Microcantilever Beam Research Articles

Assessing the fracture toughness in Tungsten-based nanocomposites: A micro-mechanical approach

Nanocrystalline tungsten-copper composites can favorably combine the outstanding material properties of both elements. This work investigates tungsten-copper composites fabricated from elemental powders with 80 wt% tungsten and either copper or α-brass containing 20 wt% zinc, respectively. Moreover, high-pressure torsion is used to compact the powders, strengthen the resulting composite by grain refinement, and tailor the grain-size in the nanocrystalline regime by varying the deformation temperature between RT, 400 °C and 550 °C, resulting in grain-sizes of 9 nm 14 nm and 28 nm, respectively. Hardness measurements revealed a transition from normal to inverse Hall-Petch behavior for grain-sizes below 11 nm. To examine the fracture properties, micro-cantilever bending beams with a cross-section of 10x10µm2 were fabricated. Evaluation of these experiments indicated a fracture toughness of 3 MPa m. The slight decrease of fracture toughness between a grain-size of 9 nm to 14 nm indicates a reduction of the grain boundary cohesion strength. The grain-size increase to 28 nm reversed the trend in fracture toughness and raised it to 3.4 MPa m, which points to activating additional deformation mechanisms, such as dislocation-accumulation and twinning. Additionally, alloying with zinc raised the composites strength and retained the composites fracture toughness, benefiting the damage tolerance.

Effects of air damping on quality factors of different probes in tapping mode atomic force microscopy

Abstract The AFM probe in tapping mode is a continuous process of energy dissipation, from moving away from to intermittent contact with the sample surfaces. At present, studies regarding the energy dissipation mechanism of this continuous process have only been reported sporadically, and there are no systematic explanations or experimental verifications of the energy dissipation mechanism in each stage of the continuous process. The quality factors can be used to characterize the energy dissipation in TM-AFM systems. In this study, the vibration model of the microcantilever beam was established, coupling the vibration and damping effects of the microcantilever beam. The quality factor of the vibrating microcantilever beam under damping was derived, and the air viscous damping when the probe is away from the sample and the air squeeze film damping when the probe is close to the sample were calculated. In addition, the mechanism of the damping effects of different shapes of probes at different tip–sample distances was analyzed. The accuracy of the theoretical simplified model was verified using both experimental and simulation methods. A clearer understanding of the kinetic characteristics and damping mechanism of the TM-AFM was achieved by examining the air damping dissipation mechanism of AFM probes in the tapping mode, which was very important for improving both the quality factor and the imaging quality of the TM-AFM system. This study’s research findings also provided theoretical references and experimental methods for the future study of the energy dissipation mechanism of micro-nano-electromechanical systems.

An efficient and quantitative approach for fracture toughness measurement of Micron-Thick hard coatings based on crack spacing

Micron-thick hard coatings find widespread applications, with fracture toughness being a crucial property that ensures their usability. However, measuring the fracture toughness of hard coatings is time-consuming and costly due to the susceptibility to cracking and small sample size. Thus, developing a simple, effective and precise measurement method is necessary. This work presents an analytical model that calculates KC from crack spacing induced by uniaxial tension. By measuring the variation of crack spacing, this model determines the fracture toughness from the energy difference during the coating fracture, and residual stress can also be estimated. This simple method overcomes the limitations of uniaxial tension methods, does not require any in-situ observations, and offers low-cost and user-friendly testing. The KC of TiN coatings with 2 μm thickness were tested and found to match the micro-cantilever beam test results from the literature. This model used data from other literature to calculate the toughness of diamond and a-C:H thin coatings, showing its generality. Additionally, our model’s estimation of residual stress in coatings, as reported in the literature, is accurate to within 0.1 ∼ 1 GPa.

Exploiting Nonlinearities of Electrostatic MEMS Resonators for Tunable Low Pressure Sensing

In this paper, we demonstrate the potential functionalization of inherent nonlinearities associated with electrostatic MEMS resonators for low air pressure applications, with operating ranges as low as 0.65-295 mbar. The proposed pressure sensor is made of a polysilicon microplate subject to electrostatic actuation via an underneath electrode and attached to two cantilever microbeams. The pressure sensing mechanism relies on the motion-induced current method, a transduction mechanism that converts the dynamic alteration of the microplate due to pressure variations into an electrical signal detected via a lock-in amplifier. The experimental study showed evidence of the possible tunability of the pressure sensor via the deployment of different detection mechanisms to achieve superior performance in terms of sensitivity and low pressure operating range. These mechanisms rely on nonlinear dynamic features that result from the strong coupling between the microplate and the surrounding fluid along with the electrostatic actuation. These include dynamic pull-in instability, bifurcation and softening behavior associated with the elastic effect of the squeeze-film damping. The experimental results revealed that tracking the bifurcation frequency allows for the detection of low pressure levels, in the range of a few millibars. This capability is not provided by the resonance frequency shift method, which, while offering higher sensitivity, does not achieve the same low-pressure detection.

Vibration Study of Functionally Graded Microcantilever Beams in Fluids Based on Modified Couple Stress Theory by Considering the Physical Neutral Plane

Theoretical studies on the vibration of microcantilever beams in fluids, which are commonly used in micro- and nanoelectromechanical systems (MEMS/NEMS). When microcantilever beams are subjected to photo-thermal excitation, they show that the material properties such as the dynamic response and the one-dimensional temperature field will show significant differences from the macroscopic properties when the size appearance of the microbeam decreases to the scale below a dozen micrometers. In this paper, by correcting the scale constants of the beams, the photothermal vibration model of the microbeam is established using the physical neutral plane theory. The one-dimensional heat transfer equations and scale-corrected temperature field of the microcantilever beam under laser excitation are derived, which are solved by Galerkin’s method, based on the theory of thermoelasticity, the hydrodynamic model of the beams vibrating in incompressible liquids proposed by Sader et al. and the theory of Euler–Bernoulli beams. The equations governing the vibration of micro-cantilever beams corrected for scale effects in different fluids when subjected to photothermal excitation are obtained. The results show that the temperature field, resonant frequency, and quality factor of the microbeam will have a significant upward drift when the size of the microbeam is close to the scale parameter, and the scale effect has a non-negligible influence on the macroscopic performance parameters; the upward drift is gradually weakening when the thickness to scale ratio gradually increases. Finally, the property of the beam is almost the same as that of the theory when the thickness of the beam is 10 times the scale constant. The correction of the theory by the scale effect is insignificant.

Vibration Analysis of Porous Cu-Si Microcantilever Beams in Fluids Based on Modified Couple Stress Theory.

The vibrations in functionally graded porous Cu-Si microcantilever beams are investigated based on physical neutral plane theory, modified coupled stress theory, and scale distribution theory (MCST&SDT). Porous microcantilever beams define four pore distributions. Considering the physical neutral plane theory, the material properties of the beams are computed through four different power-law distributions. The material properties of microcantilever beams are corrected by scale effects based on modified coupled stress theory. Considering the fluid driving force, the amplitude-frequency response spectra and resonant frequencies of the porous microcantilever beam in three different fluids are obtained based on the Euler-Bernoulli beam theory. The quality factors of porous microcantilever beams in three different fluids are derived by estimating the equation. The computational analysis shows that the presence of pores in microcantilever beams leads to a decrease in Young's modulus. Different pore distributions affect the material properties to different degrees. The gain effect of the scale effect is weakened, but the one-dimensional temperature field and amplitude-frequency response spectra show an increasing trend. The quality factor is decreased by porosity, and the degree of influence of porosity increases as the beam thickness increases. The gradient factor n has a greater effect on the resonant frequency. The effect of porosity on the resonant frequency is negatively correlated when the gradient factor is small (n<1) but positively correlated when the gradient factor is large (n>1).

Effects of rare-earth oxides on grain boundary strength of silicon nitride ceramics

This study investigates the grain boundary (GB) strengths for Si3N4 ceramics doped with 3 wt% RE2O3 (RE = Y, La, or Lu) and 7 wt% MgO, using microcantilever beam specimens having different misorientation angles of the two adjacent grains. The measured strengths are so high that they are comparable to the theoretical strength of the intergranular glassy film (IGF). They are also widely scattered with a Weibull modulus of 3.0. The strength depends on the type of RE2O3 and increases in order of Y<La<Lu. It is suggested that the fracture occurs from the IGF/Si3N4 interfaces rather than within the IGF, and that O anions, which reside within the IGF and do not dissolve into the β-Si3N4 crystal lattice because of the high cationic field strength, reduce the IGF/grain interface strength. The GB strength also little depends on the misorientation angles, which is discussed in relation with the IGF accommodation ability of mismatch.

MEMS Resonant Beam with Outstanding Uniformity of Sensitivity and Temperature Distribution for Accurate Gas Sensing and On-Chip TGA.

Micromechanical resonators have aroused growing interest as biological and chemical sensors, and microcantilever beams are the main research focus. Recently, a resonant microcantilever with an integrated heater has been applied in on-chip thermogravimetric analysis (TGA). However, there is a strong relationship between the mass sensitivity of a resonant microcantilever and the location of adsorbed masses. Different sampling positions will cause sensitivity differences, which will result in an inaccurate calculation of mass change. Herein, an integrated H-shaped resonant beam with uniform mass sensitivity and temperature distribution is proposed and developed to improve the accuracy of bio/chemical sensing and TGA applications. Experiments verified that the presented resonant beam possesses much better uniformity of sensitivity and temperature distribution compared with resonant microcantilevers. Gas-sensing and TGA experiments utilizing the integrated resonant beam were also carried out and exhibited good measurement accuracy.

Deformation Behavior and Fracture Strength of Single‐Crystal 4H‐SiC Determined by Microcantilever Bending Tests

In this study, the deformation behaviors and mechanical properties of 4H‐SiC single crystals are investigated using microcantilever beam specimens with two different sizes, A and B (A &lt; B). Tensile stress is applied along &lt;20&gt; direction. Plastic deformation, or nonlinearity, is observed in the stress–strain curves, and yield stress, or proportional limit, coincides between the two specimens at ≈25 ± 2 GPa. Scanning transmission electron microscopy and transmission electron microscopy studies show that the plastic deformation is due to dislocation activities; multiple‐dislocation pileup areas are observed in both the specimens. Assuming {100}/&lt;110&gt; prismatic slip which most plausibly occurs in the &lt;20&gt; stress application, the critical resolved shar stress is estimated to be 10.9 GPa, which agrees well with the previous studies. Measured fracture strength is 41.9 ± 2.8 and 33.5 ± 2.4 GPa for the A and B, respectively. Dislocation–fracture relationship is discussed on the basis of dislocation‐based fracture mechanics, etc. It is suggested that cracks form within the multiple‐dislocation pileup area, by interaction with dislocation pileups, and act as fracture origins. A's strength is close to an ideal tensile strength of 4H‐SiC in the &lt;110&gt; direction, 47–55 GPa.

Development of MEMS gas sensors equipped with metal organic frameworks

In this study, we investigate the potential usage of electrostatic MEMS resonators for CO2 sensing. The MEMS sensor consists of two cantilever microbeams supporting a microplate coated with a Metal Organic Framework (MOF), namely ZIF-8. The detector material, ZIF-8, is synthesized using eco-friendly and sustainable production techniques and then deposited on the microplate to functionalize the sensor. An experimental setup, deploying the motion-induced current technique, is implemented and deployed to analyze the response of the gas sensor upon exposure to CO2. This method relies on a conversion mechanism that detects the motion of the sensor and translates it into a current signal. The experiments demonstrated the capability of the developed gas sensor to detect CO2. Motion-induced current measurements detected the nonlinear dynamic features of the sensor resulting from the presence of CO2 in various concentrations. We show effective deployment of frequency and amplitude changes in peak output current as detectors for the presence of CO2 and quantifiers of its concentration. Following the frequency-based approach, the sensor achieved a sensitivity of S=0.105 Hz/ppm. We also investigated a CO2 sensing mechanism that relies on the sudden and significant increase in the current amplitude at the onset of bifurcation. This sensing mechanism reached a sensitivity of S=0.903 pA/ppm.

Design, simulation, and testing of a tunable MEMS multi-threshold inertial switch

This paper presents a tunable multi-threshold micro-electromechanical inertial switch with adjustable threshold capability. The demonstrated device combines the advantages of accelerometers in providing quantitative acceleration measurements and g-threshold switches in saving power when in the inactive state upon experiencing acceleration below the thresholds. The designed proof-of-concept device with two thresholds consists of a cantilever microbeam and two stationary electrodes placed at different positions in the sensing direction. The adjustable threshold capability and the effect of the shock duration on the threshold acceleration are analytically investigated using a nonlinear beam model. Results are shown for the relationships among the applied bias voltage, the duration of shock impact, and the tunable threshold. The fabricated prototypes are tested using a shock-table system. The analytical results agree with the experimental results. The designed device concept is very promising for the classification of the shock and impact loads in transportation and healthcare applications.

Micro-Mechanical Fracture Investigations on Grain Size Tailored Tungsten-Copper Nanocomposites

Tungsten-copper composites are used in harsh environments because of their superior material properties. This work addresses a tungsten-copper composite made of 20 wt.% copper, which was subjected to grain refinement by high-pressure torsion, whereby the deformation temperature was varied between room temperature and 400 °C to tailor the grain size. Deformation was performed up to microstructural saturation and verified by hardness measurement and scanning electron microscopy. From the refined nanostructured material, micro-cantilever bending beams with cross-sections spanning from 5 × 5 to 35 × 35 µm2 were cut to examine possible size effects and the grain size influence on the fracture behavior. Fracture experiments were performed in situ inside a scanning electron microscope by applying a quasi-static loading protocol with partial unloading steps. Inspection of the fracture surfaces showed that all cantilevers failed in an inter-crystalline fashion. Nevertheless, remaining coarser tungsten grains impacted the resultant fracture toughness and morphology. Cantilevers fabricated from the 400 °C specimen exhibited a fracture toughness of 220 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm $$\\end{document} 50 Jm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{{\ ext{J}}}{{{\ ext{m}}}^{2}}$$\\end{document}. For the room temperature cantilevers, a fracture toughness of 410 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm $$\\end{document} 50 Jm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{{\ ext{J}}}{{{\ ext{m}}}^{2}}$$\\end{document} was observed, which declined to 340 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm $$\\end{document} 30 Jm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{{\ ext{J}}}{{{\ ext{m}}}^{2}}$$\\end{document} for cantilevers < 10 × 10 µm2, confirming a size effect. The increased fracture toughness is attributed to the delamination-like structures formed in the room temperature sample.

High-Accuracy Airborne Rangefinder via Deep Learning Based on Piezoelectric Micromachined Ultrasonic Cantilevers.

This article presents a high-accuracy air-coupled acoustic rangefinder based on piezoelectric microcantilever beam array using continuous waves. Cantilevers are used to create a functional ultrasonic rangefinder with a range of 0-1 m. This is achieved through a design of custom arrays. This research investigates various classification techniques to identify airborne ranges using ultrasonic signals. The initial approach involves implementing individual models such as support vector machine (SVM), Gaussian Naive Bayes (GNB), logistic regression (LR), k-nearest neighbors (KNNs), and decision tree (DT). To potentially achieve better performance, the study introduces a deep learning (DL) architecture based on convolutional neural networks (CNNs) to categorize different ranges. The CNN model combines the strengths of multiple classification models, aiming for more accurate range detection. To ensure the model generalizes well to unseen data, a technique called k-fold cross-validation (CV), which provides the reliability assessment, is used. The proposed framework demonstrates a significant improvement in accuracy (100%), and area under the curve (AUC) (1.0) over other approaches.

BENDING ANALYSIS OF A PERFORATED MICROBEAM WITH LAPLACE TRANSFORM

In recent years, the analysis of materials and elements with dimensions at nano/micro levels has gained momentum. While analyzing these small-scale materials and elements, higher-order elasticity theories have started to be used instead of classical elasticity theories (CETs). One of these theories, which includes a small-scale parameter in its constitutive equations, is the modified couple stress theory (MCST). In this study, the bending analysis of a cantilever perforated microbeam is investigated by MCST and Euler-Bernoulli (EB) beam theory. First, the perforation characteristics of the microbeam are described and incorporated into the equation governing the bending problem based on the modified couple stress theory found in the literature. Then, the Laplace transform is applied to the governing equation. The known boundary conditions of the cantilever microbeam are substituted into the equation and the inverse Laplace transform is applied to obtain the deflection equation.

Investigation on the Impact of Excitation Amplitude on AFM-TM Microcantilever Beam System's Dynamic Characteristics and Implementation of an Equivalent Circuit.

Alterations in the dynamical properties of an atomic force microscope microcantilever beam system in tapping mode can appreciably impact its measurement precision. Understanding the influence mechanism of dynamic parameter changes on the system's motion characteristics is vital to improve the accuracy of the atomic force microscope in tapping mode (AFM-TM). In this study, we categorize the mathematical model of the AFM-TM microcantilever beam system into systems 1 and 2 based on actual working conditions. Then, we analyze the alterations in the dynamic properties of both systems due to external excitation variations using bifurcation diagrams, phase trajectories, Lyapunov indices, and attraction domains. The numerical simulation results show that when the dimensionless external excitation g < 0.183, the motion state of system 2 is period 1. When g < 0.9, the motion state of system 1 is period 1 motion. Finally, we develop the equivalent circuit model of the AFM-TM microcantilever beam and perform related software simulations, along with practical circuit experiments. Our experimental results indicate that the constructed equivalent circuit can effectively analyze the dynamic characteristics of the AFM-TM microcantilever beam system in the presence of complex external environmental factors. It is observed that the practical circuit simulation attenuates high-frequency signals, resulting in a 31.4% reduction in excitation amplitude compared to numerical simulation results. This provides an essential theoretical foundation for selecting external excitation parameters for AFM-TM cantilever beams and offers a novel method for analyzing the dynamics of micro- and nanomechanical systems, as well as other nonlinear systems.

Deep Learning for Nonlinear Characterization of Electrostatic Vibrating Beam MEMS

In this paper, we integrate deep learning techniques with the motion-induced current method to analyze the nonlinear response of electrostatic MEMS resonators consisting of vibrating beams under electrostatic actuation. The motion-induced current method relies on a transduction mechanism that converts the motion of the resonator to a current signal. The third harmonic of the induced current captures the motion characteristics of the MEMS resonator. We conduct electrical measurements on a MEMS device comprising a microcantilever beam subject to electrostatic actuation using a side electrode. The electrical measurements are verified against their optical counterparts to confirm the suitability of the motion-induced current method to analyze the motion of the MEMS resonator. Next, we develop a model by combining deep learning methods with experimental data aiming to detect the nonlinear dynamics associated with the motion of the resonator when subjected to large actuation voltages. The results demonstrate high prediction accuracy of the data-driven model in terms of capturing the peak resonance, the onset of bifurcation, the occurrence hysteresis and its bandwidth.

Microscopic mechanical properties of silicon nitride ceramics corroded in sulfuric acid solution

The microscopic mechanical properties including the bending strength and Young’s modulus for Si3N4 ceramics doped with Y2O3 and Al2O3 which was immersed in 5 wt% sulfuric acid solution using microcantilever beam specimens was investigated in comparison with the macroscopic results obtained in conventional three-point bending tests. Both the properties sharply dropped in very short periods of the corrosion in the microcantilever tests, resulting from the dissolutions of yttrium and aluminum ions of grain boundary glass networks, followed by the hydration. After the drops at the beginning of the corrosion, they showed little degradation afterwards. The degradation behaviors of the mechanical properties are basically the same as those in conventional macroscopic approaches; however, they changes appear in very short periods of the corrosion in the microcantilever bending tests. This study also verified that a small difference of a ratio of sintering additives results in different grain boundary strengths of Si3N4 ceramics.

An analysis for support loss of micro-cantilever beam based on PML method

Support loss is the phenomenon where part of the vibration energy of a micro-cantilever is transferred to the support structure in the form of elastic waves and dissipated. Since the support loss is coupled with other dissipations, it is difficult for the experimental operator to analyze it experimentally. In this paper, the support loss of micro-cantilever beam is investigated using the perfectly matched layer method, and the support loss is calculated by using the two-dimensional and three-dimensional models, separately. Then we find that both models are consistent with the corresponding theoretical analysis, and the three-dimensional model is closer to the actual situation. In addition, we investigate the contribution of the thickness of the support substrate and the size of the micro-cantilever beam to the support loss. The result shows that the thicker the support substrate and the slimmer the micro-cantilever beam, the smaller the support loss.

Nonlocal Theory for Submerged Cantilever Beams Undergoing Torsional Vibrations

Abstract We propose a new theory for fluid–structure interactions of cantilever microbeams undergoing small amplitude vibrations in viscous fluids. The method is based on the concept of nonlocal modal hydrodynamic functions that accurately capture three-dimensional (3D) fluid loading on the structure. For short beams for which 3D effects become prominent, existing local theories based on two-dimensional (2D) fluid approximations are inadequate to predict the dynamic response. We discuss and compare model predictions in terms of frequency response functions, modal shapes, quality factors, and added mass ratios with the predictions of the local theory, and we validate our new model with experimental results.

Tracking of bifurcations and hysteresis in electrostatically actuated resonators by motion-induced current

In this work, we present an experimental technique to detect the onset of bifurcation and measure the extent of hysteresis in electrostatic MEMS. The device-under-test comprises a microcantilever beam actuated via a side electrode. The beam vibrations result in varying the resonator’s capacitance, therefore inducing a current that can be measured and used for characterization and performance analysis. The motion-induced current is measured, and its harmonics are extracted using a lock-in amplifier. Locking on the third harmonic of the induced current enables us to bypass parasitic capacitance and extract a signal directly related to the resonator motions. We show that this signal can be used to investigate the nonlinear dynamic behavior of MEMS resonators undergoing large motions. Specifically, our experiments demonstrate our technique's ability to detect various bifurcations, to track the onset of hysteresis, and to measure the hysteresis bandwidth. We also use our technique to analyze the quantitative relationships between the actuation voltage, the location of the bifurcation point, and the hysteretic bandwidth. Finally, we show that our technique can be used to generate the calibration curves for inertial MEMS sensors.