• Advances in nano research
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• v.12 no.2
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• pp.139-150
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• 2022

This paper presents sets of explicit analytical equations that compute the static displacements of nanobeams by adopting the nonlocal elasticity theory of Eringen within the framework of Euler Bernoulli and Timoshenko beam theories. Castigliano's theorem is applied to an equivalent Virtual Local Beam (VLB) made up of linear elastic material to compute the displacements. The first derivative of the complementary energy of the VLB with respect to a virtual point load provides displacements. The displacements of the VLB are assumed equal to those of the nonlocal beam if nonlocal effects are superposed as additional stress resultants on the VLB. The illustrative equations of displacements are relevant to a few types of loadings combined with a few common boundary conditions. Several equations of displacements, thus derived, matched precisely in similar cases with the equations obtained by other analytical methods found in the literature. Furthermore, magnitudes of maximum displacements are also in excellent agreement with those computed by other numerical methods. These validated the superposition of nonlocal effects on the VLB and the accuracy of the derived equations.

• Advances in nano research
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• v.17 no.4
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• pp.335-350
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• 2024

This paper investigates the mechanical behavior of a new type of functionally graded graphene-reinforced nanocomposite (FG-GRNC) doubly-curved laminated shells, referred to as cosine FG-GRNC. The study employs a refined higher-order shear deformation shell theory combined with a modified continuum nonlocal strain gradient theory. The effective Young's modulus of the GRNC shell in the thickness direction is determined using the modified Halpin-Tsai model, while Poisson's ratio and mass density are calculated using the rule of mixtures. The analysis includes two graphene-reinforced distribution patterns-FG-A CNRCs and FG-B CNRCs-along with uniform UD CNRCs. An enhanced Galerkin method is used to solve the governing equilibrium equations for the GRNC nanoshell, yielding closed-form solutions for bending deflection and critical buckling loads. The nanoshell is supported by an orthotropic elastic foundation characterized by three parameters. A detailed parametric analysis is performed to evaluate how factors such as the length scale parameter, nonlocal parameter, distribution pattern, GPL weight fraction, shell thickness, and shell geometry influence deflections and critical buckling loads.

• Journal of the Korean Ceramic Society
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• v.52 no.6
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• pp.410-416
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• 2015

Recently, a new $Y_2O_3$ coating deposited using the EB-PVD method has been developed for erosion resistant applications in fluorocarbon plasma environments. In this study, surface crack formation in the $Y_2O_3$ coating has been analyzed in terms of residual stress and elastic modulus. The coating, deposited on silicon substrate at temperatures higher than $600^{\circ}C$, showed itself to be sound, without surface cracks. When the residual stress of the coating was measured using the Stoney formula, it was found to be considerably lower than the value calculated using the elastic modulus and thermal expansion coefficient of bulk $Y_2O_3$. In addition, amorphous $SiO_2$ and crystalline $Al_2O_3$ coatings were similarly prepared and their residual stresses were compared to the calculated values. From nano-indentation measurement, the elastic modulus of the $Y_2O_3$ coating in the direction parallel to the coating surface was found to be lower than that in the normal direction. The lower modulus in the parallel direction was confirmed independently using the load-deflection curves of a micro-cantilever made of $Y_2O_3$ coating and from the average residual stress-temperature curve of the coated sample. The elastic modulus in these experiments was around 33 ~ 35 GPa, which is much lower than that of a sintered bulk sample. Thus, this low elastic modulus, which may come from the columnar feather-like structure of the coating, contributed to decreasing the average residual tensile stress. Finally, in terms of toughness and thermal cycling stability, the implications of the lowered elastic modulus are discussed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.36 no.2
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• pp.117-123
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• 2012

This paper discusses two different techniques used to measure the mechanical properties of thin films: the bulge test and the nanoindentation test. In the bulge test, a uniform pressure is applied to one side of the film. Measurement of the membrane deflection as a function of the applied pressure allows one to determine the mechanical properties such as Young's modulus, and the residual stress. A nanoindentation test is performed by pushing an indenter tip into the specimen and then withdrawing it, and then recording the indentation force as a function of the indenter position. A modified King's model is used to estimate the mechanical properties of the thin film in order to avoid the effects of the substrate layers. A combination of both the bulge test and the nanoindentation test can determine both Young's modulus and Poisson's ratio simultaneously.