Effective Young's modulus estimation of concrete

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.

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 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.

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.

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.

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.

In this paper, a study is made for the size effects on the effective Young's modulus of nano crystal copper wires. On the basis of numerical results of molecular dynamics simulation, the inhomogeneous property of the nano wires is taken into account so that the continuum model of either a rod or a beam is constructed to predict the size dependence of the effective Young's modulus. The comparison with molecular dynamics simulation based on embedded atom method shows that the new rod model enables one to predict the effective Young's modulus as accurately as existing models for the nano wires of different sizes of cross sections under axial load. Furthermore, the beam model gives better prediction than the current model for the nano wires subject to pure bending. The size effect on the elastic property can also be observed from the longitudinal and transverse natural vibration of the nano wires. In this case, the effective Young's modulus is nearly the same as that obtained through axial deformation and pure bending respectively.

Herein, the theoretical analysis of out‐of‐plane tension of a thin rectangular two‐layered plate of cubic crystals with the same orientation is provided. The dependences of effective Young's modulus and effective Poisson's ratio of the plate on Poisson's ratios of layers, the ratio of Young's moduli, and the thickness ratio are obtained. It is shown that when the ratios between Young's moduli and ratios between Poisson's ratios of the layers are equal, effective Young's modulus and effective Poisson's ratio coincide with Reuss'es means. The rules of mixtures are not fulfilled in the absence of equality of these ratios. In this case, effective Young's modulus can exceed not only Reuss'es mean but also Voigt's mean. It is demonstrated that effective Young's modulus can be larger than Young's moduli of both layers in two‐layered plates of nonauxetic−nonauxetic and auxetic−auxetic type. It is established that the behavior of effective Poisson's ratio of nonauxetic−nonauxetic plates can vary depending on the ratio of the layer thicknesses. At the same time, effective Poisson's ratio of plates from pairs of auxetics cannot be less than Poisson's ratios of both initial auxetic layers.

New models for effective Young's modulus of particulate composites

Assessing the influence of ITZ on the steady-state chloride diffusivity of concrete using a numerical model

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.

Estimating the effective Young's modulus of soft tissues from indentation tests—nonlinear finite element analysis of effects of friction and large deformation

A self-consistent method is used for the determination of the residual stress and the effective Young's modulus of thin 3C-SiC(111) grown on Si(111), and 3C-SiC(100) grown on Si(100). The developed method allows for the accurate determination of the stress and mechanical properties in a wide range of residual stress, only by a set of cantilevers and doubly clamped beams. The resulting thickness dependence of the effective Young's modulus is investigated and compared with different elasticity and surface relaxation models which are analysed in terms of validity in the ultrathin regime. It is shown that the decrease of the effective Young's modulus for SiC can approximately be described by surface relaxation. Other effects like the surface coverage with oxides or other phases can be neglected. Array of doubly clamped 3C-SiC(100) beams from 250 μm length down to 10 μm. The layer thickness is 43 nm.

A type of mechanical metamaterial is proposed, whereby the effective coefficients of thermal and moisture expansions (CTE and CME, respectively) can be tuned from positive to negative values while maintaining a consistently auxetic (negative Poisson's ratio) behavior for the overall structure. Each unit consists of a pair of equal‐armed crosses pin jointed at their centers, whereas their ends are connected via bridging beams using pin joints to facilitate free rotation. The bridging beams are of lower modulus and higher hygrothermal expansivity to permit negativity in metamaterial's overall Poisson's ratio and hygrothermal expansion. Two sets of effective Young's modulus, CME and CTE models are developed—one set for large deformation and the other for infinitesimal deformation. Results indicate that the effective Young's modulus is reduced while the expansion coefficients become more negative as the inclination angle of the equal‐armed crosses increases, and that the application of tensile and compressive loads increases and decreases the effective Young's modulus, respectively. The establishment of effective zero thermal and moisture expansion conditions facilitates the application of the metamaterial structure that requires auxetic property within highly fluctuating environmental condition.

Porous asphalt concrete (PAC) has been used to improve the traffic conditions in rainy weather due to its high porosity. Aggregate size and gradation have great impact on the connected pore structure, which ultimately affects the permeability of porous asphalt concrete. In this paper, the topological properties of connective pores including pore area, pore circularity, equivalent pore diameter, and void network of porous asphalt concrete with different nominal maximum aggregate sizes and gradations were analyzed using x-ray computer tomography scans and the image processing technique. It was observed that the maximum aggregate sizes will not have significant effect on the percentage of connected pores to total pores for porous asphalt concrete. Furthermore, the percentage of connected pores to total pores is related to the air void content, but for PAC-13 with 20% target air void content or above, the connectivity does not seem to have a sharp increase. Additionally, porous asphalt concrete with a smaller nominal particle size or lower target air void content seems to generate a more concentrated distribution of Eqdiameter. Moreover, pore circularities for porous asphalt concrete with a maximum aggregate size of 10 mm or above are independent of maximum aggregate sizes. Air void contents ranging from 16% to 21% do not have a significant effect on the voids’ circularity. Furthermore, the branching nodes in porous asphalt concrete with a smaller nominal maximum aggregate size or lower target air void content have a more uniform spatial distribution. However, the percentage of cross-linked number to total node raises as the nominal maximum aggregate size or target air void content increases.