Multilayered Composite Membranes Based on Layer‐by‐Layer Stacked Graphene Films for Ultraviolet Pellicle Applications

We determined the Young's modulus of pulsed laser deposited epitaxially grown PbZr0.52Ti0.48O3 (PZT) thin films on microcantilevers by measuring the difference in cantilever resonance frequency before and after deposition. By carefully optimizing the accuracy of this technique, we were able to show that the Young's modulus of PZT thin films deposited on silicon is dependent on the in-plane orientation, by using cantilevers oriented along the ⟨1 1 0⟩ and ⟨1 0 0⟩ silicon directions. Deposition of thin films on cantilevers affects their flexural rigidity and increases their mass, which results in a change in the resonance frequency. An analytical relation was developed to determine the effective Young's modulus of the PZT thin films from the shift in the resonance frequency of the cantilevers, measured both before and after the deposition. In addition, the appropriate effective Young's modulus valid for our cantilevers’ dimensions was used in the calculations that were determined by a combined analytical and finite-element (FE) simulations approach. We took extra care to eliminate the errors in the determination of the effective Young's modulus of the PZT thin film, by accurately determining the dimensions of the cantilevers and by measuring many cantilevers of different lengths. Over-etching during the release of cantilevers from the handle wafer caused an undercut. Since this undercut cannot be avoided, the effective length was determined and used in the calculations. The Young's modulus of PZT, deposited by pulsed laser deposition, was determined to be 103.0 GPa with a standard error of ± 1.4 GPa for the ⟨1 1 0⟩ crystal direction of silicon. For the ⟨1 0 0⟩ silicon direction, we measured 95.2 GPa with a standard error of ± 2.0 GPa.

In this paper, the effects of shape and arrangement of inclusions on the effective Young's modulus of materials are considered by the application of the finite element method through examining a model, which has two groups of periodically arranged inclusions in a matrix. Here, two groups of inclusions A and B are considered, both having equally shaped equally arranged inclusions, which have the same elastic constants but different from the ones of the matrix. This model includes square and hexagonal arrays of inclusions as its special cases. First, the effect of shape of inclusions on the Young's modulus of composite materials is considered from the comparison between the results of rectangular and elliptical inclusions. Next, when the position of group A is fixed, the effect of location of group B is considered. Then. the effective elastic Young's modulus is almost independent of the location of group B if the projected areas of groups A and B are not overlapped. In conclusion, the volume fraction of inclusion and projected area fraction of inclusions are found to be two major parameters controlling the effective Young's modulus of composites.

We developed a methodology for the evaluation of the effective Young's modulus (EYM) of the vertically aligned carbon nanofibers array (CNFA). The carbon nanofibers array is treated in this study as a continuous structural element, and, for this reason, the determined EYM might be appreciably different (actually, lower) than the Young's modulus (YM) of the material of an individual carbon nanotube or a nanofiber. The developed methodology is based on the application of a compressive load onto the carbon nanofibers array, so that each individual carbon nanofiber experiences axial compression and is expected to buckle under the compressive load. The relationship between the applied compressive stress and the induced displacement of the carbon nanofiber array is measured using a table version of an Instron tester. It has been found that the carbon nanofiber array exhibits nonlinear behavior and the EYM increases with an increase in the compressive load. The largest measured EYM of the carbon nanofiber array turned out to be about 90 GPa. It has been found also that the fragmentary pieces of lateral graphitic layer in the carbon nanofiber array resulted in substantial worsening of the quality of the carbon nanofibers. This might be one of the possible reasons why the measured EYM turned out to be much lower than the theoretical predictions reported in the literature. The measured EYM is also much lower than the reported in the literature atomic force microscopy (AFM)-based data for the EYM for multiwalled carbon nanotubes (MWCNTs) that possess uniform and straight graphitic wall structure. Our transmission electron microscope (TEM) observations have revealed indeed poor structural qualities of the plasma-enhanced chemical vapor deposition (PECVD) grown CNFs.

New models for effective Young's modulus of particulate composites

Determination of mechanical properties of thin films, such as the Young's modulus, is of fundamental importance when the films are used for coating or for materials of microelectromechanical systems (MEMS). We show a simple method to calculate the effective Young's modulus of thin films by comparing lateral and vertical expansions. The stress of the film due to expansion in the lateral direction was measured using micromechanical cantilever sensor (MCS) techniques which allow for a calculation of the lateral expansion ratio of the film. The vertical expansion was measured using ellipsometry, surface plasmon resonance (SPR) and other film thickness meters. There is no limitation by the method for a measurement of Young's modulus, even if soft and thin polymer film. We detected the influence of humidity on effective Young's modulus of a polymer material by the method, as an example.

This paper presents evaluation of the effective Young's modulus of electroplated gold micro-cantilevers. Young's modulus is one of the fundamental parameters to design MEMS (microelectromechanical systems) components. Gold electroplated MEMS structures can be used to develop highly-sensitive MEMS sensors, such as accelerometers. With a resonant frequency method, we evaluate gold-electroplated Ti/Au cantilevers by varying both the length and the width. The experimental results showed that the Young's modulus was dependent on the width, and it was found that the Young's modulus increased with an increase in the width, which would be useful to design MEMS devices.

Quantitative assessment of the biomechanical properties of limb soft tissues has become more important during the last decade because of the introduction of computer-aided design and computer-aided manufacturing (CAD/CAM) and finite element analysis to the prosthetic socket design. Because of the lack of a clinically easy-to-use apparatus, the site and posture dependences of the material properties of lower limb soft tissues have not been fully reported in the literature. In this study, an ultrasound indentation system with a pen-size hand-held probe developed earlier by the authors was used to obtain the indentation responses of lower limb soft tissues. Indentation tests were conducted on normal young subjects with four females and four males at four sites with three body postures. A linear elastic indentation solution was used to extract the effective Young's modulus from the indentation responses. The determined modulus ranged from 10.4 to 89.2 kPa for the soft tissues tested. These results were in a similar range as those reported in the literature. The thickness of the lower limb soft tissues varied slightly with body posture changes. The Young's modulus determined was demonstrated to be significantly dependent on site, posture, subject and gender. The overall mean modulus of male subjects was 40% larger than that of female subjects. No significant correlation was established between the effective Young's modulus and the thickness of entire soft tissue layers.

Porosity effect on the thermal and mechanical properties of U-50Zr alloy: A molecular dynamics study

Thin metal films are widely used in modern electro mechanical systems. The need for more integrated functionality and minimization of material and energy consumption leads to miniaturization of these systems. As a consequence, materials are processed on the micro- and nanometer scale. On this scale, material properties become a function of size. To predict performance and reliability, knowledge on the size dependence of material properties is imperative. In this work the unknown size dependence of the copper Young's modulus is determined by electrostatic pull-in experiments performed on bilayer copper-silicon nanocantilevers. The size effect is also predicted with a multi-scale (MS) method. In this method atomistic simulations predict the bulk elastic and surface properties of mono-crystalline silicon (Si) and poly-crystalline copper (Cu). These results are combined to represent the bilayer nanocantilevers of the experiment in a continuum model. The model is verified by comparison with a well documented size effect of the effective Si Young's modulus. It is shown that the experimental method can be used for determining the Young's modulus of thin Cu films in the 10 to 50 nm range. Both the experimental results and the MS simulation results show that there is a strong size effect present in Si and Cu.

This study focused on modeling and optimization of the concentration of poly (vinyl alcohol) (PVA), cellulose nanocrystals (CNC), snail shell nanoparticles (SSN), and glycerol for the development of bioplastic films. The response surface methodology using Box–Behnken experimental design was used to investigate the effect of the independent parameters (additives concentrations) on the ultimate tensile strength and Young's modulus of fabricated bioplastic films. A varied ultimate tensile strength and Young's modulus with different component loadings was observed, proving the effect of nanoparticles loading effect on the mechanical properties of bioplastic films. The quadratic polynomial model experiment data provided a coefficient of determination (R2) of 0.795 for ultimate tensile strength and 0.732 for Young's modulus, evidencing the fitness of the models to pilot the optimization space. The optimum parameters were PVA (7.820%), CNC (1079%), SSN (1241%), and glycerol (2.657%). The ultimate tensile strength and Young's modulus of 27.2 MPa and 31.2 MPa were obtained for the developed bioplastic film with optimized concentrations of each component. The bioplastic films showed improved thermal stability and degradation. The scanning electron microscopy(SEM) imaging revealed a homogeneous dispersion of SSN and CNC in the matrix, which explained the improved properties observed.

ABSTRACTThe effect of spatial variability on the effective Young's modulus of a soil mass is investigated. The soil mass is a two-dimensional plane strain square domain subjected to a simple stress state, with Young's modulus being modelled as a stationary lognormal random field. The effective Young's modulus is simulated by random field finite-element analysis. It is found that under the condition of horizontal scale of fluctuation (SOF) = vertical SOF, the effective Young's modulus can be satisfactorily approximated as the geometric average over the square domain. However, the conclusion changes dramatically when the spatial variability is highly anisotropic, e.g. horizontal scale vertical SOF. In this case, the effective Young's modulus can be approximated as the arithmetic average or harmonic average, depending on the direction of loading. A unified spatial averaging model is further proposed in this study. It is shown that the effective Young's modulus can be satisfactorily approximated by this unified model without the need to switch among arithmetic, geometric and harmonic averages.

Laser-induced surface acoustic wave spectroscopy (LISAWS) allows quick and non-destructive access to elastic properties such as the Young's Modulus of coatings, surfaces and surface-near bulk materials. Furthermore, the mechanical weakening due to cracks and pores can be evaluated, as they influence the propagation of surface waves as well. Therefore, the method is a quick and powerful tool for surface characterization and can be found today in research and development, quality control and as a precise reference method. The short measuring time of the LISAWS measurement allow the distribution of the effective Young's modulus over the coated surface to be determined with a high accuracy. For this purpose, a LISAWS measurement system was automated to allow for processing of a larger amount of samples and fast mappings. The investigated coating materials were thermally sprayed Al2O3 insulation coatings and WC-reinforced 316L steel coatings on brake discs produced by laser cladding. For the Al2O3 coatings, the correlation of the Young's modulus and its areal distribution is shown for different process parameters, such as spray gun movement direction or spraying distance, and compared with results from pull-off tests. For the WC/316L coated brake discs, the distribution of the wave velocity over the coated surfaces or the two coated sides of different discs with varying coating qualities is used to assess the coating quality and homogeneity.

Laser-induced surface acoustic wave spectroscopy (LISAWS) allows quick and nondestructive evaluation of the elastic properties such as the Young’s modulus of coatings, surfaces and surface-near bulk materials. Furthermore, the mechanical weakening due to cracks and pores can be evaluated, as they influence the propagation of surface waves as well. This makes the method a fast, accurate and versatile tool for surface characterization, and it is increasingly used in research and development, and quality control. The short measurement time of the LISAWS method allows the time-efficient distribution of the effective Young's modulus over the coated surface to be determined. For this purpose, an industrial LAwave measurement system was automated to allow for processing of a larger number of samples and fast mappings. The investigated coating materials were thermally sprayed Al2O3 insulation coatings and WC-reinforced 316L steel coatings on brake disks produced by laser cladding, respectively. For the Al2O3 coatings, the correlation between the Young's modulus and its areal distribution is shown for different process parameters, such as spray gun movement direction or spray distance, and compared with results from pull-off tests. For the WC/316L-coated brake disks, the distribution of the wave velocity over the coated surfaces or the two coated sides of different disks with varying coating qualities is used to assess the coating quality and homogeneity.

Effective Young's modulus estimation of concrete

The effect of temperature, defect and strain rate on the mechanical property of multi-layer graphene: Coarse-grained molecular dynamics study