Xiaoqing Jin

Fatigue initiation and propagation behavior in bulk-metallic glasses under a bending load

Understanding how to predict the fatigue lifetimes of bulk-metallic glass (BMG) materials is crucially important for their selection as structural alloys. In our paper, the nature of likely fatigue mechanisms for BMGs is revealed. Fatigue cracks, arising from machining/polishing damage, were experimentally observed to initiate from shear bands near defects. At the crack tip, a plastic-zone creation is observed through the formation of many shear bands, and the fatigue crack is found to propagate along these shear bands. The size of the plastic zone can be characterized by fracture-mechanics quantities, and each fatigue cycle is seen to produce a fine striation instead of a single coarse one. We propose a shear-band mechanism to explain the characteristics of the observed fatigue cracking. Numerical computations, based on linear-elastic-fracture mechanics, yield reasonably good agreement with experiments. Our findings are significant to predict the fatigue lifetimes of these materials.

An Efficient Numerical Method With a Parallel Computational Strategy for Solving Arbitrarily Shaped Inclusions in Elastoplastic Contact Problems

The plastic zone developed during elastoplastic contact may be effectively modeled as an inclusion in an isotropic half space. This paper proposes a simple but efficient computational method to analyze the stresses caused by near surface inclusions of arbitrary shape. The solution starts by solving a corresponding full space inclusion problem and proceeds to annul the stresses acting normal and tangential to the surface, where the numerical computations are processed by taking advantage of the fast Fourier transform techniques with a parallel computing strategy. The extreme case of a cuboidal inclusion with one facet on the surface of the half space is chosen to validate the method. When the surface truncation domain is extended sufficiently and the grids are dense enough, the results based on the new approach are in good agreement with the exact solutions. When solving a typical elastoplastic contact problem, the present analysis is roughly two times faster than the image inclusion approach and six times faster than the direct method. In addition, the present work demonstrates that a significant enhancement in the computational efficiency can be achieved through the introduction of parallel computation.

Novel Model for Partial-Slip Contact Involving a Material With Inhomogeneity

Contacts involving partial slip are commonly found at the interfaces formed by mechanical components. However, most theoretical investigations of partial slip are limited to homogeneous materials. This work proposes a novel and fast method for partial-slip contact involving a material with an inhomogeneity based on the equivalent inclusion method, where the inhomogeneity is replaced by an inclusion with properly chosen eigenstrains. The stress and displacement fields due to eigenstrains are formulated based on the half-space inclusion solutions recently derived by the authors and solved with a three-dimensional fast Fourier transform algorithm. The effectiveness and accuracy of the proposed method is demonstrated by comparing its solutions with those from the finite element method. The partial slip contact between an elastic ball and an elastic half space containing a cuboidal inhomogeneity is further investigated. A number of in-depth parametric studies are performed for the cuboidal inhomogeneity with different sizes and at different locations. The results reveal that the contact behavior of the inhomogeneous material is more strongly influenced by the inhomogeneity when it is closer to the contact center and when its size is larger.

A 3D EHL Simulation of CMP Theoretical Framework of Modeling

The extensive application of chemical mechanical polishing (CMP) in the semiconductor industry requires an understanding of the fundamental mechanisms involved. This paper integrates a group of mechanical models to give a framework for CMP modeling: a mixed three-dimensional (3D) soft elastohydrodynamic lubrication (EHL) model with asperity contact considered. The soft-pad mechanics, asperity-contact analysis, and slurry film description are three major components of this framework. Based on the results of a thin-layer contact analysis, the Winkler foundation model is selected to evaluate the pad deformation in bulk. By applying the macro-micro approach, the macroscopic view of the average fluid film thickness (average clearance) is related to microasperity contact. When CMP is implemented in a mixed lubrication regime, the soft polishing pad usually undergoes a displacement of the same scale as the slurry film, which may change the lubrication boundary considerably. Considering this effect, a modified Reynolds equation is derived, and a stronger coupling is found in the global force and moment balances. Finally, an effective iterative scheme is proposed and modeling results examined.

A Numerical Approach for Analyzing Three-Dimensional Steady-State Rolling Contact Including Creep Using a Fast Semi-Analytical Method

This article presents a new rolling contact solver using a semi-analytical method (SAM) to analyze three-dimensional steady-state rolling contacts, including the effects of creep. This new solver includes both the normal and tangential contact issues for the pressure and shear tractions, respectively. The accuracy and efficiency of the present method are demonstrated by comparison to existing analytical and numerical solutions. Rolling contact problems for a smooth infinite roller pressed against a half space with either a single asperity or a sinusoidal wave are investigated. The results show the complexity of pressure and shear traction. Asperities produce higher localized pressures, which demand larger local shear tractions to produce slip in such regions. Stick regions are also observed at the trailing edge of the contact.

A Comparative Study of Modeling the Magnetostatic Field in a Current-Carrying Plate Containing an Elliptic Hole

The presence of crack-like defects can cause an uneven distribution of the electric current density in a cracked conductor. To investigate the perturbation of the magnetic field resulting from the disturbed electric current, computational modeling of the magnetostatics is attempted on an infinite conductive plate, which contains an elliptic hole and is subjected to uniform current flow at infinity. Both 2-D and 3-D analyses are considered in this study. The 2-D analysis requires certain crucial assumptions and the governing Maxwells equations are solved analytically in elliptic coordinates. The 3-D numerical computation is based on superposition of the elementary solution, whose derivation utilizes the Biot-Savart law. To improve the efficiency of the 3-D calculation, an adaptive mesh refinement algorithm is implemented in the numerical discretization. Finally, through a comparative study, the validity of the introduced simplifications in the 2-D analysis is benchmarked with the 3-D computational results. The present study shows that the 2-D solution predicts the upper bound for the out-of-plane component of the magnetic field perturbed by the elliptical hole, whose semi-major axis does not exceed ten times the thickness of the plate.

Note on the fft based computational code and its application

The discrete convolution based Fast Fourier Transform algorithm (DC-FFT) has been successfully applied in numerical simulation of contact problems. The algorithm is revisited from a mathematical point of view, equivalent to a Toeplitz matrix multiplied by a vector. The nature of the convolution property permits one to implement the algorithm with fewer constraints in choosing the computational domains. This advantageous feature is explored in the present work, and is expected to be beneficial to many tribological studies.Copyright

Analytical Solution for the Stress Field of Eshelby’s Inclusion of Polygonal Shape

Recently, we developed a closed-form solution to the stress field due to a point eigenstrain in an elastic full plane. This solution can be employed as a Green’s function to compute the stress field caused by an arbitrary-shaped Eshelby’s inclusion subjected to any distributed eigenstrain. In this study, analytical expressions are derived when uniform eigenstrain is distributed in a planar inclusion bounded by line elements. Here it is demonstrated that both the interior and exterior stress fields of a polygonal inclusion subjected to uniform eigenstrain can be represented in a unified expression, which consists of only elementary functions. Singular stress components are identified at all the vertices of the polygon. These distinctive properties contrast to the well-known Eshelby’s solution for an elliptical inclusion, where the interior stress field is uniform but the formulae for the exterior field are remarkably complicated. The elementary solution of a polygonal inclusion has valuable application in the numerical implementation of the equivalent inclusion method.Copyright

A closed-form solution for the horizontally aligned thermal-porous spheroidal inclusion in a half-space and its applications in geothermal reservoirs

Abstract The inclusion model for pore pressure and near surface localized heating may be of practical importance to many geological applications including geothermal reservoirs and volcanoes. In literature, the axisymmetric inclusion problems considering vertically placed spheroidal inclusions have been examined, while the complementary problems concerning horizontal spheroidal inclusion have not drawn much attention. The latter lacks axial symmetry, and usually cannot be handled by the analytical methods developed for the symmetric case. The current work analytically explores this asymmetric problem of thermo-porous spheroidal inclusion with the assistance of geometric interpretation. The complete solution to the displacement, strain and stress is formulated in Cartesian coordinates for ease of engineering applications. The formulae are derived in compact closed-form expressions in terms of elementary functions, which are handy for analytical manipulations and computer programming. Furthermore, applications in geostructures are discussed, and benchmark examples are provided to validate the present solution.

Numerical Modeling of Partial Slip Contact Involving Inhomogeneous Materials

When solving the problems involving inhomogeneous materials, the influence of the inhomogeneity upon contact behavior should be properly considered. This research proposes a fast and novel method, based on the equivalent inclusion method where inhomogeneity is replaced by an inclusion with properly chosen eigenstrains, to simulate contact partial slip of the interface involving inhomogeneous materials. The total stress and displacement fields represent the superposition of homogeneous solutions and perturbed solutions due to the chosen eigenstrains. In the present numerical simulation, the half space is meshed into a number of cuboids of the same size, where each cuboid is has a uniform eigenstrain. The stress and displacement fields due to eigenstrains are formulated by employing the recent half-space inclusion solutions derived by the authors and solved using a three-dimensional fast Fourier transform algorithm. The partial slip contact between an elastic ball and an elastic half space containing a cuboidal inhomogeneity was investigated.Copyright