Xueli Han

Dislocation motion in anisotropic multilayer materials

Line integral forms for the elastic field of dislocations in anisotropic, multilayer materials are developed and utilized in Parametric Dislocation Dynamics (PDD) computer simulations. Developed equations account for interface image forces on dislocations as a result of elastic modulus mismatch between adjacent layers. The method is applied to study dislocation motion in multilayer thin films. The operation of dislocation sources, dislocation pileups, confined layer slip (CLS), and the loss of layer confinement are demonstrated for a duplex Cu/Ni system. The strength of a thin film of alternating nanolayers is shown to increase with decreasing layer thickness, and that the maximum strength is determined by the Koehler barrier in the absence of coherency strains. For alternating Cu/Ni nanolayers, the dependence of the strength on the duplex layer thickness is found to be consistent with experimental results, down to a layer thickness of ≈10nm.

Stress field and interaction forces of dislocations in anisotropic multilayer thin films

Utilizing Fourier transforms, the elastic field of three-dimensional dislocation loops in anisotropic multilayer materials is developed. Greens functions and their derivatives, obtained first in the Fourier domain and then in the real domain by numerical inversion, are used in integrals to determine the elastic field of dislocation loops. The interaction forces between dislocations and free surfaces or interfaces in multilayer thin films are then investigated. The developed method is based on rigorous elasticity solutions for dislocations approaching to within one to two atomic planes from the interface. For a dislocation in one layer, the interface image force is determined mainly by the elastic moduli and thicknesses of neighbouring layers. When a dislocation approaches an interface between two layers, within 10–20 atomic planes, the image force changes rapidly. Interaction forces are then kept constant up to the interface. The model shows that, when a dislocation crosses an interface from a soft to a hard layer, additional external forces must be applied to overcome an elastic mismatch barrier. The developed method extends the concept of the Kohler barrier in 2D, and shows that the interface force barrier not only depends on the relative ratio of the elastic moduli of neighbouring layers, but also on the 3D shape of the dislocation, the number of interacting adjacent layers, and on layer thicknesses.

Parametric dislocation dynamics of anisotropic crystals

Efficient computational methods for the elastic field, self force and interaction forces of three-dimensional (3D) dislocations in anisotropic elastic crystals are developed for 3D dislocation dynamics (DD). The elastic field of a general dislocation loop is determined by incorporating numerically evaluated derivatives of Greens functions in the fast sum method of Ghoniem and Sun. Self-forces of dislocation loops are calculated by numerical integrations performed on the dislocation line, and several approximation methods to the full integration are also explored. Strong effects of elastic anisotropy on many ingredients of DD are shown (e.g. the elastic field, self-forces, operation of Frank–Read sources, dipole formation and break-up and dislocation junction strength). Large-scale 3D DD simulations are carried out for copper single crystals. It is found that the dislocation microstructure and strain-hardening behaviour are also strong functions of elastic anisotropy.

Interacting multiple cracks in piezoelectric materials

In this paper, a method is presented to calculate the plane electro-elastic fields in piezoelectric materials with multiple cracks. The cracks may be distributed randomly in locations, orientations and sizes. In the method, each crack is treated as a continuous distributed dislocations with the density function to be determined according to the conditions of external loads and crack surfaces. Some numerical examples are given to show the interacting effect among multiple cracks.

Interface crack between two different viscoelastic media

The plane (including antiplane) problem of an interfacial crack between different viscoelastic (including viscoelastic and elastic) media is considered. By using the Laplace transform method, the viscoelastic problem is reduced to an associated elastic one. The corresponding elastic analysis results in the viscoelastic solutions in the transformed field. The crack tip fields and fracture parameters of the viscoelastic interface crack are derived through an approximate Laplace inverse transform method. As an example, numerical calculations for an interfacial crack between viscoelastic and elastic materials are carried out. It is shown that the simple formulae of the crack line (and tip) fields and fracture parameter (energy release rate) of the viscoelastic interface crack, derived by the approximate method, are quite accurate. When the bimaterial is subject to a remote uniform and constant tensile loading, the normal stress along the crack line (including tip) is almost time independent. In contrast, the relative crack surface displacements and crack energy release rate do change with time, and are very much dependent on the creep compliance of the viscoelastic material. The tendencies of the crack advancing along the interface, and kinking out of the interface, are estimated and discussed.

Fields induced by three-dimensional dislocation loops in anisotropic magneto-electro-elastic bimaterials

The coupled elastic, electric and magnetic fields produced by an arbitrarily shaped three-dimensional dislocation loop in general anisotropic magneto-electro-elastic (MEE) bimaterials are derived. First, we develop line-integral expressions for the fields induced by a general dislocation loop. Then, we obtain analytical solutions for the fields, including the extended Peach–Koehler force, due to some useful dislocation segments such as straight line and elliptic arc. The present solutions contain the piezoelectric, piezomagnetic and purely elastic solutions as special cases. As numerical examples, the fields induced by a square and an elliptic dislocation loop in MEE bimaterials are studied. Our numerical results show the coupling effects among different fields, along with various interesting features associated with the dislocation and interface.

Toughening of ferroelectric ceramics under polarization switching

For ferroelectric ceramics under coupled mechanical and electrical loading, the intensified stress and electric fields in the vicinity of a crack tip lead to domain switching. The switched domain induces incompatible strain, and consequently changes the apparent fracture toughness. In this paper, the toughness variation induced by domain switching is analysed via a domain switching strip model. A local energy release rate at the crack tip is used to evaluate toughening and weakening in ferroelectric ceramics induced by domain switching. It is shown that the crack growth can be either enhanced or retarded depending on the magnitude, the direction, and type of the applied electrical load. The prediction based on the present model explains the conflicting experimental data on toughness variations with respect to the applied electric field. It is also shown that a substantial enhancement in toughness is possible due to domain switching, and domain switching in the field of a crack tip provides the requisite energy absorption mechanism for enhancement of fracture toughness.

Analysis of two-dimensional finite solids with microcracks

A general method is presented for solving the plane elasticity problem of finite plates with multiple microcracks. The method directly accounts for the interactions between different microcracks and the effect of outer boundary of a finite plate. Analysis is based on a superposition scheme and series expansions of the complex potentials. By using the traction-free conditions on each crack surface and resultant forces relations along outer boundary, a set of governing equations is formulated. The governing equations are solved numerically on the basis of a boundary collocation procedure. The effective Youngs moduli for randomly oriented cracks and parallel cracks are evaluated for rectangular plates with microcracks. The numerical results are compared with those from various micromechanics models and experimental data. These results show that the present method provides a direct and efficient approach to deal with finite solids containing multiple microcracks.

Interaction among interface, multiple cracks and dislocations

Abstract The interaction problem of a number of arbitrary oriented and distributed cracks and/or dislocations in bonded bi-material half planes, are considered in a unified method. The basic solution of a single dislocation in a bonded half plane and the superposition technique, are used. The method has high accuracy and computational efficiency. It can treat the combined interaction of cracks, dislocations and interface. Several examples are given to show certain interaction effects, especially among cracks near an interface.

A crack near the interface of bonded elastic–viscoelastic planes

Abstract The plane problem for bonded elastic–viscoelastic half planes containing an arbitrarily oriented crack in the vicinity of the interface is investigated. By using the Laplace transformation, the viscoelastic problem is first reduced to an associated elastic one. The complex function method is used to solve the associated elastic problem. Then, the solution of viscoelastic problem is obtained by using the inverse Laplace transformation of the associated elastic results. The fracture parameters, such as the stress intensity factors and strain energy release rates, and the probable directions of crack propagation are determined for various crack orientation and distance from the interface. The effect of elastic–viscoelastic interface on a crack approaching it from either medium is discussed.