SiC f Finite Element Simulation Method for Ultrasonic Vibration-Assisted Cutting of SiC

Abstract

The application relates to a SiC f ultrasonic vibration assisted cutting finite element simulation method of SiC, which comprises the following steps: (1) establishing a three-dimensional micro-geometric model (workpiece model and tool model); (2) dividing the grid; setting the tool model as a rigid body; setting the grid element type and grid size of the workpiece model and the tool model; (3) defining the boundary conditions; the boundary conditions comprise: a) all six degrees of freedom of the bottom of the workpiece model are completely constrained; b) the cutting speed of the tool model is equal to the actual cutting speed of the tool in the experiment; c) the motion speed function of the tool model under three cutting conditions satisfies a specific expression; (4) defining the material constitutive model and the damage criterion; (5) defining the contact condition; (6) calculating and precision control; (7) submitting the task and carrying out the finite element simulation calculation. The application can make up for the defects of the prior art and realize the simulation of the material removal mechanism of SiC f / SiC in ultrasonic vibration assisted cutting.

Description

Technical Field

[0001] This invention belongs to the field of composite material processing technology, and relates to a SiC f / SiC ultrasonic vibration-assisted cutting finite element simulation method. Background Technology

[0002] Compared to most single-phase materials, SiC f / SiC composites are composed of phases with different properties. The synergistic effect between the high-hardness matrix, the anisotropic fiber reinforcement phase, and the weak interface phase is beneficial to improving the material's performance, but at the same time, it significantly reduces the material's machinability. Carbon fibers, silicon carbide fibers, and silicon carbide matrices are all highly brittle materials, and are easily damaged by localized high stress during processing, resulting in relatively serious mechanical damage. Under the action of the cutting edge, continuous fibers will debond and deform from the matrix during processing, leading to machining defects (mainly surface pits, edge tears, and delamination). Extensive research has shown that ultrasonic vibration-assisted machining technology has the potential to play a positive role in reducing machining damage and improving the quality of machined surfaces. In 2014, Wang Minghai et al. published "Simulation Study on Cutting Force of Ultrasonic Vibration Milling of Ceramic Matrix Composites" in "Mechanical Design and Manufacturing," which focused on ultrasonic-assisted milling of C with carbide end mills. f Finite element analysis of C / SiC composites revealed that ultrasonic vibration helps reduce cutting forces. Liu et al., in their paper "Experimental study on cutting force and surface quality in ultrasonic vibration-assisted milling of C / SiC composites" published in *The International Journal of Advanced Manufacturing Technology*, conducted conventional milling and ultrasonic vibration-assisted milling using diamond-coated milling cutters, proposing that ultrasonic vibration-assisted milling reduces tool wear and improves machining quality. However, there is currently little research on using cutting edge tools for C / SiC milling. f The mechanism of material removal in ultrasonic vibration-assisted cutting of SiC composite materials remains unclear.

[0003] As a fiber-rich material, SiC f In SiC composites, fiber breakage and damage during machining play a decisive role in the finished surface. This study aims to elucidate the effect of ultrasonic vibration-assisted machining technology on improving the surface finish of SiC composites. fThe effectiveness of machining the surface quality of SiC composite materials requires a deep understanding of fiber fracture and removal mechanisms under ultrasonic vibration-assisted cutting conditions. Currently, at ultrasonic frequencies of tens of kilohertz and high cutting speeds, no suitable high-frame-rate high-speed camera can meet the observation requirements. Furthermore, because the fibers are encapsulated within the matrix, existing microscopic detection techniques struggle to clearly capture the fiber fracture process. Finite element method (FEM) simulation technology provides a means to observe the physical field changes (such as stress and strain fields) and details of material fracture during the material removal process. Therefore, FEM has become a crucial tool for in-depth research on the effects of ultrasonic vibration-assisted cutting technology on SiC. f Effective methods to address the impact of SiC composite material removal mechanisms during machining processes are currently unavailable. f Research on the finite element simulation of material removal mechanism in the machining of SiC composite materials. Summary of the Invention

[0004] The purpose of this invention is to solve the problems existing in the prior art and provide a SiC f / SiC ultrasonic vibration-assisted cutting finite element simulation method.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] SiC f The steps of the finite element simulation method for ultrasonic vibration-assisted cutting of SiC are as follows:

[0007] (1) Establish a three-dimensional microscopic geometric model;

[0008] The three-dimensional micro-geometric model consists of a workpiece model and a tool model;

[0009] The workpiece model is a cubic structure, consisting of an equivalent homogeneous body and a three-dimensional micro-geometric model of composite materials arranged in parallel along the length direction;

[0010] The three-dimensional micro-geometric model of the composite material consists of a silicon carbide ceramic matrix and cylindrical fibers arranged in a regular matrix within it. The central axis of the cylindrical fibers is parallel to the height of the workpiece model, and the row direction of the regular matrix is ​​parallel to the length of the workpiece model.

[0011] The workpiece model satisfies the following condition: the stress in the height direction during cutting is zero at the bottom surface of the workpiece model;

[0012] The diameter of the cylindrical fibers is equal to the average diameter of the silicon carbide fibers used in the actual experiment; the center-to-center distance of the cylindrical fibers is equal to that of the SiC fibers used in the actual experiment. f The average center-to-center distance of silicon carbide fibers in the / SiC composite material;

[0013] The shape and size of the tool model are the same as those of the tool used in the actual test;

[0014] The tool model is located on the side of the composite workpiece geometry model away from the equivalent homogeneous body. The cutting direction is parallel to the length of the workpiece model, and the distance between the position of the tool tip and the top surface of the composite workpiece geometry model is equal to the cutting depth. Since the equivalent homogeneous body is set on the side of the composite workpiece geometry model away from the tool model along the cutting direction, the present invention can support the composite workpiece geometry model and prevent it from collapsing during the cutting process.

[0015] (2) Divide the grid;

[0016] The tool model is set as a rigid body, given that the modulus of PCD tools is much higher than that of SiC. f Since the tool model is set as a rigid body, and tool wear is not considered, the tool is made of SiC composite material.

[0017] Set the mesh element type of the workpiece model and tool model to 3D 8-node reduced integral solid element C3D8R;

[0018] Set the mesh size of the workpiece model. The mesh size should be smaller than the smallest material element size that is removed during material fracture in the cutting process. In addition, the mesh size should not be too small. Computational efficiency should also be considered. The smaller the mesh, the lower the computational efficiency. The specific mesh size should be determined through multiple trials in the simulation.

[0019] Set the mesh size of the tool model. The mesh size at the blunt circle of the tool cutting edge is smaller than the radius of the blunt circle. Since the tool is a rigid body, it will not produce mesh deformation. Therefore, there is no requirement for the mesh size from a calculable point of view. However, since the tool cutting edge has a blunt circle and the size is on the micrometer scale, the mesh size at the blunt circle of the cutting edge must be smaller than the radius of the blunt circle to ensure the geometric integrity of the tool.

[0020] (3) Define boundary conditions;

[0021] The boundary conditions are as follows:

[0022] a) All six degrees of freedom at the bottom of the workpiece model are fully constrained. In actual processing, the workpiece is clamped and fixed on the worktable. Therefore, in the finite element simulation, all six degrees of freedom at the bottom of the workpiece model are fully constrained.

[0023] b) The cutting speed of the tool model is equal to the cutting speed of the tool in the actual test;

[0024] c) To achieve ultrasonic vibration-assisted cutting along and perpendicular to the cutting direction, vibration functions in the x and z directions need to be coupled to the tool based on the cutting speed. The motion velocity functions of the tool model under the three cutting conditions are shown in the following equations:

[0025]

[0026] Among them, ① corresponds to cutting condition without ultrasonic vibration, ② corresponds to cutting condition with ultrasonic vibration along the cutting direction, and ③ corresponds to cutting condition with ultrasonic vibration perpendicular to the cutting direction; v x (t), v y (t), v z (t) represents the velocity of the tool model along the x, y, and z directions, respectively, all in mm / s; v c f represents the cutting speed of the tool model, in mm / s. FEM The vibration frequency, measured in Hz, is equal to the vibration frequency of the ultrasound in the actual experiment; A FEM t represents the vibration amplitude in μm, which is equal to the vibration amplitude of the ultrasonic wave in the actual test; t represents the time in seconds.

[0027] (4) Define the material constitutive model and damage criterion;

[0028] The constitutive models of silicon carbide fibers and silicon carbide matrix are based on the brittle cracking model, while the constitutive model of the fiber-matrix interface is based on the cohesive force within zero-thickness elements (CZM).

[0029] (5) Define the contact conditions;

[0030] The finite element simulation contact model considers two different types of interaction between the workpiece and the tool: compression along the normal direction and friction along the tangential direction, such as... Figure 4 As shown in Figure a;

[0031] The classic pure kinematic master-slave contact algorithm is used to describe compression along the normal direction. First, the kinematic state of the finite element model is proposed. Then, the normal contact force is determined based on the contact penetration depth and process-related mass to counteract penetration. Considering that the focus of the study is the workpiece behavior, the workpiece is set as the slave component and the tool as the master component. In the pure kinematic master-slave contact algorithm, slave nodes cannot penetrate the master surface, while master nodes can penetrate the slave surface, such as... Figure 4 As shown in b;

[0032] A modified Coulomb friction model is used to describe tangential friction. Friction at the tool-workpiece contact surface affects cutting force and surface quality. Therefore, choosing a suitable friction model to define the tool-chip contact problem is crucial for simulation. The tangential interaction between the workpiece and the tool includes both adhesion and slippage. Therefore, the modified Coulomb friction model is adopted, which considers both adhesion and slippage contact zones at the tool-chip contact surface. The formula is as follows:

[0033] ;

[0034] In the formula, τ is the shear stress, with units of MPa; τ max , where is the ultimate shear stress, in MPa; μ is the average friction coefficient of the tool-chip contact surface. In this invention, the friction coefficient between the matrix and the fiber is set to 0.3, the friction coefficient between fibers is set to 0.3, the friction coefficient between the fiber and the tool is set to 0.2, and the friction coefficient between the matrix and the tool is set to 0.2.

[0035] (6) Calculation and precision control;

[0036] An explicit central difference algorithm is used to solve the model. Explicit algorithms are more suitable for analyzing and solving dynamic nonlinear numerical problems than implicit algorithms. The principle of the central difference algorithm is to use differences instead of differentials, and to use linear extrapolation for the derivatives of displacement and acceleration. It does not require balancing iterations and has a fast calculation speed. In dynamic explicit algorithms (explicit central difference algorithm is a type of dynamic explicit algorithm), the solution of the next step is directly based on the solution of the current step. Therefore, the total calculation time is the sum of the time increments of each single step. Thus, the total calculation time of dynamic explicit algorithms depends on the length of the increment step. However, for the stability of the algorithm, the stability condition of dynamic explicit algorithms is that the time step increment is less than the limit. In fact, in finite element simulation, the selection of the time step increment is quite complex. It is necessary to balance the contradiction between the accuracy, stability and computational efficiency. Theoretically, the smaller the time step increment, the higher the model solution accuracy and the easier it is for the dynamic explicit algorithm to converge, but the calculation time increases accordingly. Therefore, choosing a reasonable single-step time increment (the default setting is used in ABAQUS, and the software will dynamically adjust it during the calculation) is crucial for reducing computation time while ensuring solution accuracy, especially for research on SiC. f The problem of material fracture and removal during the cutting of SiC composite materials is difficult to balance between computational cost and accuracy due to the small mesh size, large number of meshes and complex contact relationships.

[0037] Due to the limitations of time increments, this model employs mass scaling to reduce computational costs while ensuring computational accuracy, and also reasonably reduces the total time. Mass scaling artificially increases the density of the material, thereby increasing the settling time increment, reducing increment steps, and shortening the computation time. The premise of mass scaling is to ensure that the kinetic energy in the calculation is less than 10% of the total work done. Based on this, an appropriate mass scaling factor and actual computation time are determined. The expression for the settling time is as follows:

[0038] ;

[0039] In the formula, L e c is the length of the feature unit, in mm. dρ is the propagation wave velocity of the material, in m / s; E is the elastic modulus of the material, in MPa; ρ is the density of the material, in g / mm³. 3 ;

[0040] (7) Submit the task and perform finite element simulation calculations to realize SiC f Simulation of the material removal mechanism in ultrasonic vibration-assisted cutting of SiC composite materials.

[0041] As a preferred technical solution:

[0042] SiC as described above f / SiC ultrasonic vibration assisted cutting finite element simulation method, in step (1), the number of rows of the regular matrix is ​​7 and the number of columns is 3, that is, the geometric model of the composite material workpiece contains 21 cylindrical fibers. The 21 fibers can meet the requirements of showing the fiber fracture and damage during the cutting process, and the amount of calculation will not be too large.

[0043] SiC as described above f / SiC ultrasonic vibration-assisted cutting finite element simulation method, in step (1), there are two workpiece models, one with a cutting depth of less than 8μm and the other with a cutting depth of more than 11μm; for SiC f In the machining of SiC composite materials, two important material removal mechanisms of the fibers are microscopic brittle fracture and macroscopic brittle fracture. Therefore, two separate models are needed for simulation to cover the different material removal mechanisms. Experiments have shown that SiC… f The critical cutting depth for micro-brittle fracture and macro-brittle fracture of SiC composites during machining is 8-11 μm. Micro-brittle fracture occurs when the cutting depth is less than this value. Therefore, to simulate the effect of ultrasonic vibration of the cutting edge on the material removal mechanism and damage behavior of the fiber in the micro-brittle fracture domain, a cutting depth of less than 8 μm was selected. Similarly, macro-brittle fracture occurs when the cutting depth is greater than this value. Therefore, to simulate the effect of ultrasonic vibration of the cutting edge on the material removal mechanism and damage behavior of the fiber in the macro-brittle fracture domain, a cutting depth of more than 11 μm was selected.

[0044] SiC as described above f / SiC ultrasonic vibration assisted cutting finite element simulation method, in step (1), the difference in cutting depth between the two workpiece models is not less than 10μm, otherwise the simulation results will not have sufficient differences.

[0045] SiC as described above f / SiC ultrasonic vibration-assisted cutting finite element simulation method, in step (1), the heights of the two workpiece models are different, and the height of the workpiece model with a larger cutting depth is greater than that of the workpiece model with a smaller cutting depth. This is because the physical field distribution depth and subsurface damage depth of the workpiece model with a smaller cutting depth are much smaller than those of the workpiece model with a larger cutting depth. Therefore, if the height of the workpiece model with a smaller cutting depth is set to be consistent with the height of the workpiece model with a larger cutting depth, a large number of unnecessary elements will be generated, which will greatly reduce the calculation efficiency.

[0046] SiC as described above f / SiC ultrasonic vibration assisted cutting finite element simulation method, in step (2), the mesh size of each workpiece model increases linearly downward from the cutting plane, which is beneficial to improve the calculation efficiency.

[0047] SiC as described above f / SiC ultrasonic vibration assisted cutting finite element simulation method, in step (4), since a three-dimensional micro finite element model is used, the material behavior of three micro components, namely silicon carbide fiber, silicon carbide matrix and silicon carbide fiber-silicon carbide matrix interface, is involved in the cutting process. Considering that silicon carbide fiber and silicon carbide matrix are both brittle materials, the same constitutive model is used for silicon carbide fiber and silicon carbide matrix, but the model coefficients are different. The constitutive model of silicon carbide fiber-silicon carbide matrix interface is different from that of silicon carbide fiber.

[0048] Since both silicon carbide fibers and silicon carbide matrices are brittle materials, their yield stress is very close to their ultimate stress. Therefore, the plastic stage is not significant, and at high strain rates, the plastic stage can be ignored. Thus, the material behavior of silicon carbide fibers, silicon carbide matrices, and silicon carbide fiber-silicon carbide matrix interfaces includes two stages: an elastic stage and a degradation stage. In the elastic stage, stress and strain satisfy a linear relationship, meaning that the Young's modulus is constant in this stage. Figure 2 As shown in Stage I; in the degradation stage, when the maximum principal stress exceeds the tensile strength of the material, the material begins to fracture. At this time, Young's modulus decreases until the material fails, as shown in the diagram. Figure 2 As shown in stage II;

[0049] ① Silicon carbide fibers and silicon carbide matrix can be considered as isotropic materials. According to the theory of mechanics of materials, the stress-strain relationship of silicon carbide fibers and silicon carbide matrix in the elastic stage is a linear proportional relationship, as follows:

[0050] ;

[0051] In the formula, σ x σ y σ z These represent the stresses along the x, y, and z directions, respectively, in MPa; εx ε y ε z τ represents the strain along the x, y, and z directions, respectively; xy τ yz τ zx γ represents the shear stress tensor in the XOY, YOZ, and ZOX planes, respectively, in MPa; xy γ yz γ zx , respectively, are the angular strain tensors in the XOY, YOZ, and ZOX planes; C is the stiffness matrix, as follows:

[0052] ;

[0053] In the formula, ν xy ν yz ν zx Poisson's ratios in the XOY, YOZ, and ZOX planes, respectively; G xy G yz G zx E represents the shear modulus in the XOY, YOZ, and ZOX planes, respectively, in MPa; x E y E z These are the Young's moduli along the x, y, and z directions, respectively, in MPa; Δ is an intermediate variable, as detailed below:

[0054] ;

[0055] ② During the degradation stage, the brittle fracture of silicon carbide fibers and silicon carbide matrix exhibits two different types: Type I fracture and Type II fracture;

[0056] When it is a Type I fracture, the Rankine criterion, based on Type I fracture, is used to determine whether the material has cracked. Specifically, when the maximum principal tensile stress of the material exceeds the tensile strength σ... t At that time, the material will develop cracks;

[0057] When it is a type I fracture, the fracture energy cracking criterion based on stress-displacement response is used to describe the material behavior during crack propagation. Specifically, the material strength decreases as the crack propagates, and when the displacement reaches a set crack normal displacement δ... n When the material completely fails and experiences a complete loss of strength (generally considered as complete material failure), the formula for calculating the crack normal displacement is as follows:

[0058] ;

[0059] In the formula, δ n This represents the crack normal displacement, in μm. The fracture energy of a type I crack is expressed in N / m; σ t Tensile strength, unit is MPa; K IC The fracture toughness of the material is expressed in MPa·m. 1 / 2 E' is the equivalent Young's modulus of the material, in MPa.

[0060] When the fracture is of type II, the shear behavior of the material is described by the decrease in shear modulus during crack propagation. Based on this, Abaqus provides a shear-holding model, in which the post-crack shear stiffness is defined as a function of the cross-crack strain. In this shear-holding model, the post-crack shear modulus is defined as a portion of the uncracked shear modulus, as follows:

[0061] ;

[0062] In the formula, (=0.02) represents the crack initiation strain; (=0.2) and p (=2) are material parameters; G c G is the shear modulus of the material, in Pa; G is the shear modulus of the uncracked material, in Pa.

[0063] The cohesive force within zero-thickness elements (CZM) model is used to describe the material mechanical behavior of the pyrolytic carbon interface between the fiber and the matrix, as detailed in ③ and ④ below;

[0064] ③ In this model, the material properties of the interface are considered to be linearly elastic when there is no damage. According to the theory of mechanics of materials, the stress-strain relationship of the silicon carbide fiber-silicon carbide matrix interface in the elastic stage is a linear proportional relationship, as follows:

[0065] ;

[0066] In the formula, t is the nominal traction stress, in MPa; δ is the separation displacement, in mm; n represents the normal direction, and s and t represent the two shear directions; K n Normal stiffness, in N / mm; K s and K t Tangential stiffness, in N / mm;

[0067] ④ During the degradation stage, the damage initiation point of the silicon carbide fiber-silicon carbide matrix interface is determined using the secondary stress criterion in the cohesive model of the zero-thickness element. The formula is as follows:

[0068] ;

[0069] In the formula, t 0The contact stress required to initiate interface damage is expressed in MPa, and in this model, its value is assumed to be equal to the interface strength; t represents the contact stress, expressed in MPa; the superscript 0 indicates the moment when interface damage begins; the subscript n represents the normal direction, and s and t represent the two shear directions.

[0070] The rate of decrease in viscous stiffness after reaching the cracking criterion is described by the damage evolution law. The contact stress of interface separation in the absence of damage is predicted based on the damage variables, as shown in the following formula:

[0071] ;

[0072] In the formula, , , These are the nominal tensile stresses in the normal and two shear directions, respectively, without damage, in MPa; D' is the damage variable, used to describe the damage evolution of the interface, as follows:

[0073] ;

[0074] In the formula, δ n To effectively separate the normal component of the displacement, in mm, δ s and δ t To effectively separate the components of displacement in the two shear directions, the unit is mm; To effectively separate displacements, the unit is mm, including the normal (δ). n ) and shear direction (δ) s and δ t The components of ); the superscripts 0 and f represent the states of starting damage and completing failure, respectively; The maximum effective separation displacement obtained during the loading process, in mm;

[0075] The effective separation displacement at failure is derived using linear energy evolution, as shown in the following formula:

[0076] ;

[0077] In the formula, G represents the finite traction force at the initial damage site, expressed in Pa. c The fracture energy is taken as 8.0 J / m. 2 .

[0078] Beneficial effects:

[0079] Finite element method (FEM) simulation technology is widely used in the simulation and analysis of material removal mechanisms in composite material machining. Jia Zhenyuan et al., in their patent "A Simulation Method for Chip Formation in Cutting Fiber Reinforced Composite Materials," proposed a two-dimensional macroscopic modeling method, treating the workpiece material as a two-dimensional equivalent homogeneous body. However, this method cannot study the fracture removal behavior of each component phase in the composite material during the cutting process. Xu et al., in their paper "Elliptic vibration-assisted cutting of fibre-reinforced polymer composites: Understanding the material removal mechanisms" published in *Composites Science and Technology*, only used a brittle fracture constitutive model to simulate the material removal mechanism of unidirectional carbon fiber reinforced resin matrix composites (CFRP) under elliptical ultrasonic vibration. Currently, there is no simulation method specifically for SiC… f Finite element simulation models for SiC composite materials, which possess both brittle material and composite material properties, are insufficient due to the differences in the phase properties of the constituent phases. f The material removal mechanism of ultrasonic vibration-assisted cutting of SiC composite materials was simulated and analyzed.

[0080] This invention, based on finite element simulation technology, establishes a three-dimensional microscopic geometric model considering fibers, matrix, and interface. For the established geometric model, boundary constraints are set according to actual cutting conditions, and the tool's motion function is set based on the cutting edge trajectory during ultrasonic vibration-assisted machining. The model defines constitutive models according to the material characteristics of each constituent phase, including a brittle fracture model for silicon carbide fibers and a cohesive model for the interface phase with zero-thickness elements. A master-slave contact algorithm is used to define the contact relationship between the tool and the workpiece, and the model's computational accuracy and efficiency are improved by optimizing mesh generation and mass scaling. This invention enables the machining of SiC... f Simulations of the material removal mechanism of SiC composites during ultrasonic vibration-assisted cutting can be used to guide the development of SiC composites. f Damage suppression during machining of SiC composite materials and optimization of machining parameters assisted by ultrasonic vibration. Attached Figure Description

[0081] Figure 1 SiC f Three-dimensional micro-geometric model of ultrasonic vibration-assisted cutting of SiC composite material, where a is a finite element model with a cutting depth of 5μm and b is a finite element model with a cutting depth of 30μm.

[0082] Figure 2It is a constitutive model for brittle fracture;

[0083] Figure 3 For zero-thickness element cohesive constitutive models;

[0084] Figure 4 For the contact model, a is the workpiece-tool interaction principle diagram, and b is the kinematic master-slave contact algorithm;

[0085] Figure 5 SiC f Finite element simulation results of ultrasonic vibration-assisted cutting material removal mechanism of SiC composite material, where a is conventional cutting with a cutting depth of 5μm, b is ultrasonic vibration along the cutting direction with a cutting depth of 5μm, c is ultrasonic vibration perpendicular to the cutting direction with a cutting depth of 5μm, d is conventional cutting with a cutting depth of 30μm, e is ultrasonic vibration along the cutting direction with a cutting depth of 30μm, and f is ultrasonic vibration perpendicular to the cutting direction with a cutting depth of 30μm.

[0086] Figure 6 SiC f SEM images of the machined surface of the / SiC composite material, where a is conventional cutting with a cutting depth of 5μm and b is conventional cutting with a cutting depth of 30μm. Detailed Implementation

[0087] The present invention will be further described below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0088] SiC f The steps of the finite element simulation method for ultrasonic vibration-assisted cutting of SiC are as follows:

[0089] (1) Establish a three-dimensional microscopic geometric model;

[0090] The three-dimensional micro-geometric model consists of a workpiece model and a tool model;

[0091] The workpiece model is a cubic structure, consisting of an equivalent homogeneous body and a three-dimensional micro-geometric model of composite materials arranged in parallel along the length direction;

[0092] like Figure 1As shown, the three-dimensional micro-geometric model of the composite material consists of a silicon carbide ceramic matrix and cylindrical fibers arranged in a regular matrix within it. The central axis of the cylindrical fibers is parallel to the height of the workpiece model, and the row direction of the regular matrix is ​​parallel to the length of the workpiece model. The regular matrix has 7 rows and 3 columns, meaning that the composite material workpiece geometric model contains a total of 21 cylindrical fibers. These 21 fibers can meet the requirements of showing fiber fracture and damage during the cutting process, and the computational load is not too large.

[0093] The workpiece model satisfies the following condition: the stress in the height direction during cutting is zero at the bottom surface of the workpiece model;

[0094] Two workpiece models were used, one with a cutting depth of 5 μm and the other with a cutting depth of 30 μm. The reason for choosing cutting depths of 5 μm and 30 μm is that experiments have shown that SiC... f The critical cutting depth for micro-brittle fracture and macro-brittle fracture of SiC composites during machining is 8-11 μm. Micro-brittle fracture occurs when the cutting depth is less than this value. Therefore, to simulate the effect of ultrasonic vibration of the cutting edge on the material removal mechanism and damage behavior of the fiber in the micro-brittle fracture domain, a cutting depth of 5 μm was selected. Similarly, when the cutting depth is greater than this value, macro-brittle fracture occurs. Therefore, to simulate the effect of ultrasonic vibration of the cutting edge on the material removal mechanism and damage behavior of the fiber in the macro-brittle fracture domain, a cutting depth of 30 μm was selected.

[0095] Obviously, the physical field distribution depth and subsurface damage depth of the workpiece model with a cutting depth of 5μm are much smaller than those of the workpiece model with a cutting depth of 30μm. Therefore, if the height of the workpiece model with a cutting depth of 5μm is set to be the same as that of the workpiece model with a cutting depth of 30μm, a large number of unnecessary elements will be generated, which will significantly reduce the computational efficiency. Therefore, when building the model, the dimensions of the workpiece model with a cutting depth of 5μm are set to 100μm long × 44μm wide × 60μm high, and the dimensions of the workpiece model with a cutting depth of 30μm are set to 100μm long × 44μm wide × 160μm high.

[0096] The diameter of the cylindrical fiber is 12 μm; the center-to-center distance of the cylindrical fiber is 14 μm.

[0097] The shape and size of the tool model are the same as those of the actual tool used in the experiment. In this example, the rake angle of the tool is 3°, the clearance angle is 10°, and the blunt radius of the tool tip is 5μm.

[0098] The tool model is located on the side of the composite workpiece geometry model away from the equivalent homogeneous body. The cutting direction is parallel to the length of the workpiece model, and the distance between the position of the tool tip and the top surface of the composite workpiece geometry model is equal to the cutting depth. Since the equivalent homogeneous body is set on the side of the composite workpiece geometry model away from the tool model along the cutting direction, the present invention can support the composite workpiece geometry model and prevent it from collapsing during the cutting process.

[0099] (2) Divide the grid;

[0100] The tool model is set as a rigid body, given that the modulus of PCD tools is much higher than that of SiC. f Since the tool model is set as a rigid body, and tool wear is not considered, the tool is made of SiC composite material.

[0101] Set the mesh element type of the workpiece model and tool model to 3D 8-node reduced integral solid element C3D8R;

[0102] The mesh size of the workpiece model was set as follows: For the workpiece model with a cutting depth of 5μm, the cutting depth is relatively small, so to ensure the reliability of the simulation results, the mesh of the cutting layer was refined to 1μm×1μm×1μm. At the same time, to improve the computational efficiency, the mesh size was set to increase linearly from the cutting plane downwards. For the workpiece model with a cutting depth of 30μm, due to the larger cutting depth, the mesh size of the model was set to 2μm×2μm×2μm, thereby improving the computational efficiency while ensuring the computational accuracy.

[0103] Set the mesh size of the tool model. The mesh size at the blunt circle of the tool cutting edge is smaller than the radius of the blunt circle. Since the tool is a rigid body, it will not produce mesh deformation. Therefore, there is no requirement for the mesh size from a calculable point of view. However, since the tool cutting edge has a blunt circle and the size is on the micrometer scale, the mesh size at the blunt circle of the cutting edge must be smaller than the radius of the blunt circle to ensure the geometric integrity of the tool.

[0104] (3) Define boundary conditions;

[0105] The boundary conditions are as follows:

[0106] a) All six degrees of freedom at the bottom of the workpiece model are fully constrained. In actual processing, the workpiece is clamped and fixed on the worktable. Therefore, in the finite element simulation, all six degrees of freedom at the bottom of the workpiece model are fully constrained.

[0107] b) The cutting speed of the tool model is equal to the cutting speed of the tool in the actual test. In this example, it is set to 1000 mm / s.

[0108] c) To achieve ultrasonic vibration-assisted cutting along and perpendicular to the cutting direction respectively, vibration functions in the x and z directions need to be coupled to the tool based on the cutting speed. Figure 1 The motion velocity functions of the tool model under the three cutting conditions shown are as follows:

[0109]

[0110] Among them, ① corresponds to cutting condition without ultrasonic vibration, ② corresponds to cutting condition with ultrasonic vibration along the cutting direction, and ③ corresponds to cutting condition with ultrasonic vibration perpendicular to the cutting direction; v x (t), v y (t), v z (t) represents the velocity of the tool model along the x, y, and z directions, respectively, all in mm / s; v c f represents the cutting speed of the tool model, in mm / s. FEM The vibration frequency is expressed in Hz and is equal to the actual vibration frequency of the ultrasound in the test (20.6 kHz in this example); A FEM t represents the vibration amplitude in μm, which is equal to the vibration amplitude of the ultrasonic wave in the actual test (3 μm in this example); t represents the time in seconds.

[0111] (4) Define the material constitutive model and damage criterion;

[0112] Given the adoption of a three-dimensional micro-finite element model, the material behavior of three micro-components—silicon carbide fiber, silicon carbide matrix, and silicon carbide fiber-silicon carbide matrix interface—is involved during the cutting process. Considering that silicon carbide fiber and silicon carbide matrix are both brittle materials, the same constitutive model is used for silicon carbide fiber and silicon carbide matrix, but the model coefficients are different. The constitutive model of silicon carbide fiber-silicon carbide matrix interface is different from that of silicon carbide fiber.

[0113] Since both silicon carbide fibers and silicon carbide matrices are brittle materials, their yield stress is very close to their ultimate stress. Therefore, the plastic stage is not significant, and at high strain rates, the plastic stage can be ignored. Thus, the material behavior of silicon carbide fibers, silicon carbide matrices, and silicon carbide fiber-silicon carbide matrix interfaces includes two stages: an elastic stage and a degradation stage. In the elastic stage, stress and strain satisfy a linear relationship, meaning that the Young's modulus is constant in this stage. Figure 2 As shown in Stage I; in the degradation stage, when the maximum principal stress exceeds the tensile strength of the material, the material begins to fracture. At this time, Young's modulus decreases until the material fails, as shown in the diagram. Figure 2 As shown in stage II;

[0114] ① Silicon carbide fibers and silicon carbide matrix can be considered as isotropic materials. According to the theory of mechanics of materials, the stress-strain relationship of silicon carbide fibers and silicon carbide matrix in the elastic stage is a linear proportional relationship, as follows:

[0115] ;

[0116] In the formula, σ x σ y σ z These represent the stresses along the x, y, and z directions, respectively, in MPa; ε x ε y ε z τ represents the strain along the x, y, and z directions, respectively; xy τ yz τ zx γ represents the shear stress tensor in the XOY, YOZ, and ZOX planes, respectively, in MPa; xy γ yz γ zx , respectively, are the angular strain tensors in the XOY, YOZ, and ZOX planes; C is the stiffness matrix, as follows:

[0117] ;

[0118] In the formula, ν xy ν yz ν zx Poisson's ratios in the XOY, YOZ, and ZOX planes, respectively; G xy G yz G zx E represents the shear modulus in the XOY, YOZ, and ZOX planes, respectively, in MPa; x E y E z These are the Young's moduli along the x, y, and z directions, respectively, in MPa; Δ is an intermediate variable, as detailed below:

[0119] ;

[0120] ② During the degradation stage, the brittle fracture of silicon carbide fibers and silicon carbide matrix exhibits two different types: Type I fracture and Type II fracture;

[0121] When it is a Type I fracture, the Rankine criterion, based on Type I fracture, is used to determine whether the material has cracked. Specifically, when the maximum principal tensile stress of the material exceeds the tensile strength σ... t At that time, the material will develop cracks;

[0122] When it is a type I fracture, the fracture energy cracking criterion based on stress-displacement response is used to describe the material behavior during crack propagation. Specifically, the material strength decreases as the crack propagates, and when the displacement reaches a set crack normal displacement δ... n When the material completely fails and experiences a complete loss of strength (generally considered as complete material failure), the formula for calculating the crack normal displacement is as follows:

[0123] ;

[0124] In the formula, δ n This represents the crack normal displacement, in μm. The fracture energy of a type I crack is expressed in N / m; σ t Tensile strength, unit is MPa; K IC The fracture toughness of the material is expressed in MPa·m. 1 / 2 E' is the equivalent Young's modulus of the material, in MPa.

[0125] When the fracture is of type II, the shear behavior of the material is described by the decrease in shear modulus during crack propagation. Based on this, Abaqus provides a shear-holding model, in which the post-crack shear stiffness is defined as a function of the cross-crack strain. In this shear-holding model, the post-crack shear modulus is defined as a portion of the uncracked shear modulus, as follows:

[0126] ;

[0127] In the formula, (=0.02) represents the crack initiation strain; (=0.2) and p (=2) are material parameters; G c G is the shear modulus of the material, in Pa; G is the shear modulus of the uncracked material, in Pa.

[0128] The material behavior of an interface includes two phases: an elastic phase and a degradation phase, such as... Figure 3 As shown, the present invention uses the zero-thickness element cohesion (CZM) model to describe the material mechanical behavior of the pyrolytic carbon interface between the fiber and the matrix, as detailed in ③ and ④ below;

[0129] ③ In this model, the material properties of the interface are considered to be linearly elastic when there is no damage. According to the theory of mechanics of materials, the stress-strain relationship of the silicon carbide fiber-silicon carbide matrix interface in the elastic stage is a linear proportional relationship, as follows:

[0130] ;

[0131] In the formula, t is the nominal traction stress, in MPa; δ is the separation displacement, in mm; n represents the normal direction, and s and t represent the two shear directions; K n Normal stiffness, in N / mm; K s and K t Tangential stiffness, in N / mm;

[0132] ④ During the degradation stage, the damage initiation point of the silicon carbide fiber-silicon carbide matrix interface is determined using the secondary stress criterion in the cohesive model of the zero-thickness element. The formula is as follows:

[0133] ;

[0134] In the formula, t 0 The contact stress required to initiate interface damage is expressed in MPa, and in this model, its value is assumed to be equal to the interface strength; t represents the contact stress, expressed in MPa; the superscript 0 indicates the moment when interface damage begins; the subscript n represents the normal direction, and s and t represent the two shear directions.

[0135] The rate of decrease in viscous stiffness after reaching the cracking criterion is described by the damage evolution law. The contact stress of interface separation in the absence of damage is predicted based on the damage variables, as shown in the following formula:

[0136] ;

[0137] In the formula, , , These are the nominal tensile stresses in the normal and two shear directions, respectively, without damage, in MPa; D' is the damage variable, used to describe the damage evolution of the interface, as follows:

[0138] ;

[0139] In the formula, δ n To effectively separate the normal component of the displacement, in mm, δ s and δ t To effectively separate the components of displacement in the two shear directions, the unit is mm; To effectively separate displacements, the unit is mm, including the normal (δ). n ) and shear direction (δ) s and δ t The components of ); the superscripts 0 and f represent the states of starting damage and completing failure, respectively; The maximum effective separation displacement obtained during the loading process, in mm;

[0140] The effective separation displacement at failure is derived using linear energy evolution, as shown in the following formula:

[0141] ;

[0142] In the formula, G represents the finite traction force at the initial damage site, expressed in Pa. c The fracture energy is taken as 8.0 J / m. 2 ;

[0143] (5) Define the contact conditions;

[0144] The finite element simulation contact model considers two different types of interaction between the workpiece and the tool: compression along the normal direction and friction along the tangential direction, such as... Figure 4 As shown in Figure a;

[0145] The classic pure kinematic master-slave contact algorithm is used to describe compression along the normal direction. First, the kinematic state of the finite element model is proposed. Then, the normal contact force is determined based on the contact penetration depth and process-related mass to counteract penetration. Considering that the focus of the study is the workpiece behavior, the workpiece is set as the slave component and the tool as the master component. In the pure kinematic master-slave contact algorithm, slave nodes cannot penetrate the master surface, while master nodes can penetrate the slave surface, such as... Figure 4 As shown in b;

[0146] A modified Coulomb friction model is used to describe tangential friction. Friction at the tool-workpiece contact surface affects cutting force and surface quality. Therefore, choosing a suitable friction model to define the tool-chip contact problem is crucial for simulation. The tangential interaction between the workpiece and the tool includes both adhesion and slippage. Therefore, the modified Coulomb friction model is adopted, which considers both adhesion and slippage contact zones at the tool-chip contact surface. The formula is as follows:

[0147] ;

[0148] In the formula, τ is the shear stress, with units of MPa; τ max , where is the ultimate shear stress, in MPa; μ is the average friction coefficient of the tool-chip contact surface. In this invention, the friction coefficient between the matrix and the fiber is set to 0.3, the friction coefficient between fibers is set to 0.3, the friction coefficient between the fiber and the tool is set to 0.2, and the friction coefficient between the matrix and the tool is set to 0.2.

[0149] (6) Calculation and precision control;

[0150] An explicit central difference algorithm is used to solve the model. Explicit algorithms are more suitable for analyzing and solving dynamic nonlinear numerical problems than implicit algorithms. The principle of the central difference algorithm is to use differences instead of differentials, and to use linear extrapolation for the derivatives of displacement and acceleration, eliminating the need for equilibrium iterations and resulting in fast computation. In dynamic explicit algorithms (explicit central difference algorithm is a type of dynamic explicit algorithm), the solution for the next step is directly based on the solution of the current step. Therefore, the total computation time is the sum of the time increments of each single step. Thus, the total computation time of dynamic explicit algorithms depends on the length of the increment step. However, for algorithm stability... The stability condition of the dynamic explicit algorithm is that the time step increment is less than a limit. In fact, the selection of the time step increment in finite element simulation is quite complex, requiring a balance between computational accuracy, stability, and efficiency. Theoretically, the smaller the time step increment, the higher the model solution accuracy and the easier it is for the dynamic explicit algorithm to converge, but the computation time increases accordingly. Therefore, choosing a reasonable single-step time increment (using the default setting in ABAQUS, which the software dynamically adjusts during the calculation process) to reduce computation time while ensuring solution accuracy is crucial, especially for SiC research. f The problem of material fracture and removal during the cutting of SiC composite materials is difficult to balance between computational cost and accuracy due to the small mesh size, large number of meshes and complex contact relationships.

[0151] Due to the limitations of time increments, this model employs mass scaling to reduce computational costs while ensuring computational accuracy, and also reasonably reduces the total time. Mass scaling artificially increases the density of the material, thereby increasing the settling time increment, reducing increment steps, and shortening the computation time. The premise of mass scaling is to ensure that the kinetic energy in the calculation is less than 10% of the total work done. Based on this, an appropriate mass scaling factor and actual computation time are determined. The expression for the settling time is as follows:

[0152] ;

[0153] In the formula, L e c is the length of the feature unit, in mm. d ρ is the propagation wave velocity of the material, in m / s; E is the elastic modulus of the material, in MPa; ρ is the density of the material, in g / mm³. 3 ;

[0154] (7) Submit the task and perform finite element simulation calculations to realize SiC f Simulation of the material removal mechanism in ultrasonic vibration-assisted cutting of SiC composite materials;

[0155] The material properties of the fiber, matrix, and fiber-matrix interface used in this finite element model are shown in the table below;

[0156]

[0157] like Figure 5 The figures show the finite element simulation results for the micro-brittle domain (5 μm) and macro-brittle domain (30 μm), respectively, under conditions of no ultrasonic vibration, ultrasonic vibration along the cutting direction, and ultrasonic vibration perpendicular to the cutting direction. Overall, when ultrasonic vibration is applied along the cutting direction, the maximum cutting speed and strain rate increase, leading to a concentration of stress in the cutting zone. This is beneficial for reducing cutting force, surface roughness, and subsurface damage layer depth in both the micro-brittle fracture domain and the macro-brittle fracture domain. When ultrasonic vibration is applied perpendicular to the cutting direction, the maximum cutting depth increases in the micro-brittle fracture domain, and the stress distribution penetrates deeper into the material along the cutting speed direction, thus worsening the machining quality. However, in the macro-brittle fracture domain, the perpendicular vibration of the cutting edge generates additional tensile / compressive stress cycles during friction with the fiber, resulting in multi-regional stress concentration in the fiber, increasing the number of potential fiber fracture points, reducing fiber chip length, promoting fiber fracture, and thus facilitating chip removal and reducing the subsurface damage layer depth.

[0158] Figure 6 SiC f SEM images of the machined surface of SiC composite material, where a) represents conventional cutting at a depth of 5 μm, and b) represents conventional cutting at a depth of 30 μm. Experimental results show that at a cutting depth of 5 μm, microscopic brittle fracture occurs in the fibers, with these small-scale fractures occurring within the fibers. A single fiber undergoes several brittle fractures, resulting in a relatively smooth machined surface. At a cutting depth of 30 μm, macroscopic brittle fracture occurs, with the entire fiber undergoing brittle fracture. A single fiber experiences only one brittle fracture, the fracture location is highly random, and the machined surface is relatively rough. These experimental results demonstrate the validity of the proposed method for machining SiC composite materials. f The finite element simulation method for material removal mechanism in SiC composite machining shows high consistency with actual conditions and can accurately simulate SiC. f / SiC composite material ultrasonic vibration assisted cutting material removal mechanism.

[0159] This invention enables the realization of SiC f This study simulates the material removal mechanism of SiC composites during ultrasonic vibration-assisted cutting, providing an effective analytical method for investigating the fiber fracture removal mechanism and damage behavior caused by ultrasonic vibration at the cutting edge. This method can then be used to guide the research on SiC... f Damage suppression during machining of SiC composite materials and optimization of machining parameters assisted by ultrasonic vibration.

Claims

1. SiC f The finite element simulation method for ultrasonic vibration-assisted cutting of SiC is characterized by... The steps are as follows: (1) Establish a three-dimensional microscopic geometric model; The three-dimensional micro-geometric model consists of a workpiece model and a tool model; The workpiece model is a cubic structure, consisting of an equivalent homogeneous body and a three-dimensional micro-geometric model of composite materials arranged in parallel along the length direction; The three-dimensional micro-geometric model of the composite material consists of a silicon carbide ceramic matrix and cylindrical fibers arranged in a regular matrix within it. The central axis of the cylindrical fibers is parallel to the height of the workpiece model, and the row direction of the regular matrix is ​​parallel to the length of the workpiece model. The workpiece model satisfies the following condition: the stress in the height direction during cutting is zero at the bottom surface of the workpiece model; The diameter of the cylindrical fiber is equal to the average diameter of the silicon carbide fiber used in the actual experiment; The center-to-center distance of the cylindrical fibers is equal to that of the SiC used in the actual experiment. f The average center-to-center distance of silicon carbide fibers in the / SiC composite material; The shape and size of the tool model are the same as those of the tool used in the actual test; The tool model is located on the side of the composite workpiece geometry model away from the equivalent homogeneous body. The cutting direction is parallel to the length of the workpiece model, and the distance between the position of the tool tip and the top surface of the composite workpiece geometry model is equal to the cutting depth. (2) Divide the grid; Set the tool model to a rigid body; Set the mesh element type of the workpiece model and tool model to 3D 8-node reduced integral solid element C3D8R; Set the mesh size of the workpiece model to be smaller than the smallest material element size that is removed during material fracture in the cutting process; Set the mesh size of the tool model so that the mesh size at the blunt circle of the tool cutting edge is smaller than the radius of the blunt circle; (3) Define boundary conditions; The boundary conditions are as follows: a) All six degrees of freedom at the bottom of the workpiece model are fully constrained; b) The cutting speed of the tool model is equal to the cutting speed of the tool in the actual test; c) The motion velocity functions of the tool model under the three cutting conditions are shown in the following equations: ① ② ③ Among them, ① corresponds to cutting condition without ultrasonic vibration, ② corresponds to cutting condition with ultrasonic vibration along the cutting direction, and ③ corresponds to cutting condition with ultrasonic vibration perpendicular to the cutting direction; v x (t), v y (t), v z (t) represents the velocity of the tool model along the x, y, and z directions, respectively, all in mm / s; v c f represents the cutting speed of the tool model, in mm / s. FEM The vibration frequency, measured in Hz, is equal to the vibration frequency of the ultrasound in the actual experiment; A FEM t represents the vibration amplitude in μm, which is equal to the vibration amplitude of the ultrasonic wave in the actual test; t represents the time in seconds. (4) Define the material constitutive model and damage criterion; The constitutive models of silicon carbide fibers and silicon carbide matrix are based on a brittle fracture model, while the constitutive model of fiber-matrix interface is based on a zero-thickness element cohesion model. (5) Define contact conditions; Compression along the normal direction is described using a pure kinematic master-slave contact algorithm; Friction along the tangential direction is described using a modified Coulomb friction model; (6) Calculation and precision control; The model is solved using an explicit central difference algorithm; a quality scaling method is used to reduce computational costs and reasonably reduce the total time. (7) Submit the task and perform finite element simulation calculation.

2. The SiC according to claim 1 f The finite element simulation method for ultrasonic vibration-assisted cutting of SiC is characterized by... In step (1), the rule matrix has 7 rows and 3 columns.

3. The SiC according to claim 1 f The finite element simulation method for ultrasonic vibration-assisted cutting of SiC is characterized by... In step (1), there are two workpiece models, one with a cutting depth of less than 8 μm and the other with a cutting depth of more than 11 μm.

4. The SiC according to claim 3 f The finite element simulation method for ultrasonic vibration-assisted cutting of SiC is characterized by... In step (1), the difference in cutting depth between the two workpiece models is not less than 10 μm.

5. The SiC according to claim 3 f The finite element simulation method for ultrasonic vibration-assisted cutting of SiC is characterized by... In step (1), the two workpiece models have different heights, and the workpiece model with a larger cutting depth has a greater height than the workpiece model with a smaller cutting depth.

6. The SiC according to claim 1 f The finite element simulation method for ultrasonic vibration-assisted cutting of SiC is characterized by... In step (2), the mesh size of each workpiece model increases linearly downwards from the cutting plane.

7. The SiC according to claim 1 f The finite element simulation method for ultrasonic vibration-assisted cutting of SiC is characterized by... In step (4), the material behavior includes two stages: the elastic stage and the degradation stage; In the elastic stage, the stress-strain relationship between silicon carbide fibers and silicon carbide matrix is ​​linearly proportional. During the degradation stage, brittle fracture of silicon carbide fibers and silicon carbide matrix exhibits two distinct types: Type I fracture and Type II fracture. When it is Type I fracture, the Rankine criterion, based on Type I fracture, is used to determine whether the material has cracked. When it is Type II fracture, the fracture energy cracking criterion based on stress-displacement response is used to describe the material's behavior during crack propagation. When it is a type II fracture, the decrease in shear modulus during crack propagation is used to describe the shear behavior of the material; In the elastic stage, the stress-strain relationship at the silicon carbide fiber-silicon carbide matrix interface is a linear proportional relationship. The damage initiation point of the cohesive model within a zero-thickness element was determined using the secondary stress criterion at the silicon carbide fiber-silicon carbide matrix interface during the degradation stage. The rate of decrease in viscous stiffness after reaching the cracking criterion is described by the damage evolution law, and the contact stress of interface separation under no-damage conditions is predicted based on the damage variables. The effective separation displacement at failure is derived by using the linear evolution of energy.

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