A 2D level set finite element grain coarsening study with heterogeneous grain boundary energies

In a previous article (Fausty et al., 2018) a new level-set finite element formulation for pure grain growth with heterogeneous grain boundary energies (i.e. one energy per grain interface) was developed and validated for simple configurations. In this work, the authors apply this new tool to the simulation of two dimensional grain growth of polycrystals using different disorientation dependent grain boundary energy functions. The results of these full-field calculations are assessed using the time dependent evolution of the following criteria: grain size, grain number, total interface energy, grain boundary disorientation distribution, grain boundary energy distribution and number of neighboring grains distribution. Of particular interest is the relationship between the grain boundary energy function and the evolution of the grain boundary network in the sense of both its morphology and its constitution. Some notable results are that the disorientation distribution evolution is inversely correlated to the grain boundary energy function itself and that the kinetics of grain growth are heavily effected by the heterogeneity of the system.     

Numerical modelling of solidification of castings made of two‐component alloys

The paper deals with a numerical modelling of equiaxed microstructure formation during the solidification of two‐component alloys. The basic enthalpy formulation was applied to model the solidification. The equiaxed grain size was dependent on the average cooling velocity at the moment when the liquid metal reaches the liquidus temperature. The experimentally determined dependence between grain radius and cooling velocity was used in the calculation of average grain radii distribution.     

Cosserat continuum modelling of grain size effects in metal polycrystals

The global response of polycrystalline aggregates is investigated, in order to simulate grain size effects in IF ferritic steels. The mechanics of generalized continua is used to describe the studied phenomena. The polycrystal is regarded as a heterogeneous Cosserat medium, and the overall properties are estimated using a specific homogenization technique. To illustrate the capabilities of the model, some simple bidimensionnal computations are presented for different grain sizes. Afterwards tridimensionnal computations are shown in order to extract the global effect on the mechanical behaviour for grain sizes ranging from 5 µm to 120 µm. The finite element response is harder for the smallest grain size, but the model still underestimate the grain size effect on the tensile response. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simultaneous observation of tunnel-type GMR and intrinsic CMR in nanometer perovskite

The nanometer-sized perovskite L_80.85 S_ro.15 MnO₃ is synthesized by a sol-gel method. And, through controlling the conditions of heat-treatment, a series of polycrystalline perovskite with different grain sizes is obtained. The resistance measurements with changing temperatures show that with the increase in grain size the transport properties of this kind of granular perovskite, including the giant magnetoresistanee (GMR) effect, systematically change from an interfacial effect-controlled form to the crystal intrinsic type. Meanwhile, the magnetoresistance effect transforms from an interfacial tunneling GMR to the intrinsic colossal magnetoresistance (CMR). For the sample with a suitable grain size (≈100 nm), the two magnetoresistance effects can be observed simultaneously. And the action of both magnetoresistances in common can make a “plain” on the curve of magnetoresistance versus temperature (MRT); that is, the magnetoresistance effect of the granular perovskite does not change with temperature in a wide range.     

纳米晶体弹性模量的模拟研究

通过分子动力学(MD)方法模拟纳米晶体(1～3nm)的结构,并对模拟的结果进行了X射线衍射的点阵常数、结合能及弹性模量等模拟计算.结果表明纳米晶体无论是晶界和晶粒都与传统的粗晶粒晶体材料没有根本的区别,只是由于晶粒尺寸变小以及晶界的体积分数等的作用而导致诸如弹性模量大幅度减少等一系列不同性能.     

Crack propagation at bi-material interfaces

There is currently a gap in the understanding of how crack propagation by intergranular versus transgranular fracture varies with changes in material properties and grain size. Much of the prior work in this area has been in terms of LEFM and criterion based on toughness alone. More recent work has shown that a toughness-and-strength approach is required. In this study a strength-and-energy approach is applied to intergranular-versus-transgranular fracture through a cohesive-zone approach implemented in a finite element model. Results show that intergranular fracture becomes more likely, and has an increasing shear component, as grain toughness increases and grain stiffness and grain size decrease. These results can help guide material development. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microstructure analysis on IN 718 alloy round rod by FEM in the hot continuous rolling process

Based on physical metallurgy rules and experiential equations, models for microstructure analysis on IN 718 alloy in the round rod hot continuous rolling process has been developed using the finite element method (FEM) on the software ANSYS/LS-DYNA. The dynamic and metadynamic recrystallization models in and after deformation, the grain growth models in the compensated reheating process for IN 718 alloy are regressed, and corresponding processes are involved in these models. For a real rolling practice, the calculated central grain sizes were examined and are in good agreement with the measured ones. The element in the center of the workpiece is a typical one possessing the maximum of the effective strain, the temperature and the grain size in the rolling process. In the hot continuous rolling process, the relationship between the final grain size of the typical element and the inlet velocity of the first stand has been regressed by FE analysis, and the lower rolling speed is beneficial to the grain refinement.     

Optimization model of recrystallization hot rolling of titanium-vanadium steels

An optimization model was built based on the data of a pilot-scale (4.5 MN load, 225 KW power capacity) rolling mill to minimize the austenite grain sizes of Ti–V steels, which prevail at the instant of completion of the static recrystallization during hot rolling. A computer program developed for this optimization model was run for the rolling schedule, which is designed according to the complete recrystallization case. An energy optimization model developed previously was applied to different rolling schedules. The grain size optimization results demonstrate the effectiveness of these modelling approaches in terms of final grain size, final plate thickness, measured and computed roll force and torque values for both the design of the thermomechanical schedules which produce plate with fine-grained microstructures, high strength, and notch toughness and the temperature-reduction schedules of conventional controlled rolling.     

坡度对坡面土壤侵蚀的影响分析

在运动波理论基础上,就影响土壤侵蚀的主要因素,包括降雨超渗净雨量,坡面流水深、流速和切应力,以及土壤抗冲蚀能力等随坡度的变化关系进行了理论分析。并进一步对坡面土壤侵蚀的坡度界限做了较细致分析,表明坡度界限是一个变量,随颗粒粒径、容重、坡面糙率、径流长度、降雨入渗差值(净雨量),以及土壤摩擦系数等因素的不同而改变,给出了界限坡度的变化规律,并得出一般情况下土壤侵蚀的坡度界限值应在415°～50°范围内的结论。     

Simulation of Size Effects in Ferroelectric Materials using a Phase Field Model

An electro-mechanically coupled phase field model for domain evolution in ferroelectric materials is presented. The inner length scale introduced by the model gives rise to size effects, especially in the context of the poling behavior of polycrystals. Such size effects are investigated by 2D numerical simulations for barium titanate polycrystals. Ferroelectric hysteresis curves and coercive fields are calculated for two different transition conditions for the order parameter at the grain boundaries. The results show that there is a significant size effect for the investigated polycrystal systems. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

各向异性双晶和三晶体晶界附近应力场分析

采用率相关晶体滑移有限元程序对不同取向晶粒构成的双晶体和三晶体在晶界和三晶交点附近的应力集中特性进行了计算分析．双晶体的数值结果表明,不同取向晶粒的晶界附近应力场具有较大的应力梯度,存在应力集中现象;三晶体由于晶界之间的相互作用使得三晶交点可能造成应力集中地,也可能不造成应力集中,晶界附近的应力结构与双晶体晶界附近的应力结构亦不相同,这主要取决于三个晶粒的晶体取向．对双晶体和三晶体的分析说明,不同取向的晶粒具有不同的变形规律．因此研究金属材料的损伤、断裂问题至少需要采用晶体滑移理论从细观的角度分析不同晶粒之间的相互作用．     

Application of Strain Gradient Plasticity to Micro-torsion Experiments

The applicability of a strain gradient crystal plasticity model to size effects observed on microwires in torsion experiments is discussed. Finite Element simulations of simplified cylindrical grain aggregations are presented and the resulting overall mechanical response is compared to experimental data for gold from the literature. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new stabilized finite element method for advection‐diffusion‐reaction equations

In this article, a new stabilized finite element method is proposed and analyzed for advection‐diffusion‐reaction equations. The key feature is that both the mesh‐dependent Péclet number and the mesh‐dependent Damköhler number are reasonably incorporated into the newly designed stabilization parameter. The error estimates are established, where, up to the regularity‐norm of the exact solution, the explicit‐dependence of the diffusivity, advection, reaction, and mesh size (or the dependence of the mesh‐dependent Péclet number and the mesh‐dependent Damköhler number) is revealed. Such dependence in the error bounds provides a mathematical justification on the effectiveness of the proposed method for any values of diffusivity, advection, dissipative reaction, and mesh size. Numerical results are presented to illustrate the performance of the method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 616–645, 2016     

Effects of orientation and interaction of grains on coercivity for sintered NdFeB magnets

The coercivity of NdFeB magnets is determined by the coercivity of individual grains and the interaction between the grains composed of the magnets. The coercivity of individual grains and the intergrain interaction depend on the degree of the grain alignment, “tanθ type” Gaussian function is applied to describing the degree of the grain alignment. According to different coercivity mechanisms, there are different formula on the coercivity and the angular dependence of coercivity. The interaction between grains can be classified as the long-range magnetostatic interaction and the exchange-coupling interaction of neighboring grains. For the sintered magnet, the grain size is large and the grain boundaries are mostly separated by the non-magnetic phase. So, the long-range magnetostatic interaction is much stronger than the exchange coupling interaction and it makes the coercivity of the magnet composed of misaligned grains be bigger than that of the magnet composed of ideally aligned grains. The effects of coercivity of individual grains and the intergrain interactions are taken into account, and the starting field theory is in agreement with the experimental result for the coercivity of sintered NdFeB magnets. Project supported by the National Natural Science Foundation of China (Grant No. 59571017).     

The functional limit theorem for the canonical U-processes defined on dependent trials

The functional limit theorem is proven for a sequence of normalized U-statistics (the socalled U-processes) of arbitrary order with canonical (degenerate) kernels defined on samples of φ-mixing observations of growing size. The corresponding limit distribution is described as that of a polynomial of a sequence of dependent Wiener processes with some known covariance function.     

Computational mechanics-based modeling of size-dependent hardening in polycrystals

It has been well-known for a number of years that the macroscopic material response of polycrystalline metals is influenced by the size and morphology of grains. Different size effects may occur, one of which is the Hall-Petch effect. The key aim of this contribution is the computational modeling of grain-size-dependent hardening in polycrystals using a microstructural approach. Here, the focus is on the influence of the microscopic grain boundary conditions on the simulation results. In particular, micro-flexible boundary conditions are discussed and compared to micro-hard and micro-free assumptions. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Barrier lake formation due to landslide impacting a river: A numerical study using a double layer-averaged two-phase flow model

A granular landslide impacting a river may lead to the formation of a landslide dam blocking the streamflow, and subsequently create a barrier lake. Should a barrier lake outburst, the flood may be destructive and spell disastrous consequences downstream. The last decade or so has witnessed a number of experimental and numerical investigations on barrier lake outburst flooding, whilst studies on barrier lake formation remain rare – a physically enhanced and practically viable mathematical model is still missing. Generally, barrier lake formation is characterized by multi-physical, interactive processes between water flow, multi-sized sediment transport and morphological evolution. Here, a new double layer-averaged two-phase flow model is proposed, which is an advance on existing continuum models that involve a single-phase flow assumption and presume a single sediment size, and discrete models that preclude fine grains and assume narrow grain size distributions. The proposed model is first validated against data from previous laboratory experiments of waves due to landslides impacting reservoirs and landslide dam formation over dry valleys. Then it is applied to explore the complicated mechanism and threshold for barrier lake formation. The water and grain velocities are shown to be disparate, characterizing the primary role of grains in driving water movement during subaqueous landslide motion and also demonstrating the need for a two-phase flow approach. The grain size effects are revealed, i.e., coarse grains and grain-size uniformity favour barrier lake formation. A new threshold condition is proposed for barrier lake formation, integrating the landslide-to-river momentum ratio and grain size effects. The present work facilitates a promising modelling framework for solving barrier lake formation, thereby underpinning the assessment of flood hazards due to barrier lakes.     

Modelling of recrystallization behavior and austenite grain size evolution during the hot rolling of GCr15 rod

In this paper, four 3-D finite element models are developed to simulate the whole rod rolling process of GCr15 steel. The distribution and evolution of different field-variables, such as effective strain, effective strain rate and temperature, are obtained. Based on the simulated results and the microstructure evolution models of the steel, the paper designs a FORTRAN program to predict the evolution of recrystallization behavior and austenite grain size in rolled piece during the rolling. The surface temperatures of rolled piece calculated by FEM agree well with measured values. Comparison between calculated values and measured ones of grain size shows the validity of the program.     

2014“高教社杯”全国大学生数学建模竞赛颁奖仪式在海军航空工程学院青岛校区举行

<正>2014年12月20日,2014"高教社杯"全国大学生数学建模竞赛颁奖仪式暨工作会议在海军航空工程学院青岛校区隆重举行。全国大学生数学建模竞赛组委会主任、复旦大学李大潜院士,海军航空工程学院政委龚理华少将,山东省教育厅宋承祥副厅长,高等教育出版社林金安副总编辑,中国科学院袁亚湘院士,全国大学生数学建模竞赛组委会副主任、专家组组长、浙江大学陈叔平教授等160余人出席了颁奖仪式。颁奖仪式由全国组委会秘书长、清华大学谢金星教授主持。颁奖仪式上,学院龚理华