Effect Of Material Nonhomogeneity Research Articles

Numerical analysis of frictional contact in the presence of a surface crack in a functionally graded coating substrate system

In this paper, the frictional two-dimensional contact in the presence of a surface crack in a functionally graded coating substrate system is studied for rigid circular and flat stamps. A computational method based on finite difference (FD) is developed to evaluate the contact stresses and also the fracture parameters, which are KI and KII due to mixed mode fracture. The FD method applied here, uses a mapping technique which enable the analysis to consider any geometry of the punch and the crack. The Coulomb's dry friction law is considered in the contact area. The advantage of this study, compared to the efforts done by other researchers, is the ability to analysis a system with any arbitrary material properties distribution. Here, the elastic material properties distribution is estimated by TTO model which takes into account the interaction between the constituting phases as well, and the Poisson's ratio is assumed to be constant. The effect of material nonhomogeneity, the interaction of the constituting phases, the thickness of the graded coating layer, the size of the punch and the coefficient of friction is studied. In a general case, the findings of this research show that increasing the size of the punch, the coefficient of friction and the thickness of the graded layer increase the contact force and hence the contact stress; however, the interaction of the constituting phases does not have any effects on the contact parameters. In frictionless contact, the stress intensity factor is negative. In addition, increasing the coefficient of friction increases KI but decreases KII. These results are valid for any materials properties distribution.

Probabilistic model of fatigue crack propagation and estimation of probability-confidence bounded a–N curves

ABSTRACTThe fatigue crack growth model is expressed as a function of mechanical properties. The uncertainties associated with the crack growth process are incorporated assuming them as random variable following a statistical distribution. The effect of material nonhomogeneity is included in the model through a random process parameter of Gaussian type. Assuming fatigue life as a random variable, probability-confidence bounded mean crack growth relation is developed and an algorithm is presented. The model is validated through the experimental and predicted results from several data sets.

Analysis of a propagating crack tip in orthotropic functionally graded materials

Crack tip stress and displacement fields for a propagating crack at constant velocity along a gradient in orthotropic functionally graded materials (OFGMs) with an exponential variation of the shear modulus and density are developed. The crack tip fields are obtained by using wave potentials and the Airy stress function through an asymptotic analysis. Solutions are obtained for orthotropic characteristics of two kinds. Using the stress fields, the effects of material nonhomogeneity on the stress components are investigated. In addition, contours of the constant maximum shear stress at a propagating crack tip are generated and the effects of material nonhomogeneity on the isochromatics are discussed.

Mode III stress intensity factor in two-dimensional functionally graded material with lengthwise linearly varying properties

Mode III fracture is considered in a two-dimensional functionally graded material with an internal crack. The material properties are assumed to vary linearly along two planar directions. The problem has been analyzed via two different methods. Primarily, the governing partial differential equations are derived, and using the method of separating variables and Hankel transforms, the equations are solved. Then, finite element technique is employed to analyze the problem. The effects of material non-homogeneity on the value of stress intensity factor are studied. Finally, the obtained stress intensity factors, calculated by two different methods, are compared.

Effect of material nonhomogeneity on the mechanical behaviors of a thick-walled functionally graded sandwich cylindrical structure

In this investigation, the effect of material nonhomogeneity on the mechanical behaviors of a thick-walled sandwich cylindrical structure embedded with a functionally graded (FG) interlayer is investigated. The inner of the sandwich cylindrical structure is a homogeneous and isotropic layer. The outer is a homogeneous and orthotropic layer and the middle is a transition layer. A three-parameter model is presented to model the transitional form of the FG interlayer. The laminate approach method is employed to tackle the material nonhomogeneity. The analytical solutions are obtained by employing the initial parameter method. Numerical results show that the material nonhomogeneity plays important roles on the mechanical behaviors of a sandwich cylindrical structure.

The Role of Nonuniformity in Convective Heat and Mass Transfer through Porous Media, Part 1

Through-air drying is commonly used in the drying of high-quality tissue and towel products. A representative elementary volume method was used to model the fluid flow and heat and mass transfer during through drying in heterogeneous porous biobased materials such as tissue and towel products. Results of flow both upstream and downstream of a modeled porous sheet allowed visualization of the effects of mixing at the top and bottom of the porous medium. The effect of initial nonuniformity on fluid flow and convective heat and mass transfer in heterogeneous porous media was studied. The effect of material nonhomogeneity and associated transport properties on moisture content of the porous material as a function of drying time was studied. Modeling results indicate that for the first time it is possible to simulate the effect of nonuniformity on fluid flow and convective heat and mass transfer in porous media during through-air drying of paper. Moisture and structural nonuniformity contributing to nonuniformity in air flow might contribute significantly to drying nonuniformity. Depending on the moisture regimes and degree of saturation of the convective medium, heat and mass transfer coefficients may have varying effects on the overall drying.

Geometrically Induced Stress Singularities of a Thick FGM Plate Based on the Third-Order Shear Deformation Theory

Asymptotic solutions for a functionally graded material (FGM) plate are developed to elucidate stress singularities at a plate corner, using a third-order shear deformation theory. The characteristic equations are given explicitly for determining the order of stress singularity at the vertex of a corner with two radial edges having various boundary conditions. The non-homogeneous elasticity properties are present only in the characteristic equations for a corner with one of its two edges simply supported. The effects of material non-homogeneity on the stress singularities are extensively examined. The present results are very useful for developing accurate numerical solutions for an FGM plate under static or dynamic loading when the plate involves stress singularities, such as a V-notch or crack.

Stresses in FGM pressure tubes under non-uniform temperature distribution

The effects of material nonhomogeneity and nonisothermal conditions on the stress response of pressurized tubes are assessed by virtue of a computational model. The modulus of elasticity, the Poisson's ratio, the yield strength, and the coefficient of thermal expansion, are assumed to vary nonlinearly in the tube. A logarithmic temperature distribution within the tube is proposed. Under these conditions, it is shown that the stress states and the magnitudes of response variables are affected significantly by both the material nonhomogeneity and the existence of the radial temperature gradient.

Torsional impact response of a penny-shaped crack in a functional graded strip

The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived. And it is shown that, as crack driving force, they are equivalent for the present crack problem. Investigated are the effects of material nonhomogeneity and strip's highness on the dynamic fracture behavior. Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus, and that the dynamic behavior varies little with the adjusting of the strip's highness.

Dynamic stress field for torsional impact of a penny-shaped crack in a transversely isotropic functional graded strip

The torsional impact response of a penny-shaped crack in a transversely isotropic strip is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Investigated are the effects of material nonhomogeneity and orthotropy and strip’s highness on the dynamic stress intensity factor. The peak of the dynamic stress intensity factor can be suppressed by increasing the shear moduli’s gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface. The dynamic behavior varies little with the increasing of the strip’s highness.

Effect of material nonhomogeneity on stress distribution in the vicinity of a thin elastic inclusion

A problem of a matrix of exponentially nonhomogeneous material has been discussed in a case a thin elastic inclusion of a similar type of nonhomogeneity. A stress function for elastic solids of exponential non-homogeneity varying with x and y has been derived.

Effect of material nonhomogeneity on crack propagation characteristics

The influence of material nonhomogeneity on the behavior of a moving crack is investigated. The model assumes a running crack in a material whose elastic properties may differ from those of the surrounding material. Theoretical calculations showed that the energy stored in elements ahead of the crack can be raised or lowered depending on the crack velocity, the crack length and the degree of material nonhomogeneity which is associated with the ratio of the shear moduli and the distance between the crack and the neighboring material with different elastic properties. Based on the strain energy density theory, predictions are made on how material nonhomogeneity can influence the initiation and/or arrest characteristics of cracks.