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In this paper, a simple approach is presented to determine the Muskhelishvili potential function in a generic quasi-static contact problem between two elastically similar half planes. As an example, this approach is applied to the symmetric indentation of a flat surface by a bi-quadratic punch to obtain the interior elastic stress field of the indented lower half plane  

The analytical formulation of the fully coupled and the uncoupled rolling contact mechanics problems for all possible stick/slip regimes are derived in Part I (Alinia et al., 2013). In this part, we focus on the numerical algorithm, the iteration procedure and the numerical results. The coupled and the uncoupled solutions corresponding to each of the assumed stick/slip regimes are provided. The uncoupled solution provides an acceptable approximation to the problem for small coefficient of friction values. However, for high values of the coefficient of friction the problem should be solved in fully coupled form. In addition, the effect of several parameters such as the stiffness ratio, the... 

In this study, the rolling contact problem of two elastically similar cylinders coated with functionally graded materials is investigated. The singular integral equations approach is utilized to extract the governing equations of the problem. The governing equations are discretized into systems of algebraic equations by virtue of the Gauss-Chebyshev integration method. Comprehensive parametric study is performed to examine the effects of mechanical properties, coating thickness and external loads on the surface stress components, stick/slip transition, creep ratio and power loss. This study aimed to emphasize the capability of graded materials in improving the rolling contact fatigue of... 

In this study, the tractive rolling contact problem between a rigid cylinder and a graded coating is investigated. The main objective of this study is to investigate the effect of the stiffness ratio, the coefficient of friction and the coating thickness on the surface contact tractions, the surface in-plane stress, the stick zone length and the creep ratio parameter that may have a bearing on the fatigue life of the component. Assuming that the shear modulus varies exponentially through the thickness of the coating, the governing integral equations associated with the rolling contact problem are constructed. Furthermore, it is supposed that the contact patch is controlled by a central stick... 

In this article, the sliding frictional contact problem for a half-plane which is graded in two dimensions is studied. The effect of medium properties gradient and coefficient of friction in contact mechanics of two dimensional (2D) graded materials which is loaded by a flat stamp have been investigated by developing two Finite Element (FE) models, in macro and micro scales. Discretizing the graded half-plane by quadrants for whose material properties are specified at the centroids by Mori-Tanaka method in both directions has been used to model the 2D FGM in macro scale. In micro scale, the ideal solid quadrant particles which are spatially distributed in a homogeneous matrix used to model... 

The two-dimensional contact problem for an elastic body indenting an elastically similar half plane resulting in double contacts is important for various applications. In this paper, a generic quasi-static two-dimensional symmetric double contact problem with nonsingular end points between two elastically similar half planes, under the constant normal and oscillatory tangential loading, is analyzed. The classical singular integral equations approach is utilized to extract the pressure and shear functions in the contact zones; subsequently boundary conditions at end points are applied and a new side condition is derived and titled "the consistency condition" for symmetric double contacts.... 

The thermoelastic rolling contact problem for an FGM-coated half plane under the plane strain deformation is studied in this paper. A rigid roller rolls over the surface of coating with constant translational velocity generating frictional heating in the slip zones of the contact patch. The material properties of the FGM vary exponentially along the thickness direction. It is assumed that the contact area consists of a central stick zone and two slip zones of the same sign. The transfer matrix method and Fourier integral transform technique are used to achieve a system of two Cauchy singular integral equations. The coupling effect of tangential traction is eliminated by adapting the... 

In this paper, we analyze a general quasi-static two-dimensional multiple contact problem between two elastically similar half-planes under the constant normal (including applied moments) and oscillatory tangential loading utilizing the classical singular integral equations approach. Boundary conditions at nonsingular edges of discrete contact zones are applied and new side conditions are extracted and named “the consistency conditions” for multiple contacts. These conditions are mandatory for determination of the positions of the nonsingular edges of the contact and stick zones, when the number of them exceeds the number of the discrete contact and stick zones, respectively. Consequently, a... 

The two-dimensional thermoelastic tractive rolling contact problem for a half-plane which is coated with a functionally graded material (FGM), under the plane strain deformation, is studied in this paper. A rigid cylinder rolls over the surface of an FGM coating with constant translational velocity, generating frictional heating in the slip zones of the contact area. Thermomechanical properties of the FGM vary exponentially along the thickness direction. It is assumed that the contact area consists of a central stick zone and two slip zones of the same sign. The transfer matrix method and Fourier integral transform technique are used to achieve a system of two Cauchy singular integral... 

Epoxy resins and their derivatives, such as composites and epoxy adhesives, are widely used in various industries. However, epoxy resins have low performance against dynamic loading and crack propagation. Graphene-based nanomaterials can improve the mechanical performance of polymeric composites because of their appropriate mechanical properties and high surface area. This study aimed to investigate the effect of Two-Dimensional Graphene Oxide (2DGO) and Three-Dimensional Nitrogen-Doped Graphene (3D(N)G) nanomaterials on the fatigue behavior of epoxy resin. 2DGO was produced by the modified Hummer's method and 3D(N)G was synthesised by hydrothermal process, followed by freeze-drying.... 

In this paper, a relation is introduced that simplifies the determination of the Muskhelishvilis potential function in plane contact problems. The relation is (z)=1/2[p(z)iq(z)], which is correct for all uncoupled-elastic contact problems. This relation is proved in a mathematical way and utilized to obtain the potential function in several contact problems. A complete agreement has been observed between our results and the potential functions that have been obtained from complicated methods in the past. Utilization of the relation simplifies the solution of contact problems and analytical calculation of the stress and displacement fields, which is helpful in the analytical studies of... 

Asymmetric contact problem of an elastic wedge and an elastic half-plane has been considered. Contact pressure distributions as well as the lengths of the contact zones are extracted analytically. The results have been compared with the results of the symmetric problem and also the FE modelling of the problem which show excellent agreement. The method of approach is a completely analytical method based on the singular integral equations. In this method, the boundary conditions of the problem are stated as some singular integrals and distribution of the contact pressure is determined. Then, with the aid of the equilibrium equations and the consistency conditions of the singular integral... 

The efficiency of fiber/matrix interface bonding in composites has an important influence on their overall performance. This article deals with the simulation of interface imperfection effect as it grows under fatigue loading. The relations have been derived based on the constituents' properties for the primary damage mode in unidirectional composites and boundary conditions defined for elements of the micromechanics model. Conformation of model stiffness predictions with the best described residual stiffness model indicates the way to find the remaining constants in the simulated relation. Finally through this relation, cyclic corrected stress components in constituents could be determined.... 

The overall mechanical properties of composite materials are dependent on the mechanical response of individual constituents and their interactions while they may be relatively easy to determine. This paper represents a simulation process by which the cyclic stresses and fatigue loadings on its constituents could be predicted for an under fatigue loading lamina. Hence, the unidirectional composites fatigue would be studied through its constituents. The proposed model introduces a new coupled stiffness/strength technique by relating lamina stiffness to the stress field in its constituents. Therefore, the stress field and strength considerations in its constituents could be studied when the... 

This research explored the corrosion effect of NaCl solution on the surface quality of AZ31 magnesium alloy. Cubic-shaped specimens were immersed in standard 3.5% NaCl solution for 1, 2, 3, and 4 hours. The size of corrosion pits, fatigue crack propagation area, and surface topology were characterized. Fatigue tests were carried out on pre-corroded AZ31 specimens under different stress amplitudes. The correlation between the corrosion time and the virtual crack size was obtained. The virtual crack size is a new parameter that can relate the corrosion to the fatigue life. A new model was proposed to map the surface topology on the virtual crack size of pre-corroded AZ31 magnesium alloy. The... 

Prediction of the creep behavior of metal matrix whiskers reinforced composites is the subject of many analytical and experimental research works. However, application of the FEM modeling to this area has not been so successful. The present research work highlights the shortcomings of the previous FEM studies and combines the analytical findings with the power of FEM modeling. More specifically, the fiber/matrix debonding parameter ξ is incorporated into the modeling. In contrary to the analytical results, it is shown that the value of ξ could only change in the range of zero to 0.5. The results indicate that the exponential creep law along with the modified ξ-σ relationship, and the newly... 

Road roughness-induced vibrations are the main source of fatigue damage accumulation in vehicles. Hence, road surface profile modeling and simulation are of high importance when it comes to vehicle fatigue damage assessment. This research focuses on uncovering the statistical distributions that describe the characteristics of road loads that affect fatigue damage accumulation. Particle filtering is deployed to estimate the log-volatility of the road surface profile by assuming a random walk behavior for the hidden log-volatility. The skew-normal distribution with three parameters is fitted to the estimated log-volatility. The inferred parameters are used for synthesizing artificial road... 

This research explored the corrosion effect of NaCl solution on the surface quality of AZ31 magnesium alloy. Cubic-shaped specimens were immersed in standard 3.5% NaCl solution for 1, 2, 3, and 4 hours. The size of corrosion pits, fatigue crack propagation area, and surface topology were characterized. Fatigue tests were carried out on pre-corroded AZ31 specimens under different stress amplitudes. The correlation between the corrosion time and the virtual crack size was obtained. The virtual crack size is a new parameter that can relate the corrosion to the fatigue life. A new model was proposed to map the surface topology on the virtual crack size of pre-corroded AZ31 magnesium alloy. The... 

This paper investigates the subsurface stress field induced by a rigid cylinder rolling over a functionally graded coating-substrate system. The Fourier transform is employed to extract the stress components within the graded coating and the homogeneous substrate. The distributions of the stresses are given through the depth and along the coating-substrate interface. The contour plots of normalized Von Mises stresses are provided as well. The results indicate that continuous variation of the shear modulus substantially reduces the difference between the in-plane stresses along the interface. Also, the softening coating leads to the minimum value of the stress concentration near the contact... 

In this paper, the fully coupled rolling contact problem of a graded coating/substrate system under the action of a rigid cylinder is investigated. Using the singular integral equation approach, the governing equations of the rolling contact problem are constructed for all possible stick/slip regimes. Applying the Gauss-Chebyshev numerical integration method, the governing equations are converted to systems of algebraic equations. A new numerical algorithm is proposed to solve these systems of equations. Both the coupled and the uncoupled solutions to the problem are found through an implemented iterative procedure. In Part I of this paper, the analytical formulation of the rolling contact...