Effect Of Material Inhomogeneity Research Articles

Micromechanical methodology for fatigue in cardiovascular stents

A finite element based micromechanical methodology for cyclic plasticity and fatigue crack initiation in cardiovascular stents is presented. The methodology is based on the combined use of a (global) three-dimensional continuum stent-artery model, a local micromechanical stent model, the development of a combined kinematic–isotropic hardening crystal plasticity constitutive formulation, and the application of microstructure sensitive crack initiation parameters. The methodology is applied to 316L stainless steel stents with random polycrystalline microstructures, based on scanning electron microscopy images of the grain morphology, under realistic elastic–plastic loading histories, including crimp, deployment and in vivo systolic–diastolic cyclic pressurisation. Identification of the micromechanical cyclic plasticity and failure constants is achieved via application of an objective function and a unit cell representative volume element for 316L stainless steel. Cyclic stent deformations are compared with the J2-predicted response and conventional fatigue life prediction techniques. It is shown that micromechanical fatigue analysis of stents is necessary due to the significant predicted effects of material inhomogeneity on micro-plasticity and micro-crack initiation.

Elasticity Solution of a Cantilever Functionally Graded Beam

This paper considers the plane stress problem of a cantilever functionally graded beam subjected to linearly distributed load. The material properties of the functionally graded beam are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a functionally graded cantilever beam.

Influence of Crack Length on Ductile Fracture Initiation in Welded Joints with one and Two Weld Metals

Among various micromechanical models for ductile fracture analysis using local approach, those based on the Gurson plastic flow criterion have been intensively developed in the past three decades. However, their application is still subject of many researches, with the aim to improve the assessment of ductile fracture in various, mainly metallic, materials. In this work, Gurson criterion is applied to welded joints produced with one or two different weld metals (one of these is overmatched, while the other is undermatched). Welded single-edge notched bend (SENB) specimens are examined, with an initial pre-crack located in the symmetry plane of each joint. Local approach is chosen for assessment of behaviour of the joints under the external loading, to capture the effect of material inhomogeneity and initial crack length on deformation and ductile fracture initiation in analysed specimens.

Effect of material in-homogeneity on electro-thermo-mechanical behaviors of functionally graded piezoelectric rotating shaft

In this article, a hollow circular shaft made from functionally graded piezoelectric material (FGPM) such as PZT_5 has been studied which is rotating about its axis at a constant angular velocity ω. This shaft subjected to internal and external pressure, a distributed temperature field due to steady state heat conduction with convective boundary condition, and a constant potential difference between its inner and outer surfaces or combination of these loadings. All mechanical, thermal and piezoelectric properties except for the Poisson’s ratio are assumed to be power functions of the radial position. The governing equation in polarized form is shown to reduce to a system of second-order ordinary differential equation for the radial displacement. Considering six different sets of boundary conditions, this differential equation is analytically solved. The electro-thermo-mechanical stress and the electric potential distributions in the FGPM hollow shaft are discussed in detail for the piezoceramic PZT_5. The presented results indicate that the material in-homogeneity has a significant influence on the electro-thermo-mechanical behaviors of the FGPM rotating shaft and should therefore be considered in its optimum design.

Effect of material inhomogeneity on the rotating functionally of a graded orthotropic hollow cylinder

The effect of the material inhomogeneity on the stress field of a rotating orthotropic infinite hollow cylinder made of functionally graded materials is investigated. The original functionally graded hollow cylinder is approximated by the laminate model, of which the solution will gradually approach the exact one with the increase in number of fictitious layers. The analysis is performed by means of the state space method. The validity of the solution is verified by utilizing the exact solution of a special non-homogeneous rotating hollow cylinder and earlier results. The distributions of the radial and tangential stresses of the internally pressurized rotating functionally graded hollow cylinder for various material inhomogeneity parameters are depicted graphically. The degree of the orthotropy on the stress fields is also discussed.

Anti-plane interaction of a crack and reinforced elliptic hole in an infinite matrix

Anti-plane interaction of a crack with a coated elliptical hole embedded in an infinite matrix under a remote uniform shear load is considered in this paper. Analytical treatment of the present problem is laborious due to the presence of material inhomogeneities and geometric discontinuities. Nevertheless, based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, general expressions for displacements and stresses in the coated layer and the matrix are derived explicitly in closed form. By applying the existing complex function solutions for a dislocation, the integral equations for a line crack are formulated and mode-III stress intensity factors are obtained numerically. Some numerical examples are given to demonstrate the effects of material inhomogeneity and geometric discontinuities on mode-III stress intensity factors.

Time and depth dependent poisson’s ratio of cartilage explained by an inhomogeneous orthotropic fiber embedded biphasic model

A time- and depth-dependent Poisson’s ratio has been observed during unconfined compression experiments on articular cartilage, but existing cartilage models have not fully addressed these phenomena. The goal of this study was to develop a model which is able to predict and explain these phenomena, while also being able to fit other experimental scenarios on full depth cartilage specimens such as confined and unconfined compressions. A biphasic (poroelastic), fiber-embedded cartilage model was developed. The heterogeneous material properties of the cartilage (aggregate modulus, void ratio tensile modulus) were extracted from reported experiments on individual layers of bovine articular cartilage. The nonlinear permeability material constants were found by fitting the overall response to published experimental data from confined compression. The matrix of the cartilage was modelled as an inhomogeneous isotropic biphasic material with nonlinear strain dependent permeability. Orthotropic layers were added as embedded elements to represent collagen fibers. Material parameters for these layers were derived from tensile tests of different layers of cartilage. With these predefined tensile parameters, the model showed a good fit with multi-step confined and unconfined compression experiments ( R 2=0.984 and 0.977, respectively) and could also predict the depth-dependent Poisson’s ratio ( R 2=0.981). The highlight of the model is the ability to explain the time-depth dependent Poisson's ratio and, by association, the strong effect of material inhomogeneity on local stress and strain patterns within the cartilage layer. This material model’s response may provide valuable new insight into potential initiation of cartilage fibrillation or delamination in whole-joint simulations.

Effect of material inhomogeneity on electromechanical behaviors of functionally graded piezoelectric spherical structures

Based on the three-dimensional linear piezoelectric theory, the elastic analysis is carried out for functionally graded, radially polarized piezoelectric spherical structure subjected to mechanical and electrical loads. The material properties are assumed to be exponential function of the radial position. Frobenius series method is employed to solve the second-order ordinary differential equation with variable coefficient and the closed-form displacement solution is obtained. The obtained solution converges very quickly and is convenient to treat in analyzing the electromechanical fields in the exponentially graded piezoelectric (EGP) hollow sphere subjected to different mechanical and electric loads. The presented numerical results show that the material inhomogeneity has a significant influence on the electromechanical behaviors of the EGP spherical structures.

Gradation of mechanical properties in gas-diffusion electrode. Part 2: Heterogeneous carbon fiber and damage evolution in cell layers

In PEM fuel cell, gas-diffusion electrode (GDE) plays very significant role in force transmission from bipolar plate to the membrane. This paper investigates the effects of geometrical heterogeneities of gas-diffusion electrode layer (gas-diffusion layer (GDL) and catalyst layer (CL)) on mechanical damage evolution and propagation. We present a structural integrity principle of membrane electrode assembly (MEA) based on the interlayer stress transfer capacity and corresponding cell layer material response. Commonly observable damages such as rupture of hydrophobic coating and breakage of carbon fiber in gas-diffusion layer are attributed to the ductile to brittle phase transition within a single carbon fiber. Effect of material inhomogeneity on change in modulus, hardness, contact stiffness, and electrical contact resistance is also discussed. Fracture statistics of carbon fiber and variations in flexural strength of GDL are studied. The damage propagation in CL is perceived to be influenced by the type of gradation and the vicinity from which crack originates. Cohesive zone model has been proposed based on the traction–separation law to investigate the damage propagation throughout the two interfaces (carbon fiber/CL and CL/membrane).

A Numerical Fatigue Damage Model for Life Scatter of MEMS Devices

This paper presents a fatigue damage model to estimate fatigue lives of microelectromechanical systems (MEMS) devices and account for the effects of topological randomness of material microstructure. For this purpose, the damage mechanics modeling approach is incorporated into a new Voronoi finite-element model (VFEM). The VFEM developed for this investigation is able to consider both intergranular crack initiation (debonding) and propagation stages. The model relates the fatigue life to a damage parameter " <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> " which is a measure of the gradual material degradation under cyclic loading. The fatigue damage model is then used to investigate the effects of microstructure randomness on the fatigue of MEMS. In this paper, three different types of randomness are considered: (1) randomness in the microstructure due to random shapes and sizes of the material grains; (2) the randomness in the material properties considering a normally (Gaussian) distributed elastic modulus; and (3) the randomness in the material properties considering a normally distributed resistance stress, which is the experimentally determined material property controlling the ability of a material to resist the damage accumulation. Thirty-one numerical models of MEMS specimens are considered under cyclic axial and bending loading conditions. It is observed that the stress-life results obtained are in good agreement with the experimental study. The effects of material inhomogeneity and internal voids are numerically investigated.

Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness

We analyze axisymmetric deformations of a rotating disk with its thickness, mass density, thermal expansion coefficient and shear modulus varying in the radial direction. The disk is made of a rubberlike material that is modeled as isotropic, linear thermoelastic and incompressible. We note that the hydrostatic pressure in the constitutive relation of the material is to be determined as a part of the solution of the problem since it cannot be determined from the strain field. The problem is analyzed by using an Airy stress function φ. The non-homogeneous ordinary differential equation with variable coefficients for φ is solved either analytically or numerically by the differential quadrature method. We have also analyzed the challenging problem of tailoring the variation of either the shear modulus or the thermal expansion coefficient in the radial direction so that a linear combination of the hoop stress and the radial stress is constant in the disk. For a rotating annular disk we present the explicit expression of the thermal expansion coefficient for the hoop stress to be uniform within the disk. For a rotating solid disk we give the exact expressions for the shear modulus and the thermal expansion coefficient as functions of the radial coordinate so as to achieve constant hoop stress. Numerical results for a few typical problems are presented to illuminate effects of material inhomogeneities on deformations of a hollow and a solid rotating disk.

Symplectic analysis of plane problems of functionally graded piezoelectric materials

This paper develops an analytical method to investigate the plane problems of functionally graded piezoelectric materials within the symplectic framework. The material constants, including the elastic, piezoelectric and dielectric constants are assumed to vary along the length in an identical exponential form. A matrix state equation is derived by introducing new stress and electric displacement components, and is solved using the method of separation of variables. The operator matrix in the state equation is found to have similar properties as Hamiltonian matrix for homogeneous materials. Its eigenvectors (and hence eigensolutions) corresponding to particular eigenvalues (0 and − α) are derived; while the former also present in the homogeneous materials, the latter bear complete different forms. A detailed analysis shows, however, that the − α-group eigensolutions can degenerate to the ones for the homogeneous materials after eliminating certain rigid motions. Numerical results are given to show the effect of material inhomogeneity on these eigensolutions.

Simulating material inhomogeneities and defects in CIGS thin‐film solar cells

AbstractThin‐film CIGS solar cells are simulated using a hybrid model consisting of a distributed form of the analytical one diode model paired with a numerical finite element model of the d.c. conduction in the front contact layers. Variations in material quality over the substrate surface, from measured J–V curves, are incorporated into the model and the effects of cell width and window layer thickness are evaluated for homogeneous and inhomogeneous material quality. Furthermore, the effects of discrete shunt defects of different sizes are modelled, and in different positions on the cell surface. The results from optimizing cell width and window layer thickness show that the effects of material inhomogeneities include a small shift of the optimal parameters together with a less pronounced maximum. As expected, the defect size is important to the shunt conductance parameter of the resulting J–V curves. The passivating effect of the highly resistive ZnO layer is confirmed. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Three-dimensional analytical solution for a transversely isotropic functionally graded piezoelectric circular plate subject to a uniform electric potential difference

This paper studies the problem of a functionally graded piezoelectric circular plate subjected to a uniform electric potential difference between the upper and lower surfaces. By assuming the generalized displacements in appropriate forms, five differential equations governing the generalized displacement functions are derived from the equilibrium equations. These displacement functions are then obtained in an explicit form, which still involve four undetermined integral constants, through a step-by-step integration which properly incorporates the boundary conditions at the upper and lower surfaces. The boundary conditions at the cylindrical surface are then used to determine the integral constants. Hence, three-dimensional analytical solutions for electrically loaded functionally graded piezoelectric circular plates with free or simply-supported edge are completely determined. These solutions can account for an arbitrary material variation along the thickness, and thus can be readily degenerated into those for a homogenous plate. A numerical example is finally given to show the validity of the analysis, and the effect of material inhomogeneity on the elastic and electric fields is discussed.

Effects of material inhomogeneity on the dynamic behavior of cracked piezoelectric solids: a BIEM approach

AbstractTreated is an arbitrarily shaped anti‐plane shear crack in a finite inhomogeneous piezoelectric domain under time‐harmonic loading. Within a unified scheme different types of inhomogeneity are considered for which the material parameters may vary in two directions. The problem is solved by using a numerically efficient non‐hypersingular traction based boundary equation method (BIEM). The fundamental solutions for the different inhomogeneity types are derived in closed form. This is done by an appropriate functional transformation of the displacement vector in order to obtain a wave equation with constant coefficients and subsequently by application of the Radon transform. Numerical results for the stress intensity factors (SIF) are discussed for several examples. They show the effect of the material inhomogeneity and the efficiency of the method.

Investigation of a Mode III Crack in Functionally Graded Magnetoelectroelastic Materials

In this study, an anti-plane crack in a functionally graded magnetoelectroelastic materials is investigated. It is assumed that the material properties such as elastic stiffness c44(y), piezoelectric coefficient e15(y), dielectric constant ε11(y), piezomagnetic coefficient α15(y), magnetoelectric coupling coefficient μ11(y) and magnetic permeability υ11(y) vary one-dimensionally on the ycoordinate with a series of functions f(y).An asymptotic analysis is done and the problem is solved by means of singular integral equation technique. The influence of the material inhomogeneity on crack tip stress, electric displacement and magnetic induction intensity factors are studied. The results are considered to reveal the effect of material inhomogeneity and geometry of the crack on the field intensity factors.

Influence from front contact sheet resistance on extracted diode parameters in CIGS solar cells

AbstractThe extraction of one‐diode model parameters from a current–voltage (J–V) curve is problematic, since the model is one‐dimensional while real devices are indeed three‐dimensional. The parameters obtained by fitting the model curve to experimental data depend on how the current is collected, and more specifically the geometry of the contact. This is due to the non‐uniform lateral current flow in the window layers, which leads to different parts of the device experiencing different front contact voltage drop, and hence different operating points on the ideal J–V curve. In this work, finite element simulations of three‐dimensional contact structures are performed and compared to experimental data on Cu(In,Ga)Se2‐based solar cell devices. It is concluded that the lateral current flow can influence the extracted parameters from the one‐diode model significantly if the resistivity of the front contact material is high, or if there is no current collecting grid structure. These types of situations may appear in damp heat‐treated cells and module type cells, respectively. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk

This paper considers the bending of transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate, subject to a transverse load in the form of qr k ( k is zero or a finite even number). The differential equations satisfied by stress functions for the particular problem are derived. An elaborate analysis procedure is then presented to derive these stress functions, from which the analytical expressions for the axial force, bending moment and displacements are obtained through integration. The method is then applied to the problem of transversely isotropic functionally graded circular plate subject to a uniform load, illustrating the procedure to determine the integral constants from the boundary conditions. Analytical elasticity solutions are presented for simply-supported and clamped plates, and, when degenerated, they coincide with the available solutions for an isotropic homogenous plate. Two numerical examples are finally presented to show the effect of material inhomogeneity on the elastic field in FGM plates.

Linear buckling analysis of orthotropic inhomogeneous rectangular plates under uniform in-plane compression

A linear buckling analysis is carried out for orthotropic inhomogeneous rectangular plates under uniform in-plane compression. It is assumed that material inhomogeneities of Young's modulus and shear modulus of elasticity are continuously changed in the thickness direction with the power law of the coordinate variable, while Poisson's ratio is assumed to be constant. The buckling equation can be successfully constructed as the linearized von Karman plate model by introducing the newly defined position of the reference plane which enables us to easily deal with the problem. The critical buckling loads of the simply supported rectangular plate are presented using the derived fundamental relations. Effects of material inhomogeneity, material orthotropy, aspect ratio, width-to-thickness ratio and load ratio are discussed.

Pure bending of simply supported circular plate of transversely isotropic functionally graded material

This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogeneous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).