Interaction of a screw dislocation in the interphase layer with the inclusion and matrix

The interaction of a screw dislocation in the interphase layer with the circular inhomogeneity and matrix was dealt with . An efficient method for multiply connected regions was developed by combining the sectionally subholomorphic function theory, Schwatz symmetric principle and Cauchy integral technique. The Hilbert problem of the complex potentials for three material regions was reduced to a functional equation in the complex potential of the interphase layer, resulting in an explicit series solution . By using the present solution the interaction energy and force acting dislocation were evaluated and discussed.     

Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper at mesoscale

Constitutive laws are critical in the investigation of mechanical behavior of single crystal or polycrystalline materials in applications spanning from microscale to macroscale. In this investigation, a combined FEM simulation and experimental nanoindentation approach was taken to determine the mechanical behavior of single crystal copper incorporating the mesoplastic constitutive model. This model was implemented in a user-defined subroutine in 3D ABAQUS/Explicit code. Nanoindentation was modeled using the multiscale modeling technique involving mesoplasticity and elasticity, i.e., mesoplastic constitutive model was used near the local nanoindentation region (where the dislocations are generated) while elastic constitutive model was used in rest of the region in the workmaterial. The meso-mechanical behavior of the crystalline structure and the effect of the mesoplastic parameters on the nanoindentation load-displacement relationships were investigated in the FEM analysis. Nanoindentation tests were conducted on single crystal copper to determine load-displacement relationships. Appropriate mesoplastic parameters were determined by fitting the simulated load-displacement curves to the experimental data. The mesoplastic model, with appropriate parameters, was then used to determine the stress-strain relationship of a single crystal copper at meso-scale. The effect of indenter radius (3.4-) on material hardness under nanoindentation was simulated and found to match the experimental data for several indenter radii (3.4, 10 and ). A comparison of the topographies of nanoindentation impressions in the experiments with FEM results showed a reasonably good agreement.     

A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface

The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method. The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4 π rule. The solid angle for the open surface is treated in direct method based on its definition. Several kinds of configurations for the bubbles and free surface have been investigated. The pressure contours during the evolution of bubbles are obtained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface. The bubble dynamics and their interactions have close relation with the standoff distances, buoyancy parameters and initial sizes of bubbles. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under different parameters can be observed in our model, as demonstrated in our calculation results.     

A viscoplastic study of crack-tip deformation and crack growth in a nickel-based superalloy at elevated temperature

Viscoplastic crack-tip deformation behaviour in a nickel-based superalloy at elevated temperature has been studied for both stationary and growing cracks in a compact tension (CT) specimen using the finite element method. The material behaviour was described by a unified viscoplastic constitutive model with non-linear kinematic and isotropic hardening rules, and implemented in the finite element software ABAQUS via a user-defined material subroutine (UMAT). Finite element analyses for stationary cracks showed distinctive strain ratchetting behaviour near the crack tip at selected load ratios, leading to progressive accumulation of tensile strain normal to the crack-growth plane. Results also showed that low frequencies and superimposed hold periods at peak loads significantly enhanced strain accumulation at crack tip. Finite element simulation of crack growth was carried out under a constant ΔK-controlled loading condition, again ratchetting was observed ahead of the crack tip, similar to that for stationary cracks.A crack-growth criterion based on strain accumulation is proposed where a crack is assumed to grow when the accumulated strain ahead of the crack tip reaches a critical value over a characteristic distance. The criterion has been utilized in the prediction of crack-growth rates in a CT specimen at selected loading ranges, frequencies and dwell periods, and the predictions were compared with the experimental results.     

A computationally efficient solution of the wave equation for the transient response of infinite reservoirs

In this paper, the transient response of an infinite reservoir is analyzed using the dual-reciprocity boundary element method. A vertical and an inclined-face rigid dam are analyzed under a transient loading. Sharan-type boundary-condition transmission is implemented in the formulation. The results are compared with the exact solution and those obtained by using the finite element method. It is seen that the application of the dual-reciprocity boundary element method is simpler and the results are in very good agreement with the exact solution and those obtained by using the finite element method.     

Cohesive zone laws for fatigue crack growth: Numerical field projection of the micromechanical damage process in an elasto-plastic medium

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loading, but the model parameters are phenomenological and are not closely tied to the underlying micromechanics of the problem. In this paper, we will inversely extract the cohesive zone laws for fatigue crack growth in an elasto-plastic ductile solid using a field projection method (FPM), which projects the equivalent tractions and separations at the cohesive crack-tip from field information outside the process zone. In our small-scale yielding model, a single row of discrete voids is deployed directly ahead of a crack in an elasto-plastic medium subjected to cyclic mode I K-field loading. Damage accumulation under cyclic loading is captured by the growth of voids within the micro-voiding zone ahead of the crack, while the evolution of the cohesive zone law representing the micro-voiding zone is inversely extracted via the FPM. We show that the field-projected cohesive zone law captures the essential micromechanisms of fatigue crack growth in the ductile medium: from loading and unloading hysteresis caused by void growth and plastic hardening, to the softening damage locus associated with crack propagation via a void by void growth mechanism. The results demonstrate the effectiveness of the FPM in obtaining a micromechanics-based cohesive zone law in-place of phenomenological models, which opens the way for a unified treatment of fatigue crack problems.     

A 3D finite element method for the simulation of thermoconvective flows and its performances on a vector-parallel computer

A three-dimensional finite element method for the simulation of thermoconvective flows is presented. Vector-parallel performances of some preconditioned conjugate gradient methods are compared for solving both large linear systems and the Stokes problem. As significant examples, numerical experiments on the steady two- and three-dimensional Rayleigh-Bénard convection at high Prandtl number are reported.     

Surface tension-driven shape-recovery of micro/nanometer-scale surface features in a Pt57.5Ni5.3Cu14.7P22.5 metallic glass in the supercooled liquid region: A numerical modeling capability

Recent experiments in the literature show that micro/nano-scale features imprinted in a Pt-based metallic glass, Pt_57.5Ni_5.3Cu_14.7P_22.5, using thermoplastic forming at a temperature above its glass transition temperature, may be erased by subsequent annealing at a slightly higher temperature in the supercooled liquid region (Kumar and Schroers, 2008). The mechanism of shape-recovery is believed to be surface tension-driven viscous flow of the metallic glass. We have developed an elastic-viscoplastic constitutive theory for metallic glasses in the supercooled liquid temperature range at low strain rates, and we have used existing experimental data in the literature for Pt_57.5Ni_5.3Cu_14.7P_22.5 (Harmon et al., 2007) to estimate the material parameters appearing in our constitutive equations. We have implemented our constitutive model for the bulk response of the glass in a finite element program, and we have also developed a numerical scheme for calculating surface curvatures and incorporating surface tension effects in finite element simulations. By carrying out full three-dimensional finite-element simulations of the shape-recovery experiments of Kumar and Schroers (2008), and using the independently determined material parameters for the bulk glass, we estimate the surface tension of Pt_57.5Ni_5.3Cu_14.7P_22.5 at the temperature at which the shape-recovery experiments were conducted. Finally, with the material parameters for the underlying elastic-viscoplastic bulk response as well as a value for the surface tension of the Pt-based metallic glass fixed, we validate our simulation capability by comparing predictions from our numerical simulations of shape-recovery experiments of Berkovich nanoindents, against corresponding recent experimental results of Packard et al. (2009) who reported shape-recovery data of nanoindents on the same Pt-based metallic glass.     

A finite element method for analysis of fluid flow,heat transfer and free interfaces in Czochralski crystal growth

A finite element algorithm is presented for simultaneous calculation of the steady state, axisymmetric flows and the crystal, melt/crystal and melt/ambient interface shapes in the Czochralski technique for crystal growth from the melt. The analysis is based on mixed Lagrangian finite element approximations to the velocity, temperature and pressure fields and isoparametric approximations to the interface shape. Galerkin's method is used to reduce the problem to a non-linear algebraic set, which is solved by Newton's method. Sample solutions are reported for the thermophysical properties appropriate for silicon, a low-Prandtl-number semiconductor, and for GGG, a high–Prandtl–number oxide material. The algorithm is capable of computing solutions for both materials at realistic values of the Grashof number, and the calculations are convergent with mesh refinement. Flow transitions and interface shapes are calculated as a function of increasing flow intensity and compared for the two material systems. The flow pattern near the melt/gas/crystal tri-junction has the asymptotic form predicted by an inertialess analysis assuming the meniscus and solidification interfaces are fixed.     

A spectral projection method for the analysis of autocorrelation functions and projection errors in discrete particle simulation

Discrete particle simulation is a well‐established tool for the simulation of particles and droplets suspended in turbulent flows of academic and industrial applications. The study of some properties such as the preferential concentration of inertial particles in regions of high shear and low vorticity requires the computation of autocorrelation functions. This can be a tedious task as the discrete point particles need to be projected in some manner to obtain the continuous autocorrelation functions. Projection of particle properties on to a computational grid, for instance, the grid of the carrier phase, is furthermore an issue when quantities such as particle concentrations are to be computed or source terms between the carrier phase and the particles are exchanged. The errors committed by commonly used projection methods are often unknown and are difficult to analyse. Grid and sampling size limit the possibilities in terms of precision per computational cost. Here, we present a spectral projection method that is not affected by sampling issues and addresses all of the above issues. The technique is only limited by computational resources and is easy to parallelize. The only visible drawback is the limitation to simple geometries and therefore limited to academic applications. The spectral projection method consists of a discrete Fourier‐transform of the particle locations. The Fourier‐transformed particle number density and momentum fields can then be used to compute the autocorrelation functions and the continuous physical space fields for the evaluation of the projection methods error. The number of Fourier components used to discretize the projector kernel can be chosen such that the corresponding characteristic length scale is as small as needed. This allows to study the phenomena of particle motion, for example, in a region of preferential concentration that may be smaller than the cell size of the carrier phase grid. The precision of the spectral projection method depends, therefore, only on the number of Fourier modes considered. Copyright © 2008 John Wiley & Sons, Ltd.     

Stress state in the vicinity of an inclined elliptical defect and stress intensity factors for biaxial loading of a plate

The problem of determining the stress state of a plate with an inclined elliptical notch under biaxial loading is considered. The Kolosov-Muskhelishvili method is used to obtain an expression for the stress near the vertex of an inclined ellipse, whose particular case are expressions for the stress in the case of an inclined crack. The stress intensity factors K _I and K _II were determined experimentally by holographic interferometry in the case of extension of a plate with an inclined crack-like defect. The calculation results are compared with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 118–127, January–February, 2009.     

岩石断裂韧度试样CCNBD临界应力强度因子的全新数值标定

国际岩石力学学会（ISRM）提出的用人字型切槽巴西圆盘（Cracked Chevron Notched Brazilian Disc—CCNBD）测试岩石I型断裂韧度所必需的量纲为一的临界应力强度因子Y＊min的精度需要进一步改进。本文对CCNBD试样的Y＊min进行了系统的重新标定,CCNBD的几何参数有效范围为0.44≤αB≤1.04、0≤α0≤0.69、0.4≤α1≤0.8。采用有限单元法对CCNBD做三维数值分析,得到了435种CCNBD试样的Y＊min值标定结果;在此基础上全面修正了CCNBD试样Y＊min计算公式中u和v的取值表;给出了不用查表直接确定CCNBD试样Y＊min值的近似表达式,该表达式计算结果与标定结果的相对误差绝对值在1.87%以内。对于ISRM建议的CCNBD标准试样的Y＊min值：ISRM标定值0.84比本文结果0.957小12.2%;分片合成法标定值0.947比本文结果小1.0%;子模型法标定值0.943比本文结果小1.5%。本文特别强调了任何CCNBD试样Y＊min的取值必须在它对应的上限和下限所限定的范围内,这一要求对判断Y＊min标定值是否合理是很重要的。     

Adaptive finite elements for the steady free fall of a body in a Newtonian fluid

The numerical simulation of the free fall of a solid body in a viscous fluid is a challenging task since it requires computational domains which usually need to be several order of magnitude larger than the solid body in order to avoid the influence of artificial boundaries. Toward an optimal mesh design in that context, we propose a method based on the weighted a posteriori error estimation of the finite element approximation of the fluid/body motion. A key ingredient for the proposed approach is the reformulation of the conservation and kinetic equations in the solid frame as well as the implicit treatment of the hydrodynamic forces and torque acting on the solid body in the weak formulation. Information given by the solution of an adequate dual problem allows one to control the discretization error of given functionals. The analysis encompasses the control of the free fall velocity, the orientation of the body, the hydrodynamic force and torque on the body. Numerical experiments for the two dimensional sedimentation problem validate the method. To cite this article: V. Heuveline, C. R. Mecanique 333 (2005).