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In this paper, the first principle method based on density functional theory is adopted to establish the interface model of WC/WC-Co through the software Materials Studio (MS). On the basis of this interface structure, rare earth element Y is doped, and then the energy of WC/WC-Co before and after doping is calculated respectively. The electronic structure is analyzed, and the calculation results of the two structures are compared. Finally, the grain growth is simulated by cellular automata of matlab to verify our calculation and analysis results. The results show that the interfacial adhesion work increases and the interface structure is more stable after doping Y element. The interface energy decreases and plays a role in grain refinement.

We investigate a spectral Galerkin method for the two-dimensional fractional diffusion-reaction equations on a disk. We first prove regularity estimates of solutions in the weighted Sobolev space. Then we obtain optimal convergence orders of a spectral Galerkin method for the fractional diffusion-reaction equations in the L 2 L^2 and energy norm. We present numerical results to verify the theoretical analysis.

In this paper, the well-known shifted Grunwald–Letnikov formula is revisited to solve the two-dimensional fractional boundary value problems (FBVPs) with non-smooth solution. Both stability analysi...

In this work, we revisit the spectral Petrov-Galerkin method for fractional elliptic equations with the general fractional operators. To prove the optimal convergence of the method, we first present the ultra-weak formulation and establish its well-posedness. Then, based on such a novel formulation, we are able to prove the discrete counterpart and obtain the optimal convergence of the spectral method in the weighted L 2 -norm. For simple and easy implementation of the method, we also describe the fast solver with linear storage and quasilinear complexity. To support our theory, we carry out the numerical experiments and provide several numerical results to show the accuracy and efficiency of our method.

Ni-based alloys are widely used in aerospace because of their high strength and high temperature oxidation resistance. CBN tool is suitable for precision machining of Ni-based alloy. Diffusion wear is an important wear form of CBN tool in the process of cutting Ni-based alloy. Therefore, it is of great significance to study the diffusion phenomenon in the process of cutting Ni-based alloy with CBN tool. In this paper, the cutting model of Ni-based alloy containing γ′ phase (Ni3Al) with CBN tool is established based on the molecular dynamics (MD) simulation method. The self diffusion activation energy of all kinds of atoms in the workpiece and the formation energy of several point defects in the tool are calculated, so as to study in depth the atom diffusion mechanism according to the simulation results. The results show that the atoms in the crystal boundary of the workpiece are the most easily diffused, followed by the atoms in the phase boundary, and the atoms in the lattice are the most difficult to diffuse. When the workpiece atoms diffuse into the tool, it is easier to diffuse into the tool grain boundary than to form interstitial impurity atoms or displacement impurity atoms. It is more difficult to form the substitutional impurity atom than to form the interstitial impurity atom.

Nickel based single crystal alloys have excellent properties such as heat resistance, corrosion resistance and creep resistance, which are widely used in aerospace and other national defense fields. Severe work hardening occurs in the process of cutting nickel based single crystal alloy. How to improve the machining quality and grasp the cutting deformation mechanism has become the research focus. In this paper, the effect of work hardening on the surface of workpiece during the atomic and close-to-atomic scale (ACS) cutting process is studied. The model of S i 3 N 4 ceramic tool cutting the nickel based single crystal alloy was established, and the ACS cutting process was simulated by the molecular dynamics method. The existing strain rate conversion model was modified to make it suitable for the process of ACS cutting into nano compression with the same strain rate. The results show that the dislocation density of Ni-based single crystal alloy workpiece changes greatly with the change of cutting distance. According to the change of microstructure in the workpiece, a new staged work hardening mechanism is proposed. The development of work hardening in the cutting process is divided into three stages, and the transition node of each hardening stage is defined. An important sign of the transformation from the first stage to the second stage of work hardening is the occurrence of a large number of dislocation pile-up group, dislocation tangles and the appearance of non-basal slip lines. The distinctive feature of the transformation from the second stage to the third stage of work hardening is that a large number of screw dislocations are cross-slip and the dislocation pile-up group is destroyed. At the same time, the different hardening mechanisms in each stage and the reasons for the change of work hardening mechanism in different stages are summarized. The research content is believed to be helpful to understand the mechanism of significant work hardening effect in nickel-based alloys.

Inconel 718 is one kind of nickel-based superalloy containing γ′ precipitates (Ni3Al). It has been widely used in aerospace field due to its high strength, high oxidation resistance, and corrosion resistance at high temperature. Considering the influence of the strengthening phase γ′ on the cutting deformation, and the inability of traditional classical mechanics to describe the characteristic scale of materials and to accurately explain some phenomena in the machining process, the model of enhanced phase γ′ with cohesive element in cutting Inconel 718 is established in this paper. Moreover, the strain gradient theory is introduced to establish constitutive model. The effects of γ′ phase on stress, strain, and temperature and the distribution of stress field at the crack tip are analyzed from the point of view of material micro-plasticity mechanics and material dislocation theory. The strain gradient strengthening effect is studied by changing the size of γ′ phase.

Nickel-based single crystal superalloy is widely used in the field of aerospace and nuclear reaction equipment due to its good properties. Ultra-precision machining technology is an important means to ensure the surface quality of parts. However, the anisotropy of materials has great influence on the evolution of surface and subsurface defects and the removal of materials in the process of machining. In this paper, The MD (molecular dynamics) modeling and simulation verification of cutting anisotropic nickel-based single crystal superalloy workpiece with silicon nitride tool is carried out by using the mixed potential function simulation. Through cutting simulation and visualization, the types, number, deformation area and dislocation evolution of the machined surface defects and inside of the workpiece defect of nickel-based single crystal superalloy with different crystal orientations are analyzed. The evolutionary mechanism of the machined surface defects and the law of material removal are discussed. The research content provides a theoretical basis for parameter optimization and improvement of machining quality in the atomic and close-to-atomic scale (ACS) cutting process, and technical support for efficient and precise machining process of the nickel-based superalloy.

Nickel-based single crystal alloys are widely used in aerospace and other important fields of national defense due to their excellent properties. Phase transformation occurs during high-speed cutting of nickel-based single crystal alloy, which seriously affects the surface quality. It is of great significance to carry out theoretical research on phase transformation for improving the machining quality of nickel-based alloy. In this paper, molecular dynamics method is used to study the nano-cutting of single crystal nickel-based alloy with silicon nitride ceramic tool. The mechanism of phase transformation and the effect of cutting speed on phase transformation in workpieces are studied in detail. The nano-cutting model is established. Morse potential functions for molecular dynamics simulation are calculated, and EAM and Tersoff potential functions are selected. The effect of cutting speed on phase transformation was studied by using radial distribution function, coordination number analysis, common neighbor analysis, and the deep reasons for the sharp change of lattice structure were analyzed from many aspects. Finally, in order to verify the universality of the research results and explore the new properties of compression, nano compression (the same strain rate as the nano cutting process) was simulated. The results show that the increase of cutting speed leads to the increase of hydrostatic stress, the increase of energy in crystal and the rise of cutting temperature. As a result, the change of lattice structure becomes more and more intense, and the conversion rate of different crystal structures increases greatly.

In this paper, an efficient algorithm is presented by adopting the extrapolation technique to improve the accuracy of finite difference schemes for two-dimensional space-fractional diffusion equations with non-smooth solution. The popular fractional centered difference scheme is revisited and the stability and error estimation of numerical solution are given in maximum norm. Based on the analysis of leading singularity of exact solution for the underlying problem, the extrapolation technique and numerical correction method are exploited to enhance the accuracy and convergence rate of the computation. Two numerical examples are provided to validate the theoretical prediction and efficiency of the algorithm. It is shown that, by using the proposed algorithm, both accuracy and convergence rate of numerical solutions can be significantly improved and the second-order accuracy can even be recovered for the equations with large fractional orders.

We investigate a spectral Galerkin method for the fractional advection-diffusion-reaction equations in one dimension. We first prove sharp regularity estimates of solutions in nonweighted and weigh...

In this paper, the Johnson-Cook constitutive model is modified by considering the influence of hard point such as TiC and NbC in the matrix of Inconel718 on the deformation stress. The theoretical model of cutting specific energy in the main deformation zone of Inconel718 is modified based on the new constitutive model by combining the strain gradient theory. The effect of different cutting parameters on cutting specific energy is studied, and the effect of cutting specific energy on cutting deformation and the resulting dimensional effect are also analyzed. The research results show that cutting specific energy increases with the increase of cutting speed. With the increase of cutting thickness, the cutting specific energy reduced, and the trend is non-linear. The change of undeformed chip thickness will cause size effect. The cutting specific energy increases with the reduction of the thickness of undeformed chip, and the impact of the thickness of undeformed chip on the cutting specific energy becomes smaller and smaller as the speed increases. The existence of hard points makes the main deformation zone generate a large amount of heat energy and deformation energy, which leads to dimensional effects and makes the material be more prone to adiabatic shear instability, then leads to the increase of cutting specific energy. With the increase of cutting specific energy, the width of adiabatic shear band is narrowed, the degree of serration is aggravated, and the chip morphology is closer to the experimental results.

In this paper, we propose a conservative three-layer linearized difference scheme for the two-dimensional nonlinear Schrodinger equation with fractional Laplacian. The difference scheme can be strictly proved to be uniquely solvable, conservation of mass and energy in the discrete sense. Furthermore, it is shown that the difference scheme is unconditionally convergent and stable under $$l^{\infty }$$ -norm by discrete energy method. The convergence order is $$\mathcal {O}(\tau ^2+h^2)$$ with time step $$\tau $$ and mesh size h. Numerical examples are given to demonstrate the theoretical results.

Nickel-based alloy Inconel 718 is widely used in aircraft engine industry because of its good mechanical properties. Inconel 718 is a typical difficult-to-machine material and its price is relatively expensive. Therefore, accurate prediction of Inconel 718 machined surface roughness with small sample space can improve machining efficiency, optimize process parameters and reduce machining cost. In this paper, a method is proposed to characterize the influence of cutting parameters on roughness by stablishing the corresponding relationship between the proportional hyperparameters in the multivariate kernel function and the cutting speed, cutting deep, feed rate and the rake angle of the tool. A multi input single output (MISO) multivariate Gaussian process regression (GPR) surface roughness prediction model with cutting speed, cutting depth, feed rate and tool rake angle as input variables and surface roughness as output variables is established. The model can not only output the predicted value of surface roughness, but also give the reliability of the predicted value. Experimental results show that the proportional hyperparameter has an independent adjustment function, and the influence of the process parameters characterized by the proportional hyperparameter on the surface roughness is consistent with the experimental results. The experimental results show that the average relative error of MISO multivariate GPR surface roughness prediction model proposed in this paper is 1.5%, which can accurately predict the surface roughness in small sample space.

Inconel718 is nickel-based alloy and is also a multi-component complex alloy. There exist complex cutting deformation and serrated chip in machining Inconel718, which have been the focus concern of academia and business. In this paper, the failure behavior of shear band in the process of chip formation was studied by means of cutting experiment, numerical simulation and theoretical analysis. The stress triaxiality and Lode angle were used to reveal the relationship between different cutting conditions and fracture. The results show that the material in the upper region of the chip cross section is easy to be pulled off, and the ductile fracture occurred, and the stress triaxiality was positive. At the same time, it can be seen that a large number of shear dimples distributed in the bottom of the chip (near the tool-chip interface) and the shear fracture occurred, and the stress triaxiality was negative. When the value of stress triaxiality is between the above two ranges, the dimples and ductile fracture can be observed simultaneously in the chip cross section. Finally, combining with the law of the Lode angle and the fracture strain, the material fracture damage mechanism of the shear zone is revealed.

The nickel-based alloy Inconel718 is a multi-component complex alloy. There exists complex cutting deformation, higher cutting temperature, higher cutting force and formation of serrated chip in the machining process. However, the formation time of every saw tooth unit in serrated chip is very short. It is difficult to use traditional method to analyze the chip at any time. Simulation analysis, integrated with the experimental results, was used to study the whole process of cutting deformation. The Johnson—Cook (JC) constitutive model of Inconel718 under high speed and high strain rate is established through split Hopkinson pressure bar (SHPB) test. The finite element method was used to study the deformation process. Combining the analysis of metallographic pictures which were obtained in the cutting experiment, the plastic behavior evolution of material in the cutting zone is deeply studied to further reveal the forming mechanism of serrated chip. The results showed that the local temperature in the cutting zone increased rapidly. The appearance of thermal softening of materials led to the change of stress distribution in the cutting zone. The thermoplastic shear instability further appeared which resulted in the shear localization, subsequently leading to the uneven deformation of chip and then serrated chip formed.

Nickel-based superalloy is widely used in aerospace field for its excellent comprehensive performance, such as oxidation resistance and high temperature resistance. The key surfaces of most of the heat-resistant parts are obtained by precision cutting or ultra-precision cutting. Nickel-based superalloy belongs to NixFeyCrz series alloy because its main component is nickel (Ni), iron (Fe) and chromium (Cr). However, the high cutting temperature generated in cutting process caused that chemically worn is easy to occur in cutting tools. The main manifestation is that the tool wear caused by the weakening of tool strength with the fusion between the workpiece and tool atoms at tool-chip interface. In order to study the mechanism of diffusion wear in precision cutting process, the cutting model that using silicon carbide tool to cut Nickel-based superalloy is established, and the Morse potential energy function between different atoms is calculated. The simulation of the cutting process is carried out by means of MD (molecular dynamic) method. Besides, the simulation results are visualized and the interaction mechanism between the tool and workpiece material in the process of cutting simulation is studied. The MSD (Mean Square Displacement) method is used to describe the diffusion process between the workpiece atoms in the silicon carbide more accurately. The diffusion activation energy of the Ni, Cr and Fe atoms are calculated. Furthermore, the vacancy formation energy and the interstitial atom formation energy of the three atoms in the complete silicon carbide lattice are also calculated. The results show that the main diffusion mechanism of Ni, Cr and Fe atoms in cutting tools is grain boundary (GB) diffusion. The present study can make a more perfect microcosmic explanation for tool wear mechanism.

The traditional material constitutive model can effectively simulate the mechanical properties during the cutting process. However, the scale characteristics contained in materials are not considered in the traditional cutting model, and the inherent scale effect of materials is also ignored. Therefore, the traditional cutting constitutive model cannot effectively reflect the size effect in the cutting process, and then cannot obtain the accurate stress, strain, and temperature. In this present paper, a material constitutive model which can reflect the scale effect is established based on the strain gradient plasticity theory. Through the established model and secondary development of abaqus, the two-dimensional dynamic finite element simulation model of cutting Inconel 718 is established. By comparing the cutting experiment results with the simulation results, the established simulation model can more accurately reflect the effects of temperature, strain gradient effect, equivalent stress, and its scale effect on cutting deformation during the machining process.

In the cutting process of nickel-based superalloys, because of the high strain rate and cutting temperature, the cutting deformation is complex and there exist hardening and softening pheno...

More and more experiments have shown that particle-reinforced metal matrix composites (PMMC) exhibit obvious size effects. The aclassic plasticity theory does not contain internal length scale and cannot explain this size effect. In this paper, based on the Taylor relationship, the concept of "geometrically necessary dislocations" and the mechanism of dislocation multiplication, slippage and extinguishing, a constitutive equation for SiCp/Al composites related to strain gradient is established. The established equation is imported into Abaqus for simulation by writing a user subroutine Vumat. Combining the simulation and experimental results, the effects of stress, temperature, cutting force, strain gradient effect and its dimensional effect on cutting deformation during machining SiCp/Al composites are analyzed from the perspectives of material micro-plasticity mechanics and material dislocation theory. The results show that the presence of SiC particles changes the microstructure of the matrix material, and induce a high strain gradient in the matrix. This high strain gradient makes the material more prone to shear deformation localization. In the cutting process, the defects and breakage of the SiC particles themselves will lead to the formation of micro-cracks. The growth of micro-cracks in the shearing area is an important factor in the generation of chips. By comparing the simulation results with the experimental results, the modified constitutive model is closer to the experimental results, indicating that the established theoretical model based on the strain gradient can better reflect the cutting process of particle-reinforced metal matrix composites.

This paper develops a Galerkin approach for two-sided fractional differential equations with variable coefficients. By the product rule, we transform the problem into an equivalent formulation which additionally introduces the fractional low-order term. We prove the existence and uniqueness of the solutions of the Dirichlet problems of the equations with certain diffusion coefficients. We adopt the Galerkin formulation, and prove its error estimates. Finally, several numerical examples are provided to illustrate the fidelity and accuracy of the proposed theoretical results.

Nickel-based alloy Inconel718 is one kind of complex alloy with multiple components. There is complex cutting deformation (shear localization of material) in high-speed cutting process. The chip shows a serrated shape. Through analyzing the chip morphology, the change of microstructure and development of shear band is analyzed, and the formation mechanism of the shear band is revealed. Based on the formation mechanism of shear band, the coupled elastoplastic-damage constitutive model is proposed to describe the shear stress during the cutting process. The shear band width has been determined by micrographic observations and theoretical model calculation. The experimental and theoretical results show that the shear band width in chip formation decreases linearly with an increase in the cutting speed.

Nickel-based superalloy Inconel718 has excellent properties such as good fatigue resistance, creep resistance, oxidation resistance and corrosion resistance. It has been widely used in aerospace industry. However, nickel-based superalloy is a kind of typical difficult-to process-material. The alloying elements which enhanced material exist in the form of high hardness compound (TiC, NbC and other interphase hard point). These high hardness compounds led to complicate cutting deformation, high cutting temperature, large cutting force and severe tool wear. According to the characteristics in cutting Inconel718 and the microstructure of cemented carbide tool, the wear properties and mechanism of carbide tool in cutting Inconel718 process are revealed by multi-scale analysis method. The main wear forms that wear debris peeled from the tool substrate are given and the evolution mechanism of tool wear caused by the crack in the cutting process is deeply studied.

Inconel718 is one kind of nickel-based superalloy strengthened by body centered tetragonal γ ″ and face centered cubic γ ′ precipitation, which has a high yield strength, high corrosion resistance and oxidation resistance at high temperature. Alloying elements exist in the form of high hardness compounds, such as TiC, NbC and other interphase hard point. These high hardness compounds result in the presence of high cutting temperature, large plastic deformation, especially the generation of residual stress in the machined surface. In this paper, the multi-scale finite element model of Inconel718 is established, and the cohesive element is added into the brittle phase particles to conduct the cutting simulation process. The accuracy of the established model is verified according to the chip morphology and the cutting force. The formation mechanism and distribution law of residual stress in the machined surface is studied deeply. The results show that the simulation results of the multi-scale finite element model which adds the brittle phase particles are closer to the experimental results. The larger the size of the brittle phase particles is, the smaller the residual stress of the workpiece is. Along the depth direction of workpiece, the influence of the brittle phase particles on the residual stress is getting smaller and smaller. This study provides a theoretical basis and reference for the further optimization of Inconel718 cutting performance and surface integrity.

Cemented carbide is widely used as tool material since it has a series of excellent properties such as high hardness, wear resistance, good strength and toughness. The addition of rare earth elements can improve the high temperature crack resistance and deformation resistance of WC-Co cemented carbide. In this paper, a WC-Co model was established based on the first-principles method. The energy of the structure doped with rare earth elements in four positions is calculated to determine the most stable structure, and then carry out the model optimization. The elastic constants, electronic properties, and thermodynamic properties of WC-Co before and after doping were calculated. Furthermore, the elastic properties of the two materials was analyzed by comparing the parameters of Young's modulus and Poisson's ratio. Their thermodynamic properties were explored by calculating the enthalpy, entropy, free energy and specific heat capacity of the two structures. The results shows that the comprehensive performance of cemented carbide materials doped with rare earth elements is significantly improved.

In this paper, we propose a three-level linearized finite difference scheme for the high-dimensional nonlinear Ginzburg–Landau equation with fractional Laplacian. The Crank–Nicolson scheme is used for time discretization, and the fractional Laplacian is discretized by the fractional centered difference scheme. The proposed difference scheme (i.e. a linear system) can be solved efficiently by fast Fourier transform (FFT) and complex conjugate gradient method, since the coefficient matrix is a multi-level block Toeplitz matrix. Furthermore, we analyze the unique solvability and boundedness of solution of the difference scheme by the discrete energy method. It is also proved that the difference scheme is unconditionally stable and second-order accurate in time and space with respect to l ∞ -norm. Finally, several numerical examples are provided to validate the theoretical results.

Nickel-based superalloy Alloy 718 is widely used in aerospace and power industry due to its mechanical and physical properties at elevated temperature. In the process of high-speed cutting Alloy 718, plastic behavior of material in the cutting zone is investigated by quick-stop tests and split-Hopkinson pressure bar (SHPB) test at elevated temperatures with strain rates ranging from 5 × 103 s−1 to 10.5 × 103 s−1 and temperatures between 500 and 800 °C. The results show that a significant thermal softening effect occurs in the process of material deformation. Based on the kinematics of the dynamic recrystallization, the combined flow stress constitutive equations of the work hardening and softening are established for describing the plastic behavior of the material in high speed cutting of Alloy 718. Finally, the predicted results of the model quite coincide with the experimental values, showing that the established constitutive model can well reflect the deformation characteristics in high-speed machining of Alloy 718.

The lightweight aluminum 3D curved structure part has the characteristics of high structural strength, excellent aerodynamic performance, and flowing geometric shape. It is increasingly used in the fields of railway transportation, aerospace, and other high-end vehicle manufacture industry. However, with the increase of forming dimensions, as well as the large, thin-walled, complex forming features, it is urgent to study the precise plastic forming method for this kind of difficult-to-deform materials. Based on the new type of flexible multi-points 3D stretch-bending (3D FSB) process, the precision forming method for these hard-to-deform parts was studied in this paper. Extensive numerical simulations for the 3D FSB forming of the target parts have been performed by finite element methods. The simulation results show good agreement with the experiment results, and the max shape error of springback prediction is less than 0.3 mm. Then, based on the measured shape error of the 3D formed parts, an iterative overbending method for envelope surface of the multi-point die (MPD) is proposed to realize precise forming of the 3D curved structure parts. After four times adjustment of MPD, the simulation results show that the contour error is reduced from 1.01 to 0.06%, the maximum springback error changes from 30.16 to 1.66 mm. According to the adjustment parameters acquired in the optimization process, the actual experimental measured contour error is 0.05%, the maximum springback error is 1.41 mm, which achieved the forming requirements of the target parts and verified the effectiveness of the compensation method.

The nickel-based alloy Inconel718 is widely used in the field of aerospace because it has a high yield strength, high corrosion resistance, and high-temperature oxidation resistance. These excellent performances were obtained through the precipitation strengthening and since it has the phase of body-centered tetragonal γ ″ and face-centered cubic γ ′.The alloying elements which make material strengthen exist in the form of high hardness compounds, such as TiC, NbC, and other interphase hard point. These high hardness compounds result in complex cutting deformation of cutting process. In this paper, the multi-scale finite element model of Inconel718 is established and the cohesive element is added into the brittle phase particles to conduct the cutting simulation. The simulation results obtained by the proposed multi-scale simulation model are closer to the experimental results, so as to illustrate the accuracy of the proposed model. On the basis, the action mechanism of the brittle phase on the grain dislocation slip and the effect of brittle phase on the morphology evolution of serrated chip are analyzed.

Self-reinforced SiAlON ceramic tool materials, due to its unique properties such as high wear resistance, high hardness and low affinity with metal, is widely used in machining nickel-based alloy. The self-reinforced SiAlON ceramic tool was used in the experimental process of high speed milling nickel-based alloy Inconel718. The results obtained through observing the tool wear morphology and further analysis showed that when cutting speed vc = 50- 200 m/min, abrasive wear and lamellar spalling was the main cause of tool wear. When cutting speed vc = 350, 500 m/min, the bond strength between b-SiAlON whisker and SiAlON matrix reduced, and then the tool material fell off, which led to the formation of hole and groove. When the hole and groove mark connected, the crack nucleation formed. The crack propagation resulted in fracture eventually. At last, according to the tool wear mechanism, tool wear model was established and the optimal cutting temperature range, which can lead to minimum tool wear in milling Inconel718 using self-reinforced SiAlON ceramic tool, was obtained.

In this paper, an efficient algorithm is presented by the extrapolation technique to improve the accuracy of finite difference schemes for solving the fractional boundary value problems with nonsmooth solution. Two popular finite difference schemes, the weighted shifted Grunwald difference (WSGD) scheme and the fractional centered difference (FCD) scheme, are revisited and stability of the schemes is shown in maximum norm. Based on the analysis of leading singularity of exact solution for the underlying problem, it is demonstrated that, with the use of the proposed algorithm, the improved WSGD and FCD schemes can achieve higher accuracy than the original ones for nonsmooth solution. To further improve the accuracy for solving problems with small fractional order, an extended algorithm dealing with two-term singularities correction is also developed. Several numerical examples are given to validate our theoretical prediction. It is shown that both accuracy and convergence rate of numerical solutions can be significantly improved by using the proposed algorithms.

In order to investigate the antiferromagnetic coupling of Co and Mn atoms in Cu2−xCoxMn1+yAl1−y, a Heusler alloy, under Mn rich condition, our basic research objects are Cu2MnAl with only one kind of magnetic atoms and Co2MnAl which remain ferromagnetic in Mn rich conditions. After a large number of calculations, we found that because the Co atom is higher than the d-band center of Cu atom, then the anti-bonding state of Mn atom is pushed above Fermi level, thus changing the d-orbital electron arrangement of Mn atom, making the original antiferromagnetic Mn atom become ferromagnetic. Based on this theory, a method of applying stress to the alloy to adjust the lattice size to change the magnetic moment of Mn atom is proposed to achieve the same effect as doping special atoms. In addition, it was also inferred that the ferromagnetism of the parent phase and the ferromagnetism of the martensite phase are closely related to the d-band center caused by the change of lattice size.

In this work we study the finite difference method for the fractional diffusion equation with high-dimensional hyper-singular integral fractional Laplacian. We first propose a simple and easy-to-implement discrete approximation, i.e., fractional centered difference scheme with γth-order ( γ ≤ 2 ) convergence for the fractional operator. Based on the established approximation, we then construct a finite difference scheme to solve fractional diffusion equations and analyze the stability and convergence in discrete energy norm ( 0 α ≤ 2 ) and in discrete maximum norm ( 1 α ≤ 2 ). We further present a fast solver for the linear system which is obtained by discretization on rectangular domain and use the fictitious domain method to extend the fast solver to the non-rectangular one. Several numerical results are provided to support our theoretical results.

The numerical solution for the one-dimensional complex fractional Ginzburg–Landau equation is considered and a linearized high-order accurate difference scheme is derived. The fractional centered difference formula, combining the compact technique, is applied to discretize fractional Laplacian, while Crank–Nicolson/leap-frog scheme is used to deal with the temporal discretization. A rigorous analysis of the difference scheme is carried out by the discrete energy method. It is proved that the difference scheme is uniquely solvable and unconditionally convergent, in discrete maximum norm, with the convergence order of two in time and four in space, respectively. Numerical simulations are given to show the efficiency and accuracy of the scheme. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 105–124, 2017

This article is devoted to the study of some high-order difference schemes for the distributed-order time-fractional equations in both one and two space dimensions. Based on the composite Simpson formula and Lubich second-order operator, a difference scheme is constructed with convergence in the L1(L∞)-norm for the one-dimensional case, where τ,h and σ are the respective step sizes in time, space and distributed-order. Unconditional stability and convergence are proven. An ADI difference scheme is also derived for the two-dimensional case, and proven to be unconditionally stable and convergent in the L1(L∞)-norm, where h1 and h2 are the spatial step sizes. Some numerical examples are also given to demonstrate our theoretical results.

In machining titanium alloys, due to the low thermal conductivity and high chemical activity of titanium alloys, tool wear is serious and processing efficiency is very low. To avoid the effects of impurities, which were brought by the cutting fluid, the uncoated cemented carbide tool (WC-Co), which was suitable for cutting titanium alloys, was used for the experiments of dry-turning titanium alloy Ti-6Al-4V. A scanning electron microscopy (SEM) equipped with energy-dispersive X-ray spectrometer (EDS) was used to analyze tool wear mechanism. Based on analyzing the friction characteristic of tool–chip interface, tool wear mechanism was also studied and a physical evolution model of tool wear was established. The results showed that there existed serious adhesion, diffusion and oxidation at tool–chip interface and increasing cutting speed accelerated their occurrence. The physical evolution of tool wear behavior can reflect the loss process of tool material very well.