• Journal of the Korean Society for Nondestructive Testing
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• v.18 no.2
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• pp.112-120
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• 1998

A nondestructive evaluation technique was developed for the quantitative determination of the reinforcement volume fractions in particulate reinforced metal matrix composites. The proposed technique employed a composite micromechanics which accounts for the microstructure of the composite medium together with the measurement of anisotropic electrical conductivity. When the measured conductivity was coupled with the theoretically predicted conductivity, the unknown reinforcement volume fraction was calculated. An analytical model based on the Mori-Tanaka method was described which relates the NDE signatures to the composite microstructure. The volume fractions were calculated using eddy current measurements made on a wide range of silicon carbide particulate ($SiC_p$) reinforced aluminum (Al) matrix composites. The calculated $SiC_p$ volume fractions were in good agreement with the measured volume fractions in the range of 0-30%. The technique was also found to be effective in estimating the total volume percentage of reinforcement and intermetallic compound formed during the processing stage.

• Composites Research
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• v.25 no.4
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• pp.117-125
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• 2012

Warpage of the film insert molded (FIM) part is caused by an asymmetric residual stress distribution. Asymmetric residual stress and temperature distribution is generated by the retarded heat transfer in the perpendicular direction to the attached film surface. Since warpage was not prevented by controlling injection molding conditions, glass fiber (GF) filled composites were employed as substrates for film insert molding to minimize the warpage. Distribution of short GFs was evaluated by using micro-CT equipment. Proper models for micro mechanics, anisotropic thermal expansion coefficients, and closure approximation should be selected in order to calculate fiber orientation tensor and warpage of the FIM part with the composite substrate. After six kinds of micro mechanics models, three models of the thermal expansion coefficient and five models of the closure approximation had been considered, the Mori-Tanaka model, the Rosen and Hashin model, and the third orthotropic closure approximation were selected in this study. The numerically predicted results on fiber orientation tensor and warpage were in good agreement with experimental results and effects of GF reinforcement on warpage of the FIM composite specimen were identified by the numerical results.

• Journal of the Microelectronics and Packaging Society
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• v.9 no.4
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• pp.35-45
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• 2002

The stresses of the underfill/chip interface due to thermal loading was studied using the finite element method. At first, the effective properties of underfill for several volume fractions of silica particles were calculated by Mori-Tanaka method for three different material sets, and the parameters of singularity for the bimaterial edge and the bimaterial wedge were calculated. Consequently, the stresses at the underfill/chip interface with volume fraction of silica particles were investigated. Five different geometric models of flip-chip assembly involving two kinds of bimaterial strips and three kinds of three-layer models were considered under the assumption that the underfill is homogeneous. It was assumed that all components of the flip-chip assembly were linear elastic and isotropic, and their properties were temperature independent. The analysis was conducted in the context of the uncoupled plane thermo-elasticity under a plane strain assumption.

• Steel and Composite Structures
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• v.38 no.5
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• pp.477-496
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• 2021

The main objective of this paper is to study vibration of sandwich open cylindrical panel with damaged core and FG face sheets based on three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. Three complicated equations of motion for the panel under consideration are semi-analytically solved by using 2-D differential quadrature method. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions. It is seen that for the large amount of power-law index "P", increasing this parameter does not have significant effect on the non-dimensional natural frequency parameters of the FG sandwich curved panel. Results indicate that by increasing the value of isotropic damage parameter "D" up to the unity (fully damaged core) the frequency would tend to become zero. One can dictate the fiber variation profile through the radial direction of the sandwich panel via the amount of "P", "b" and "c" parameters. It should be noticed that with increase of volume fraction of fibers, the frequency parameter of the panels does not increase necessarily, so by considering suitable amounts of power-law index "P" and the parameters "b" and "c", one can get dynamic characteristics similar or better than the isotropic limit case for laminated FG curved panels.

• Steel and Composite Structures
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• v.44 no.1
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• pp.65-79
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• 2022

The main goal of this paper is to study the vibration of damaged core laminated annular plates with FG face sheets based on a three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. In this study the effect of microcracks on the vibrational characteristic of the sandwich plate is considered. In particular, the structures are made by an isotropic core that undergoes a progressive uniform damage, which is modeled as a decay of the mechanical properties expressed in terms of engineering constants. These defects are uniformly distributed and affect the central layer of the plates independently from the direction, this phenomenon is known as "isotropic damage" and it is fully described by a scalar parameter. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular plate is assumed to have any arbitrary boundary conditions at the circular edges including simply supported, clamped and, free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution, and boundary conditions.

• Steel and Composite Structures
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• v.48 no.1
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• pp.1-17
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• 2023

The main goal of this paper is to study vibration of damaged core laminated sectorial plates with Functionally graded (FG) face sheets based on three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular sector plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions.

• Composites Research
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• v.34 no.2
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• pp.123-128
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• 2021

This paper dealt with multi-scale natural frequency characteristics of wavy CNT (carbon nanotube) reinforced composites by applying the Mori-Tanaka method, rule of mixture, and Halpin-Tsai equation. By compelling benefit of an ad-hoc Eshelby tensor, the load-transfer characteristics of CNT with a waviness implanted in the polymer matrix was determined. The numerical results obtained are in good agreement with those reported by other investigators. Furthermore, the new results reported in this paper show the interactions between CNT weight, waviness ratios and layup sequences of laminated composites. Key observation points are discussed and significant considerations are given in practical designing of CNT reinforced composites.

• Steel and Composite Structures
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• v.36 no.6
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• pp.631-642
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• 2020

This paper studies nonlinear stability behavior of a nanocrystalline silicon curved nanoshell considering strain gradient size-dependency. Nanocrystallines are composite materials with an interface phase and randomly distributed nano-size grains and pores. Imperfectness of the curved nanoshell has been defined based on an initial deflection. The formulation of nanocrystalline nanoshell has been established by thin shell theory and an analytical approach has been used in order to solve the buckling problem. For accurately describing the size effects related to nano-grains or nano-pores, their surface energies have been included. Nonlinear stability curves of the nanoshell are affected by the size of nano-grain, curvature radius and nano-pore volume fraction. It is found that increasing the nano-pore volume fraction results in lower buckling loads.

• Advances in aircraft and spacecraft science
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• v.5 no.1
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• pp.21-49
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• 2018

In this paper, geometric nonlinear bending characteristics of single wall carbon nanotube reinforced composite (SWCNTRC) doubly curved shell panels subjected to uniform transversely loadings are investigated. The nonlinear mathematical model is developed for doubly curved SWCNTRC shell panel on the basis of higher-order shear deformation theory and Green- Lagrange nonlinearity. All nonlinear higher order terms are included in the mathematical model. The effective material properties of SWCNTRC are estimated by using Eshelby-Mori-Tanaka micromechanical approach. The governing equation of the shell panel is obtained using the total potential energy principle and a Newton-Raphson iterative method is employed to compute the nonlinear displacement and stresses. The present results are compared with published literature. The effect of SWCNT volume fraction, width-to-thickness ratio, radius-to-width ratio (R/a), boundary condition, linear and nonlinear deflection, stresses and different types of shell geometry on nonlinear bending response is investigated.

• Computers and Concrete
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• v.19 no.6
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• pp.745-753
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• 2017

Dynamic analysis of a concrete pipes armed with Silica ($SiO_2$) nanoparticles subjected to earthquake load is presented. The structure is modeled with first order shear deformation theory (FSDT) of cylindrical shells. Mori-Tanaka approach is applied for obtaining the equivalent material properties of the structure considering agglomeration effects. Based on energy method and Hamilton's principle, the motion equations are derived. Utilizing the harmonic differential quadrature method (HDQM) and Newmark method, the dynamic displacement of the structure is calculated for the Kobe earthquake. The effects of different parameters such as geometrical parameters of pipe, boundary conditions, $SiO_2$ volume percent and agglomeration are shown on the dynamic response of the structure. The results indicate that reinforcing the concrete pipes by $SiO_2$ nanoparticles leads to a reduction in the displacement of the structure during an earthquake.