Jianmin Qu

The effect of slightly weakened interfaces on the overall elastic properties of composite materials

Abstract The effect of imperfect interfaces on the overall elastic properties of composites is studied in this paper. The imperfect interface is modeled by a linear spring-layer of vanishing thickness. The Mori-Tanaka estimate and its modification are used to evaluate the effective moduli of composites having slightly weakened interfaces. An interface is said to be slightly weakened, if the compliance of the spring-layer is very small. As an example, a composite consisting of aligned ellipsoidal particles is considered in detail. Explicit expressions of the Mori-Tanaka estimates of the effective moduli are derived when the particles are spherical. Based on classical minimum energy principles, upper and lower bounds of the effective moduli of composites with imperfect interfaces are also derived.

Interfacial dislocation and its applications to interface cracks in anisotropic bimaterials

Interfacial dislocations and cracks in anisotropic bimaterials are considered. The displacement and the stress fields due to an interfacial dislocation are obtained in a real and simple form. Explicit solutions to the traction along the interface and the crack opening displacement for a Griffith interface crack are derived. Possible definitions of stress intensity factors are given which reduce to the classical definition for a crack in a homogeneous medium. It is found that a planar interface between dissimilar anisotropic solids is completely characterized by no more than 9 independent parameters. Some invariant properties of the dislocation and crack solutions under coordinate transformation are also discussed.

An electrochemomechanical theory of defects in ionic solids. I. Theory

Charged defects diffuse through an ionic solid under electrochemical driving forces. Such a diffusion process can be affected by mechanical stresses in the solid. A deviation of defect concentration from its stoichiometric value during diffusion can cause volumetric strains in the solid. Such strains will result in mechanical stresses if the ionic solid is under mechanical constraint, or if the defect distribution is non-uniform. We develop a framework to account for the coupling between mechanical stresses and diffusion of charged defects in ionic solids. The framework consists of a system of nonlinear differential/algebraic equations governing the defect concentrations, electrostatic potential and the mechanical stresses. It is believed that this framework is the first fully coupled theory for the interaction between mechanical stresses and electrochemical forces in ionic solids.

Interfacial Fracture Mechanics for Anisotropic Bimaterials

This paper focuses on aspects of fracture mechanics of interface cracks in anisotropic bimaterials. In this case there is a coupling of all three crack-tip fracture modes in the natural interface-crack coordinate system, whereas in the isotropic case, mode 3 is decoupled from modes 1 and 2. This paper intends to shed light on how to interpret the crack-tip fields which are given explicitly along the interface in terms of two (real 3x3) bimaterial matrices W and D . A matric function Y is defined in terms of W and D which determines the coupling and oscillations in the cracktip fields. Explicit expressions for the crack-tip fields and the associated stress intensity factors are given as well as for the energy release rate. The finite (Griffith) interface crack is considered in detail.

Developing a second nearest-neighbor modified embedded atom method interatomic potential for lithium

This paper reports the development of a second nearest-neighbor modified embedded atom method (2NN MEAM) interatomic potential for lithium (Li). The 2NN MEAM potential contains 14 adjustable parameters. For a given set of these parameters, a number of physical properties of Li were predicted by molecular dynamics (MD) simulations. By fitting these MD predictions to their corresponding values from either experimental measurements or ab initio simulations, these adjustable parameters in the potential were optimized to yield an accurate and robust interatomic potential. The parameter optimization was carried out using the particle swarm optimization technique. Finally, the newly developed potential was validated by calculating a wide range of material properties of Li, such as thermal expansion, melting temperature, radial distribution function of liquid Li and the structural stability at finite temperature by simulating the disordered–ordered transition. (Some figures may appear in colour only in the online journal)

Evaluation of thermomechanical properties of non-stoichiometric gadolinium doped ceria using atomistic simulations

It is well known that gadolinium doped ceria (GDC), when subjected to reducing conditions, undergoes significant volumetric expansion and changes its elastic stiffness. In this paper, a methodology based on a semi-analytical formulation in conjunction with molecular dynamic (MD) simulation is presented to determine the coefficient of compositional expansion (CCE) and the complete elastic stiffness tensor of two common forms of GDC at various levels of non-stoichiometry and temperatures. The CCE is determined by comparing the volumes of the MD simulation cell before and after the reduction at a given temperature. To compute the elastic constants, MD simulations are first conducted to determine the equilibrium (relaxed) positions of each atom. Then, the constants are obtained through an analytical method that uses the relaxed positions of the atoms in the simulation cell. It is found that the elastic stiffness tensor of the non-stoichiometric structures remain cubic. The elastic constant C11 decreases with increasing vacancy concentration, while the changes in C12 and C66 were found to be negligible. In addition, both the elastic constants and the CCE are found to be insensitive to temperature.

An electrochemomechanical theory of defects in ionic solids. Part II. Examples

In this paper, a boundary value problem formulated previously by N. Swaminathan, J. Qu, Y. Sun, Phil. Mag. 2006 (this volume) is solved to obtain the defect, stress distributions in a planar electrolyte in solid oxide fuel cells. It is found that analytical solutions from the coupled theory reduce to the known results from electrochemistry literature when the coefficient of compositional expansion is set to zero, i.e. when there is no coupling between electrochemical and mechanical fields. For the case of non-zero coefficient of compositional expansion, extensive numerical results are presented which show that there is a significant interaction between mechanical stresses and defect distribution.

A coarse-grained model for epoxy molding compound

We present a coarse-grained model for molecular dynamics simulations of an epoxy system composed of epoxy phenol novolac as epoxy monomer and bisphenol-A as the cross-linking agent. The epoxy and hardener molecules are represented as short chains of connected beads, and cross-linking is accomplished by introducing bonds between reactive beads. The interbead potential, composed of Lennard-Jones, bond stretching, and angle bending terms, is parametrized through an optimization process based on a particle swarm optimization method to fit certain key thermomechanical properties of the material obtained from experiments and previous full atomistic simulations. The newly developed coarse-grained model is capable of predicting a number of thermomechanical properties of the epoxy system. The predictions are in very good agreement with available data in the literature. More importantly, our coarse-grained model is capable of predicting tensile failure of the epoxy system, a capability that no other conventional molecular dynamic simulation model has. Finally, our coarse-grained model can speed up the simulations by more than an order of magnitude when compared with traditional molecular dynamic simulations.

A study of highly crosslinked Epoxy Molding Compound and its interface with copper substrate by molecular dynamic simulations

A novel Epoxy Molding Compound (EMC) with a crosslinked network structure was formed by curing tri-/tetra-functionalized EPN1180 with Bisphenol-A. A full atomistic model reflecting the network nature of the material was constructed by applying an iterative crosslinking algorithm to an amorphous cell with 3D periodic boundary condition containing the stoichiometric mixture of constitutive monomers. The geometry of the model was then optimized using the COMPASS force-field in Materials Studio [1]. The variation of system density and volume against temperature was simulated using a cooling down profile, which was employed to derive the glass transition temperature and coefficient of thermal expansion of the system. Furthermore, the Youngs modulus and Poissons ratio were calculated by uni-axial tensile molecular statics simulations. The material properties computed by molecular dynamics/mechanics simulations were in good agreement with experiment measurements. An epoxy resin/copper interface model was constructed and the interfacial adhesion energy was calculated as the energy difference between the total energy of the entire system and the sum of the energies of individual materials. The traction-displacement law of the interface was derived when the system was subjected to a molecular statics uniaxial tension. The work of separation and the peak traction, considered as the two key parameters required by cohesive zone finite element simulation, were extracted from the traction-displacement law.

An investigation of the tensile deformation and failure of an epoxy/Cu interface using coarse-grained molecular dynamics simulations

In this study, a coarse-grained model is developed to describe the interatomic interactions between a cross-linked epoxy and a copper substrate. Based on this model, the tensile deformation and failure of an epoxy/Cu bimaterial is studied. Attention is given to the microstructural evolution near the epoxy/Cu interface, and its effects on the overall stress–strain behavior of the bimaterial. It is found that, under uniaxial strain, plastic deformation in the epoxy/Cu bimaterial is localized to a thin layer of epoxy next to the epoxy/Cu interface. This discovery enables the definition of an interfacial zone. Consequently, a cohesive zone model at the continuum level could potentially be constructed where the separation of the interface is given by the stretching of the interfacial zone computed from the coarse grain simulations.