A micromechanical study on the existence of the interphase layer in particle-reinforced nanocomposites

Ghanbari, Jaafar; Rashidi, Zahra

doi:10.1088/2053-1591/aa99e7

Cited by 4 publications

(5 citation statements)

References 35 publications

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“…Since the volume fraction of the reinforcing phase (and the interphase layer) depends on the coordinates of the macroscopic problem, we propose a multiscale scheme to determine the mechanical properties of the beam as a function of coordinates. For the FG nanocomposite beam, the effective mechanical properties are determined using the micromechanical model based on Green's function and the interface operator 37 . According to this model, the effective elasticity tensor for a three‐phase nanocomposite is given as,

C_{ijmn}^{eff} = C_{ijmn}^{m} + f_{I} ((), C_{ijkl}^{I} - C_{ijkl}^{m}) A_{klmn}^{I} + f_{c} ((), C_{ijkl}^{c} - C_{ijkl}^{m}) A_{klmn}^{c}

where

C_{ijmn}^{eff}

is the equivalent elasticity tensor of the nanocomposite, and

C_{ijkl}^{m}

C_{ijkl}^{I}

C_{ijkl}^{c}

are elasticity tensors of the matrix, inclusion (the nanoparticle), and the interphase layer between the inclusion and the matrix, respectively; f I and f c being volume fractions of the nanoparticle inclusion and the interphase layer; and

A_{klmn}^{I}

and

A_{klmn}^{c}

are the strain concentration tensors for the inclusion and the interphase, respectively, given by

\begin{matrix} centertrue \\ A_{italicijrs}^{I} = ([], \begin{array}{c} \frac{f_{I}}{f_{I} + f_{c}} ((), I_{ijrs} + T_{ijkl} ((), C^{eff}) normalΔ C_{klrs}^{I}) \\ + \frac{f_{c}}{f_{I} + f_{c}} ((), I) \end{array}) \end{matrix}

…”

Section: Microscale Problemmentioning

confidence: 99%

“…According to Hill, 38 it is given as,

\begin{matrix} centertrue \\ ε_{italicij}^{2} - ε_{italicij}^{1} = P_{italicijkl} (boldn, C^{2}) Δ C_{italicklmn}^{12} ε_{italicmn}^{1} \end{matrix}

where

ε_{ij}^{1}

and

ε_{ij}^{2}

are strain tensors in region 1 and 2; and Δ C 12 = C 1 − C 2 with C 1 and C 2 being elasticity tensors of regions 1 and 2, and n is the unit normal vector to the interface, respectively. For a detailed discussion on the micromechanical method employed here, the reader is referred to References [37, 39, 40].…”

Section: Microscale Problemmentioning

confidence: 99%

“…For the FG nanocomposite beam, the effective mechanical properties are determined using the micromechanical model based on Green's function and the interface operator. 37 According to this model, the effective elasticity tensor for a three-phase nanocomposite is given as,…”

Section: Microscale Problemmentioning

confidence: 99%

See 2 more Smart Citations

An analytical micromechanics‐based multiscale model for the analysis of functionally graded nanocomposites

Ghanbari

Rashidi

2020

Polymer Composites

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An analytical multiscale model is presented in this article for the analysis of functionally graded nanocomposites. The multiscale scheme is composed of a microscale problem whose solution provides the constitutive model for the macroscale problem. For nanoparticle‐reinforced composites, the microscale problem consists of three phases, namely the nanoparticle, the matrix, and an interphase layer between the matrix and the nanoparticle. An analytical micromechanical model based on Green's function is employed to solve the triple‐phase microscale problem. The homogenized properties of the FG nanocomposite are determined by the micromechanical problem and used in the macroscale level, at every macroscopic material point in which the constitutive model is required. As an example, a nanocomposite beam under bending is considered as the macroscale problem which is investigated by classical, first‐order, and third‐order shear deformation theories. The results obtained from the presented method are compared with the relevant data for similar problems using various higher‐order elasticity theories. By comparing the results of higher‐order theories and those obtained by the presented multiscale method, the internal length parameter of the higher‐order theories is correlated to the volume fraction of the interphase layer between the nanoparticle and the matrix.

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C_{ijmn}^{eff} = C_{ijmn}^{m} + f_{I} ((), C_{ijkl}^{I} - C_{ijkl}^{m}) A_{klmn}^{I} + f_{c} ((), C_{ijkl}^{c} - C_{ijkl}^{m}) A_{klmn}^{c}

where

C_{ijmn}^{eff}

is the equivalent elasticity tensor of the nanocomposite, and

C_{ijkl}^{m}

C_{ijkl}^{I}

C_{ijkl}^{c}

A_{klmn}^{I}

and

A_{klmn}^{c}

are the strain concentration tensors for the inclusion and the interphase, respectively, given by

\begin{matrix} centertrue \\ A_{italicijrs}^{I} = ([], \begin{array}{c} \frac{f_{I}}{f_{I} + f_{c}} ((), I_{ijrs} + T_{ijkl} ((), C^{eff}) normalΔ C_{klrs}^{I}) \\ + \frac{f_{c}}{f_{I} + f_{c}} ((), I) \end{array}) \end{matrix}

…”

Section: Microscale Problemmentioning

confidence: 99%

“…According to Hill, 38 it is given as,

\begin{matrix} centertrue \\ ε_{italicij}^{2} - ε_{italicij}^{1} = P_{italicijkl} (boldn, C^{2}) Δ C_{italicklmn}^{12} ε_{italicmn}^{1} \end{matrix}

where

ε_{ij}^{1}

and

ε_{ij}^{2}

Section: Microscale Problemmentioning

confidence: 99%

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An analytical micromechanics‐based multiscale model for the analysis of functionally graded nanocomposites

Ghanbari

Rashidi

2020

Polymer Composites

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“…Yet, continuum modeling of nanocomposite materials has been increasingly used and has proven to be a practical tool to validate the material mechanical behavior of PNCs [26,[29][30][31], often with high accuracy when compared with experiments [3,13] and MD simulations [32,33]. In addition, continuum mechanics can incorporate interface energy analysis [25,26] and the effects of the PNC interphase layer as a ternary phase on the effective properties of the composite via homogenization techniques [34]. The latter approach has been extensively investigated using FE models, Halpin-Tsai model, Mori-Tanaka model, and equivalent continuum model; a detailed discussion can be found in [26].…”

Section: Introductionmentioning

confidence: 99%

Decoupling subsurface inhomogeneities: a 3D finite element approach for contact nanomechanical measurements

Malavé

Killgore²,

Garboczi³

2019

Nanotechnology

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Novel material properties can be attained when embedding three-dimensional (3D) nanoparticles (NPs) in a variety of polymeric matrices. These inhomogeneities influence the bulk mechanical response due to the local high modulus mismatch between the particles and the matrix. The degree of the mechanical mismatch that is seen near a composite surface depends on the geometry/shape and spatial location and orientation of the particle with respect to the external contact loading. Isolating each particle’s contribution to the surrounding elastic field can be numerically discerned but is experimentally complex, as there are limited direct characterization approaches available at the nanoscale. Atomic force microscopy (AFM) instrumentation is one such method that can quantify subsurface particle stiffness effects on nanocomposites with a resolution of a few nanometers. This work studies the spatial and geometrical effects of subsurface silver NPs on the local composite stiffness of a polystyrene matrix using 3D finite element (FE) models to interpret contact resonance (CR) AFM measurements. The present FE-AFM findings suggest both particle shape and particle orientation have a significant role in the degree of uniformity of the stiffness distribution in the embedding matrix. The applied CR-AFM technique shows that the NP geometry can be clearly distinguished when such inhomogeneities are relatively close, 17 nm, to a free surface whereas material-interface measurements at deeper subsurfaces are obscured by experimental noise. This work demonstrates that (i) numerical solutions can assist in qualitatively elucidating nanoinstrumentation stiffness profiles in terms of particle shape and orientation and (ii) CR-AFM measurements can quantify the influence of particle geometry and orientation on the surface nanomechanics of nanocomposite materials.

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“…In addition, the mechanical properties of SMPs reduce with the increase in temperature (Cho and Lee, 2004; Liu et al, 2006). To overcome this difficulty, the reinforcing phase at micro- or nanoscale is usually added to the SMP matrix (Chung et al, 2012; Farshad, 2001; Fejős et al, 2012; Ghanbari and Rashidi, 2017; Meng and Hu, 2009; Nafar Dastgerdi et al, 2013; Pulla et al, 2016; Yu et al, 2013) to obtain high-performance polymer composites (Cho and Lee, 2004; Kwon et al, 2008; Liu et al, 2016; Tang et al, 2011; Wang et al, 2005). According to the previous experimental and theoretical investigations (Ansari et al, 2016b; Dragatogiannis et al, 2016; Gholami and Ansari, 2017; Gholami et al, 2017, 2018; Kleinjan et al, 2008; Odegard et al, 2005; Rosso et al, 2006; Sun et al, 2011; Zhang et al, 2006), further improvement in the overall properties of polymer composites would be gained with the reduction in the particle size of reinforcements from micrometric to nanometric scale.…”

Section: Introductionmentioning

confidence: 99%

Effects of added SiO₂ nanoparticles on the thermal expansion behavior of shape memory polymer nanocomposites

Mahmoodi

Hassanzadeh-Aghdam

Ansari

2018

Journal of Intelligent Material Systems and Structures

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In this study, a unit cell–based micromechanical approach is proposed to analyze the coefficient of thermal expansion of shape memory polymer nanocomposites containing SiO2 nanoparticles. The interphase region created due to the interaction between the SiO2 nanoparticles and shape memory polymer is modeled as the third phase in the nanocomposite representative volume element. The influences of the temperature, volume fraction, and diameter of the SiO2 nanoparticles on the thermal expansion behavior of shape memory polymer nanocomposite are explored. It is observed that the coefficient of thermal expansion of shape memory polymer nanocomposite decreases with the increase in the volume fraction up to 12%. Also, the results reveal that with the increase in temperature, the shape memory polymer nanocomposite coefficient of thermal expansion linearly increases. The role of interphase region on the thermal expansion response of the shape memory polymer nanocomposite is found to be very important. In the presence of interphase, the reduction in nanoparticle diameter leads to lower coefficient of thermal expansion for shape memory polymer nanocomposite, while the variation of nanoparticles diameter does not affect the coefficient of thermal expansion in the absence of interphase. Based on the simulation results, the shape memory polymer nanocomposite coefficient of thermal expansion decreases as the interphase thickness increases. In addition, the contribution of interphase coefficient of thermal expansion to the shape memory polymer nanocomposite coefficient of thermal expansion is more significant than that of interphase elastic modulus.

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A micromechanical study on the existence of the interphase layer in particle-reinforced nanocomposites

Cited by 4 publications

References 35 publications

An analytical micromechanics‐based multiscale model for the analysis of functionally graded nanocomposites

An analytical micromechanics‐based multiscale model for the analysis of functionally graded nanocomposites

Decoupling subsurface inhomogeneities: a 3D finite element approach for contact nanomechanical measurements

Effects of added SiO₂ nanoparticles on the thermal expansion behavior of shape memory polymer nanocomposites

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A micromechanical study on the existence of the interphase layer in particle-reinforced nanocomposites

Cited by 4 publications

References 35 publications

An analytical micromechanics‐based multiscale model for the analysis of functionally graded nanocomposites

An analytical micromechanics‐based multiscale model for the analysis of functionally graded nanocomposites

Decoupling subsurface inhomogeneities: a 3D finite element approach for contact nanomechanical measurements

Effects of added SiO2 nanoparticles on the thermal expansion behavior of shape memory polymer nanocomposites

Contact Info

Product

Resources

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Effects of added SiO₂ nanoparticles on the thermal expansion behavior of shape memory polymer nanocomposites