Materials Science Forum Vols. 492-493

Abstract: This paper presents a Galerkin boundary element method for solving crack problems governed by potential theory in nonhomogeneous media. In the simple boundary element method, the nonhomogeneous problem is reduced to a homogeneous problem using variable transformation. Cracks in heat conduction problem in functionally graded materials are investigated. The thermal conductivity varies parabolically in one or more coordinates. A three dimensional boundary element implementation using the Galerkin approach is presented. A numerical example demonstrates the eáciency of the method. The result of the test example is in agreement with ßnite element simulation results.

Abstract: In this study the three – dimensional surface cracking of a graded coating bonded to a homogeneous substrate is considered. The main objective is to model the subcritical crack growth process in the coated medium under a cyclic mechanical or thermal loading. Because of symmetry, along the crack front conditions of mode I fracture and plane strain deformations are assumed to be satisfied. Thus, at a given location on the crack front the crack propagation rate would be a function of the mode I stress intensity factor. A three – dimensional finite element technique for nonhomogeneous elastic solids is used to solve the problem and the displacement correlation technique is used to calculate the stress intensity factor.

Abstract: The thermal fracture and its dependence on time-dependent behavior in functionally graded yttria stabilized zirconia - NiCoCrAlY bond coat alloy thermal barrier coatings was studied. The response of three coating architectures of similar thermal resistance to laser thermal shock tests was considered, experimentally and computationally.

Abstract: The fracture of the functionally graded thermal barrier coating (TBC) under the thermal loads is a key for the engineering application of this kind of materials. In the previous studies, the functionally graded TBC is usually simplified into a laminate by homogenizing the material of each interlayer as an isotropic layer. Nevertheless, this method is a macro equivalent method, which neglected the microstructure characteristics of materials. In this paper, the computational micromechanics method (CMM) is employed to study the fracture problem of the functionally graded TBC with the interface crack. Essentially, CMM is a finite element analytical method based on the real microstructure of materials, which combines the digital image processing technique, the auto mesh generation technique with the finite element method. Firstly, the microstructure photos of the functionally graded TBC are required. Secondly, the digital image processing technique and the auto mesh generation technique are used to construct the finite element model. Finally, the finite element method is utilized for the fracture analysis of the functionally graded TBC under the thermal shock loads. Moreover, the problem is also analyzed using the macro equivalent method and the results from the two methods are compared. The temperature field obtained using CMM is basically consistent with the one obtained from the macro equivalent method and the influences of the interface crack on the temperature fields are limited in a local region. But results of the driving forces for the crack propagation, J-integrals, from the two methods are quite different. Comparing with the CMM results, J-integrals from the macro equivalent method are smaller. It means that the macro equivalent method tends to underestimate the driving force of the interface crack. On the other hand, the prediction of the critical location of the interface crack from the two methods is also different. Since the influence of the microstructure is taken into account by CMM, results of the present work may suggest that CMM is a more useful and accuracy method for the fracture analysis of the functionally graded TBC.

Abstract: A micromechanics-based elastic model is developed for two-phase functionally graded composites with locally pair-wise particle interactions. In the gradation direction, there exist two microstructurally distinct zones: particle-matrix zone and transition zone. In the particle-matrix zone, the homogenized elastic fields are obtained by integrating the pair-wise interactions from all other particles over the representative volume element. In the transition zone, a transition function is constructed to make the homogenized elastic fields continuous and differentiable in the gradation direction. The averaged elastic fields are solved for transverse shear loading and uniaxial loading in the gradation direction.

Abstract: A general methodology is constructed for the fundamental solution of a crack in the homogeneous half-plane interacting with a crack at the interface between the homogeneous elastic half-plane and the nonhomogeneous elastic coating in which the shear modulus varies exponentially with one coordinate. The problem is solved under plane strain or generalized plane stress condition using the Fourier integral transform method. The stress field in the homogeneous half plane is evaluated by the superposition of two states of stresses, one is associated with a local coordinate system in the infinite fractured plate, while the other in the infinite half plane defined in a structural coordinate system.

Abstract: This paper revisits the interaction integral method to evaluate both the mixed-mode stress intensity factors and the T-stress in functionally graded materials under mechanical loading. A nonequilibrium formulation is developed in an equivalent domain integral form, which is naturally suitable to the finite element method. Graded material properties are integrated into the element stiffness matrix using the generalized isoparametric formulation. The type of material gradation considered includes continuum functions, such as an exponential function, but the present formulation can be readily extended to micromechanical models. This paper presents a fracture problem with an inclined center crack in a plate and assesses the accuracy of the present method compared with available semi-analytical solutions.

Abstract: This paper presents numerical simulation of mixed-mode crack propagation in functionally graded materials by means of a remeshing algorithm in conjunction with the finite element method. Each step of crack growth simulation consists of the calculation of the mixedmode stress intensity factors by means of a non-equilibrium formulation of the interaction integral method, determination of the crack growth direction based on a specific fracture criterion, and local automatic remeshing along the crack path. A specific fracture criterion is tailored for FGMs based on the assumption of local homogenization of asymptotic crack-tip fields in FGMs. The present approach uses a user-defined crack increment at the beginning of the simulation. Crack trajectories obtained by the present numerical simulation are compared with available experimental results.

Abstract: Journal bearings are graded systems with a metal-metal composite as the functional layer. Estimation of the microscale stress distributions is used to analyse the interaction between microstructure, material properties and damage mechanisms during wear. The analysis is executed by means of simple plane-strain finite element models mimicking experimentally observed microstructures. It is found that under realistic macrosstress conditions no tensile microstresses are induced in the triboalloy and that plastic flow is inhibited by the graded structure.