase (DP500/800) steel sheet (1.6 mm thickness) was evaluated by means of low cycle fatigue (LCF). The fatigue properties of the material were assessed by means of the cyclic elastic modulus determination at half-life as well as by the plastic strain amplitude measurements. Both methods show a good correlation and high reliability, however, the plastic strain amplitude approach tends to fit better to the experimental results. From a parametric analysis performed, it was observed that the plastic strain amplitude approximation could be more suitable to assess the fatigue properties for LCF of the material due to an improved correlation of the computed cyclic elastic modulus in comparison to the cyclic elastic modulus measurements at half-life. Both methods showed that, for strain amplitudes higher than εa = 0.004, the cyclic elastic modulus tends to be lower than 210 GPa, meanwhile for lower strain amplitudes, the cyclic elastic modulus tends to increase. An evaluation by X-ray Diffraction technique allowed to determine that the increment of residual equivalent strain contributes to the cyclic elastic modulus diminution.

Determination of the Complex-Valued Elastic Moduli of Polymers by Electrical-Impedance Spectroscopy for Ultrasound Applications

A method is presented for the determination of complex-valued compression and shear elastic moduli of polymers for ultrasound applications. The resulting values, which are scarcely reported in the literature, are found with uncertainties typically around 1% (real part) and 6% (imaginary part). The method involves a setup consisting of a cm-radius, mm-thick polymer ring glued concentrically to a disk-shaped piezoelectric transducer. The ultrasound electrical-impedance spectrum of the transducer is computed numerically and fitted to measured values as an inverse problem in a wide frequency range, typically from 500 Hz to 5 MHz, both on and off resonance. The method is validated experimentally by ultrasonic through transmission around 1.9 MHz. The method is low cost, not limited to specific geometries and crystal symmetries, and, given the developed software, easy to execute. The method has no obvious frequency limitations before severe attenuation sets in above 100 MHz.

Investigations on the Characterization of Various Adhesive Joints by Means of Nanoindentation and Computer Tomography

The mechanical properties of cured wood adhesive films were tested in a dry state by means of nanoindentation. These studies have found that the application of adhesives have an effect on the accuracy of the hardness and elastic modulus determination. The highest values of hardness among the tested adhesives at 20 °C have condensation resins: MF (0.64 GPa) and RPF (0.52 GPa). Then the decreasing EPI (0.43 GPa), PUR (0.23 GPa) and PVAc (0.14 GPa) adhesives. The values of the elastic modulus look a little bit different. The highest values among the tested adhesives at 20 °C have EPI (11.97 GPa), followed by MF (10.54 GPa), RPF (7.98 GPa), PVAc (4.71 GPa) and PUR (3.37 GPa). X-ray micro-computed tomography was used to evaluate the adhesive joint by the determination of the voids. It has been proven that this value depends on the type of adhesive, glue quantity and reactivity. The highest values of the void ratio achieve the PUR (17.26%) adhesives, then PVAc (13.97%), RRF (6.88%), MF (1.78%) and EPI (0.03%). The ratio of the gaps increases with the higher joint thickness. A too high proportion of voids may weaken the adhesive joint.

Determination of Polypropylene Fiber-Reinforced Concrete Compressive Strength and Elasticity Modulus via Ultrasonic Pulse Tests

Compressive strength and elasticity modulus are the main mechanical properties of concrete. The non-destructive ultrasound pulse test can be used to determine these properties without compromising the structure’s integrity. This study seeks to assess whether a correlation exists (1) between the Reinforcement Index (RI) and the mechanical properties, (2) between the RI and the dynamic properties, and (3) among the dynamic properties of polypropylene fiber-reinforced concrete. The RI was modified through fiber volume fraction (0, 0.4, 0.8 and 1.2%) and fiber length (40, 50 and 60 mm). The dynamic properties were assessed through dynamic elasticity modulus and ultrasonic pulse velocity (UPV), which were determined by direct, semi-direct, and indirect prospect methods. Finally, compressive strength, static elasticity modulus, and Poisson’s ratio were assessed through destructive tests. Their relationship with UPV and the dynamic elasticity modulus is also subsequently studied. The results reveal a correlation between RI and compressive strength and UPV; however, the static elasticity modulus only exhibits a correlation with UPV in one of its measurement methods. Finally, empirical models were developed for predicting compressive strength, elasticity modulus as a function of ultrasonic pulse velocity and RI, and dynamic elasticity modulus as a function of compressive strength and RI.

Machine learning framework for determination of elastic modulus without contact model fitting

Many contact models have been proposed for determining the elastic modulus of materials based on AFM force measurement. However, contact model fitting could be a challenging task since the elastic modulus usually varies depending on the tip parameters (i.e., radius and half-opening angle) which are difficult to determine in practice. Therefore, this study proposes a supervised machine learning (SML) regression framework for determining the elastic modulus without the need to either select an appropriate contact model or perform contact model fitting. In the proposed approach, the SML regressor learns the relationship between the force-displacement (FZ) features and the elastic modulus, and then predicts the elastic modulus of unseen samples directly from their FZ features. The predictive power of the proposed framework is demonstrated using both homogeneous materials (polydimethylsiloxane, polymethyl methacrylate, and polyvinyl alcohol), and heterogeneous materials (Staphylococcus aureus bacteria and methylammonium lead iodide). It is shown that the Gaussian process regression (GPR) model achieves a higher prediction accuracy than the multiple linear regression (MLR), random forest (RF), and support vector regression (SVR) models for both groups of materials. Particularly, GPR achieves a testing coefficient of determination value of up to 91.55% for homogeneous materials, and 82.73% for heterogeneous materials. Overall, the results confirm that the proposed SML regression framework is capable of determining the elastic modulus of both homogeneous and heterogeneous materials without the need for both contact model fitting and knowledge of tip shape.

Giant magnetostriction in low-concentration magnetorheological elastomers

Magnetorheological elastomers (MREs) are smart composite materials that can vary their mechanical properties under the influence of an external magnetic field. In the present work, we report the giant magnetostriction of low-concentration isotropic and anisotropic MREs, by combining a soft elastomer matrix with helicoidal-shaped particles. Magnetic characterization has shown high magnetic sensitivity of the anisotropic MREs near H ≅ 0, which can be up to 400% larger comparing to the isotropic counterparts. The determination of tensile elastic modulus (E) of the MREs indicates that the anisotropic samples become softer when the magnetic field is increased from H = 0 to H = 200 Oe. Due to the higher field sensitivity of the anisotropic composites, the magneto-induced elongation contributes to the increase in the overall strain when measuring the elastic modulus at low deformation. This compliance of the MRE explains the decrease in E from H = 0 to H = 200 Oe. Magnetostriction measurements were performed and giant strain values up to 3731 ppm were obtained for isotropic samples with 3.4 vol% of Hiperco particles under a field of H = 3500 Oe. This result stands out from the literature due to the giant induced elongation, with reduced volume fraction of particles. The developments of this work are a step forward on improving smart and efficient composites, that can have many applications, such as switches, controllable valves, and vibration attenuators.