Three-phase Composite Cylinder Model Research Articles

Damping of thickly coated fibrous composites with viscous interfaces under longitudinal shear

We study the damping of thickly coated fibrous composites with viscous fiber-coating and coating-matrix interfaces under longitudinal shear loads. The specific damping capacity is derived by means of the three-phase composite cylinder model. Our analysis indicates that the specific damping capacity depends on six dimensionless parameters: the fiber and coating volume fractions, two stiffness ratios, and two interface parameters arising from rate-dependent interface sliding.

A wedge disclination dipole interacting with a coated cylindrical inhomogeneity

A three-phase composite cylinder model is utilized to study the interaction of a wedge disclination dipole with a coated cylindrical inhomogeneity. The explicit expression of the force acting on the wedge disclination dipole is calculated. The motilities and the equilibrium positions of the disclination dipole near the coated inhomogeneity are discussed for various material combinations, relative thicknesses of the coating layer and the features of the disclination dipole. The results show that the material properties of the coating layer have a major part to play in alteringi the strengthening effect or toughening effect produced by the coated inhomogeneity.

Dislocation stability in three-phase nanocomposites with imperfect interface

Interface imperfection can significantly affect the mechanical properties and failure mechanisms as well as the strength and toughness of nanocomposites. The elastic behavior of a screw dislocation in nanoscale coating with imperfect interface is studied in the three-phase composite cylinder model. The interface between inner nanoinhomogeneity and intermediate coating is assumed as perfectly bonded. The bonding between intermediate coating and outer matrix is considered to be imperfect with the assumption that interface imperfection is uniform, and a linear spring model is adopted to describe the weakness of imperfect interface. The explicit expression for image force acting on dislocation is obtained by means of a complex variable method. The analytic results indicate that inner interface effect and outer interface imperfection, simultaneously taken into account, would influence greatly image force, equilibrium position and stability of dislocation, and various critical parameters that would change dislocation stability. The weaker interface is a very strong trap for glide dislocation and, thus, a more effective barrier for slip transmission.

Interaction between edge dislocations and amorphous interphase in carbon nanotubes reinforced metal matrix nanocomposites incorporating interface effect

Dislocations mobility and stability in the carbon nanotubes (CNTs)-reinforced metal matrix nanocomposites (MMNCs) can significantly affect the mechanical properties of the composites. However, current processing techniques often lead to the formation of coated CNT (amorphous interphase exists between the reinforcement and metal matrix), which have large impact upon the image force exerting on dislocations. Even though the importance of the interphase zone formed in metal matrix composites has been demonstrated by many studies for elastic properties, the influence of interphase on the local elastoplastic behavior of CNT-reinforced MMNCs is still an open issue. This paper puts forward a three-phase composite cylinder model with new boundary conditions. In this model, the interaction between edge dislocations and a coated CNT incorporating interface effect is investigated. The explicit expressions for the stress fields and the image force acting on an edge dislocation are proposed. In addition, plastic flow occurring around the coated reinforcement is addressed. The influences of interface condition and the material properties of coated CNT on the glide/climb force are clearly analyzed. The results indicate that the interface effect becomes remarkable when the radius of the coated reinforcement is below 10nm. In addition, different from the traditional particles, the coated CNT attracts the adjacent edge dislocations, causing pronounced local hardening at the interface between the interphase and the metal matrix under certain conditions. It is concluded that the presence of the interphase can have a profound effect on the local stress field in CNT-reinforced MMNCs. Finally, the condition of the dislocations stability and the equilibrium numbers of dislocations at a given size grain are evaluated for considering the interface effect.

Image force and stability of a screw dislocation inside a coated cylindrical inhomogeneity with interface stresses

The image force and stability of a screw dislocation inside a coated cylindrical inhomogeneity with interface stresses are analyzed. A three-phase composite cylinder model is utilized to study the issues. The stress boundary condition at the interface of the coating layer is modified by incorporating surface/interface stress. The analytical solution of complex functions of the inhomogeneity, the coating layer, and the infinite matrix is derived by means of the complex variable method. With the aid of the obtained stress fields and the Peach–Koehler formula, the explicit expression of the image force acting on the screw dislocation is obtained. The critical radius of the inhomogeneity where the screw dislocation stays is evaluated. The influence of the interface stresses on the image force and the critical radius of the inhomogeneity is derived. The results indicate that the negative interface stresses attract the dislocation, and the positive interface stresses repel the dislocation. The critical radius of inhomogeneity will increase for considering the negative interface stresses and will decrease for considering the positive interface stresses.

A piezoelectric screw dislocation in a three-phase composite cylinder model with an imperfect interface

The electroelastic coupling interaction between a piezoelectric screw dislocation and the embedded circular cross-section inclusions with imperfect interfaces in piezoelectric solids is investigated by using a three-phase composite cylinder model. By means of a complex variable technique, the explicit solutions of electroelastic fields are obtained. With the aid of the Peach–Koehler formula, the explicit expression for the image force exerted on the piezoelectric screw dislocation is derived. The image force on the dislocation and its equilibrium positions near one of the inclusions are discussed for variable parameters (interface imperfection and material electroelastic dissimilarity) and the influence of nearby inclusions is also considered. The results show that when compared with the previous solution (the perfect interface), more equilibrium positions of the screw dislocation in the matrix may be available due to the effect of the interface imperfection when the dislocation is close to the electroelastic stiff inclusion. It is also found that the magnitude of the image force exerted on the piezoelectric screw dislocation produced by multiply inclusions is always smaller than that produced by a single inclusion and the impact of nearby inclusions on the mobility of the screw dislocation is very important.

Interaction between screw dislocations and inclusions with imperfect interfaces in fiber-reinforced composites

A three-phase composite cylinder model is utilized to study the elastic interaction between screw dislocations and embedded multiple circular cross-section inclusions (fibers) with imperfect interfaces in composites. By means of complex variable techniques, the explicit solutions of stress and displacement fields are obtained. With the aid of the Peach–Koehler formula, the explicit expressions of image forces exerted on screw dislocations are derived. The equilibrium positions of the appointed screw dislocation near one of the inclusions are discussed for variable parameters (interface imperfection, material mismatch and dislocation position) and the influence of the nearby inclusions and dislocations is also considered. The results show that, if the inclusion is stiffer than the matrix and the magnitude of the degree of interface imperfection reaches the certain value, a new equilibrium position for the screw dislocation in the matrix can always be produced in comparison with the previous solution (the perfect interface). The effect of elastic constants of the inclusion on the image force and the equilibrium position of the appointed screw dislocation is weak when the interface imperfection is strong. It is also seen that the magnitude of the image force exerted on the appointed dislocation caused by multiple inclusions is always smaller than that produced by a single inclusion. The impact of the closer dislocations on the mobility of the appointed dislocation is very significant.

Screw Dislocations in a Three-Phase Composite Cylinder Model With Interface Stress

A three-phase composite cylinder model is utilized to study the interaction between screw dislocations and nanoscale inclusions. The stress boundary condition at the interface between nanoscale inclusion and the matrix is modified by incorporating surface/interface stress. The explicit solution to this problem is derived by means of the complex variable method. The explicit expressions of image forces exerted on screw dislocations are obtained. The mobility and the equilibrium positions of the dislocation near one of the inclusions are discussed. The results show that, compared to the classical solution (without interface stress), more equilibrium positions of the screw dislocation may be available when the dislocation is close to the nanoscale inclusion due to consider interface stress. Also, the mobility of the dislocation in the matrix will become more complex than the classical case.

A Piezoelectric Screw Dislocation in a Three-phase Composite Cylinder Model with Electrically Conductive Interfacial Rigid Lines

The problem of the electro-elastic coupling interaction between a piezoelectric screw dislocation and a three-phase circular inclusion with interfacial electrically conductive rigid lines (anti-cracks) is investigated. An efficient and concise method for complex multiply connected region is developed, in terms of which explicit series form solutions of the complex potentials in the matrix, the interphase layer and the inclusion regions are derived. Based on the complex potentials, the image force on the piezoelectric screw dislocation is then calculated by using the generalized Peach–Koehler formula. The equilibrium position of the dislocation is discussed in detail for various rigid line geometries, intrephase layer thicknesses, and piezoelectric material property combinations. The main results show that the interfacial rigid lines have significant perturbation effect on the motion of the piezoelectric screw dislocation near the circular inclusion surrounded by an interphase layer. The solutions of complex potentials in the article can be used as Green's functions to solve the problem on the interaction between interfacial rigid lines and arbitrary shape cracks in piezoelectric composites.

A screw dislocation interacting with inclusions in fiber-reinforced composites

A closed-form analytical solution is given for the stress field due to a screw dislocation interacting with nearby inclusions (the fibers) in a fiber-reinforced composite material. The dislocation is assumed near one of the inclusions, while the influence of other surrounding inclusions on the dislocation is taken into consideration through the three-phase composite cylinder model. The formulation procedure is based on the Muskhelishvili complex variable method of elasticity theory. The force on the dislocation is then derived. It is shown that, in comparison with the two-phase model adopted by Dundurs, the three-phase model allows the dislocation to have equilibrium positions near the fiber.

An Edge Dislocation in a Three-Phase Composite Cylinder Model With a Sliding Interface

An exact elastic solution is derived in a decoupled manner for the interaction problem between an edge dislocation and a three-phase circular inclusion with circumferentially homogeneous sliding interface. In the three-phase composite cylinder model, the inner inclusion and the intermediate matrix phase form a circumferentially homogeneous sliding interface, while the matrix and the outer composite phase form a perfect interface. An edge dislocation acts at an arbitrary point in the intermediate matrix. This three-phase cylinder model can simultaneously take into account the damage taking place in the circumferential direction at the inclusion-matrix interface and the interaction effect between the inclusions. As an application, we then investigate a crack interacting with the slipping interface.

A Zener–Stroh crack in a fiber-reinforced composite material

A Zener–Stroh crack is formed by coalescing a dislocation pileup and therefore is a net dislocation loaded crack. In this paper, the interaction between a Zener–Stroch crack and surrounding cylindrical fibers in a fiber-reinforced composite material has been investigated. The crack is located in the matrix and near a fiber, while the influence of other fibers on the crack is considered through the three-phase composite cylinder model. Using the solution of stress field for a single dislocation in a three-phase cylinder as the Green’s function, the crack is represented by a continuous distribution of dislocations. A set of singular integral equations are thus formulated and solved numerically. The stress intensity factor (SIF) on the crack tip due to crack–inclusions interaction is calculated. The results show that the volume concentration of fibers has non-negligible influence on the SIF of the crack.

Energies of circular inclusions: sliding versus bonded interfaces

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Lubarda V. A. and Markenscoff X. 1999Energies of circular inclusions: sliding versus bonded interfacesProc. R. Soc. Lond. A.455961–974http://doi.org/10.1098/rspa.1999.0344SectionRestricted accessEnergies of circular inclusions: sliding versus bonded interfaces V. A. Lubarda V. A. Lubarda Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093-0411, USA Google Scholar Find this author on PubMed Search for more papers by this author and X. Markenscoff X. Markenscoff Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093-0411, USA Google Scholar Find this author on PubMed Search for more papers by this author V. A. Lubarda V. A. Lubarda Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093-0411, USA Google Scholar Find this author on PubMed Search for more papers by this author and X. Markenscoff X. Markenscoff Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093-0411, USA Google Scholar Find this author on PubMed Search for more papers by this author Published:08 March 1999https://doi.org/10.1098/rspa.1999.0344AbstractThe elastic strain energies of circular inclusions with sliding and bonded interfaces are compared. It is shown that the energy in the inclusion with a sliding interface due to uniform eigenstrain is greater than the energy in the inclusion with a bonded interface if the Poisson ratio of the material is less than 1/6, and smaller if it is greater than 1/6. The total energy in the inclusion and the matrix due to uniform eigenstrain is always smaller in the case of a sliding inclusion. The opposite is true for the inclusion under remote uniform loading at infinity. The relationships between the energies of sliding and bonded inhomogeneities are also derived. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Firooz S, Steinmann P and Javili A (2021) Homogenization of Composites With Extended General Interfaces: Comprehensive Review and Unified Modeling, Applied Mechanics Reviews, 10.1115/1.4051481, 73:4, Online publication date: 1-Jul-2021. Lubarda V (2017) On elastic fields of perfectly bonded and sliding circular inhomogeneities in an infinite matrix, Acta Mechanica, 10.1007/s00707-017-2033-y, 229:4, (1597-1611), Online publication date: 1-Apr-2018. Lubarda V (2017) An analysis of edge dislocation pileups against a circular inhomogeneity or a bimetallic interface, International Journal of Solids and Structures, 10.1016/j.ijsolstr.2017.09.004, 129, (146-155), Online publication date: 1-Dec-2017. Kattis M, Karalis N and Gkouti E (2013) Energy Changes In a Stressed Unbounded Matrix Containing a Inhomogeneity Due to Formation of a Non-perfect Interface, International Journal of Fracture, 10.1007/s10704-013-9910-8, 185:1-2, (217-224), Online publication date: 1-Jan-2014. Zhou K, Hoh H, Wang X, Keer L, Pang J, Song B and Wang Q (2013) A review of recent works on inclusions, Mechanics of Materials, 10.1016/j.mechmat.2013.01.005, 60, (144-158), Online publication date: 1-Jul-2013. Kattis M and Karalis N (2012) Elastic Energies in Circular Inhomogeneities: Imperfect Versus Perfect Interfaces, Journal of Elasticity, 10.1007/s10659-012-9397-y, 111:2, (131-151), Online publication date: 1-Apr-2013. Xu B, Mueller R and Wang M (2009) The Eshelby property of sliding inclusions, Archive of Applied Mechanics, 10.1007/s00419-009-0391-1, 81:1, (19-35), Online publication date: 1-Jan-2011. Lubarda V (2003) Circular inclusions in anti-plane strain couple stress elasticity, International Journal of Solids and Structures, 10.1016/S0020-7683(03)00227-0, 40:15, (3827-3851), Online publication date: 1-Jul-2003. Wang X and Shen Y (2002) An Edge Dislocation in a Three-Phase Composite Cylinder Model With a Sliding Interface, Journal of Applied Mechanics, 10.1115/1.1467090, 69:4, (527-538), Online publication date: 1-Jul-2002. Lubarda V and Markenscoff X (1998) On the Stress Field in Sliding Ellipsoidal Inclusions With Shear Eigenstrain, Journal of Applied Mechanics, 10.1115/1.2791922, 65:4, (858-862), Online publication date: 1-Dec-1998. This Issue08 March 1999Volume 455Issue 1983 Article InformationDOI:https://doi.org/10.1098/rspa.1999.0344Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/03/1999Published in print08/03/1999 License: Citations and impact KeywordsEshelby inclusionseigenstrainsliding interfacePapkovich–Neuber potentialsstrain energy

The influence of interphase regions on local thermal displacements in composites

Although the exact physical and chemical mechanisms are not clearly understood, it is widely believed that an interphase region with properties that differ from those of the plain matrix is developed near fiber surfaces in polymer matrix composites. The current study involves experimental investigation and theoretical modeling of the influence of the interphase on local thermal displacements. Experimental studies have centered on the development of a scanning microinterferometer for in-situ measurements of thermal displacements in the interphase. Thermal displacement measurements have been successfully made for specimens containing a single carbon fiber embedded in an epoxy matrix. A three-phase composite cylinder model is adopted to predict the thermal displacements of the single fiber specimen. Comparison of the theoretical displacement predictions with the experimental profiles measured by the interferometer indicate that the value of the matrix properties near the fiber surface differs from the value in the bulk resin. The data provide evidence of the existence of a lower glass transition temperature in the interphase.