Fracture analysis of a functionally graded coating-substrate structure with a crack perpendicular to the interface - Part II: Transient problem

In Part I of this paper, the static problem of a functionally graded coating-substrate system with an internal or edge crack perpendicular to the interface has been studied. In this part, the transient response of the structure is considered under an in-plane impact. Laplace and Fourier transforms are applied to reduce the mixed boundary value problem to a singular integral equation which is solved in the Laplace domain numerically. The dynamic stress intensity factors (DSIFs) are obtained by numerical Laplace inversion technique. The influences of material constants and geometry parameters on the dynamic stress intensity factors are studied. It is found that the DSIFs for an internal crack rise rapidly to a peak and then tend to the steady value without obvious oscillations, but the DSIFs for an edge crack have more obvious oscillations after rising to a peak with the increasing of the nonhomogeneity constant.     

On debonding of graded thermal barrier coatings

Thermal barrier coatings generally consist of a metallic substrate which is the primary structural component, a metallic bond coat which serves as oxygen diffusion barrier, a very thin layer of thermally grown oxide and a ceramic top coat that provides the main thermal shielding. Homogeneous ceramic coatings as top coats appear to have certain undesirable features such as high residual and thermal stresses, generally low toughness and relatively poor bonding strength. The new concept of compositional grading of the top coat may help to overcome some of these shortcomings by eliminating the material property discontinuities. A common mode of failure in thermal barrier coatings seems to be the debonding of the top coat. In this study the related interface crack problem for a graded ceramic/metal top coat is considered. It is assumed that the thermophysical properties of the top coat continuously vary between that of the bond coat at the top coat-bond coat interface and that of the ceramic at and near the free surface. The main objective of the study is to examine the influence of the material nonhomogeneity parameters and relative dimensions on the stress intensity factors and the crack opening displacements.     

CAD modeling for the components made of multi heterogeneous materials and smart materials

There appear more critical requirements for special functions of components/products in various areas, which can be satisfied only by using heterogeneous materials and/or smart materials. The heterogeneous materials include composite materials, functionally graded materials, and heterogeneous materials with a periodic microstructure. To design and manufacture the components made of these materials, the computer models for representing them need first to be built so that further analysis, optimization and manufacturing can be implemented based on the models. This paper develops such a modeling method, which can be implemented by employing the functions of current CAD graphic software and obtain the model that includes all the material information (about periodic microstructures, constituent composition, inclusions, and embedded parts) along with geometry information in 3D solid modeling without the problem arising from too much data.     

功能梯度涂层热残余应力

涂层中的残余应力严重影响着涂层零件的机械完整性与操作可靠性。对于功能梯度涂层,由于各界面位移协调条件的限制,很难得到涂层内部残余应力的闭合解。基于传统的悬臂梁理论,获得了功能梯度涂层热残余应力的闭合解;这一分析模型的优点是残余应力的闭合解与涂层层数无关。讨论了采用传统的近似解所带来的误差, 针对含不同层数的ZrO2/NiCoCrAlY功能梯度涂层内部的残余应力进行了计算。另外,对应力诱导的涂层失效模型也进行了分析。     

Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments

Nonlinear bending analysis is presented for a simply supported, functionally graded rectangular plate subjected to a transverse uniform or sinusoidal load and in thermal environments. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations of a functionally graded plate are based on Reddy's higher-order shear deformation plate theory that includes thermal effects. Two cases of the in-plane boundary conditions are considered. A mixed Galerkin-perturbation technique is employed to determine the load-deflection and load-bending moment curves. The numerical illustrations concern nonlinear bending response of functional graded rectangular plates with two constituent materials. The influences played by temperature rise, the character of in-plane boundary conditions, transverse shear deformation, plate aspect ratio and volume fraction distributions are studied.     

In-plane and out-of-plane buckling of arches made of FGM

The mechanical buckling of curved beams made of functionally graded materials is studies in this paper. The equilibrium and stability equations of curved beams under mechanical loads are derived. Using proper approximate functions for the displacement components, the stability equations are employed to obtain the related eigenvalues associated with the buckling load of the curved beam. Closed-form solutions are obtained for mechanical buckling of curved beams with doubly symmetric cross section subjected to uniform distributed radial load and pure bending moment. The results are validated with the known data in the literature for beams with isotropic materials.     

A state space differential reproducing kernel method for the 3D analysis of FGM sandwich circular hollow cylinders with combinations of simply-supported and clamped edges

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) sandwich circular hollow cylinders with combinations of simply-supported and clamped edges and under sinusoidally (or uniformly) distributed loads. The strong formulation of this 3D elasticity problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler–Lagrange equations of this problem and its associated boundary conditions. The primary field variables are expanded as the single Fourier series in the circumferential coordinate, then interpolated in the axial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The present state space DRK solutions can then be obtained by means of the transfer matrix method. In the illustrative examples, three different edge conditions, the simple-simple (SS), simple-clamped (SC), and clamped–clamped (CC) edges, are considered, and the accuracy and convergence of this method are examined by comparing their solutions with the exact 3D ones available in the literature and the solutions using the ANSYS commercial software.     

Simulation Charpy impact energy of functionally graded steels by modified stress-strain curve through mechanism-based strain gradient plasticity theory

In the present work, Charpy impact energy of functionally graded steels produced by electroslag remelting composed of graded ferritic or austenitic layers in both crack divider and crack arrester configurations has been modeled by finite element method. The yield stress of each layer was related to the density of the statistically stored dislocations of that layer and assuming by Holloman relation for the corresponding stress-strain curves, tensile strengths of the constituent layers were determined via numerical method. By using load-displacement curves acquired from instrumented Charpy impact tests on primary specimens, the obtained stress-strain curves from uniaxial tensile tests were modified. The data used for each layer in finite element modeling were predicted modified stress-strain curves obtained from strain gradient plasticity theory. A relatively good agreement between experimental results and those obtained from simulation was observed.     

On the dynamical thermoelasticity problem for a hollow funtionally graded cylinder

A thermoelasticity problem of a pressurized infinite cylinder made of functionally graded material is solved analytically where material properties vary with radial position. Time dependent thermal and mechanical boundary conditions are assumed to act on the inner and outer surfaces of the cylinder. For thermal boundary conditions, temperature is prescribed on both surfaces, whereas for mechanical boundary conditions, tractions are prescribed on the boundaries. Obtaining distribution of temperature throughout the cylinder, the dynamical structural problem is solved and closed form relations are extracted for distributions of stress components.     

Solid lubricant behavior of MoS2 and WSe2-based nanocomposite coatings

Abstract

Tribological coatings made of MoS₂ and WSe₂ phases and their corresponding combinations with tungsten carbide (WC) were prepared by non-reactive magnetron sputtering of individual targets of similar composition. A comparative tribological analysis of these multiphase coatings was done in both ambient air (30–40% relative humidity, RH) and dry nitrogen (RH<7%) environments using the same tribometer and testing conditions. A nanostructural study using advanced transmission electron microscopy of the initial coatings and examination of the counterfaces after the friction test using different analytical tools helped to elucidate what governs the tribological behavior for each type of environment. This allowed conclusions to be made about the influence of the coating microstructure and composition on the tribological response. The best performance obtained with a WSe_x film (specific wear rate of 2 × 10^?8 mm³ N^–1m^–1 and a friction coefficient of 0.03–0.05) was compared with that of the well-established MoS₂ lubricant material.