Effect of forced lamina flow on microsegregation simulated by phase field method quantitatively

The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled with flow field. The microsegregation, concentration maximum value, boundary thickness of concentration near upstream dendrite and normal to flow dendrite, and downstream dendrite were studied quantitatively in the case of forced lamia flow. The simulation results show that solute field and flow field interact complexly. Compared with melt without flow, in front of upstream dendrite tip, the concentration boundary thickness is the lowest and the concentration maximum value is the smallest for melt with flow. However, in front of downstream dendrite tip, the results are just the opposite. The zone of poor Cu in upstream dendrite where is the most severely microsegregation and shrinkage cavity is wider and the concentration is lower for melt with flow than that without flow.

Ageing process of pre-precipitation phase in Ni_(0.75)Al_(0.05)Fe_(0.2) alloy based on phase field method

By utilizing phase field method combined with analysis on free energy and interatomic potentials, pre-precipitation phase formation and transformation process of Ni0.75Al0.05Fe0.2 alloy in early precipitation stage during the ageing process under 1 000 K were studied. And free energy, microstructures, compositions and volume fractions of pre-precipitation phase and equilibrium phase were analyzed. The simulation results indicate that nonstoichiometric Llo pre-precipitation phase formed first, and then would gradually transform into L12 equilibrium phase. It is discovered that the phase transformation process was closely related to free energy and interatomic potentials. Additionally, it is revealed that free energy of Llo pre-precipitation phase was higher and interatomic potential was smaller than that of L12 equilibrium phase. Therefore, it is concluded that Llo phase was unstable, and phase transformation would occur to L12 which was more stable.

Phase field method simulation of faceted dendrite growth with arbitrary symmetries

A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.

Rolling Force and Rolling Moment in Spline Cold Rolling Using Slip-line Field Method

Rolling force and rolling moment are prime process parameter of external spline cold rolling. However, the precise theoretical formulae of rolling force and rolling moment are still very fewer, and the determination of them depends on experience. In the present study, the mathematical models of rolling force and rolling moment are established based on stress field theory of slip-line. And the isotropic hardening is used to improve the yield criterion. Based on MATLAB program language environment, calculation program is developed according to mathematical models established. The rolling force and rolling moment could be predicted quickly via the calculation program, and then the reliability of the models is validated by FEM. Within the range of module of spline m=0.5-1.5 mm, pressure angle of reference circle α=30.0°-45.0°, and number of spline teeth Z=19-54, the rolling force and rolling moment in rolling process （finishing rolling is excluded） are researched by means of virtualizing orthogonal experiment design. The results of the present study indicate that： the influences of module and number of spline teeth on the maximum rolling force and rolling moment in the process are remarkable; in the case of pressure angle of reference circle is little, module of spline is great, and number of spline teeth is little, the peak value of rolling force in rolling process may appear in the midst of the process; the peak value of rolling moment in rolling process appears in the midst of the process, and then oscillator weaken to a stable value. The results of the present study may provide guidelines for the determination of power of the motor and the design of hydraulic system of special machine, and provide basis for the farther researches on the precise forming process of external spline cold rolling.

Simulation of faceted dendrite growth of non-isothermal alloy in forced flow by phase field method

Numerical simulation based on a new regularized phase field model was presented to simulate the dendritic shape of a non-isothermal alloy with strong anisotropy in a forced flow. The simulation results show that a crystal nucleus grows into a symmetric dendrite in a free flow and into an asymmetry dendrite in a forced flow. As the forced flow velocity is increased, both of the promoting effect on the upstream arm and the inhibiting effects on the downstream and perpendicular arms are intensified, and the perpendicular arm tilts to the upstream direction. With increasing the anisotropy value to 0.14, all of the dendrite arms tip velocities are gradually stabilized and finally reach their relative saturation values. In addition, the effects of an undercooling parameter and a forced compound flow on the faceted dendrite growth were also investigated.

On the field method in non-holonomic mechanics

This paper deals with the generalization of the fieldmethod to non-holonomic systems whose motion is subject toeither non-linear constraints or those of a higher order,whiletheir motion is modeled by the generalized Lagrange equa-tions of the second kind.Two examples are given to illustratethe theory.

Average vector field methods for the coupled Schrdinger KdV equations

The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.

Anisotropic growth of multigrain in equiaxial solidification simulated with the phase field method

The phase field method has been mainly used to simulate the growth of a single crystal in the past. But polycrystalline materials predominate in engineering. In this work, a phase field model for multigrain solidification is developed, which takes into account the random crystallographic orientations of crystallites and preserves the rotational invariance of the free energy. The morphological evolution of equiaxial multigrain solidification is predicted and the effect of composition on transformation kinetics is studied. The numerical results indicate that due to the soft impingement of grains the Avrami exponent varies with the initial melt composition and the solidification fraction.

Analysis on high-temperature oxidation and growth stress of iron-based alloy using phase field method

High-temperature oxidation is an important property to evaluate thermal protection materials. However, since oxidation is a complex process involving microstructure evolution, its quantitative analysis has always been a challenge. In this work, a phase field method （PFM） based on the thermodynamics theory is developed to simulate the oxidation behavior and oxidation induced growth stress. It involves microstructure evolution and solves the problem of quantitatively computational analysis for the oxidation behavior and growth stress. Employing this method, the diffusion process, oxidation performance, and stress evolution axe predicted for Fe-Cr-A1-Y alloys. The numerical results agree well with the experimental data. The linear relationship between the maximum growth stress and the environment oxygen concentration is found. PFM provides a powerful tool to investigate high-temperature oxidation in complex environments.

Numerical Simulations of Equiaxed Dendrite Growth Using Phase Field Method

Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in a metallic system. In this paper, the equiaxed dendrite evolution during the solidification of a pure material was numerically simulated using the phase field model. The equiaxed dendrite growth in a two-dimensional square domain of undercooled melt (nickel) with four-fold anisotropy was simulated. The phase field model equations was solved using the explicit finite difference method on a uniform mesh. The formation of various equiaxed dendrite patterns was shown by a series of simulations, and the effect of anisotropy on equiaxed dendrite morphology was investigated.

A FIELD METHOD FOR INTEGRATING THE EQUATIONS OF MOTION OF NONHOLONOMIC CONTROLLABLE SYSTEMS

This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems. An example is given to illustrate the application of the method.

A field method for integrating the equations of motion of mechanico-electrical coupling dynamical systems

A field method for integrating the equations of motion for mechanico-electrical coupling dynamical systems is studied. Two examples in mechanico-electrical engineering are given to illustrate this method.

Field Method Research for Leak-off Coefficient Analysis Using Instantaneous Shut-in Pressure

The accurate monitor and prediction of fracturing pressure for formation is very important to hydraulic fracturing treatment operation, but whether hydraulic fracturing is successful or not, the fracturing fluid plays a very important role, leak-off coefficient is the most leading parameters of fracturing fluids. Mini-frac test was the most commonly used tools for leak-off coefficient analysis, but it has the shortcoming of time-consuming and costly that can not meet the requirement of the production. The main purpose of this paper is to introduce a simple and convenient leak off coefficient analysis method with more inexpensive and time-saving than former methods. Based on ISIP （instantaneous shut-in pressure） method, a new field method of leak off coefficient field analysis model was presented. According to twice ISIP of the fracturing treatment in field operation, therefore, fluid leak off coefficient and formation characteristic can be studied quickly and reliably. More than 40 wells were fractured using this field method. The results show that average liquid rates of post-fracturing was 20 m3/d which double improvement compared with the past treatment wells. It had an important role for fracturing treatments in low permeability used in field application. reservoirs, the new model for real time analysis and adjust is successful

Multi-Behavior Fusion Based Potential Field Method for Path Planning of Unmanned Surface Vessel

The problem of the unmanned surface vessel (USV) path planning in static and dynamic obstacle environments is addressed in this paper. Multi-behavior fusion based potential field method is proposed, which contains three behaviors: goal-seeking, boundary-memory following and dynamic-obstacle avoidance. Then, different activation conditions are designed to determine the current behavior. Meanwhile, information on the positions, velocities and the equation of motion for obstacles are detected and calculated by sensor data. Besides, memory information is introduced into the boundary following behavior to enhance cognition capability for the obstacles, and avoid local minima problem caused by the potential field method. Finally, the results of theoretical analysis and simulation show that the collision-free path can be generated for USV within different obstacle environments, and further validated the performance and effectiveness of the presented strategy.

Univector field method-based multi-agent navigation for pursuit problem in obstacle environments

The pursuit problem is a well-known problem in computer science. In this problem, a group of predator agents attempt to capture a prey agent in an environment with various obstacle types, partial observation, and an infinite grid-world. Predator agents are applied algorithms that use the univector field method to reach the prey agent, strategies for avoiding obstacles and strategies for cooperation between predator agents. Obstacle avoidance strategies are generalized and presented through strategies called hitting and following boundary(HFB); trapped and following shortest path(TFSP); and predicted and following shortest path(PFSP). In terms of cooperation, cooperation strategies are employed to more quickly reach and capture the prey agent. Experimental results are shown to illustrate the efficiency of the method in the pursuit problem.

Crack propagation simulation in brittle elastic materials by a phase field method

To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations,the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable(x)∈[0,1]to characterize discontinuous cracks in brittle materials.This method can well describe the crack initiation and propagation without assuming the shape,size and orientation of the initial crack in advance.In this paper,a phase field method based on Miehe's approach[Miehe et al.,Comp.Meth.App.Mech.Eng.(2010)]is applied to simulate different crack propagation problems in twodimensional(2D),isotropic and linear elastic materials.The numerical implementation of the phase field method is realized within the framework of the finite element method(FEM).The validity,accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in literature.Several numerical examples are presented to show the effects of the loading type(tension and shear),boundary conditions,and initial crack location and orientation on the crack propagation path and force-displacement curve.Furthermore,for a single edge-cracked bi-material specimen,the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and discussed.It is demonstrated that the phase field method is an efficient tool for the numerical simulation of the crack propagation problems in brittle elastic materials,and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.

3D anisotropy simulation of dendrites growth with phase field method

The anisotropy problem of 3D phase-field model was studied,and various degrees of anisotropy were simulated by numerical calculation method.The results show that with the change of interface anisotropy coefficients,from smooth transition to the appearance of angle,equilibrium crystals shape morphology has a critical value,and 3D critical value is 0.3.The growth of dendrites is stable and the interface is smooth when it is less than critical value;the interface is unstable,rolling edge appears and the growth is discontinuous when it is more than critical value.With the increase of anisotropy coefficients,the dendrites grow faster under the same condition.

A FIELD METHOD FOR SOLVING THE EQUATIONS OF MOTION OF NONHOLONOMIC SYSTEMS

In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrate its application.

Field Method for Integrating the First Order Differential Equation

An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.