# Three-Dimensional Finite Element Numerical Simulation and Analysis of Solid-State Processing of Metal Material

Authors: Guang Su; Aimin Zhang
Journal: Complexity
 (2020)

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## Abstract

Solid-state processing of metal material is a very complex physical and chemical process, which is coupled by a series of variations including heat transfer, momentum transfer, mass transfer, and phase change. Applying three-dimensional (3D) finite element numerical method to the simulation of solid-state processing can perform analysis of metal material’s forging processes before production trial production, can obtain their relevant information such as material flow law, temperature field, and strain field under the minimum physical test conditions, thereby predicting metal material’s forming defects and improving their forging quality. On the basis of summarizing and analyzing previous research works, this paper expounded the current status and significance of solid-state processing of metal materials, elaborated the development background, current status, and future challenges of 3D finite element numerical simulation, introduced the discrimination method and free surface solution method of numerical simulation calculation, conducted finite element model’s geometric assumptions, material selection, element division, model establishment, parameter selection, and initial and boundary condition determination, and simulated and analyzed rheological casting, remelting heating, thixoforming, and rotary piercing processes of metal materials. The results show that the 3D finite element numerical method can not only simulate various processes of flow field, temperature field, stress field, and microstructure in solid-state processing but also can provide a reliable basis for effectively obtaining a reasonable description and finding a more optimized design plan for metal material processing in a short time, which plays an important role in understanding and analyzing solid metal forming process, controlling and optimizing process parameters, guiding and mastering rheological casting, and secondary heating and rotary piercing of metal materials.


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## Body

## 1. Introduction

Solid-state processing of metal material is a very complex physical and chemical process, which is coupled by a series of variations including heat transfer, momentum transfer, mass transfer, and phase change. The simulation of temperature field and strain field in the solid-state processing of metal materials is to simulate the process of metal transforming from liquid to solid from the perspective of heat transfer, and the numerical solution of the thermal differential equation is obtained in the presence of phase change [1]. With the help of numerical simulation technology of temperature field and strain field, the formation mechanism of major casting defects, such as shrinkage cavity, shrinkage porosity, thermal cracking, and macrosegregation, optimizes the design of the casting process, ensures the quality of castings, shortens the trial production cycle, and reduces production costs [2]. Solid-state processing of metal material refers to the deformability that a material can achieve without damage during plastic processing and is an important indicator of the material's bulk forming ability [3]. Material processing includes two aspects and the first one is stress state processing, which is related to the processing technology, mold and friction state, and can be controlled by changing the geometric size of the deformation area and the applied stress state; the other is internal workability, which reflects the decisive microstructure evolution under certain temperature, strain rate, and strain conditions through the flow stress curve of the material and is very sensitive to the initial state of the material [4].Applying three-dimensional (3D) finite element numerical method to the simulation of solid-state processing can perform analysis of metal material’s forging processes before production trial production, can obtain their relevant information such as material flow law, temperature field, and strain field under the minimum physical test conditions, and thereby predicting metal material’s forming defects and improving their forging quality [5]. The accurate simulation of these processes requires the constitutive equation of the liquid-solid mixture, and the contribution of the liquid to the deformation mechanism of mixture needs to be accurately described. Stress and strain field analysis is the basis for optimizing the rolling process. The key to accurate simulation is the establishment of solid material models and the optimization of simulation parameters, and the 3D simulation has further increased the difficulty [6]. Through numerical simulation, researchers can answer questions that cannot be answered in empirical design and understand the whole process of metal plastic forming, including the filling of materials at each stage of the metal forming process, the trend of material deformation, the stress, strain, and strain rate and forming inside the material load and velocity vector field [7]. This has great practical significance for the metal plastic forming process design, mold design, metal blank design, press selection, and forming quality control. Therefore, scholars have conducted a lot of research studies on the numerical simulation of metal material’s solid-state processing and have obtained many research results [8].On the basis of summarizing and analyzing previous research works, this paper expounded the current status and significance of solid-state processing of metal materials, elaborated the development background, current status, and future challenges of 3D finite element numerical simulation, introduced the discrimination method and free-surface solution method of numerical simulation calculation, conducted finite element model’s geometric assumptions, material selection, element division, model establishment, parameter selection, and initial and boundary condition determination, and simulated and analyzed rheological casting, remelting heating, thixoforming, and rotary piercing processes of metal materials. The study results of this paper provide a reference for further research studies of 3D finite element numerical simulation and analysis of solid-state processing of metal material. The detailed chapters are arranged as follows. Section2 introduces the discrimination method and free surface solution method of numerical simulation calculation. Section 3 conducts finite element model’s geometric assumptions, material selection, element division, model establishment, parameter selection, and initial and boundary condition determination. Section 4 simulates the rheological casting and remelting heating processes of metal materials. Section 5 analyzes the thixoforming and rotary piercing processes of metal materials. Section 6 is conclusion.


## 2. Methods and Principles

### 2.1. Discrimination Method of Numerical Simulation Calculation

Rheological casting is actually a 3D heat conduction process, but the rheological casting used for solid-state processing of metal materials mainly prepares cylindrical billets, which is a symmetric problem. The differential equations for solving the thermal field problem of continuous casting semisolid cylindrical ingots can be written as follows:(1)∂raTx∂x+∂rbTy∂y+∂rcTz∂z=fsx∂Ta∂tdL+fsy∂Tb∂tdL+fsz∂Tc∂tdL,where Tx, Ty, and Tz are the thermal conductivity in the x, y, and z directions, respectively; d is the material density; L is the latent heat of crystallization; and Ta, Tb, and Tc are the specific heat; a, b, and c are the axial displacement, fs(x) The above differential equation can be solved by applying the finite element method or the difference method as the power consumption function.According to the general viscosity model of early suspensions, the correlation between apparent viscosity and solid phase ratio and microstructure is(2)w=fs1+−dL2λk+1/Cp,where w is the apparent viscosity of the liquid alloy; λk is the critical solid phase rate, which mainly depends on the cooling rate and shear rate; and Cp is the specific surface area of the solid phase particles.The central content of the theory of plasticity of metallic materials is the establishment of yield criterion. Since the complex physical characteristics of metal material deformation are difficult to describe with a very accurate mathematical model, the yield criterion based on the relationship between equivalent stress and equivalent strain increment is expressed as follows:(3)K=1γm2σ+d2L2w−P,where K is the uniaxial yield stress; m is the stress component tensor; P is the hydrostatic pressure; and σ is the function of relative density, which can be obtained through uniaxial compression experiments and 3D compression experiments.Previous studies have shown that the viscosityη and the shear rate of the alloy melt continuously cooled at a certain shear rate are [9]. The relationship of γ can usually be expressed as follows:(4)η=K−fsCp−mr1+bfsann/k,where a and b are the critical solid fraction and instantaneous solid fraction related to the cooling rate and the shear rate, respectively, and m and n are the consecutive times; the other parameters are empirical constants.The thermal strainδij is related to the temperature and the thermal expansion coefficient of the material, and its expression is(5)δij=αijT−Tη,i=j,αijT+Tη,i≠j,where αij is the thermal expansion coefficient of mental material; T is the temperature; and Tη is the reference temperature and one is the direct coupling unit. In addition to the displacement freedom of the ordinary unit, the unit also has the temperature freedom. After being affected by the local temperature, the temperature field in the unit is first calculated according to the heat conduction theory, and the temperature is taken as the temperature field. The external load is applied to the element and then combined with the element force and displacement constraints, and the internal force distribution of the element is obtained.


### 2.2. Free Surface Solution Method

The change of the free surface of liquid metal belongs to the category of interface dynamics, which is a difficult problem to deal with in the simulation of the metal flow process. In this method, the coordinate system is established on the fluid mass, and the grid moves with the mass, so the calculation method is simple and the determination of the free surface is more convenient. However, the flow and deformation of the mass will inevitably cause the grid to be distorted and distorted so that they are kinked with each other and even the grids may intersect, making the calculation impossible [10].Since it is assumed that the solid material is equivalent to the porous material, the elastic deformation can be ignored. From the relationship between the strain rate tangent and the instantaneous stress, the rigid-constitutive equation of the solid material can be obtained as follows:(6)VI=γI∂T∂r,where VI is the yield function and r is the material constant. The rheological behavior of solid metals is mainly affected by factors such as shear rate, solid phase volume fraction, solid phase particle morphology, and agglomeration degree, which can be expressed as follows:(7)hx,y,z=ηγ,fs,m,c,where η is the apparent viscosity, γ is the shear rate, m is the morphology parameter of solid particles, and c is the parameter of the degree of agglomeration of solid particles.Therefore, when calculating the rolling force during the forming process, generally only the average total rolling force is calculated. The calculation formula is as follows:(8)Be=haσbVID+DcnσbVDe−n/L,where Be is the average total rolling force, ha is a parameter related to the taper of the core and uneven deformation, σb is a parameter that depends on the degree of hardening of the metal or alloy, D is the outer diameter of the rolled tube, Dc is the outer diameter of the tube, n is the amount of feed, and L is the length of the working part of the groove excluding the sizing section. If expressed in terms of heat capacity based on unit mass, the equation can be expressed as follows:(9)dW=mCpdT,where m is the mass of the object and Cp is the heat capacity per unit mass, that is, the specific heat capacity of the object. The total power absorbed by the material per unit volume during thermal processing can be expressed by the sum of two complementary functions:(10)U=∫0υσdυ+∫0συdσ.TheU value in the formula represents the power consumption due to plastic deformation, most of which is converted into heat. The dissipation margin is the power consumption related to the change of the structure during the deformation of the material, so the change also represents the change of the microstructure.


## 2.1. Discrimination Method of Numerical Simulation Calculation

Rheological casting is actually a 3D heat conduction process, but the rheological casting used for solid-state processing of metal materials mainly prepares cylindrical billets, which is a symmetric problem. The differential equations for solving the thermal field problem of continuous casting semisolid cylindrical ingots can be written as follows:(1)∂raTx∂x+∂rbTy∂y+∂rcTz∂z=fsx∂Ta∂tdL+fsy∂Tb∂tdL+fsz∂Tc∂tdL,where Tx, Ty, and Tz are the thermal conductivity in the x, y, and z directions, respectively; d is the material density; L is the latent heat of crystallization; and Ta, Tb, and Tc are the specific heat; a, b, and c are the axial displacement, fs(x) The above differential equation can be solved by applying the finite element method or the difference method as the power consumption function.According to the general viscosity model of early suspensions, the correlation between apparent viscosity and solid phase ratio and microstructure is(2)w=fs1+−dL2λk+1/Cp,where w is the apparent viscosity of the liquid alloy; λk is the critical solid phase rate, which mainly depends on the cooling rate and shear rate; and Cp is the specific surface area of the solid phase particles.The central content of the theory of plasticity of metallic materials is the establishment of yield criterion. Since the complex physical characteristics of metal material deformation are difficult to describe with a very accurate mathematical model, the yield criterion based on the relationship between equivalent stress and equivalent strain increment is expressed as follows:(3)K=1γm2σ+d2L2w−P,where K is the uniaxial yield stress; m is the stress component tensor; P is the hydrostatic pressure; and σ is the function of relative density, which can be obtained through uniaxial compression experiments and 3D compression experiments.Previous studies have shown that the viscosityη and the shear rate of the alloy melt continuously cooled at a certain shear rate are [9]. The relationship of γ can usually be expressed as follows:(4)η=K−fsCp−mr1+bfsann/k,where a and b are the critical solid fraction and instantaneous solid fraction related to the cooling rate and the shear rate, respectively, and m and n are the consecutive times; the other parameters are empirical constants.The thermal strainδij is related to the temperature and the thermal expansion coefficient of the material, and its expression is(5)δij=αijT−Tη,i=j,αijT+Tη,i≠j,where αij is the thermal expansion coefficient of mental material; T is the temperature; and Tη is the reference temperature and one is the direct coupling unit. In addition to the displacement freedom of the ordinary unit, the unit also has the temperature freedom. After being affected by the local temperature, the temperature field in the unit is first calculated according to the heat conduction theory, and the temperature is taken as the temperature field. The external load is applied to the element and then combined with the element force and displacement constraints, and the internal force distribution of the element is obtained.


## 2.2. Free Surface Solution Method

The change of the free surface of liquid metal belongs to the category of interface dynamics, which is a difficult problem to deal with in the simulation of the metal flow process. In this method, the coordinate system is established on the fluid mass, and the grid moves with the mass, so the calculation method is simple and the determination of the free surface is more convenient. However, the flow and deformation of the mass will inevitably cause the grid to be distorted and distorted so that they are kinked with each other and even the grids may intersect, making the calculation impossible [10].Since it is assumed that the solid material is equivalent to the porous material, the elastic deformation can be ignored. From the relationship between the strain rate tangent and the instantaneous stress, the rigid-constitutive equation of the solid material can be obtained as follows:(6)VI=γI∂T∂r,where VI is the yield function and r is the material constant. The rheological behavior of solid metals is mainly affected by factors such as shear rate, solid phase volume fraction, solid phase particle morphology, and agglomeration degree, which can be expressed as follows:(7)hx,y,z=ηγ,fs,m,c,where η is the apparent viscosity, γ is the shear rate, m is the morphology parameter of solid particles, and c is the parameter of the degree of agglomeration of solid particles.Therefore, when calculating the rolling force during the forming process, generally only the average total rolling force is calculated. The calculation formula is as follows:(8)Be=haσbVID+DcnσbVDe−n/L,where Be is the average total rolling force, ha is a parameter related to the taper of the core and uneven deformation, σb is a parameter that depends on the degree of hardening of the metal or alloy, D is the outer diameter of the rolled tube, Dc is the outer diameter of the tube, n is the amount of feed, and L is the length of the working part of the groove excluding the sizing section. If expressed in terms of heat capacity based on unit mass, the equation can be expressed as follows:(9)dW=mCpdT,where m is the mass of the object and Cp is the heat capacity per unit mass, that is, the specific heat capacity of the object. The total power absorbed by the material per unit volume during thermal processing can be expressed by the sum of two complementary functions:(10)U=∫0υσdυ+∫0συdσ.TheU value in the formula represents the power consumption due to plastic deformation, most of which is converted into heat. The dissipation margin is the power consumption related to the change of the structure during the deformation of the material, so the change also represents the change of the microstructure.


## 3. Finite Element Model and Parameter Selection

### 3.1. Basic Assumptions of the Geometric Model

The assumptions for the solid-state processing of metal materials are as follows: the metal material is a compressible continuum; the elastic deformation of the material is ignored during the forming process of the metal material; the solid material is a non-Newtonian fluid. Thixoforming is to cool and solidify the semisolid billet obtained by special processes such as stirring, then cut the material according to the required size, then reheat it to the semisolid temperature, and then place it in the mold cavity for forming. The heating and conveying of semisolid metal blanks are very convenient, the forming process is easy to control, and it is convenient to realize automated production [11]. At present, most processes use thixoforming. After holding the alloy melt for a certain period of time near the liquids temperature, it is cast to obtain a semisolid slurry method suitable for thixoforming, and liquid casting alloy has a low melt temperature, almost no overheating, and a uniform temperature field. During the casting process, a large number of crystal nuclei are uniformly generated in the melt to form small, uniform, and semisolid slurry, and the method is simple, efficient, energy saving, and material saving. The alloy ingot with the structure is heated and sheared during the transportation process through a heating source and a special spiral propulsion system so that it has importance and is injected into the mold cavity to form injection molding which is essentially a kind of rheological technology.


### 3.2. Material Selection and Unit Division

This paper chooses TC11 alloy as the experimental metal material. TCll alloy is a kind ofa-β-type heat-strength alloy with good comprehensive properties, which has excellent heat-strength properties below 500°C and high room temperature strength. The alloy is mainly used to manufacture parts such as compressor discs, blades, and drums of aero engines, as well as aircraft structural parts.From the perspective of forging, the upper boss of the forging is not easy to be filled, so the upper boss is placed on the upper die. Although the shape of the bottom of the forging is complex, it is easy to fill. The size of the blank is obtained according to previous calculations and experiments and the initial heating temperature is 950°C. Considering the heat loss during the transfer process, the blank temperature is set to 930°C in the simulation. The size of the material is obtained according to previous calculations and experiments with its size of 400 mm × 120 mm. The blank is divided into 40,000 tetrahedral units (Figure1).Figure 1
Metal material model and unit division for simulation and analysis of solid-state processing.


### 3.3. Establishment of Geometric Model

Finite element software is used to simulate the forming process, and two kinds of blanks, cylindrical and stepped, are used for forming research, respectively. At the same time, in order to reduce the number of unit divisions and increase the calculation speed and time, only a certain proportion of the blank is taken as the simulation research object. Tetrahedral elements are used to discriminate the blank and redraw according to the grid distortion at any time during the calculation process to ensure the accuracy and convergence of the calculation. The points on the symmetry plane are constrained so that their normal velocity along the symmetry plane is zero (Figure2). The deformation of the mold is not considered during the simulation, and its material property is a rigid body. In this paper, a simple and convenient parent element method is used to generate the grid of the initial blank. That is to say, the blank must be divided into simple sub-blocks and coordinate transformation, then transformed into a unit rectangle or a unit parallelepiped in the local coordinate system, and finally the grid is divided according to the specified grid division ratio in each direction.Figure 2
Establishment of the geometric model and its unit division of the metal material in solid-state processing.During the deformation process, high temperature and large deformation are often generated in a local area to cause mesh distortion, which will reduce the accuracy of the solution or cause the mold to be embedded in the blank and penetrate, so adaptive mesh re-partitioning technology is required. As the deformation intensifies, the initial grid of the blank will be severely distorted, which may result in the inability to continue the calculation. Therefore, in order to overcome the computational difficulties and low accuracy caused by grid distortion, when the finite element grid is distorted to a certain extent, the calculation must be stopped, the grid suitable for the calculation must be redivided, and the modified boundary conditions must be determined and then continued to calculate. The automatic mesh redraw technology can correct the distorted or distorted mesh caused by excessive deformation. According to a certain set criterion, such as mold penetration, plastic strain, and incremental step criterion, it can automatically regenerate a good-shaped mesh. The state variables in the original old grid are mapped to the newly divided grid to ensure subsequent calculations and improve calculation accuracy. Grid redrawing is generally divided into three steps of judgment of grid distortion, new grid generation, and data conversion between old and new grids [12].


### 3.4. Determination of Initial and Boundary Conditions

The processing of the boundary conditions is the determination of the representative section of the tool and work-piece shape in the calculation, taking into account the geometric conditions, thermal effects, and other aspects. Such as work-piece cooling caused by tools or temperature rise caused by plastic deformation, as well as mechanical effects, including elastic flattening and bouncing of metal materials, are not considered. These simplifications are made to reduce the required calculation time, and the basic assumption makes the physical influence not play a major role when analyzing the influence of the equipment structure on the uneven flow of materials. These steps apply boundary condition constraints on geometric objects or finite element meshes, apply symmetric boundary conditions to corresponding symmetric nodes, and establish a set of two boundary nodes:Y = 0 node X displacement and Y and Z rotation is 0 and X = 0 node Y displacement and X and Z rotation is 0.The metal material processing process mainly involves the heat transfer during the plastic deformation of the sheet surface. During the processing, the upper surface of the sheet material in contact with the air is a free surface, and the initial temperature of the sheet material and room temperature during the simulation is 24°C. The main heat exchange model is expressed as follows:(11)−k∂T∂x=λcT−T0,where k is the heat transfer coefficient between the metal material and the air and T is the absolute temperature. When calculating the temperature field, it is necessary to impose thermodynamic boundary conditions, including constant temperature boundary conditions and thermal convection boundary conditions. The constant temperature boundary condition simulates the surrounding external ambient temperature; the thermal convection boundary condition simulates the heat exchange on the contact surface between the structure and the air, assuming that the convective heat transfer coefficient is constant.In the model, the speed of the contact surface with the cooling boot is 0, that is,vx = 0, vy = 0, and vz = 0. The speed of the contact surface with the work roll is the work roll speed:(12)vxi=v0cosαi,vyi=v0sinαi,where v0 is the rotation speed of the work roll and i is the number of the node in the heat conduction matrix. The convective heat transfer coefficient on the entire contact surface changes with the temperature of the alloy and the mold and the contact state between the two, and it is accurately determined quite difficult. The metal material moves down at a constant speed, and the die adopts a floating structure, that is, during the pressing process of the metal material, the metal material forces the die to move downward together at the same speed. In the simulation process, it is assumed that the mold does not undergo plastic deformation and is a rigid body; in the incremental calculation, each reduction is taken as a certain value of the initial blank height.


## 3.1. Basic Assumptions of the Geometric Model

The assumptions for the solid-state processing of metal materials are as follows: the metal material is a compressible continuum; the elastic deformation of the material is ignored during the forming process of the metal material; the solid material is a non-Newtonian fluid. Thixoforming is to cool and solidify the semisolid billet obtained by special processes such as stirring, then cut the material according to the required size, then reheat it to the semisolid temperature, and then place it in the mold cavity for forming. The heating and conveying of semisolid metal blanks are very convenient, the forming process is easy to control, and it is convenient to realize automated production [11]. At present, most processes use thixoforming. After holding the alloy melt for a certain period of time near the liquids temperature, it is cast to obtain a semisolid slurry method suitable for thixoforming, and liquid casting alloy has a low melt temperature, almost no overheating, and a uniform temperature field. During the casting process, a large number of crystal nuclei are uniformly generated in the melt to form small, uniform, and semisolid slurry, and the method is simple, efficient, energy saving, and material saving. The alloy ingot with the structure is heated and sheared during the transportation process through a heating source and a special spiral propulsion system so that it has importance and is injected into the mold cavity to form injection molding which is essentially a kind of rheological technology.


## 3.2. Material Selection and Unit Division

This paper chooses TC11 alloy as the experimental metal material. TCll alloy is a kind ofa-β-type heat-strength alloy with good comprehensive properties, which has excellent heat-strength properties below 500°C and high room temperature strength. The alloy is mainly used to manufacture parts such as compressor discs, blades, and drums of aero engines, as well as aircraft structural parts.From the perspective of forging, the upper boss of the forging is not easy to be filled, so the upper boss is placed on the upper die. Although the shape of the bottom of the forging is complex, it is easy to fill. The size of the blank is obtained according to previous calculations and experiments and the initial heating temperature is 950°C. Considering the heat loss during the transfer process, the blank temperature is set to 930°C in the simulation. The size of the material is obtained according to previous calculations and experiments with its size of 400 mm × 120 mm. The blank is divided into 40,000 tetrahedral units (Figure1).Figure 1
Metal material model and unit division for simulation and analysis of solid-state processing.


## 3.3. Establishment of Geometric Model

Finite element software is used to simulate the forming process, and two kinds of blanks, cylindrical and stepped, are used for forming research, respectively. At the same time, in order to reduce the number of unit divisions and increase the calculation speed and time, only a certain proportion of the blank is taken as the simulation research object. Tetrahedral elements are used to discriminate the blank and redraw according to the grid distortion at any time during the calculation process to ensure the accuracy and convergence of the calculation. The points on the symmetry plane are constrained so that their normal velocity along the symmetry plane is zero (Figure2). The deformation of the mold is not considered during the simulation, and its material property is a rigid body. In this paper, a simple and convenient parent element method is used to generate the grid of the initial blank. That is to say, the blank must be divided into simple sub-blocks and coordinate transformation, then transformed into a unit rectangle or a unit parallelepiped in the local coordinate system, and finally the grid is divided according to the specified grid division ratio in each direction.Figure 2
Establishment of the geometric model and its unit division of the metal material in solid-state processing.During the deformation process, high temperature and large deformation are often generated in a local area to cause mesh distortion, which will reduce the accuracy of the solution or cause the mold to be embedded in the blank and penetrate, so adaptive mesh re-partitioning technology is required. As the deformation intensifies, the initial grid of the blank will be severely distorted, which may result in the inability to continue the calculation. Therefore, in order to overcome the computational difficulties and low accuracy caused by grid distortion, when the finite element grid is distorted to a certain extent, the calculation must be stopped, the grid suitable for the calculation must be redivided, and the modified boundary conditions must be determined and then continued to calculate. The automatic mesh redraw technology can correct the distorted or distorted mesh caused by excessive deformation. According to a certain set criterion, such as mold penetration, plastic strain, and incremental step criterion, it can automatically regenerate a good-shaped mesh. The state variables in the original old grid are mapped to the newly divided grid to ensure subsequent calculations and improve calculation accuracy. Grid redrawing is generally divided into three steps of judgment of grid distortion, new grid generation, and data conversion between old and new grids [12].


## 3.4. Determination of Initial and Boundary Conditions

The processing of the boundary conditions is the determination of the representative section of the tool and work-piece shape in the calculation, taking into account the geometric conditions, thermal effects, and other aspects. Such as work-piece cooling caused by tools or temperature rise caused by plastic deformation, as well as mechanical effects, including elastic flattening and bouncing of metal materials, are not considered. These simplifications are made to reduce the required calculation time, and the basic assumption makes the physical influence not play a major role when analyzing the influence of the equipment structure on the uneven flow of materials. These steps apply boundary condition constraints on geometric objects or finite element meshes, apply symmetric boundary conditions to corresponding symmetric nodes, and establish a set of two boundary nodes:Y = 0 node X displacement and Y and Z rotation is 0 and X = 0 node Y displacement and X and Z rotation is 0.The metal material processing process mainly involves the heat transfer during the plastic deformation of the sheet surface. During the processing, the upper surface of the sheet material in contact with the air is a free surface, and the initial temperature of the sheet material and room temperature during the simulation is 24°C. The main heat exchange model is expressed as follows:(11)−k∂T∂x=λcT−T0,where k is the heat transfer coefficient between the metal material and the air and T is the absolute temperature. When calculating the temperature field, it is necessary to impose thermodynamic boundary conditions, including constant temperature boundary conditions and thermal convection boundary conditions. The constant temperature boundary condition simulates the surrounding external ambient temperature; the thermal convection boundary condition simulates the heat exchange on the contact surface between the structure and the air, assuming that the convective heat transfer coefficient is constant.In the model, the speed of the contact surface with the cooling boot is 0, that is,vx = 0, vy = 0, and vz = 0. The speed of the contact surface with the work roll is the work roll speed:(12)vxi=v0cosαi,vyi=v0sinαi,where v0 is the rotation speed of the work roll and i is the number of the node in the heat conduction matrix. The convective heat transfer coefficient on the entire contact surface changes with the temperature of the alloy and the mold and the contact state between the two, and it is accurately determined quite difficult. The metal material moves down at a constant speed, and the die adopts a floating structure, that is, during the pressing process of the metal material, the metal material forces the die to move downward together at the same speed. In the simulation process, it is assumed that the mold does not undergo plastic deformation and is a rigid body; in the incremental calculation, each reduction is taken as a certain value of the initial blank height.


## 4. Simulation Results and Analyses

### 4.1. Rheological Casting Simulation of Solid-State Processing of Metallic Materials

A closed die is used to actively load the isothermal extrusion to form a curved metal material. By optimizing the cavity structure of the concave mold, the nondevelopable surface can be directly forged to achieve a net shape or an approximate net shape processing. The simulation results show that the metal flows smoothly, the forming effect is good, and there are no defects such as folding and dissatisfaction with the filling, which proves that the isothermal extrusion forming of curved metal materials is feasible. As shown in Figure3, when the load is 2 kPa, the vector change of the true radial plastic strain of the working cone is mainly deformed by wall reduction and the amount of wall reduction is evenly distributed; when the load is 3 kPa, the true radial plastic strain has remained unchanged and its value is the largest in the entire forming process because this stage is in the sizing stage of the cold rolling process; when the load is 6 kPa, the residual deformation of the short-side simply supported plate is similar to that of the free plate, which is greater than the deformation of the short-side fixed plate. It can be seen from the simulated load curve that the deformation process is roughly divided into three stages, namely, the initial deformation, cavity filling, and final forming [13]. In the initial stage of deformation, the load curve rises gently and the deformation force is small; the upward trend of the load curve increases with the increase of displacement, which shows that deformation is becoming more and more difficult.Figure 3
3D finite element numerical simulation results of rheological casting processing of metal material. (a) Load = 2 kPa. (b) Load = 3 kPa. (c) Load = 6 kPa.
(a)(b)(c)In the process of multistroke cold rolling of metal materials, the vector change of the true radial plastic strain of the working cone is divided into three stages. From the beginning to the section, the true radial plastic strain gradually increases, and its increasing trend is the largest. This is because at this stage, the working cone is mainly reduced in diameter and the amount of reduction is the largest, while the reduction in wall deformation is not obvious, which is usually called the empty reducing stage, so the value of this stage is relatively small. The radial plastic true strain also gradually increases, but the increasing trend decreases. This is because at this stage the working cone is mainly deformed by wall reduction and the amount of wall reduction is evenly distributed, while the reduction deformation carried out with the wall reduction is relatively large. The true radial plastic strain has remained unchanged and its value is the largest in the entire forming process because this stage is in the sizing stage of the cold rolling process, and the value remains unchanged. The axial length of the outer surface of the rolled tube is greater than the axial length of the neutral layer, and the axial length of the neutral layer is greater than the axial length of the inner surface, which indicates that the degree of anisotropy of the rolled tube ranges from the outer surface to the neutral layer and to the inner surface. The wall-reducing deformation of the material in the final stage is much greater than the diameter-reducing deformation, and the degree of anisotropy of the rolled tube decreases from the outer surface to the neutral layer to the inner surface.Under different constraint conditions, the magnitude of the residual stress and the residual deformation are different. The boundary constraint of the short-side fixed plate is the strongest and the deformation inside and outside the plane is restricted, the deformation amount is the smallest, but the residual stress is the largest. The residual deformation of the short-side simply supported plate is similar to that of the free plate, which is greater than the deformation of the short-side fixed plate, but the residual stress is smaller. Comparing the calculation results with or without heat preservation after processing, whether in terms of residual deformation or residual stress, the performance with heat preservation conditions is significantly better than that without heat preservation. When there is heat preservation, after the material is cooled to the heat preservation temperature, the temperature field is distributed uniformly through heat transfer, and the temperature difference gradient is small. After the heat preservation is removed, the whole material can be uniformly cooled to the on-site ambient temperature; compared with the case of no heat preservation, the material with heat preservation. The degree of uneven cooling is small so that the residual deformation and residual stress are small, indicating that heat preservation measures are indispensable for controlling the residual deformation and residual stress. During the processing and construction of the material shear wall, lateral supports are often set on the two wall panels that need to be processed to limit the effect of the out-of-plane deformation of the material during the processing. After the processing is completed, the support is removed, and the out-of-plane deformation of the material increases [14].


### 4.2. Remelting and Heating Simulation of Solid-State Processing of Metal Materials

In the process of metal deformation, the deformation temperature has a great influence on the metal deformation. The temperature change during the piercing process has a great influence on the plastic deformation resistance of the metal. When the temperature increases, the plasticity of the metal increases, the deformation resistance weakens, and the metal is easily deformed. On the contrary, the metal deformation resistance increases and the metal are difficult to deform. In addition, temperature is also the key influencing factor for the phase transition of metals, and the phase transition structure is the determining factor for the final mechanical properties of metals and the temperature distribution during the sample rolling process is not uniform. In the direct contact area between the roll and the sample, due to the relative sliding friction between the roll and the sample, it is mainly back slip, causing the temperature in the contact area between the sample and the roll to be higher than the rest (Figure4). The temperature in the area is tens of degrees higher. The metal equivalent strain in the cross-rolling piercing deformation is the highest near the roll transition cone, and gradually decreases to both sides. The largest deformation occurs in the contact area between the sample and the roll, which corresponds to the stress distribution. During the piercing process, the surface of the plug is subject to high temperature, high pressure, and high shear stress and is prone to wear, melt loss, and steel sticking, which shortens the service life of the plug and deteriorates the inner surface quality of the steel pipe. During the cross-rolling and piercing process, the maximum stress on the outer surface of the tube blank occurs in the contact area between the tube blank and the roll and the contact area with the guide plate.Figure 4
Numerical simulation results of displacement increment for mental material at different remelting temperature in solid-state processing.
(a)(b)(c)(d)This is because the plastic deformation of the semisolid slurry of the granular structure is mainly achieved by liquid flow. As the deformation temperature increases, the volume fraction of the liquid phase increases, and the liquid phase is gradually connected into a network to separate the solid particles and the particle rotation and movement are easier to proceed. The solid phase ratio is a key factor affecting the deformation characteristics of the semisolid slurry. Generally speaking, the longer the opening and drawing time, the closer the position of the crack is to the lower opening of the mold, that is, the length of the retained layer in the mold becomes longer with the extension of the opening and drawing time [15]. The greater the heat flux density, the closer the crack position is to the lower mouth of the crystallizer, that is, the length of the retention layer in the crystallizer increases as the heat flux density increases. The greater the heat flux density, the closer the crack position is to the lower mouth of the crystallizer, that is, the length of the retention layer in the crystallizer increases as the heat flux density increases (Figure 5). The longer the opening time or the greater the heat flux density, the greater the thickness of the solidified shell at the crack, which is consistent with common sense. From the perspective of the corresponding relationship between the crack position and the crack thickness, in general, the lower the crack position, the thicker the thickness of the solidified shell at the crack. If a crack occurs due to excessive drawing resistance, the position of the crack will be lower. Figure 5 concludes that during repeated grinding and deformation, since it is a new deformation based on the plastic deformation of the last pass, the surface metal has undergone work hardening after plastic deformation, so the deformation resistance is greater.Figure 5
Relationship between equivalent stress and load ratio. (a) Heat flux. (b) Processing temperature. (c) Pull speed. (d) Different processing effects.
(a)(b)(c)(d)The finite element analysis of solid-state rolling is a highly nonlinear problem. Considering material nonlinearity, boundary nonlinearity, and temperature nonlinearity, the use of simple geometric models is a means to make research progress. In order to study the change of solid state during rolling, two rolling methods, flat rolling and closed pass rolling, were used; in flat rolling, the solid slurry is simplified into a round bar. In the pass rolling, under the restriction of the pass and side sealing tools, the solid slurry has better fluidity and will form a small hole above the hole; therefore, the solid slurry can be simplified into cuboids. Because flat rolling has no restriction on the side of the rolled piece, the horizontal extension is large. At the same time, due to the friction force of the rolling, the contact part of the rolling piece head and the rolling piece extends in the longitudinal direction to form a spiral depression [16]. The downward pulling force causes the remaining part of the rolled piece to shrink and become thinner. Because the solid material has low flow stress and good fluidity, it can be rolled with a large amount of deformation, but at the same time, it is easy to cause uneven stress distribution on the cross-section. The stress distribution on the cross-section of the deformation zone is uneven, decreasing from the core to the side on the same cross-section; the longitudinal changes of the stress gradient on the surface of the deformation zone are inconsistent.


## 4.1. Rheological Casting Simulation of Solid-State Processing of Metallic Materials

A closed die is used to actively load the isothermal extrusion to form a curved metal material. By optimizing the cavity structure of the concave mold, the nondevelopable surface can be directly forged to achieve a net shape or an approximate net shape processing. The simulation results show that the metal flows smoothly, the forming effect is good, and there are no defects such as folding and dissatisfaction with the filling, which proves that the isothermal extrusion forming of curved metal materials is feasible. As shown in Figure3, when the load is 2 kPa, the vector change of the true radial plastic strain of the working cone is mainly deformed by wall reduction and the amount of wall reduction is evenly distributed; when the load is 3 kPa, the true radial plastic strain has remained unchanged and its value is the largest in the entire forming process because this stage is in the sizing stage of the cold rolling process; when the load is 6 kPa, the residual deformation of the short-side simply supported plate is similar to that of the free plate, which is greater than the deformation of the short-side fixed plate. It can be seen from the simulated load curve that the deformation process is roughly divided into three stages, namely, the initial deformation, cavity filling, and final forming [13]. In the initial stage of deformation, the load curve rises gently and the deformation force is small; the upward trend of the load curve increases with the increase of displacement, which shows that deformation is becoming more and more difficult.Figure 3
3D finite element numerical simulation results of rheological casting processing of metal material. (a) Load = 2 kPa. (b) Load = 3 kPa. (c) Load = 6 kPa.
(a)(b)(c)In the process of multistroke cold rolling of metal materials, the vector change of the true radial plastic strain of the working cone is divided into three stages. From the beginning to the section, the true radial plastic strain gradually increases, and its increasing trend is the largest. This is because at this stage, the working cone is mainly reduced in diameter and the amount of reduction is the largest, while the reduction in wall deformation is not obvious, which is usually called the empty reducing stage, so the value of this stage is relatively small. The radial plastic true strain also gradually increases, but the increasing trend decreases. This is because at this stage the working cone is mainly deformed by wall reduction and the amount of wall reduction is evenly distributed, while the reduction deformation carried out with the wall reduction is relatively large. The true radial plastic strain has remained unchanged and its value is the largest in the entire forming process because this stage is in the sizing stage of the cold rolling process, and the value remains unchanged. The axial length of the outer surface of the rolled tube is greater than the axial length of the neutral layer, and the axial length of the neutral layer is greater than the axial length of the inner surface, which indicates that the degree of anisotropy of the rolled tube ranges from the outer surface to the neutral layer and to the inner surface. The wall-reducing deformation of the material in the final stage is much greater than the diameter-reducing deformation, and the degree of anisotropy of the rolled tube decreases from the outer surface to the neutral layer to the inner surface.Under different constraint conditions, the magnitude of the residual stress and the residual deformation are different. The boundary constraint of the short-side fixed plate is the strongest and the deformation inside and outside the plane is restricted, the deformation amount is the smallest, but the residual stress is the largest. The residual deformation of the short-side simply supported plate is similar to that of the free plate, which is greater than the deformation of the short-side fixed plate, but the residual stress is smaller. Comparing the calculation results with or without heat preservation after processing, whether in terms of residual deformation or residual stress, the performance with heat preservation conditions is significantly better than that without heat preservation. When there is heat preservation, after the material is cooled to the heat preservation temperature, the temperature field is distributed uniformly through heat transfer, and the temperature difference gradient is small. After the heat preservation is removed, the whole material can be uniformly cooled to the on-site ambient temperature; compared with the case of no heat preservation, the material with heat preservation. The degree of uneven cooling is small so that the residual deformation and residual stress are small, indicating that heat preservation measures are indispensable for controlling the residual deformation and residual stress. During the processing and construction of the material shear wall, lateral supports are often set on the two wall panels that need to be processed to limit the effect of the out-of-plane deformation of the material during the processing. After the processing is completed, the support is removed, and the out-of-plane deformation of the material increases [14].


## 4.2. Remelting and Heating Simulation of Solid-State Processing of Metal Materials

In the process of metal deformation, the deformation temperature has a great influence on the metal deformation. The temperature change during the piercing process has a great influence on the plastic deformation resistance of the metal. When the temperature increases, the plasticity of the metal increases, the deformation resistance weakens, and the metal is easily deformed. On the contrary, the metal deformation resistance increases and the metal are difficult to deform. In addition, temperature is also the key influencing factor for the phase transition of metals, and the phase transition structure is the determining factor for the final mechanical properties of metals and the temperature distribution during the sample rolling process is not uniform. In the direct contact area between the roll and the sample, due to the relative sliding friction between the roll and the sample, it is mainly back slip, causing the temperature in the contact area between the sample and the roll to be higher than the rest (Figure4). The temperature in the area is tens of degrees higher. The metal equivalent strain in the cross-rolling piercing deformation is the highest near the roll transition cone, and gradually decreases to both sides. The largest deformation occurs in the contact area between the sample and the roll, which corresponds to the stress distribution. During the piercing process, the surface of the plug is subject to high temperature, high pressure, and high shear stress and is prone to wear, melt loss, and steel sticking, which shortens the service life of the plug and deteriorates the inner surface quality of the steel pipe. During the cross-rolling and piercing process, the maximum stress on the outer surface of the tube blank occurs in the contact area between the tube blank and the roll and the contact area with the guide plate.Figure 4
Numerical simulation results of displacement increment for mental material at different remelting temperature in solid-state processing.
(a)(b)(c)(d)This is because the plastic deformation of the semisolid slurry of the granular structure is mainly achieved by liquid flow. As the deformation temperature increases, the volume fraction of the liquid phase increases, and the liquid phase is gradually connected into a network to separate the solid particles and the particle rotation and movement are easier to proceed. The solid phase ratio is a key factor affecting the deformation characteristics of the semisolid slurry. Generally speaking, the longer the opening and drawing time, the closer the position of the crack is to the lower opening of the mold, that is, the length of the retained layer in the mold becomes longer with the extension of the opening and drawing time [15]. The greater the heat flux density, the closer the crack position is to the lower mouth of the crystallizer, that is, the length of the retention layer in the crystallizer increases as the heat flux density increases. The greater the heat flux density, the closer the crack position is to the lower mouth of the crystallizer, that is, the length of the retention layer in the crystallizer increases as the heat flux density increases (Figure 5). The longer the opening time or the greater the heat flux density, the greater the thickness of the solidified shell at the crack, which is consistent with common sense. From the perspective of the corresponding relationship between the crack position and the crack thickness, in general, the lower the crack position, the thicker the thickness of the solidified shell at the crack. If a crack occurs due to excessive drawing resistance, the position of the crack will be lower. Figure 5 concludes that during repeated grinding and deformation, since it is a new deformation based on the plastic deformation of the last pass, the surface metal has undergone work hardening after plastic deformation, so the deformation resistance is greater.Figure 5
Relationship between equivalent stress and load ratio. (a) Heat flux. (b) Processing temperature. (c) Pull speed. (d) Different processing effects.
(a)(b)(c)(d)The finite element analysis of solid-state rolling is a highly nonlinear problem. Considering material nonlinearity, boundary nonlinearity, and temperature nonlinearity, the use of simple geometric models is a means to make research progress. In order to study the change of solid state during rolling, two rolling methods, flat rolling and closed pass rolling, were used; in flat rolling, the solid slurry is simplified into a round bar. In the pass rolling, under the restriction of the pass and side sealing tools, the solid slurry has better fluidity and will form a small hole above the hole; therefore, the solid slurry can be simplified into cuboids. Because flat rolling has no restriction on the side of the rolled piece, the horizontal extension is large. At the same time, due to the friction force of the rolling, the contact part of the rolling piece head and the rolling piece extends in the longitudinal direction to form a spiral depression [16]. The downward pulling force causes the remaining part of the rolled piece to shrink and become thinner. Because the solid material has low flow stress and good fluidity, it can be rolled with a large amount of deformation, but at the same time, it is easy to cause uneven stress distribution on the cross-section. The stress distribution on the cross-section of the deformation zone is uneven, decreasing from the core to the side on the same cross-section; the longitudinal changes of the stress gradient on the surface of the deformation zone are inconsistent.


## 5. Discussion

### 5.1. Thixoforming Simulation of Solid-State Processing of Metallic Materials

From the relationship between volume change rate and pressing time under different load conditions, it can be seen that, in the initial stage of pressing, the volume changes more drastically. This is mainly due to the rapid decrease of the void density between the compact particles and the gradual compaction of the metal material particles. As the pressing progresses, the volume change trend is relatively gentle. At this stage, the metal material particles are rearranged and plastically deformed. From the comparison between the experimental value and the simulated value, it can be seen that the change of the average density goes through three stages with the increase of the load: the rapid growth stage, the gentle growth stage, and the saturation stage. The density distribution is in a stepped layered distribution that gradually increases from bottom to top in parallel to the movement direction of the die punch (Figure6). The maximum and minimum relative density of the compact are located at the end corners of the upper and lower surfaces, respectively, inside the press. The density distribution is more uniform than the outer surface, and the density distribution is a contour surface, which indicates that the radial flow and axial flow of the metal material are in a balanced state on this surface. The density distribution is layered parallel to the movement direction of die punching, and the density distribution on the outer surface is basically gradually increasing from bottom to top, and is basically parallel to the top surface. In the interior of the press, the density distribution is stepped. Gradually, except for the upper and lower corners, the density distribution inside the pressing piece is more even than the outer surface [17].Figure 6
Relationship between stress change and strain rate. (a) Displacement. (b) Mental material in the solid-state processing.
(a)(b)The flow velocity of the melt in the longitude direction is much larger than the axial casting velocity. The electromagnetic field in the velocity field presents a distribution and reaches its maximum value on the middle surface of the stator. The equivalent flow trajectory length of all solidified particles increases with the progress of casting, and the residence time of solid particles in the solidification zone is also significantly different. This method can accurately process free surfaces, effectively track the deformation history of fluid masses, conveniently realize grid optimization, obtain local accurate physical images, and can handle larger grid deformations. Numerical simulation technology can not only simulate the changes in the flow field, temperature field, stress field, and microstructure of the metal processing process but also predict the formation of defects in the metal processing process. Therefore, it has control over the understanding and analysis of the solid metal forming process, and optimization of process parameters can play an effective guiding role for rheological casting, secondary heating, and near-net thixoforming of parts. However, solid metal forming is a solid-liquid two-phase flow process and has importance, and its deformation resistance or apparent viscosity is not only related to the shear rate but also closely related to time. Therefore, the numerical simulation method must be able to track the fluid deformation process.Under the same reduced pressure condition, the surface of the plate is milled by single milling and repeated milling. The comparison of the effective strain shows that the cumulative effect of repeated milling on the effective strain is very obvious [17]. The reason for this result is that the deformation of the metal material during processing consists of two parts: elastic deformation and plastic deformation. The elastic deformation is restored after each grinding process, and the plastic deformation remains in the deformation area. During repeated grinding and deformation, since it is a new deformation based on the plastic deformation of the last pass, the surface metal has undergone work hardening after plastic deformation, so the deformation resistance is greater. In order to continue the deformation, the plate must be the material exerts greater compressive stress, which is also the reason why more effective strain can be obtained by multipass grinding under the same lower pressure condition. With the increase of milling passes, the maximum effective strain gradually increases. When the number of milling passes exceeds the second, even if the number of milling passes increases, the maximum effective strain does not increase much, indicating that the strengthening effect produced by strong plastic deformation tends to be saturated. No matter which milling method is used, the effective strain increases with the increase of milling times, and the curve is close to the linear change law.


### 5.2. Rotary Piercing Simulation of Solid-State Processing of Metal Materials

The alloy ingot with the structure is heated and sheared during the transportation process through a heating source and a special spiral propulsion system so that it has importance and is injected into the mold cavity to form injection molding which is essentially a kind of rheological technology. As shown in Figure7, in stage (1), wall thickness changes everywhere are not gradually and slowly, and the change at the beginning quickly reaches the final change result; in stage (2), the bending part of the tube gradually moves to the rear end of the tube as the bending angle increases; in stage (3), the wall thickness is still the initial value; as the bending angle increases, the deformation zone moves to this point; in stage (4), tensile and compressive stresses are generated on the pipe wall, resulting in a change in the wall thickness; in stage (5), no bending deformation occurs, and the wall thickness at this time remains basically unchanged; in stage (6), the inner concave edge of the elbow is compressed to increase the wall thickness, while the outer convex edge is stretched to reduce the wall thickness. The total change of the equivalent stress value during the bending deformation process of the pipe fitting increases with the increase of the bending angle, and the stress value of the inner concave side pipe wall of the curved pipe fitting is larger than that of the outer convex side pipe wall. The inner wall is subjected to compressive stress and the outer wall is subjected to compressive stress. The equivalent strain value of the inner pipe wall is larger than the outer pipe wall. In the bending process, due to the small bending radius and large bending deformation, the inner concave edge of the elbow is compressed to thicken the inner wall, while the outer convex edge is stretched to make the outer wall thinner [18].Figure 7
Rotary piercing simulation results of solid-state processing of metal materials. (a) Stage (1). (b) Stage (2). (c) Stage (3). (d) Stage (4). (e) Stage (5). (f) Stage (6).When the strain rate is low, driven by the pore pressure gradient, the liquid seeps out of the free surface, and the resulting pore pressure is much smaller than the total macroscopic pressure. At the other extreme, if the deformation is fast, the liquid does not have enough time to migrate to low pressure zone and causes the accumulation of pressure and the deformation in this case is nondraining [19]. In the nondraining deformation, the increased pressure reduces the pressure component of the equivalent stress, resulting in a reduction in the three-way equivalent stress because the reduction of the cohesive force is directly related to the partial stress of the applied stress. In the case of no drainage, the solid skeleton is destroyed, which easily causes deformation concentration. Without ignoring the pressure of the liquid, there is a lack of understanding of the behavior of metals in liquid-filled porous media both theoretically and experimentally. Because these relationships are not only theoretical, technological processes such as continuous casting and solid forging are likely to generate a large amount of liquid pressure. The accurate simulation of these processes requires the constitutive equation of the liquid-solid mixture, and the contribution of the liquid to the deformation mechanism of the mixture needs to be accurately described. The asymmetry of the metal solid down-compression deformation behavior and the use of liquid compression experiment, nondraining liquid compression experiment, and shear experiment verified the correctness of the model [20].In the actual forming process, the size range of different partitions is constantly changing, and the related areas are also constantly transformed. When they are in the stable deformation stage, the metal volume from the force transmission zone into the deformation zone and transfer from the deformation zone to the deformed volume of the zone is equal. With the progress of the deformation process, the force-transmitting zone keeps decreasing; the deformed zone keeps increasing, while the size of the deformed zone and the numerical distribution of stress remain unchanged [21]. During the deformation process, the degree of deformation, the diameter, thickness, length of the tube blank, and the adjustment of the structural parameters of the rotary wheel will all have a direct impact on the deformation state. When the feed depth is constant, the deformation resistance is reduced when the working angle is small, which is more conducive to metal deformation, but on the contrary, the distance of metal flow increases, and the deformation zone is correspondingly elongated, which increases the contact area between the blank and the surface of the rotary wheel. When the working angle of the rotary wheel is large, the contact area between the blank and the rotary wheel is reduced, and the deformation of the metal is more difficult, resulting in an increase in the deformation force. In the process of necking forming, the deformation zone is mainly affected by radial and axial compressive stresses, which reduces the diameter and increases the wall thickness and length. For thin-walled cylinders, when the radial compressive stress is too large, it is easy to cause wrinkling and instability in the deformed thin-walled area.


## 5.1. Thixoforming Simulation of Solid-State Processing of Metallic Materials

From the relationship between volume change rate and pressing time under different load conditions, it can be seen that, in the initial stage of pressing, the volume changes more drastically. This is mainly due to the rapid decrease of the void density between the compact particles and the gradual compaction of the metal material particles. As the pressing progresses, the volume change trend is relatively gentle. At this stage, the metal material particles are rearranged and plastically deformed. From the comparison between the experimental value and the simulated value, it can be seen that the change of the average density goes through three stages with the increase of the load: the rapid growth stage, the gentle growth stage, and the saturation stage. The density distribution is in a stepped layered distribution that gradually increases from bottom to top in parallel to the movement direction of the die punch (Figure6). The maximum and minimum relative density of the compact are located at the end corners of the upper and lower surfaces, respectively, inside the press. The density distribution is more uniform than the outer surface, and the density distribution is a contour surface, which indicates that the radial flow and axial flow of the metal material are in a balanced state on this surface. The density distribution is layered parallel to the movement direction of die punching, and the density distribution on the outer surface is basically gradually increasing from bottom to top, and is basically parallel to the top surface. In the interior of the press, the density distribution is stepped. Gradually, except for the upper and lower corners, the density distribution inside the pressing piece is more even than the outer surface [17].Figure 6
Relationship between stress change and strain rate. (a) Displacement. (b) Mental material in the solid-state processing.
(a)(b)The flow velocity of the melt in the longitude direction is much larger than the axial casting velocity. The electromagnetic field in the velocity field presents a distribution and reaches its maximum value on the middle surface of the stator. The equivalent flow trajectory length of all solidified particles increases with the progress of casting, and the residence time of solid particles in the solidification zone is also significantly different. This method can accurately process free surfaces, effectively track the deformation history of fluid masses, conveniently realize grid optimization, obtain local accurate physical images, and can handle larger grid deformations. Numerical simulation technology can not only simulate the changes in the flow field, temperature field, stress field, and microstructure of the metal processing process but also predict the formation of defects in the metal processing process. Therefore, it has control over the understanding and analysis of the solid metal forming process, and optimization of process parameters can play an effective guiding role for rheological casting, secondary heating, and near-net thixoforming of parts. However, solid metal forming is a solid-liquid two-phase flow process and has importance, and its deformation resistance or apparent viscosity is not only related to the shear rate but also closely related to time. Therefore, the numerical simulation method must be able to track the fluid deformation process.Under the same reduced pressure condition, the surface of the plate is milled by single milling and repeated milling. The comparison of the effective strain shows that the cumulative effect of repeated milling on the effective strain is very obvious [17]. The reason for this result is that the deformation of the metal material during processing consists of two parts: elastic deformation and plastic deformation. The elastic deformation is restored after each grinding process, and the plastic deformation remains in the deformation area. During repeated grinding and deformation, since it is a new deformation based on the plastic deformation of the last pass, the surface metal has undergone work hardening after plastic deformation, so the deformation resistance is greater. In order to continue the deformation, the plate must be the material exerts greater compressive stress, which is also the reason why more effective strain can be obtained by multipass grinding under the same lower pressure condition. With the increase of milling passes, the maximum effective strain gradually increases. When the number of milling passes exceeds the second, even if the number of milling passes increases, the maximum effective strain does not increase much, indicating that the strengthening effect produced by strong plastic deformation tends to be saturated. No matter which milling method is used, the effective strain increases with the increase of milling times, and the curve is close to the linear change law.


## 5.2. Rotary Piercing Simulation of Solid-State Processing of Metal Materials

The alloy ingot with the structure is heated and sheared during the transportation process through a heating source and a special spiral propulsion system so that it has importance and is injected into the mold cavity to form injection molding which is essentially a kind of rheological technology. As shown in Figure7, in stage (1), wall thickness changes everywhere are not gradually and slowly, and the change at the beginning quickly reaches the final change result; in stage (2), the bending part of the tube gradually moves to the rear end of the tube as the bending angle increases; in stage (3), the wall thickness is still the initial value; as the bending angle increases, the deformation zone moves to this point; in stage (4), tensile and compressive stresses are generated on the pipe wall, resulting in a change in the wall thickness; in stage (5), no bending deformation occurs, and the wall thickness at this time remains basically unchanged; in stage (6), the inner concave edge of the elbow is compressed to increase the wall thickness, while the outer convex edge is stretched to reduce the wall thickness. The total change of the equivalent stress value during the bending deformation process of the pipe fitting increases with the increase of the bending angle, and the stress value of the inner concave side pipe wall of the curved pipe fitting is larger than that of the outer convex side pipe wall. The inner wall is subjected to compressive stress and the outer wall is subjected to compressive stress. The equivalent strain value of the inner pipe wall is larger than the outer pipe wall. In the bending process, due to the small bending radius and large bending deformation, the inner concave edge of the elbow is compressed to thicken the inner wall, while the outer convex edge is stretched to make the outer wall thinner [18].Figure 7
Rotary piercing simulation results of solid-state processing of metal materials. (a) Stage (1). (b) Stage (2). (c) Stage (3). (d) Stage (4). (e) Stage (5). (f) Stage (6).When the strain rate is low, driven by the pore pressure gradient, the liquid seeps out of the free surface, and the resulting pore pressure is much smaller than the total macroscopic pressure. At the other extreme, if the deformation is fast, the liquid does not have enough time to migrate to low pressure zone and causes the accumulation of pressure and the deformation in this case is nondraining [19]. In the nondraining deformation, the increased pressure reduces the pressure component of the equivalent stress, resulting in a reduction in the three-way equivalent stress because the reduction of the cohesive force is directly related to the partial stress of the applied stress. In the case of no drainage, the solid skeleton is destroyed, which easily causes deformation concentration. Without ignoring the pressure of the liquid, there is a lack of understanding of the behavior of metals in liquid-filled porous media both theoretically and experimentally. Because these relationships are not only theoretical, technological processes such as continuous casting and solid forging are likely to generate a large amount of liquid pressure. The accurate simulation of these processes requires the constitutive equation of the liquid-solid mixture, and the contribution of the liquid to the deformation mechanism of the mixture needs to be accurately described. The asymmetry of the metal solid down-compression deformation behavior and the use of liquid compression experiment, nondraining liquid compression experiment, and shear experiment verified the correctness of the model [20].In the actual forming process, the size range of different partitions is constantly changing, and the related areas are also constantly transformed. When they are in the stable deformation stage, the metal volume from the force transmission zone into the deformation zone and transfer from the deformation zone to the deformed volume of the zone is equal. With the progress of the deformation process, the force-transmitting zone keeps decreasing; the deformed zone keeps increasing, while the size of the deformed zone and the numerical distribution of stress remain unchanged [21]. During the deformation process, the degree of deformation, the diameter, thickness, length of the tube blank, and the adjustment of the structural parameters of the rotary wheel will all have a direct impact on the deformation state. When the feed depth is constant, the deformation resistance is reduced when the working angle is small, which is more conducive to metal deformation, but on the contrary, the distance of metal flow increases, and the deformation zone is correspondingly elongated, which increases the contact area between the blank and the surface of the rotary wheel. When the working angle of the rotary wheel is large, the contact area between the blank and the rotary wheel is reduced, and the deformation of the metal is more difficult, resulting in an increase in the deformation force. In the process of necking forming, the deformation zone is mainly affected by radial and axial compressive stresses, which reduces the diameter and increases the wall thickness and length. For thin-walled cylinders, when the radial compressive stress is too large, it is easy to cause wrinkling and instability in the deformed thin-walled area.


## 6. Conclusions

This paper conducted finite element model’s geometric assumptions, material selection, element division, model establishment, parameter selection, and initial and boundary condition determination and simulated and analyzed rheological casting, remelting heating, thixoforming, and rotary piercing processes of metal materials. From the relationship between volume change rate and pressing time under different load conditions, it can be seen that, in the initial stage of pressing, the volume changes more drastically. This is mainly due to the rapid decrease of the void density between the compact particles and the gradual compaction of the metal material particles. At this stage, the metal material particles are rearranged and plastically deformed and the density distribution is in a stepped layered distribution that gradually increases from bottom to top in parallel to the movement direction of the die punch. The maximum and minimum relative density of the compact are located at the end corners of the upper and lower surfaces, respectively, inside the press. The density distribution is more uniform than the outer surface, and the density distribution is a contour surface, which indicates that the radial flow and axial flow of the metal material are in a balanced state on this surface. The results show that the 3D finite element numerical method can not only simulate various processes of flow field, temperature field, stress field, and microstructure in solid-state processing but also can provide a reliable basis for effectively obtaining a reasonable description and finding a more optimized design plan for metal material processing in a short time, which plays an important role in understanding and analyzing solid metal forming process, controlling and optimizing process parameters, guiding and mastering rheological casting, and secondary heating and rotary piercing of metal materials.



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*Source: 8819745-2020-11-16.xml*