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The interaction of dislocations and hydrogen-vacancy complexes and its importance for deformation-induced proto nano-voids formation in α-Fe

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 74卷 175-191页

作者： Li, Suzhi Li, Yonggang Lo, Yu-Chieh Neeraj, Thirumalai Srinivasan, Rajagopalan Ding, Xiangdong Sun, Jun Qi, Liang Gumbsch, Peter Li, Ju Xi An Jiao Tong Univ State Key Lab Mech Behav Mat Xian 710049 Peoples R China Xi An Jiao Tong Univ Frontier Inst Sci & Technol Xian 710049 Peoples R China MIT Dept Nucl Sci & Engn Cambridge MA 02139 USA MIT Dept Mat Sci & Engn Cambridge MA 02139 USA Karlsruhe Inst Technol Inst Appl Mat D-76131 Karlsruhe Germany Chinese Acad Sci Inst Solid State Phys Key Lab Mat Phys Hefei 230031 Peoples R China ExxonMobil Res & Engn Co Corp Strateg Res Annandale NJ 08801 USA Fraunhofer Inst Werkstoffmech IWM D-79108 Freiburg Germany

By using molecular dynamics and cluster dynamics simulations, we probed the role of hydrogen-vacancy complexes on nucleation and growth of proto nano-voids upon dislocation plasticity in alpha-Fe. Our atomistic simulations reveal that, unlike a lattice vacancy, a hydrogen-vacancy complex is not absorbed by dislocations sweeping through the lattice. Additionally, this complex has lower lattice diffusivity;therefore, it has a lower probability of encountering and being absorbed by various lattice sinks. Hence, it can exist metastably for a rather long time. Our large-scale molecular dynamics simulations show that when metals undergo plastic deformation in the presence of hydrogen at low homologous temperatures, the mechanically driven out-of-equilibrium dislocation processes can produce extremely high concentrations of hydrogen-vacancy complex (10(-5) similar to 10(-3)). Under such high concentrations, these complexes prefer to grow by absorbing additional vacancies and act as the embryos for the formation of proto nano-voids. The current work provides one possible route for the experimentally observed nano-void formation in hydrogen embrittlement of steels and bridges atomic-scale events and damage with macroscopic failure. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Fracture mechanisms Crystal plasticity Corrosion and embrittlement numerical algorithms

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Disorder is good for you: the influence of local disorder on strain localization and ductility of strain softening materials

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INTERNATIONAL JOURNAL OF FRACTURE 2017年第2期205卷 139-150页

作者： Tuzes, Daniel Ispanovity, Peter Dusan Zaiser, Michael Eotvos Lorand Univ Dept Mat Phys Pazmany Peter Setany 1-A H-1117 Budapest Hungary Friedrich Alexander Univ Inst Mat Simulat WW8 Dr Mack Str 77 D-90762 Furth Germany

We formulate a generic concept model for the deformation of a locally disordered, macroscopically homogeneous material which undergoes irreversible strain softening during plastic deformation. We investigate the influence of the degree of microstructural heterogeneity and disorder on strain localization (formation of a macroscopic shear band) in such materials. It is shown that increased microstructural heterogeneity delays strain localization and leads to an increase of the plastic regime in the macroscopic stress-strain curves. The evolving strain localization patterns are characterized.

关键词： Fracture Microstructures Inhomogeneous material numerical algorithms Probability and statistics

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Efficient Scalable Parallel Higher Order Direct MoM-SIE Method With Hierarchically Semiseparable Structures for 3-D Scattering

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2017年第5期65卷 2467-2478页

作者： Manic, Ana B. Smull, Aaron P. Rouet, Francois-Henry Li, Xiaoye Sherry Notaros, Branislav M. Colorado State Univ Dept Elect & Comp Engn Ft Collins CO 80523 USA Lawrence Berkeley Natl Lab Computat Res Div Berkeley CA 94720 USA

A novel fast scalable parallel algorithm is proposed for the solution of large 3-D scattering problems based on: 1) the double (geometrical and current-approximation) higher order (DHO) method of moments (MoM) in the surface integral equation (SIE) formulation and 2) a direct solver for dense linear systems utilizing hierarchically semiseparable (HSS) structures. Namely, an HSS matrix representation is used for compression, factorization, and solution of the system matrix. In addition, a rank-revealing QR decomposition for memory compression is used, with a stopping criterion in terms of the relative rank tolerance value. A method for geometrical preprocessing of the scatterers based on the cobblestone distance sorting technique is employed in order to enhance the HSS algorithm accuracy and parallelization. numerical examples show how the accuracy of the DHO HSS-MoM-SIE method is easily controllable by using the relative tolerance for the matrix compression. Moreover, the examples demonstrate low memory consumption, as well as much faster simulation time, when compared to the direct LU decomposition. The method enables dramatically faster monostatic scattering computations than iterative solvers and reduced number of unknowns when compared to low-order discretizations. Finally, great scalability of the algorithm is demonstrated on more than one thousand processes.

关键词： Curved parametric elements direct solvers fast solvers hierarchically semiseparable (HSS) structures higher order (HO) modeling low-rank matrix approximation method of moments (MoM) multilevel matrix compression numerical algorithms parallelization polynomial basis functions scalability scattering surface integral equation (SIE)

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On the energy conservation during the active deformation in molecular dynamics simulations

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2015年 77卷 146-157页

作者： Yang, Fan Zhong, Zheng Tongji Univ Sch Aerosp Engn & Appl Mech Shanghai 200092 Peoples R China

In this paper, we examined the energy conservation for the current schemes of applying active deformation in molecular dynamics (MD) simulations. Specifically, two methods are examined. One is scaling the dimension of the simulation box and the atom positions via an affine transformation, suitable for the periodic system. The other is moving the rigid walls that interact with the atoms in the system, suitable for the non-periodic system. Based on the calculation of the external work and the internal energy change, we present that the atom velocities also need to be updated in the first deformation method;otherwise the energy conservation cannot be satisfied. The classic updating scheme is examined, in which any atom crossing the periodic boundary experiences a velocity delta that is equal to the velocity difference between the opposite boundaries. In addition, a new scheme which scales the velocities of all the atoms according to the strain increment is proposed, which is more efficient and realistic than the classic scheme. It is also demonstrated that the Virial stress instead of its interaction part is the correct stress definition that corresponds to Cauchy stress in the continuum mechanics. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Dynamics Polymeric material numerical algorithms Energy methods Deformation

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Computation of parabolic cylinder functions having complex argument

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APPLIED numerical MATHEMATICS 2024年 197卷 230-242页

作者： Dunster, T. M. Gil, A. Segura, J. San Diego State Univ Dept Math & Stat 5500 Campanile Dr San Diego CA 92182 USA Univ Cantabria Dept Matemat Aplicada & CC Comp ETSI Caminos Santander 39005 Spain Univ Cantabria Fac Ciencias Dept Matemat Estadist & Comp Santander 39005 Spain

numerical methods for the computation of the parabolic cylinder function U(a, z) for real a and complex z are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient functions involving simple coefficients, and stable integral representations;these two main methods can be complemented with Maclaurin series and a Poincare asymptotic expansion. We provide numerical evidence showing that the combination of these methods is enough for computing the function with 5 x 10(-13) relative accuracy in double precision floating point arithmetic.

关键词： Parabolic cylinder functions Asymptotic expansions numerical quadrature numerical algorithms

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LOW-VELOCITY IMPACT RESPONSE OF LAMINATED BEAMS SUBJECTED TO INITIAL STRESSES

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AIAA JOURNAL 1985年第12期23卷 1962-1969页

作者： SANKAR, BV SUN, CT PURDUE UNIV AERONAUT & ASTRONAUTW LAFAYETTEIN 47907

Finite element procedures are used in conjunction with a numerical algorithm to compute the impact response of a graphite-epoxy laminated beam subjected to tensile initial stresses. The effect of initial stresses on the contact duration, impact force, coefficient of restitution, and bending and shear stresses are discussed. The analytically computed contact force history and strain response are compared with some experimental results. © 1985 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Maximum Shear Stresses numerical algorithms Finite Element Modeling Linear Elasticity Energy Transfer Plastic Deformation Composite Laminates Material Properties Pneumatic Cylinders Green's Function

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A differential-exponential hardening law for non-Schmid crystal plasticity finite element modeling of ferrite single crystals

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INTERNATIONAL JOURNAL OF PLASTICITY 2017年 91卷 268-299页

作者： Mapar, A. Ghassemi-Armaki, H. Pourboghrat, F. Kumar, K. S. Michigan State Univ Dept Mech Engn E Lansing MI 48824 USA Michigan State Univ Dept Chem Engn & Mat Sci E Lansing MI 48824 USA Brown Univ Sch Engn Providence RI 02912 USA Ohio State Univ Dept Integrated Syst Engn Dept Mech & Aerosp Engn Columbus OH 43210 USA ArcelorMittal Global R&D E Chicago IN 46312 USA

Crystal plasticity finite element (CPFE) modeling of multi-phase, third generation advanced high strength steel (3GAHSS) requires finding the hardening parameters of slip systems operating in different phases (e.g. FCC, BCC, BCT). It is common to see the Schmid law used to model the deformation of BCC crystals. However, researches by Bassani and others have shown that BCC crystals could obey the non-Schmid law. In this paper we examined the differences between using a CPFE model based on the Schmid versus a non Schmid law to model the uniaxial compression of single crystal ferrite micropillars with distinct orientations carved out of dual phase DP980 and three-phase QP980 steel sheets. To accurately model the changing hardening rate of the single crystal, a new exponential hardening model was developed that would differentially harden slip systems. Criteria for transitioning from stage Ito stage II hardening of single crystals were also developed and verified. Finally, it was shown that it is not sufficient to use only one single crystal micropillar compression force-displacement curve for the calibration of the non-Schmid CPFE model. The predictions of the resulting model would be unreliable, and its accuracy highly dependent on the orientation of the micropillar chosen for calibration. However, when two mircopillar compression force-displacement curves were used for calibration, the model's predictions were consistently accurate. Using more than two curves for calibration did not result in significant improvements. (C) 2016 Published by Elsevier Ltd.

关键词： Yield condition Crystal plasticity Finite elements numerical algorithms Non-Schmid law

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Strain hardening in 2D discrete dislocation dynamics simulations: A new '2.5D' algorithm

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2016年第0期95卷 132-146页

作者： Keralavarma, S. M. Curtin, W. A. Indian Inst Technol Madras Dept Aerosp Engn Madras 600036 Tamil Nadu India Ecole Polytech Fed Lausanne Inst Engn Mech CH-1015 Lausanne Switzerland

The two-dimensional discrete dislocation dynamics (2D DD) method, consisting of parallel straight edge dislocations gliding on independent slip systems in a plane strain model of a crystal, is often used to study complicated boundary value problems in crystal plasticity. However, the absence of truly three dimensional mechanisms such as junction formation means that forest hardening cannot be modeled, unless additional so-called '2.5D' constitutive rules are prescribed for short-range dislocation interactions. Here, results from three dimensional dislocation dynamics (3D DD) simulations in an FCC material are used to define new constitutive rules for short-range interactions and junction formation between dislocations on intersecting slip systems in 2D. The mutual strengthening effect of junctions on preexisting obstacles, such as precipitates or grain boundaries, is also accounted for in the model. The new '2.5D' DD model, with no arbitrary adjustable parameters beyond those obtained from lower scale simulation methods, is shown to predict athermal hardening rates, differences in flow behavior for single and multiple slip, and latent hardening ratios. All these phenomena are well-established in the plasticity of crystals and quantitative results predicted by the model are in good agreement with experimental observations. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Dislocations Strengthening mechanisms Crystal plasticity Constitutive behavior numerical algorithms

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Nonlinear time-step constraints based on the second law of thermodynamics

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2000年第3期14卷 435-449页

作者： Camberos, JA USAF Res Lab Wright Patterson AFB OH 45433 USA

numerical calculations for a time-accurate solution of the equations of fluid dynamics often require a time-step constraint. One can reduce this constraint to an inequality relating the time step, the grid spacing, and some reference wave velocity. Historically, the literature in numerical analysis refers to this parametric cluster as the Courant number (nondimensional) and the condition for the linear case as the Courant-Friedrichs-Lewy (CFL) condition. Classically, numerical analysis relies on linearization and von Neumann's use of Fourier series to derive the CFL condition. In practice, computational fluid dynamics mostly relies on rules of thumb and heuristic arguments to justify the equation that determines time-step size and numerical stability for complicated and nonlinear calculations. The approach proposed in this paper uses the second law of thermodynamics as a way of imposing a restriction on the time step, applied to linear and nonlinear equations and systems of equations like the equations of gas dynamics. Basically, by transforming the truncation error for the numerical formula approximating a conservation equation into an equation representing the balance of entropy, one can obtain an inequality that restricts the time step to satisfy the second law. The second law as developed extends its role by analogy for the simple linear advection equation, then a nonlinear equation, and finally a system of equations representing the one-dimensional equations of gas dynamics. In each case results obtained agree with the classical approach for linear equations but differ in others, indicating that the second law has significant implications beyond its role in thermodynamics. This work develops the topic only for explicit numerical algorithms with truncation errors no greater than second order. By conjecture one expects that the most general conclusions will field for implicit and higher-order methods because of the universality of the second law and the concept o

关键词： Second Law of Thermodynamics Entropy Generation Rate Lax Friedrichs Method Courant Friedrichs Lewy Rankine Hugoniot Jump Conditions Thermophysics Conservation of Mass Thermodynamic Equilibrium Nonlinear Equation numerical algorithms

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DIRECT BLOCK TRIDIAGONALIZATION OF SINGLE-INPUT SINGLE-OUTPUT SYSTEMS

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SYSTEMS & CONTROL LETTERS 1992年第2期18卷 109-120页

作者： GOLUB, G KAGSTROM, B VANDOOREN, P UMEA UNIV INST INFORMAT PROC S-90187 UMEA SWEDEN UNIV ILLINOIS COORDINATED SCI LAB URBANA IL 61801 USA

In this paper we derive a direct method for block tridiagonalizing a single-input single-output system triple {A, b, c}. The method is connected to the nonsymmetric Lanczos procedure developed in [10, 2, 1] and also l... 详细信息

关键词： LANCZOS PROCEDURE STATE SPACE CANONICAL FORM numerical algorithms DIRECT ELIMINATION

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