International Journal of Computational Engineering Science

The concept of elastic-modulus-graded ceramics for improved resistance to quasi-static contact damage (Hertzian-indentation), sliding-contact damage, and wear is reviewed. In these graded materials, the in-plane elastic modulus (E) is low at the contact surface and high in the interior (substrate) with a continuous, or step-wise continuous, E-gradation in-between. Processing strategies for fabricating such E-graded ceramic composites in the Al₂O₃-glass, the Si₃N₄-glass, and the Si₃N₄-SiC systems are described. The Hertzian indentation (quasi-static and sliding) behavior of these composites, along with some results from wear tests, are reviewed. Computational modeling (finite-element analysis or FEA) results are also reviewed, and are used to discuss the role of E-gradients in imparting contact-damage resistance to these materials. The use of calibrated FEA models as predictive tools for the design of next-generation graded materials is also discussed.

Linear and nonlinear thermomechanical response of the functionally graded (metal-ceramic) plates subjected to static and dynamic loads is studied. The third-order plate theory of Reddy with the von Kármán geometric nonlinearity is used for the kinematic and kinetic descriptions, and two constitutent power-law distribution through the plate thickness is employed. A displacement finite element model is developed with the Newmark time integration scheme, and the Newton-Raphson iterative procedure is used for the solution of nonlinear algebraic equations. While the model is general enough to be used for any boundary conditions, the simply supported and clamped boundary conditions are used to study the parametric effect of the power-law index and surface temperatures and mechanical loads on the thermomechanical response. The most significant finding of this study is that the deflection response does not fall intermediate to those of the metal or ceramic plates. This is due to the nonlinear coupling of mechanical and thermal contributions.

A model problem is considered in which a crack propagates under ductile conditions through an edge-notched plane-strain tension strip. The strip consists of two monolithic material regions joined transversely by a thin graded layer. The material regions are elastically identical but dissimilar in their plastic and fracture-toughness properties. A range of initial crack configurations is studied, including cracks at various angles to the graded layer and with various initial positions in relation to it. A finite-element-based computational procedure containing a number of novel features is used to study the curvilinear crack growth that occurs in this problem. For the problem parameters under consideration, net-section yielding is induced in the more ductile of the two materials, even when the crack trajectory lies well inside the more brittle material. In general, it is found that the brittle material strongly attracts the crack trajectory, and that the presence of the lower-flow-stress material in conjunction with the constraining effect of the higher-flow-stress material induces a substantial toughening mechanism.

Functionally graded materials are characterized by spatially variable microstructures introduced to satisfy given performance requirements. The graded microstructure gives rise to continuously or discretely changing properties, complicating the analysis of these materials. The majority of the computational techniques use the so-called uncoupled approach which ignores the effect of microstructural gradation by employing specific spatial material property variations that are either assumed or obtained by local homogenization. In contrast, the higher-order theory for functionally graded materials is a coupled approach which takes the effect of microstructural gradation into consideration and does not ignore the local-global interaction of the spatially variable inclusion phase(s). Despite its demonstrated utility, however, the original formulation of the higher-order theory is computationally intensive. Herein, an efficient reformulation of the higher-order theory for thermal problems, based on the local/global conductivity matrix approach, is presented in order to enable efficient analysis of graded materials with different length scales. The reformulation decreases the size of the global conductivity matrix by approximately sixty percent, enabling the modeling of realistic microstructures containing fine and coarse phases. In order to model fine phase microstructures efficiently, the higher-order theory is further extended to accommodate regions with spatially variable homogenized properties. Thus the effects occurring at the small-length scale can be modeled exactly or in an homogenized manner depending on the desired level of detail or accuracy. The accuracy of the reformulated and extended higher-order theory is validated through comparison with an exact analytical solution. A graded thermal barrier coating application with fine and coarse microstructural details is presented to highlight the reformulated theory's technological significance.

Poisson's ratio is an important factor for fracture of functionally graded materials (FGMs). It may have significant influence on fracture parameters (e.g. stress intensity factors and T-stress) for a crack in FGMs under mixed-mode loading conditions, while its effect on such parameters is negligible in homogeneous materials. For instance, when tension load is applied in the direction parallel to material gradation, the fracture parameters may show significant influence on the Poisson's ratio. This paper uses a new formulation, so-called non-equilibrium formulation, of the interaction integral method. It also presents a few numerical examples where Poisson's ratio is assumed either constant or linearly varying function, and Young's modulus is assumed to be exponential or hyperbolic-tangent function.

Since the introduction of the hybrid boundary element method in 1987, it has been applied to various problems of elasticity and potential theory, including time-dependent problems. This paper focuses on establishing the conceptual framework for applying both the variational formulation and a simplified version of the hybrid boundary element method to nonhomogeneous materials. Several classes of fundamental solutions for problems of potential are derived. Thus, the boundary-only feature of the method is preserved even with a spatially varying material property. Several numerical examples are given in terms of an efficient patch test including irregularly bounded, unbounded, and multiply connected regions submitted to high gradients.

By utilizing the finite element method, the macroscopic as well as the microscopic thermal stress behaviors of a functionally graded material rectangular plate (FGP) subjected to partial heating conditions in a transient state are presented. The FGP has non-homogeneous thermal and mechanical material properties in the thickness direction, and consists of the particle-reinforced composite in the regions near both surfaces and a composite mixture in the intermediate region. A microscopic constitutive equation and the macroscopic analysis are used to treat the particle-reinforced regions and the intermediate region, respectively. Therefore, the FGP is analyzed by a combination of the macroscopic and the microscopic analyses. The elasto-plasticity and the temperature-dependent properties of the constituent materials as well as the residual stresses arising from the fabrication process are taken into account. The effects of the heating length of the partial heating conditions and the non-homogeneity function of the constituents are discussed in order to find out the optimum form of the gradation function for the FGM subjected to partial heating conditions in transient state. The two-dimensional transient temperature and two-dimensional transient thermal stresses, which include the macroscopic and microscopic components, for the FGP are analyzed and shown in figures. The character (tension or compression) of the macroscopic stresses is dependent on the functional form of gradation.