Four Phase Model: A New Formulation to Predict the Effective Elastic Moduli of Composites

2006 ◽  
Vol 129 (2) ◽  
pp. 313-320 ◽  
Author(s):  
El H. Barhdadi ◽  
P. Lipinski ◽  
M. Cherkaoui
Keyword(s):  
Elastic Moduli ◽  
Homogeneous Medium ◽  
Phase Model ◽  
Spherical Inclusions ◽  
Micromechanical Approach ◽  
Matrix Layer ◽  
Homogeneous Matrix ◽  
The Green Function ◽  
New Formulation ◽  
Good Agreement

We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing coated spherical inclusions. The composite is modeled by a four phase pattern consisting of inclusion, interphase, matrix layer, and equivalent homogeneous medium. The overall elastic moduli are obtained using a micromechanical approach based on the Green function techniques and the interfacial operators. The four phase model assumes that all constituents are elastic and perfectly bonded. The model is used to derive the effective elastic properties of representative volume element using classical averaging schemes assuming the isotropy of constituent. Finally, effect of the thickness and stiffness of interphase on the global behavior of real composite materials are examined. Comparisons with experimental results show a good agreement.

Micromechanical Approach of the Coated Inclusion Problem and Applications to Composite Materials

1994 ◽  
Vol 116 (3) ◽  
pp. 274-278 ◽  
Author(s):  
M. Cherkaoui ◽  
H. Sabar ◽  
M. Berveiller
Keyword(s):  
Hollow Spheres ◽  
Micromechanical Model ◽  
Inclusion Problem ◽  
Micromechanical Approach ◽  
Self Consistent ◽  
Polyester Matrix ◽  
Coated Inclusion ◽  
Homogeneous Matrix ◽  
Theoretical Results ◽  
Good Agreement

A micromechanical model using simultaneously Green’s function techniques and interfacial operators is proposed in order to solve the elastic inhomogeneous coated inclusion problem. For a composite material made of a non dilute concentration of coated inclusions and a homogeneous matrix, the interactions between the reinforcements are solved by a self-consistent scheme. The theoretical results for a composite of hollow spheres of glass in a polyester matrix are in good agreement with experimental measurements of Huang and Gibson.

Micromechanics of a Planar Hybrid Fibrous Network

1997 ◽  
Vol 67 (12) ◽  
pp. 907-925 ◽  
Author(s):  
Ning Pan ◽  
Julie Chen ◽  
Moon Seo ◽  
Stanley Backer
Keyword(s):  
Elastic Moduli ◽  
Fiber Types ◽  
Statistical Distributions ◽  
Fiber Volume ◽  
Fiber Network ◽  
Tensile Response ◽  
Fibrous Network ◽  
Micromechanical Approach ◽  
Bonding Area ◽  
Orientation Distributions

A micromechanical approach is proposed in this work to predict the initial tensile response under uniaxial loading of a bonded two-dimensional fibrous network consisting of two kinds of fibers. The probabilities and statistical distributions of the hybrid bonding points and free fiber lengths between the bonding points in the structure are first derived, and the deformations of both the fiber segment and the bonding area of a typical microelement of the network are analyzed and calculated. The analysis of an arbitrary microelement is then extended statistically to an intermediate level of the structure, the mesodomain, through which the macroscopic deformations of the structure are computed. Ultimately, the general expressions of elastic moduli and Poisson's ratios for a hybrid fibrous network are obtained. A parametric study examines the relationships between fiber mechanical and dimensional properties, fiber volume fractions of the two fiber types, fiber orientation distributions and the properties of the bonding areas, and the tensile behavior of the structure for an ideal planar fiber network.

PENENTUAN SIFAT KEKUKUHAN DAN KETEBALAN LAPISAN PERMUKAAN BERASFALT MENGGUNAKAN KAEDAH PENCARIAN RESONAN TAMBAHAN (ERS)

2015 ◽  
Vol 76 (1) ◽  
Author(s):  
Nur Mustakiza Zakaria ◽  
Muhammad Fakhry Md. Jaffary ◽  
Muhammad Kamal Hassan ◽  
Asmah Hamim ◽  
Nur Izzi Md. Yusoff ◽  
...  
Keyword(s):  
Elastic Moduli ◽  
Public Works ◽  
Traffic Load ◽  
Average Value ◽  
Resonance Search ◽  
Materials Used ◽  
Pavement Construction ◽  
Pavement Thickness ◽  
Good Agreement

This study was conducted to investigate the stiffness and thicknesses of asphalt surface layer using the Enhance Resonance Search (ERS) technique. A total of fifteen locations in the Universiti Kebangsaan Malaysia (UKM) Campus have been identified to carry out this experiment. The results were then compared with standards provided by the Malaysian Public Works Department (PWD), Jabatan Pembangunan dan Penyelenggaraan (JPP) UKM and Kumpulan IKRAM Sdn. Bhd. The computation found that the range of elastic moduli values of asphalt layer is between 3928.877 and 17726.012 MPa. A comparison between the experiment results and JPP UKM standard on pavement thickness showed that the different is between 20% to 60%, with the average thickness of 44.13 mm.  However, the average value of thickness is still in good agreement with the JKR and JPP UKM standards. Some stiffness values obtained are higher than the standard, probably due to the quality of materials used, the influence of the traffic load and the age of the pavement construction.

A Stochastic Nonlinear Constitutive Law for Concrete

1989 ◽  
Vol 111 (4) ◽  
pp. 443-449 ◽  
Author(s):  
A. Fafitis ◽  
Y. H. Won
Keyword(s):  
Stochastic Model ◽  
Elastic Moduli ◽  
Three Dimensional ◽  
Path Dependency ◽  
Experimental Results ◽  
Constitutive Law ◽  
Induced Anisotropy ◽  
Nonproportional Loading ◽  
Strain Relationship ◽  
Good Agreement

An incremental three-dimensional stress-strain relationship for concrete with induced anisotropy has been developed. The nonlinearity and path-dependency are modeled by expressing the elastic moduli at each increment as function of the octahedral and deviatoric strains, based on a uniaxial stochastic model developed earlier. Predictions of multiaxial response under proportional and nonproportional loading are in good agreement with experimental results.

Analyzing the effects of interphase on the effective damping properties of aligned carbon nanotube-reinforced epoxy nanocomposites using a micromechanical approach

2020 ◽  
Vol 234 (7) ◽  
pp. 910-923
Author(s):  
M Pakseresht ◽  
R Ansari ◽  
MK Hassanzadeh-Aghdam
Keyword(s):  
Carbon Nanotube ◽  
Polymer Nanocomposites ◽  
Volume Fraction ◽  
Contact Region ◽  
Damping Capacity ◽  
Damping Properties ◽  
Epoxy Nanocomposites ◽  
Damping Coefficients ◽  
Micromechanical Approach ◽  
Good Agreement

In this work, a micromechanical approach consisting of high-fidelity generalized method of cells (HFGMC) and Mori-Tanaka (M-T) model is proposed to calculate the damping properties of aligned carbon nanotube-epoxy nanocomposites. To determine the resultant directional specific damping coefficients, these models, by applying strain energy approach in the global system utilize each constituent’s specific damping coefficients and mechanical properties. The effects of interphase created in the contact region of the two initial phases—carbon nanotube and polymer matrix—are extensively investigated. Comparative studies show that the micromechanical results are in good agreement with experimental data. One major finding is the thickness and mechanical and damping properties of interphase significantly affect the overall specific damping coefficients of the carbon nanotube-polymer nanocomposites. It is found that by increasing the elastic modulus of the interphase, the longitudinal specific damping property continuously increases, while other components of damping, initially increase and then asymptotically decrease. The damping properties of polymer nanocomposites can be increased by increasing the interphase damping capacity. However, the rise of interphase thickness leads to a reduction of nanocomposite damping properties. Also, the influences of carbon nanotube volume fraction and radius are examined on the damping response of polymer nanocomposites.

The Stress Field and Intensity Factor due to Crazes Formed at the Poles of a Spherical Inhomogeneity

1994 ◽  
Vol 61 (4) ◽  
pp. 803-808 ◽  
Author(s):  
Z. M. Xiao ◽  
K. D. Pae
Keyword(s):  
Stress Intensity Factor ◽  
Intensity Factor ◽  
Stress Field ◽  
Elastic Moduli ◽  
Superposition Principle ◽  
Numerical Examples ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Good Agreement

The problem of two penny-shaped crazes formed at the top and the bottom poles of a spherical inhomogeneity has been investigated. The inhomogeneity is embedded in an infinitely extended elastic body which is under uniaxial tension. Both the inhomogeneity and the matrix are isotropic but have different elastic moduli. The analysis is based on the superposition principle of the elasticity theory and Eshelby’s equivalent inclusion method. The stress field inside the inhomogeneity and the stress intensity factor on the boundary of the craze are evaluated in the form of a series which involves the ratio of the radius of the penny-shaped craze to the radius of the spherical inhomogeneity. Numerical examples show the interaction between the craze and the inhomogeneity is strongly affected by the elastic properties of the inhomogeneity and the matrix. The conclusion deduced from the numerical results is in good agreement with experimental results given in the literature.

A Cellular Model of Lung Elasticity

1987 ◽  
Vol 109 (2) ◽  
pp. 126-131 ◽  
Author(s):  
E. Kimmel ◽  
R. D. Kamm ◽  
A. H. Shapiro
Keyword(s):  
Elastic Moduli ◽  
Individual Cell ◽  
Transpulmonary Pressure ◽  
Lung Parenchyma ◽  
Force Balance ◽  
Cellular Structures ◽  
Distorted Structure ◽  
Deformation Law ◽  
Experimental Values ◽  
Good Agreement

The mechanics of the lung parenchyma is studied using models comprised of line members interconnected to form 3-D cellular structures. The mechanical properties are represented as elastic constants of a continuum. These are determined by perturbing each individual cell from a reference state by an increment in stress which is superimposed upon the uniform stretching forces initially present in the members due to the transpulmonary pressure. A force balance on the distorted structure, together with a force-deformation law for the members, leads to a calculation of the strain increments of the members. Predictions based on the analysis of the 3-D isotropic dodecahedron are in good agreement with experimental values for the Young’s, shear, and bulk moduli reported in the literature. The model provides an explanation for the dependence of the elastic moduli on transpulmonary pressure, the geometrical details of the structure, and the stress-strain law of the tissue.

Matrix Cracking in Fiber-Reinforced Composite Materials

1991 ◽  
Vol 58 (3) ◽  
pp. 846-848 ◽  
Author(s):  
H. A. Luo ◽  
Y. Chen
Keyword(s):  
Composite Materials ◽  
Volume Fraction ◽  
Matrix Material ◽  
Homogeneous Medium ◽  
Circular Inclusion ◽  
Matrix Cracking ◽  
Phase Model ◽  
Infinite Matrix ◽  
Finite Concentration ◽  
Three Phase

Matrix cracking is a major pattern of the failure of composite materials. A crack can form in the matrix during manufacturing, or be produced during loading. Erdogan, Gupta, and Ratwani (1974) first considered the interaction between an isolated circular inclusion and a line crack embedded in infinite matrix. As commented by Erdogan et al., their model is applicable to the composite materials which contain sparsely distributed inclusions. For composites filled with finite concentration of inclusions, it is commonly understood that the stress and strain fields near the crack depend considerably on the microstructure around it. One notable simplified model is the so-called three-phase model which was introduced by Christensen and Lo (1979). The three-phase model considers that in the immediate neighborhood of the inclusion there is a layer of matrix material, but at certain distance the heterogeneous medium can be substituted by a homogeneous medium with the equivalent properties of the composite. Thus, for the problems of which the interest is in the field near the inclusion, it can reasonably be accepted as a good model. The two-dimensional version of the three-phase model consists of three concentric cylindrical layers with the outer one, labeled by 3, extended to infinity. The external radii a and b of the inner and intermediate phases, labeled by 1 and 2, respectively, are related by (a/b)2 =c, where c is the volume fraction of the fiber in composite.

Lattice Strains in Gold and Rhenium Under Non-Hydrostatic Compression

1997 ◽  
Vol 499 ◽  
Author(s):  
T. S. Duffy ◽  
G. Shen ◽  
D. L. Heinz ◽  
Y. Ma ◽  
R. J. Hemley ◽  
...  
Keyword(s):  
Elastic Moduli ◽  
Hydrostatic Compression ◽  
Cell Stress ◽  
Proper Choice ◽  
Stress Axis ◽  
Compression Curve ◽  
X Ray ◽  
Lattice Strains ◽  
Diffraction Geometry ◽  
Good Agreement

ABSTRACTLattice strains have been measured as a function of the angle, ψ, from the diamond cell stress axis in a sample of gold and rhenium at pressures of 15–37 GPa. Experiments were conducted using X-ray transparent gaskets made from beryllium. The differential stresses supported by gold and rhenium have been characterized to 37 GPa. It is also shown that proper choice of the diffraction geometry allows recovery of a quasi-hydrostatic compression curve under these highly non-hydrostatic conditions. X-ray elastic moduli have also been determined, and while good agreement with previous data is achieved for gold, there is a large discrepancy between the present results and extrapolated ultrasonic data for rhenium.

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