CFRP thermal coupling cutting modeling method based on microcosmic failure theory

Abstract

The invention discloses a CFRP thermal coupling cutting modeling method based on a microcosmic failure theory. Comprising the following steps: establishing a carbon fiber three-dimensional geometric model, a matrix three-dimensional geometric model and a cutter three-dimensional geometric model, and performing grid division and assembly to obtain a CFRP three-dimensional grid model; the method comprises the following steps: setting a multi-phase three-dimensional damage constitutive relation of a fiber phase, a matrix phase and an interface phase, setting a heat conduction equation, an initial environment temperature and a heat insulation boundary condition, inputting a heat source equation comprising main shear surface deformation heat, cutter-chip interface friction heat and cutter-workpiece interface friction heat, inputting a thermal strain equation, and finally, calculating a thermal deformation coefficient according to preset parameters and a preset time step length. And performing thermal-mechanical coupling analysis on the cutting process of the to-be-cut structure to obtain a simulation result. According to the method, the microcosmic failure theory is applied to a material constitutive model, an exponential type reduction mode better conforming to carbon fiber rigidity degradation is used, and the fibers are arranged in a staggered mode, so that the internal structure and the damage evolution process of the CFRP are reflected more truly.

Description

Technical Field

[0001] This invention relates to the field of machining technology, and more specifically to a method for modeling carbon fiber reinforced composite laminate structures based on micro-failure theory and considering thermo-mechanical coupling. Background Technology

[0002] In modern industry, composite materials, with their superior properties such as high strength, lightweight, and corrosion resistance, have been widely used in key fields such as aerospace, automotive manufacturing, and shipbuilding, becoming important materials for driving industrial upgrading and improving product performance. This has spurred research on CFRP material processing. However, with the extensive application of CFRP in high-end equipment, its subsequent processing stages face numerous challenges. In actual production, to ensure that CFRP components meet assembly and usage requirements, secondary processing operations such as cutting and drilling are often required. During these processes, CFRP materials are highly susceptible to damage such as delamination, tearing, and burrs, severely affecting the mechanical properties and service life of the components. Therefore, revealing the damage mechanism of CFRP during processing can provide a theoretical basis for optimizing processing technology and improving processing quality.

[0003] Currently, research methods for CFRP machining mainly include theoretical research, experimental research, and research combining simulation and experimentation. Theoretical research can analyze the mechanical behavior and damage patterns during the cutting process by establishing mathematical models. However, due to the complexity of CFRP structures and the dynamic nature of the cutting process, theoretical models often fail to fully and accurately reflect the actual situation. Experimental research can directly obtain data and damage phenomena during the machining process, but experiments are costly, time-consuming, and difficult to monitor unobservable physical quantities such as internal stress and strain in real time. The research method combining simulation and experimentation fully leverages the advantages of simulation technology. By constructing a virtual cutting environment, the machining process can be dynamically simulated, and experimental data can be used to verify and correct the simulation model. This allows for a more efficient and comprehensive revelation of the CFRP cutting damage mechanism, thus simulation methods have significant advantages in CFRP cutting research.

[0004] Traditional CFRP cutting simulations often employ macroscopic continuous medium models, treating CFRP as a single homogeneous and continuous material, neglecting the interfacial properties between fibers and the matrix, as well as differences in fiber orientation. However, in actual cutting processes, CFRP damage often results from interfacial failure between fibers and the matrix, as well as fiber breakage. Traditional simulation methods use equivalent anisotropic single-phase homogeneous materials, ignoring the differences between fibers and the matrix at their source. This causes the elements that should be based on fiber failure to be replaced by weaker matrix elements, leading to premature failure. This approach fails to accurately simulate these microscopic damage mechanisms, resulting in significant discrepancies between simulation results and experimental data. It also makes it difficult to accurately predict cutting forces, cutting temperatures, and damage distribution. Therefore, developing cross-scale numerical simulation techniques for CFRP cutting and conducting more accurate simulation studies of CFRP right-angle cutting is an urgent practical need. Summary of the Invention

[0005] To address the problems existing in the background technology, this invention provides a CFRP thermo-mechanical coupling cutting modeling method based on micro-failure theory.

[0006] The technical solution adopted in this invention is:

[0007] I. A Thermo-Mechanical Coupled Cutting Modeling Method for CFRP Based on Microscopic Failure Theory

[0008] The CFRP thermo-mechanical coupling cutting modeling method includes the following steps:

[0009] Step S1) In 3D modeling software, for the structure to be cut, a three-dimensional geometric model of carbon fiber, a three-dimensional geometric model of the matrix, and a three-dimensional geometric model of the tool are established. After meshing and assembly, a CFRP three-dimensional mesh model is obtained.

[0010] Specifically, the three-dimensional geometric model of the carbon fiber adopts a representative volume element model.

[0011] More specifically, in the carbon fiber three-dimensional geometric model, the carbon fiber three-dimensional geometric units are arranged in an interlaced pattern within a rectangular region, that is, arranged according to a rectangular RVE structure.

[0012] Specifically, the structure to be cut is made of carbon fiber reinforced composite material.

[0013] Step S2) In the CFRP three-dimensional mesh model, set the multiphase three-dimensional damage constitutive relation to obtain the mesoscopic simulation material model.

[0014] Specifically, the multiphase three-dimensional damage constitutive relations include the three-dimensional damage constitutive relations of the fibrous phase, the matrix phase, and the interface phase.

[0015] The three-dimensional damage constitutive relationship of the fiber phase includes: using a transversely isotropic constitutive model, setting the stress-strain equation before failure according to the generalized Hooke's law, using the Tsai-Wu failure model to determine the damage initiation, using an exponential mode to calculate the axial and transverse damage variables, using a linear mode to calculate the damage variables in the shear direction, and using the maximum stress criterion to determine complete failure.

[0016] The three-dimensional damage constitutive relation of the matrix phase is described by the Johnson-Cook constitutive model to describe the mechanical properties and fracture behavior.

[0017] The three-dimensional damage constitutive relationship of the interface phase includes: using a cohesive element constitutive model, using the Quads model to determine damage initiation and calculate damage variables, and using the Power-Law energy dissipation model to determine complete failure or cracking.

[0018] Step S3) In the microscopic simulation material model, set the heat conduction equation, initial ambient temperature and adiabatic boundary conditions, input the heat source equation including the deformation heat of the main shear surface, the frictional heat of the tool-chip interface and the frictional heat of the tool-workpiece interface, input the thermal strain equation, and then obtain the thermo-mechanical coupled finite element model.

[0019] Step S4) In the finite element software, using the thermo-coupling finite element model, according to the preset parameters and preset time step, perform thermo-coupling analysis on the cutting process of the structure to be cut, realize thermo-coupling dynamic cutting simulation, and obtain simulation results.

[0020] Specifically, the cutting is a right-angle cutting.

[0021] Specifically, in step S4), the preset parameters include the following parameters: physical property parameters of the structure to be cut, fiber direction angle, cutting direction, cutting speed, cutting depth, feed rate, tool rake angle, tool clearance angle, and environmental physical quantities.

[0022] Furthermore, the CFRP thermo-coupling cutting modeling method also includes: conducting cutting experiments using an orthogonal cutting integrated experimental platform to obtain experimental results; and comparing and verifying the simulation results with the experimental results to verify the accuracy of the simulation results.

[0023] II. An orthogonal cutting integrated experimental platform applied to the aforementioned CFRP thermo-coupled cutting modeling method

[0024] The orthogonal cutting integrated experimental platform includes:

[0025] Material cutting unit, used for cutting the structure to be cut;

[0026] The data acquisition unit includes a force gauge, an acoustic emission sensor, and a temperature measuring instrument; these are used to measure the cutting force, damage and / or failure of the structure to be cut, and cutting temperature during the cutting process, respectively.

[0027] The data processing unit is used to receive and process the data obtained by the data acquisition unit to obtain experimental results.

[0028] The beneficial effects of this invention are:

[0029] 1. This invention innovatively applies microscopic failure theory to the material constitutive model and uses an exponential reduction mode that is more consistent with the stiffness degradation of carbon fiber. At the same time, the fibers are arranged in an interlaced manner, which can more realistically reflect the internal structure and damage evolution process of CFRP.

[0030] 2. This invention designs an orthogonal cutting integrated experimental platform, compares the results with finite element simulation results, and considers the results analysis under thermo-mechanical coupling conditions. This provides more comprehensive and accurate experimental data for the verification and correction of the simulation model, effectively solves the shortcomings of traditional simulation methods, and provides strong support for revealing the damage mechanism and process optimization of CFRP cutting. Attached Figure Description

[0031] Figure 1 These are actual and model layout diagrams of carbon fibers in carbon fiber reinforced composites.

[0032] Figure 2 This is the flowchart of the VUMAT subroutine in ABAQUS / Explicit;

[0033] Figure 3 This is a schematic diagram of the failure modes of cohesive elements;

[0034] Figure 4 This is a schematic diagram of the constitutive model of the cohesive element;

[0035] Figure 5 This is a schematic diagram of the heat generation area during the processing;

[0036] Figure 6 This is a diagram illustrating heat distribution;

[0037] Figure 7 This is a schematic diagram of the CFRP finite element model and four fiber orientation angles;

[0038] Figure 8 This is a schematic diagram of an orthogonal cutting integrated experimental platform;

[0039] Figure 9 This is a schematic diagram of a cutting force measuring device;

[0040] Figure 10 This is a schematic diagram of the simulation results for a 0° fiber orientation angle;

[0041] Figure 11 This is a schematic diagram of the simulation results for a 45° fiber orientation angle;

[0042] Figure 12 This is a schematic diagram of the simulation results for a 90° fiber orientation angle;

[0043] Figure 13 This is a schematic diagram of the simulation results for a 180° fiber orientation angle;

[0044] Figure 14 This is a schematic diagram of the simulation results of the angular temperature of four fiber orientations in CFRP;

[0045] Figure 15 This is a comparison chart of experimental and simulation results of cutting forces at four fiber orientation angles;

[0046] Figure 16 This is a schematic diagram illustrating the effect of cutting depth on cutting force for four different fiber orientation angles;

[0047] Figure 17 This is a schematic diagram illustrating the effect of cutting speed on cutting force for four different fiber orientation angles;

[0048] Figure 18 This is a schematic diagram illustrating the effect of cutting depth on cutting temperature for four different fiber orientation angles;

[0049] Figure 19 This is a schematic diagram illustrating the effect of cutting speed on cutting temperature for four different fiber orientation angles. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] This invention provides a CFRP thermo-mechanical coupling cutting modeling method based on micro-failure theory, comprising the following steps:

[0052] Step S1) In 3D modeling software, a three-dimensional geometric model of carbon fiber, a three-dimensional geometric model of the matrix, and a three-dimensional geometric model of the tool are established. After meshing and assembly, a three-dimensional mesh model of CFRP is obtained.

[0053] Specifically, the three-dimensional geometric model of carbon fiber adopts a representative volume element model.

[0054] Furthermore, in the carbon fiber three-dimensional geometric model, the carbon fiber three-dimensional geometric units are arranged in an interlaced pattern within the rectangular region.

[0055] In this embodiment of the invention, the 3D modeling software is Abaqus.

[0056] Step S2) In the finite element software, for the CFRP three-dimensional mesh model, set the multiphase three-dimensional damage constitutive relation to obtain the microscopic simulation material model.

[0057] Specifically, the multiphase three-dimensional damage constitutive relations include the three-dimensional damage constitutive relations of the fibrous phase, matrix phase, and interface phase.

[0058] Specifically, the three-dimensional damage constitutive relationship of the fiber phase includes: adopting a transversely isotropic constitutive model, setting the stress-strain equation before failure according to the generalized Hooke's law (see formulas (1) to (2)), using the Tsai-Wu failure model to determine the damage initiation (see formulas (3) to (4)), using the exponential mode to calculate the axial and transverse damage variables, using the linear mode to calculate the damage variables in the shear direction (see formula (5)), and using the maximum stress criterion to determine complete failure.

[0059] Specifically, the three-dimensional damage constitutive relation of the matrix phase is described by the Johnson-Cook constitutive model to describe the mechanical properties and fracture behavior of the matrix phase.

[0060] Specifically, the three-dimensional damage constitutive relationship of the interface phase includes: using the cohesive element constitutive model, using the Quads model to determine the damage initiation and calculate the damage variables (see formulas (13) to (17)), and using the Power-Law energy dissipation model to determine complete failure or cracking (see formula (18)).

[0061] In this embodiment of the invention, the finite element software is Abaqus software.

[0062] Step S3) In the finite element software, set the heat conduction equation (see formula (19)), initial ambient temperature (see formula (20)) and adiabatic boundary conditions (see formula (21)) for the microscopic simulation material model, input the heat source equation (see formulas (22) to (24)) which includes the deformation heat of the main shear surface, the frictional heat of the tool-chip interface and the frictional heat of the tool-workpiece interface, and input the thermal strain equation (see formulas (25) to (26)) to obtain the thermo-mechanical coupling finite element model.

[0063] Step S4) In the finite element software, a thermo-coupled finite element model is used to perform thermo-coupled analysis on the cutting process of the structure to be cut according to preset parameters and preset time steps, so as to realize thermo-coupled dynamic cutting simulation and obtain simulation results.

[0064] Specifically, in the Abaqus software, the Abaqus temp-disp dynamic module is used for thermo-mechanical coupling analysis.

[0065] Optionally, the simulation results include cutting force, cutting temperature field distribution, stress distribution, strain distribution, material damage evolution, fiber fracture length, and material surface morphology.

[0066] Optionally, the experimental results may include cutting force, cutting temperature, etc.

[0067] Specifically, the structure to be cut is made of carbon fiber reinforced polymer (CFRP).

[0068] Furthermore, the CFRP thermo-coupling cutting modeling method may also include: conducting cutting experiments using an orthogonal cutting integrated experimental platform to obtain experimental results; and comparing and verifying the simulation results with the experimental results to verify the accuracy of the simulation results.

[0069] Furthermore, the CFRP thermo-mechanical coupling cutting modeling method can also include obtaining the optimal cutting parameters of the structure to be cut based on simulation results. The optimal cutting parameters include cutting direction, cutting speed, and depth of cut.

[0070] Furthermore, the CFRP thermo-mechanical coupling cutting modeling method can also include: determining the micro-cutting mechanism of the structure to be cut based on parameters such as stress distribution, temperature field distribution, and material surface morphology in the simulation results.

[0071] This invention also provides an orthogonal cutting integrated experimental platform.

[0072] The orthogonal cutting integrated experimental platform of this invention includes:

[0073] Material cutting unit, used for cutting the structure to be cut;

[0074] The data acquisition unit includes a force gauge, an acoustic emission sensor, and a temperature measuring instrument; these are used to measure the cutting force, damage and / or failure of the structure to be cut, and cutting temperature during the cutting process, respectively.

[0075] The data processing unit is used to receive and process the data obtained by the data acquisition unit to obtain experimental results.

[0076] Specific embodiments of the present invention are as follows:

[0077] This embodiment provides a three-dimensional dynamic progressive damage evolution model for carbon fiber composites based on microscopic failure criteria. Taking T800S-6K high-performance carbon fiber reinforced epoxy resin matrix composite as the object, through constructive modeling, microscopic orthogonal cutting simulation and experimental verification, it deeply analyzes the influence of orthogonal cutting at different fiber orientation angles on the fiber and matrix damage mechanism and tool-cutting surface temperature distribution, explores the correlation between process parameters and cutting force and cutting temperature, clarifies the cutting thermal law and establishes its correlation model with the machining morphology.

[0078] Micromechanics of Failure (MMF) is a strength-related theory of composite materials based on micromechanical analysis. It studies the influence of fiber, matrix, and fiber-matrix interface failure behavior on the overall mechanical properties of carbon fiber reinforced composites by establishing a periodic micromechanical model, namely the representative volume element (RVE). Furthermore, data can be extracted and analyzed from the model established by micromechanics to reflect the mechanical properties of the macroscopic material. Figure 1 (Left) This shows the actual arrangement of carbon fibers in carbon fiber-reinforced polymer (CFRP). It can be seen that the fibers are randomly distributed without a clear pattern. It is unrealistic to establish a completely accurate finite element model of the actual fiber distribution. Therefore, the actual composite interface can be equivalently represented as... Figure 1 The square RVE and rectangular RVE shown are illustrated. In the rectangular RVE model, the fiber arrangement is staggered, which is closer to the actual random fiber arrangement.

[0079] In carbon fiber reinforced composites (CFRP), the main load-bearing component is carbon fiber. Carbon fiber exhibits linear elasticity in terms of mechanical properties, meaning there is no plastic stage before material failure. This invention defines carbon fiber as a transversely isotropic material and uses the maximum stress criterion to determine carbon fiber failure. That is, when the stress in any direction reaches the ultimate strength in that direction, the fiber undergoes brittle fracture and fails, and the main load-bearing carbon fiber loses its load-bearing capacity. Before failure, the stress-strain relationship can be obtained according to Hooke's law, and the stress-strain equations are shown in equations (1) and (2).

[0080]

[0081]

[0082] In the formula: the direction along the fiber axis is defined as direction 1, and the direction perpendicular to the fiber axis is defined as directions 2 and 3. Therefore, in formulas (1) and (2), σ ii (i = 1, 2, 3) represent the normal stress along each coordinate axis, τ ij (i,j=1,2,3) represent the shear stress in each coordinate plane, ε ii and γ ij C represents the strain corresponding to normal stress and shear stress, respectively; ij E represents the stiffness coefficient before damage. ii G represents the Young's modulus in all directions. ijv is the shear modulus. ij is Poisson's ratio, and Symmetric represents symmetry, meaning that the upper right part of the matrix is ​​symmetric to the lower left part of the matrix.

[0083] For the damage initiation of carbon fiber, this embodiment uses the Tsai-Wu failure criterion to determine the damage. The mechanical properties of the fiber are transversely isotropic, which results in its longitudinal tensile and compressive strength being much higher than its transverse tensile and compressive strength. Therefore, the secondary failure criterion of first-order and second-order stress invariants can be used to evaluate the comprehensive effect of multiaxial stress. Since this embodiment establishes a three-dimensional CFRP finite element model, the failure determination of the fiber involves six stress components, as shown in formula (3).

[0084]

[0085] In the formula: f i f ij σ represents the intensity tensor in each i-direction and in the plane ij (i, j = 1, 2, 3; direction 1 is the fiber longitudinal direction); i This represents the normal stress of the fiber at the microscale.

[0086] The expressions for each intensity tensor are shown in formula (4).

[0087]

[0088] In the formula: X f Y f Z f This indicates the failure strength of the fiber in each direction at the microscopic scale. The superscript T indicates fiber tension, and the superscript C indicates fiber compression. This represents the shear strength of the fiber in the ij direction at the microscale (i,j = X, Y, Z).

[0089] When damage occurs inside the material, the material's stiffness will decrease. Existing research shows that the exponential reduction calculation mode is more consistent with the axial material stiffness degradation characteristics of carbon fiber, while the stiffness degradation in the shear direction is closer to linear. Therefore, this embodiment uses the exponential mode to calculate the axial and transverse damage variables, while the linear mode is used for the damage variables in the shear direction. The specific expression is shown in formula (5).

[0090]

[0091] In the formula: d1 and d2 represent the damage variables in the axial and transverse directions of the fiber. When d1 = 0, the material is undamaged; when d2 = 1, the material is completely damaged; d ij (i,j=1,2,3) represent the damage variables in the three shear directions; ε 0ε represents the strain at the onset of material damage. f G represents the strain at which the material reaches complete failure; G represents the fracture energy of the material under each failure mode; L c denoted by , where is the characteristic length of the element; X represents the axial damage evolution coefficient of the material, which is an inherent property of the material and is used to control the rate at which damage increases with strain; Y represents the transverse damage evolution coefficient of the material; F represents the correction coefficient, which is used to adjust the correlation between material damage and strength; subscripts t and c represent tension and compression, respectively; subscript f represents material damage; subscript m represents the transverse fiber.

[0092] The carbon fiber damage stiffness matrix used in this embodiment is shown in formula (6).

[0093]

[0094] In the formula: the subscript D represents the stiffness matrix containing damage.

[0095] During processing, the resin matrix is ​​generally considered to be an isotropic material, and the Johnson-Cook constitutive model is commonly used to describe it. In the elastic stage, the stiffness matrix of an isotropic material, considering the effect of temperature, can be expressed as formula (7):

[0096] K σ =∫ V [B] T [D T ][B]dV(7)

[0097] In the formula: K σ [B] is the structural stiffness matrix, reflecting the structure's ability to resist deformation; V is the integral volume domain; the superscript T indicates the transpose of the matrix; [B] is the shape function matrix, which can establish the relationship between intra-element displacements and nodal displacements; [D] is the structural stiffness matrix, reflecting the structure's ability to resist deformation; [D] is the integral volume domain, and [D] is the integral volume domain, reflecting the structural stiffness matrix. T The structural stress matrix, which takes temperature into account, describes the stress-strain relationship of a material under temperature conditions.

[0098] Among them, the structural stress matrix considering the effect of temperature [D] T This can be expressed as formula (8):

[0099]

[0100] The Johnson-Cook model is often used to characterize the mechanical properties of isotropic materials in the yield stage, and its expression can be shown in Equation (9):

[0101]

[0102] In the formula: σ is the equivalent stress, and ε is the equivalent strain. The ratio of the actual strain rate to the reference strain rate (dimensionless) describes the effect of strain rate on the yield strength of a material. A is the yield stress constant under standard conditions, B is the strain hardening variable, C is the strain rate hardening coefficient, n is the strain hardening factor, m is the thermal softening coefficient, and T... * To express the ratio of "the difference between the current temperature and the room temperature" to "the difference between the melting temperature and the room temperature", formula (10) is raised to the power of m to describe the softening effect of temperature on the yield strength of the material.

[0103] In the Johnson-Cook model (i.e., formula (9)), from left to right, the strain hardening effect, strain rate strengthening effect and thermal softening effect are represented respectively. The stress-strain equation of the yield stage is obtained under the combined action of the three.

[0104] The stress-strain equation for the yield stage can be expressed by formula (10):

[0105]

[0106] In the formula: The reference strain rate is given experimentally. This represents the actual strain rate. T is the ratio of the actual strain rate to the reference strain rate. * T is the ratio of "the difference between the current temperature and room temperature" to "the difference between the melting temperature and room temperature". ref For reference temperature, room temperature (25°C) is generally used. melt This is the melting temperature of the resin matrix.

[0107] In the Johnson-Cook constitutive model, the fracture strain of a material typically depends on the stress triaxiality, temperature, and strain rate. The JC damage model can be expressed as equation (11):

[0108]

[0109] In the formula, D is the damage variable of the matrix phase, and Δε p ε is the plastic strain increment. f This refers to the failure plastic strain.

[0110] When the damage variable D reaches 1, the material fails, and the failure process can be represented as shown in formula (12):

[0111]

[0112] Where: ε f For failure plastic strain, T represents the actual strain rate, used to describe the rate at which the strain of a material changes with time during deformation. *This is the ratio of "the difference between the current temperature and the room temperature" to "the difference between the melting temperature and the room temperature". a1 to a5 are failure model parameters, which can be determined through experiments or fitting. The stress triaxiality is given by σ, where σ is the mean stress. m With equivalent stress σ eq The ratio of .

[0113] The interface phase of a composite material refers to the transition region between the fiber-reinforced phase and the matrix phase. This embodiment uses a cohesive unit simulation method, treating the interface phase as a separate material. By defining the interface phase as a cohesive unit, the crack initiation and propagation of the interface are simulated. When the upper and lower surfaces of the units on both sides of the interface move relative to each other along the normal direction of the interface unit, the cracking or closure between the constituent phases on both sides of the interface can be simulated. The stress components are distributed in the normal, first tangential, and second tangential directions. The failure modes of the cohesive unit are as follows: Figure 3 As shown. The constitutive model of the interface phase cohesive element is as follows. Figure 4 As shown, the initial linear elastic stage corresponds to the element's bearing state, while the subsequent stiffness degradation stage is characterized by exponential softening behavior after element damage.

[0114] The initial damage of the Cohesive element is determined based on the Quads criterion, and the initial damage response can be shown in Equation (13):

[0115]

[0116] In the formula: n represents the normal component, s and t represent the first tangential direction (along the fiber direction) and the second tangential direction (perpendicular to the fiber direction), respectively; t i Let ε be the stress in the i-direction. i For strain in the i direction, K ii It is the elastic modulus in the i-direction (i = n, s, t). Under external load, the stress in the cohesive element gradually increases.

[0117] When the stress components in the three directions satisfy the second nominal stress criterion shown in formula (14), damage occurs in the cohesive unit, and the connected fiber and resin phases will gradually separate.

[0118]

[0119] In the formula: Let be the initial stress of the damage in the i-direction (i = n, s, t).

[0120] For a real number x, the meaning of the <·> operator is as shown in formula (15):

[0121] <x>= (x + |x|) / 2 (15)

[0122] As the load continues to act, the displacement of the cohesive element gradually increases, and the stiffness decreases linearly under the control of the damage factor H, as shown in formula (16). The stress in each direction of the element is calculated according to formula (17).

[0123]

[0124] In the formula: For the total displacement, u i Let i be the displacement component in the i-direction. These represent the displacement at the onset of damage, the displacement at complete failure, and the maximum displacement during loading, respectively. Let i be the stress in the i-direction without considering the effects of damage.

[0125] When the displacement of the cohesive element increases to the point that it satisfies the Power law failure criterion shown in formula (18), the cohesive element completely fails and the interface cracks.

[0126]

[0127] Where: G n G s G t G represents the energy dissipated in the normal and first and second tangential directions when the interface cracks. nC G sC G tC These are the critical fracture energies in the normal direction and the first and second tangential directions, respectively. α is the exponential weighting coefficient for energy dissipation in the normal direction, β is the exponential weighting coefficient for energy dissipation in the first tangential direction, and γ is the exponential weighting coefficient for energy dissipation in the second tangential direction. The contribution of energy dissipation in the three directions to the failure criterion can be adjusted, reflecting the nonlinear characteristics of damage evolution in the material in the three directions.

[0128] Due to the unique composition and structure of CFRP composites, the materials exhibit anisotropic and directional thermal properties, thus requiring consideration of heat generation and conduction processes within the material. During orthogonal cutting of CFRP, the significant heat release generated by friction between the tool and chips leads to changes in the material's mechanical properties. After determining the heat generation, accurately predicting heat transfer and diffusion is crucial for the model's accuracy. Equation (19) illustrates the fundamental relationship between cutting temperature and cutting time:

[0129]

[0130] In the formula: k x k y k z ρ is the thermal conductivity of CFRP in the x, y, and z directions, respectively; Q(t) is the total heat generation rate at time t; ρ is the material density; C is the specific heat capacity; and T is the temperature of the material during the cutting process. This is a function of spatial coordinates (x, y, z) and time (t), used to reflect the temperature distribution of the material at different positions and times during cutting.

[0131] The initial environmental temperature conditions are given according to formula (20), and the initial temperature T0 at any point in the finite element model is 25℃:

[0132]

[0133] Since the entire processing time is very short, the heat exchange between the workpiece and the surrounding environment is negligible, and constraints are added to the model to simplify it. The simplified model's overall boundary is constrained by adiabatic conditions, and no heat exchange occurs between any point on the model surface and the outside world at any time. Its constraint equation is shown in formula (21):

[0134]

[0135] In the formula: Let be the heat flux density at time t for any surface element, and n be the normal vector at the location of the element.

[0136] In CFRP machining, heat is inevitably generated. The heat source mainly consists of three parts:

[0137] (1) Heat generation from deformation of the material's principal shear plane, such as Figure 5 In region 1, the cutting tip cuts through the supporting fibers, and the resulting chips are mainly compressed by the rake face. The processed material in this region will undergo severe deformation, and the friction between the fibers and the rake face will cause the local area to heat up rapidly.

[0138] (2) Heat is generated by friction at the interface between the cutting tool and the chip, such as Figure 5 In region 2, the cutting tool exerts a squeezing and shearing effect on the CFRP, causing brittle fracture of the fibers and elastoplastic deformation of the matrix. The cutting heat in this region mainly comes from chip deformation and the work done to overcome the sliding friction between the chip and the cutting tool rake face.

[0139] (3) Frictional heat generation at the tool-workpiece interface, such as Figure 5 Region 3 generates heat primarily from the friction between the tool's flank and the workpiece surface, making this region the main heat-generating area during material removal. Specifically... Figure 5 As shown in the figure. The heat generated by plastic deformation is negligible; only the heat generated by friction is considered.

[0140] According to the law of conservation of energy, the heat generated during the cutting process will be transferred to the workpiece, the tool, and the chips, as shown in formula (22):

[0141] Q total =Q tool +Q chip +Q CFRP (twenty two)

[0142] In the formula, Q total Q represents the total heat. tool Q chip Q CFRP These are the deformation heat of the main shear plane, the frictional heat of the tool-chip interface, and the frictional heat of the tool-workpiece interface.

[0143] The percentage λ of the heat generated during machining that is transferred to the cutting tool can be expressed by formula (23), and F y This can be shown by formula (24):

[0144]

[0145]

[0146] In the formula: k is the thermal conductivity of the cutting tool; l t The thickness of CFRP under orthogonal cutting experiment is given; in machining, it can be considered as the chip thickness. L is the distance between the temperature measuring point on the tool and the tool tip; ΔT is the temperature difference at the measuring point; F x F is the force exerted on the workpiece by the cutting tool in the cutting direction. y V is the pressure exerted by the cutting tool on the workpiece. C α0 represents the cutting speed of the tool, corresponding to the linear velocity on the cutting edge of the tool in drilling conditions; α0 is the tool clearance angle; γ0 is the tool rake angle; E * R represents the equivalent elastic modulus of the tool and the workpiece. e Δh is the blade tip radius; Δh is the springback thickness; the parameter diagram is shown below. Figure 6 As shown. Figure 6 In the text, 1, 2, and 3 refer to... Figure 5 The text describes three regions corresponding to the generation of heat.

[0147] In the thermo-mechanical coupled finite element model of CFRP, CFRP is divided into many small elements. The total strain of each small element when considering thermal strain in time interval Δt can be expressed as shown in formula (25).

[0148] ε ij =ε ij 0 -α ij ·ΔT (25)

[0149] In the formula: i, j = 1, 2, 3, represent the directions of the three stress-strain components of the model; ε ij ε represents the total strain. ij 0 Indicates the initial strain; α ij ΔT represents the coefficient of thermal expansion; ΔT represents the temperature difference.

[0150] Since the heat generated by the plastic strain of CFRP is not considered, the temperature difference ΔT of the element in the time period Δt can be expressed as shown in formula (26):

[0151]

[0152] In the formula, K is the thermal conductivity, T is the temperature, and q f ρ is the heat flux density generated by friction, C is the specific heat capacity of the material, reflecting the material's heat storage capacity, and x is the cutting direction of the tool.

[0153] To model and analyze the fibers and resin matrix in the CFRP finite element model, we first assume that the prepared CFRP material is free of pores and defects, that there are clear boundaries between fibers without fiber overlap, and that there is no incompatibility between the fibers and the matrix. Since the distribution of fibers in the matrix is ​​random, we model the fibers as staggered, which better reflects reality.

[0154] like Figure 7 As shown, after establishing the models of the fiber, matrix, and tool, meshes were generated for each of the three components, and appropriate element shapes and algorithms were selected. This embodiment constructs CFRP mesoscopic right-angle cutting models for four typical fiber orientation angles: 0°, 45°, 90°, and 135°. After assembling the models of each component phase of the workpiece, full constraints were applied to all nodes on its left and bottom sides according to the constraint state of the workpiece during actual machining to fix the workpiece. For the mesoscopic part of the workpiece, tie constraints were applied between the fiber and the matrix to connect the two parts. The load and constraint conditions for the tool were implemented by setting a reference point RP: first, a reference point was defined and coupled to a point on the tool; a velocity load was applied to RP in the cutting direction, and the degrees of freedom in other dimensions were constrained to allow it to move along the cutting velocity direction; and the tool was set as a rigid body by applying rigid body constraints through the RP point.

[0155] For the established model, the next step is to assign material properties. In this example, the drill bit material is cemented carbide, and the workpiece material is assigned corresponding material properties through section assignment. When setting the analysis step and history variable output, the analysis step type is set to Dynamic, Temp-disp, Explict. The total analysis step time is set according to the actual cutting time. At the same time, the temperature field variable is selected for output in the history variables, and an appropriate interval is set. For boundary conditions and contact settings, the global contact state is first determined directly through General Contact. The general contact algorithm can adaptively handle geometric nonlinearity, material nonlinearity, and transient processes of interface separation-closure while preventing element erosion, thereby simulating the real contact evolution with higher efficiency. Building upon the Contact framework, a local Surface-to-Surface contact still needs to be constructed between the "tool cutting surface and the internal nodes of the workpiece": the tool-material contact surface is defined as the primary contact surface, and the relevant node set inside the workpiece is set as the secondary contact surface; regarding contact attributes, the normal behavior adopts "hard contact," and the constraint execution method adopts the default; the tangential behavior introduces the Penalty friction model and sets the corresponding friction coefficient; according to the actual situation, the workpiece material is fixed in the machining area by the fixture. For CFRP material, all nodes on the surrounding surface of the material are completely fixed, restricting all degrees of freedom, i.e., U1=U2=U3=UR1=UR2=UR3=0. Specific values ​​are assigned to the tool's movement along the cutting direction, while the angular displacement in the cutting direction and the displacement and angular displacement in the other two directions are completely constrained, i.e., U2=U3=UR1=UR2=UR3=0, to meet the actual machining conditions, thereby ensuring that the tool moves along the predetermined correct trajectory and ensuring the accuracy of the cutting process.

[0156] The experimental system consists of three main parts: a material cutting unit, a data acquisition unit, and a data processing unit. The system configuration is as follows: Figure 8 As shown in the figure. The experiment used a DX-650 vertical CNC machining center as the cutting platform. The CFRP right-angle cutting specimen was fixed on a Kistler-9129AA three-dimensional force gauge using a special fixture. The force gauge was installed on the worktable of the machining center and could monitor the dynamic mechanical response during the machining process in real time. At the same time, it was equipped with a KISTLER-8152C acoustic emission sensor, a computer, and a temperature measuring instrument to measure the cutting temperature and monitor the dynamics of the cutting process.

[0157] The cutting force detection device used in the experiment mainly consists of a force gauge, a charge amplifier, a data acquisition card, and a computer. The force gauge is a KISTLER-9129AA force sensor from Kistler, Switzerland, and the data acquisition software uses the company's specially developed DynoWare data acquisition and analysis system, such as... Figure 9 As shown.

[0158] When the fiber orientation angle is 0° (i.e., the fiber axis is parallel to the cutting direction Vc), the simulation cutting calculation results are as follows: Figure 10 As shown. The tool generates a significant axial compressive load at the moment of contact with the workpiece. Because the fiber arrangement coincides with the cutting path, the tool initially applies a compressive force along the fiber axis, generating high longitudinal stress. In the microscopic contact area between the tool rake face and the fiber, such as... Figure 10 (a) In region I, stress concentration is caused by the small local contact area, which leads to micro-bending or even instability of the fiber.

[0159] After fiber buckling, the interfacial phase between the fiber and the matrix begins to break down. As the tool continues to feed, the continuous pushing action of the tool tip on the fiber causes significant torsional deformation. When the degree of torsion exceeds the fiber's critical strength value, the fiber breaks, forming a machined cross-section with axial fracture characteristics, such as... Figure 10 (b) The cross-section is in the form of a bent cross-section. In regions II and III, local matrix pits caused by fiber pull-out and interface debonding can be clearly observed. The pits are caused by the fact that the ends of the fibers were not completely sheared when they broke. Instead, the shearing and dragging action during the pull-out process damaged the matrix structure, forming an interface damage morphology.

[0160] Stress distribution analysis reveals that high-stress areas are concentrated in the region where the tool and matrix directly contact each other. This indicates that under this fiber orientation, although the fiber bears axial compressive load, the main cutting load is still borne by the matrix, especially during the tool feed process, where the matrix provides support to the fiber, resulting in a higher degree of stress concentration in the matrix. Therefore, under this condition, fiber breakage and interface debonding mechanisms are mainly dominated by mechanical loads, with less influence from thermo-mechanical coupling factors, and the machining damage exhibits typical mechanical failure characteristics.

[0161] Figure 11 The simulation results of cutting at a fiber orientation angle of 45° are presented. The figure clearly reveals the three typical failure characteristics of the fiber bundle under cutting load: local buckling instability, stress concentration, and damage area expansion, indicating that there are typical mechanical asymmetric response characteristics in the material processing under this condition.

[0162] Under this condition, the stress concentration area is mainly distributed in the direction at a 45° angle to the fiber axis. The shear stress amplitude in this direction significantly exceeds the transverse shear strength threshold of carbon fiber, leading to periodic shear-dominated fracture. The fracture interface exhibits a typical 45° oblique cut morphology, which is highly consistent with the fiber direction, directly reflecting the dominant control of the shear principal stress in this specific direction. Simultaneously, in the low-stress zone far from the direct contact area, damage propagates along the interlaminar interface of the composite material. Because the energy dissipation required for the interfacial debonding process is far lower than the critical strain energy release rate that triggers delamination failure, the interface fails preferentially, inducing the generation and propagation of delamination cracks, ultimately forming a macroscopic damage band with a stepped characteristic, such as... Figure 11 (a) As shown in region I.

[0163] At the leading edge of the cutting zone, a highly localized contact area is formed between the tool and the workpiece material, bearing a continuous and highly concentrated triaxial compressive load, leading to a sharp increase in material stress at the microscale within this region. For thermosetting epoxy resin matrices, their mechanical behavior is extremely sensitive to load concentration. When the local stress approaches or even exceeds its yield limit, the matrix structure struggles to maintain its integrity, resulting in brittle fracture or delamination from the fiber surface. Notably, this failure process is not purely brittle fracture; under the combined effects of high pressure and strong shear, the matrix material simultaneously undergoes microscopic yielding accompanied by restricted plastic flow. Particularly in the narrow region at the tool leading edge, due to the inability of the material to effectively unload stress under high-speed cutting conditions, the continuously accumulated stress causes significant shear deformation and plastic flow in the matrix. This plastically deformed material is forcibly squeezed out of the cutting zone and ultimately becomes involved in the chip formation process. This phenomenon clearly demonstrates that even under room-temperature cutting conditions, epoxy resin matrices can still exhibit localized plastic deformation behavior under extreme stress gradients and actively participate in the evolution of the cutting surface morphology and chip shape.

[0164] Further focusing on the mechanical response of the fiber-matrix interface reveals that this interface is under a complex, non-uniform stress state during cutting, experiencing drastic stress gradient changes. Particularly in the direct contact area near the tool rake face, the significant stiffness mismatch between the high modulus of the carbon fiber and the low modulus of the matrix makes it difficult to effectively transfer and disperse the load from the rigid fiber to the surrounding flexible matrix material. This results in a strong stress concentration effect at the interface, making it highly susceptible to inducing localized debonding failure in the weaker areas. This microscale interfacial damage typically manifests as partial fiber pull-out or the formation of small, localized interfacial delamination areas.

[0165] Furthermore, due to the continuous dynamic contact between the cutting tool and the composite material during the cutting process, the initially formed interfacial microcracks rapidly propagate to adjacent areas under the drive of stress concentration, further weakening the overall interfacial bonding strength. As the tool continues to advance, interfacial debonding extends along the fiber axial direction, the damaged area gradually connects and expands, eventually evolving into macroscopic forms of damage such as fiber pull-out and large-area matrix peeling. These macroscopic and microscopic damage mechanisms directly affect the machined surface, forming defects such as pits, steps, and exposed fibers, becoming key factors in degrading the surface roughness and overall surface quality.

[0166] When the fiber orientation angle is 90°, i.e., the fiber alignment direction is perpendicular to the cutting direction of the tool, the CFRP composite material exhibits a completely different mechanical response characteristic during cutting compared to the 0° orientation. Under this condition, the axial stress component borne by the material is significantly reduced. The principal stress field is mainly composed of radial compressive stress generated by the tool rake face, tensile-compressive bending stress induced by fiber bending deformation, and highly localized shear stress at the interface. In particular, the dominant role of shear strain at the interface is more prominent, posing a challenge to the fiber-matrix bonding strength.

[0167] At this orientation angle, the material failure process exhibits typical progressive failure characteristics, which can be clearly divided into two stages. The first is the fiber bending instability stage: due to the continuous compression of the fiber perpendicular to the cutting edge by the tool rake, the fiber is essentially constrained by a cantilever beam-like boundary condition, resulting in significant bending along its length. When the local bending stress exceeds the fiber's ultimate bending strength, the fiber undergoes its first brittle fracture, forming a typical unilateral fracture surface. Entering the second stage, the remaining fiber, under the action of the already formed shear band, continues to undergo a top-down shear failure process, fracturing layer by layer along the fiber length, forming a multi-level, step-like "stepped" fracture structure. For example... Figure 12 As shown in regions I, II, and III in (a), it can be clearly observed that the fracture surfaces are irregularly distributed, indicating that the stress at the local interfaces is uneven.

[0168] Figure 12 (b) Further demonstrates the characteristics of the fiber cross-section under the condition of θ = 90°, showing an overall stepped distribution of the fracture surface, indicating that the fiber underwent multiple secondary fractures within the shear band. Furthermore, through comparison... Figure 12 The stress distribution contour maps in (b) and (c) show that the maximum stress is concentrated in the matrix region, indicating that under this condition, the matrix material is subjected to greater plastic deformation pressure. Due to its brittle nature, the fiber cannot effectively alleviate stress transmission, leading to stress concentration and diffusion towards the interface. Ultimately, debonding occurs between the fiber and the matrix, and tearing and peeling occur during the subsequent fracture process, severely affecting the quality of the cut surface and even jeopardizing the quality of the structural component itself.

[0169] When the fiber orientation angle is 135°, the representative volume element (RVE) of the cutting tool is subjected to highly complex multiaxial composite loads during the cutting process of the CFRP composite material. This load state manifests as follows: the compressive force applied by the tool rake face generates significant radial compressive stress; simultaneously, the relative slippage between the fiber bundle and the tool edge induces strong shear stress components; furthermore, the fibers are subjected to tensile loads along their axial direction, while the matrix mainly bears radial tensile stress. The superposition of these two factors creates a highly non-uniform and dynamically evolving stress field within the material.

[0170] exist Figure 13 (a) In region I, significant shear-compression combined stress occurs at the contact point between the tool tip and the CFRP material, forming a highly concentrated stress field. After being subjected to intense axial compression, the fiber bundle undergoes severe nonlinear buckling. When the buckling deformation exceeds the fiber's critical buckling strain, the fiber exceeds its critical instability state, resulting in brittle fracture and triggering a chain reaction of failure. This buckling fracture mechanism directly leads to the formation of highly regular serrated pits on the cutting surface, significantly reducing the workpiece surface quality and severely affecting the final machining quality.

[0171] Region II exhibits a more complex structural instability phenomenon. Under the high pressure of the cutting process, some fiber bundles experience overall structural instability, and some fiber bundles cannot maintain their original arrangement and break apart, further aggravating the damage to the cutting zone. In Region III, the pressure exerted by the cutting surface on the fibers can be clearly observed, causing secondary damage. Some fibers detach from their original positions, producing cracks and gaps, resulting in continuous destruction of the interface structure.

[0172] The overall stress distribution indicates that although the Mises equivalent stress is mainly concentrated in the area where the tool tip contacts the fiber, the reverse cutting geometry constraint (45° fiber-tool angle) severely hinders the effective release of shear stress along the fiber direction. This suppresses the originally ideal shear fracture mode, ultimately resulting in a combined buckling-peeling-tearing failure of the fiber. Compared to other fiber orientations, the 45° fiber orientation condition makes the machined surface more prone to severe defects such as interface delamination, crack propagation, and large-area tearing, reflecting its poor machinability and high damage sensitivity.

[0173] The heat generated during processing causes temperature changes in the processing area, which mainly affects the mechanical properties of the epoxy resin matrix and the cohesive strength between the fiber-matrix interface, thus affecting the response performance of CFRP composites during the cutting process. Figure 14 (a) shows the simulation results of orthogonal cutting at 25℃ with a fiber orientation angle of 0°. The results show that the cutting process exhibits typical brittle fracture characteristics. At this temperature, the matrix has a high elastic modulus and good cutting performance, but stress concentration is obvious. Due to the high rigidity of the matrix, the axial movement of the fiber is effectively constrained, resulting in the cutting stress being concentrated in the contact area between the tool rake and flank faces and the workpiece. The fracture mode is mainly fiber shear brittle fracture, accompanied by microcracks propagating along the interface and local pits caused by fiber pull-out. At the same time, the cutting area shows a local temperature rise, with the highest temperature concentrated in the tool-workpiece contact area. Since the axial thermal conductivity of carbon fiber is much higher than that of the matrix transverse thermal conductivity, a local heating area is formed at the tool-workpiece contact, and heat is significantly conducted away along the fiber axis.

[0174] Figure 14 (b) shows the orthogonal cutting results at a fiber orientation angle of 45°C at 25°C. The cutting process under this condition is mainly influenced by the synergistic effect of fiber bending resistance and interfacial shear. Simulation results show that at this temperature, the matrix is ​​in a glassy state with high rigidity. During cutting, the tool applies intense reverse bending and shearing forces to the fibers, leading to typical brittle fracture. Simultaneously, rapid interfacial peeling occurs, forming short fiber block chips, and irregular interfacial tearing and delamination structures appear on the machined surface. Furthermore, the formation of localized high-temperature zones is particularly pronounced. Heat generation mainly originates from tool wear and fiber bending deformation. The axial thermal conductivity of carbon fiber is significantly higher than that of the matrix, promoting heat conduction along the fiber direction. However, because the fibers are arranged in the opposite direction to the cutting direction, heat conduction is somewhat hindered, leading to continuous accumulation in the tool leading edge region.

[0175] Figure 14 (c) shows that at a temperature of 25℃, with a fiber orientation angle of 90°, the fiber axis is perpendicular to the cutting direction. At this temperature, the matrix maintains high rigidity, which can constrain the deformation behavior of the fiber to a certain extent. During the cutting process, the fiber mainly bears the combined effects of bending and shearing, and the fracture morphology is typical of brittle fiber failure. The matrix fails after the yielding stage, and the chips exist in the form of short fiber fragments. Surface defects mainly originate from microcracks propagating along the fiber-matrix interface. At the same time, the cutting heat mainly comes from the frictional heat generated between the tool and the workpiece and the heat generated by the deformation of the material, and the temperature field shows a certain gradient distribution characteristics. Since carbon fibers have high thermal conductivity along the axial direction, heat can easily diffuse rapidly along the fiber direction, while the transverse thermal conductivity of the matrix is ​​weak, resulting in the formation of a local high-temperature zone in the tool-workpiece contact area. At this time, the rigid matrix can play a strong role in constraining the bending deformation of the fiber, and the fiber mainly undergoes brittle fracture in the transverse shear manner.

[0176] Figure 14 (d) shows that at a temperature of 25℃, the maximum Mises stress can reach 288.4MPa when the fiber orientation angle is 135°. High stress is concentrated at the intersection of the tool leading edge and the fiber-matrix interface, indicating that this area is a typical stress concentration center. Since the fibers are arranged at a 135° angle, the stress mode is a combination of tension and shear. Local areas experience step-like fractures due to stress exceeding the transverse tensile strength of T800S fibers. The matrix is ​​subjected to shearing, resulting in microcracks and ultimately brittle-dominated local cracking behavior. Meanwhile, the temperature field of CFRP composite material during orthogonal cutting is mainly affected by friction between the tool and the workpiece. Due to the high friction coefficient between the workpiece and the tool surface, the cutting heat mainly comes from the following two aspects: (1) The fiber forms a rough cross-section during shearing fracture, which generates significant frictional heat due to continuous contact with the rake face; (2) The chip rubs violently on the rake face, causing the temperature gradient in the cutting zone to rise sharply, local heat to accumulate rapidly, and conduct out along the fiber axis.

[0177] Figure 15 The experimental cutting force curves and corresponding simulation results are shown at 25℃ with different fiber orientation angles θ. The comparison between experimental data and simulation results shows that the fiber orientation angle significantly affects the change of cutting force data. The mechanical response characteristics of orthogonal cutting of CFRP composite materials can be seen from the image.

[0178] When the cutting direction angle θ = 0°, in the initial contact stage, the collision between the tool and the workpiece causes a sharp increase in the cutting force signal recorded by the force gauge. However, as the cutting process progresses, continuous strip-shaped chips appear in the material, which causes the collected cutting force signal to change downward. When the tool contacts the workpiece, the stress is mainly concentrated in the longitudinal direction, and the axial stress concentration of the fibers is relatively low. Most of the cutting load is borne by the matrix. Therefore, the stress at the microscopic scale at a fiber direction angle of 0° is still smaller than that under other fiber tilt angle conditions, thus effectively suppressing the impact load in the initial stage. As the cutting process enters the stable cutting stage, the cutting force shows a fluctuating growth trend, eventually stabilizing at around 230N, with a maximum cutting force of 240.4N.

[0179] When the cutting direction angle θ = 45°, the tool will be subjected to a complex combination of multiple loads when cutting into the workpiece. During the machining process, the rake face will generate a large radial compressive stress on the material. At the same time, the fiber will slip relative to each other during the shearing process, which will also bring shear stress. In addition, the fiber will be subjected to tensile load along the axial direction during the removal process, and the matrix will also be subjected to radial tensile stress at this stage. Therefore, when machining materials with a 45° fiber direction angle, the cutting force will be complex and frequently changing, with a maximum cutting force of 186.6 N.

[0180] When the cutting angle θ = 90°, the cutting of the material by the tool is equivalent to cantilever beam cutting. At this time, the axial component of the material is reduced, and the resistance encountered during cutting mainly comes from the radial compression and bending of the fibers. The main challenge is overcoming the radial strength of the fibers. In this case, the fibers bend before being sheared, so the cutting force becomes significantly unstable. Compared to 45°, the cutting force is more stable and smaller at 90°, with a maximum cutting force of 229.5 N.

[0181] When the cutting direction angle θ = 135°, the fiber is tilted in the opposite direction to the cutting direction. This causes the spiral chips to accumulate continuously at the leading edge of the tool, and the chips are difficult to remove. This chip accumulation effect causes continuous fluctuations in the cutting force, and the fluctuation frequency is significantly higher than that at other angles. The maximum cutting force reaches 269.3N.

[0182] Figure 16 This study demonstrates the effect of different cutting speeds on cutting forces for materials with different fiber orientation angles at the same cutting depth of 40 mm. Figure 16 In (a), when the fiber orientation angle is 0° and the cutting speed is 100 mm / min (black curve), the material's elastic deformation and the squeezing effect of the cutting edge are significant at the moment the tool enters the workpiece, causing the cutting force to rise sharply. Subsequently, the cutting process gradually stabilizes, and the cutting force decreases and stabilizes at around 60 N. During this stage, the lower cutting speed allows for more interaction time between the tool and the material, resulting in a relatively smoother process of fiber breakage and matrix cutting.

[0183] When the cutting speed increases to 150 mm / min (red curve), the dynamic interaction between the tool and the material intensifies, leading to rapid accumulation of cutting heat and softening of the resin matrix. While matrix softening reduces friction between the fiber and the tool, the impact effect at the moment of tool entry is more significant, resulting in a more dramatic initial increase in cutting force. However, the cutting force stabilizes and drops to around 35 N. This is because matrix softening alters the force transmission path during cutting; the fiber is cut in a smoother matrix environment, reducing the required cutting force.

[0184] Figure 16 In (b), when the fiber orientation angle is 45°, the cutting force exhibits a "sudden initial increase followed by a stable fluctuation" characteristic at all cutting speeds. In the initial stage of cutting, the tool is in direct contact with the workpiece, and the oblique interface between the fiber and the matrix is ​​instantly subjected to load, leading to a sharp increase in cutting force. At a cutting speed of 100 mm / min (black curve), the stable cutting force is 180 N. At lower cutting speeds, the interaction time between the tool and the material is longer, and the combined effect of fiber breakage and matrix cutting is continuous and sufficient, maintaining a high cutting force. At a cutting speed of 150 mm / min (red curve), the stable cutting force drops to 160 N. As the cutting speed increases, the increased cutting heat softens the matrix locally, alleviating the cutting force to some extent, but the fiber's fracture characteristics under oblique cutting still keep the cutting force at a high value. At a cutting speed of 200 mm / min (blue curve), the stable cutting force further decreases to 60 N. During high-speed cutting, a large amount of cutting heat is generated, the matrix softening range expands, the interaction mode between the fiber and the tool changes, and the cutting force is significantly reduced. The cutting force at this fiber orientation angle is significantly higher than that at 0°, because the 45° fiber orientation causes the tool to bear the dual loads of fiber shearing and matrix cutting at the same time, and the interlayer stress is more complex.

[0185] exist Figure 16 In (c) and (d), when the fiber orientation angle is 45°, the cutting speed is 100 mm / min (black curve). The tool cuts the fiber perpendicularly. The energy required for fiber breakage is high, but the relatively low cutting speed makes the cutting process relatively smooth, with a stable cutting force of 30 N. At a cutting speed of 150 mm / min (red curve), the dynamic effect is enhanced, the synergistic effect of fiber breakage and matrix cutting changes, and the stable cutting force rises to 40 N. At a cutting speed of 200 mm / min (blue curve), the accumulation of cutting heat leads to a large amount of softening of the matrix, the fiber cutting environment changes, and the stable cutting force reaches 130 N.

[0186] When the fiber orientation angle is 135°, the cutting speed is 100 mm / min (black curve). The interaction between the tool and the fiber results in low initial cutting resistance and a stable cutting force of 20 N. When the cutting speed is 150 mm / min (red curve), the interaction strength between the fiber and the matrix increases, and the stable cutting force rises to 40 N. When the cutting speed is 200 mm / min (blue curve), the combined effects of cutting heat and dynamic action result in a stable cutting force of 60 N.

[0187] While high cutting speeds can shorten machining cycles, they significantly increase cutting forces and cause severe fluctuations. CFRPs with different fiber orientation angles exhibit significant differences in their adaptability to cutting speeds: materials with a 90° fiber orientation angle show improved efficiency in vertical fiber cutting at high cutting speeds, and high-speed cutting makes fiber breakage more "brittle," resulting in lower and more stable cutting forces, making them more suitable for high-speed machining; materials with a 135° fiber orientation angle, under low-speed conditions, can gradually release stress by extending the cutting contact time, avoiding interlayer damage caused by high-speed impacts, thus making them more suitable for low-speed machining.

[0188] Figure 17 The correlation between cutting depth and cutting force is presented for CFRP materials with different fiber orientation angles at a constant cutting speed of 150 mm / min. For example... Figure 17 As shown in (a), when the cutting depth is 20 mm (black curve), the tool enters the fiber bundle in a parallel cutting state. Due to the extremely high axial strength of carbon fiber, the fiber mainly bears the cutting load during the cutting process, and the stress distribution in the cutting area is uniform, resulting in the lowest peak cutting force and overall force value. The peak cutting force only reaches 130 N, and in the later stable stage of cutting, the cutting force is maintained at around 45 N.

[0189] As the depth of cut increased to 40mm (red curve), the cutting force spiked to 300N the instant the tool entered the material. This was due to the uneven distribution of fibers within the material and the difference in the bonding strength between the resin matrix and the fiber interface. However, as the tool continued to feed, the cutting area gradually stabilized, and the cutting force dropped and stabilized at around 30N. This is because the interaction between the tool and the material entered a relatively uniform stage, and the synergistic cutting effect between the fiber and the matrix tended to stabilize.

[0190] When the depth of cut further increases to 60 mm (blue curve), the contact area between the cutting edge and the material increases significantly, and the cutting force rapidly rises to 170.1 N in the initial stage of cutting. Subsequently, due to the change in the local failure mode of the material, the synergistic effect of fiber fracture and matrix breakage causes the cutting force to fluctuate, eventually stabilizing at around 230 N. During this process, the complex effects of multi-layer shearing of the fiber bundles inside the material and the extrusion and breakage of the matrix collectively lead to the change in cutting force.

[0191] Figure 17 (b) illustrates the relationship between cutting force and depth when the fiber orientation angle is 45°. At a cutting depth of 20 mm (black curve), the tool acts simultaneously on the oblique interface between the fiber and the matrix, resulting in a relatively uniform stress distribution. The fiber and matrix breakage during cutting is relatively synergistic, minimizing cutting force fluctuations and stabilizing at approximately 70 N. As the cutting depth increases to 40 mm (red curve), the cutting layer thickness increases, intensifying the combined effects of fiber breakage and matrix cutting. At this point, the difficulty of fiber breakage under oblique stress increases, and the energy required for matrix cutting increases, both contributing to maintaining the overall cutting force at around 150 N. When the cutting depth reaches 60 mm (blue curve), the interlaminar stress concentration effect of the material significantly intensifies. During cutting, the difficulty of synergistic breakage between the interlaminar fibers and the matrix increases, exacerbating the uneven stress distribution and causing larger cutting force fluctuations, with the maximum cutting force reaching 185 N. This is because at large cutting depths, the combined shearing and tensile effects of the interlaminar fibers, along with the large-scale fragmentation of the matrix, jointly trigger significant fluctuations in cutting force.

[0192] Figure 17 (c) and (d) show the experimental results for fiber orientation angles of 90° and 135°. Under these two fiber orientation angles, the trend of cutting force with depth is roughly similar to that under the 45° condition, but the peak value and fluctuation amplitude differ due to the different fiber orientations. When the fiber orientation angle is 90°, at a cutting depth of 20 mm, the tool cuts vertically into the fiber layer, and the fiber needs to be directly cut by the tool. The initial cutting force is relatively large, and the cutting force stabilizes at around 110 N. When the cutting depth is 40 mm, the combined effect of fiber cutting and matrix cutting is enhanced, and the stable cutting force rises to 140 N. When the cutting depth is 60 mm, the difficulty of cutting interlayer fibers and the cutting resistance of the matrix further increase, and the stable cutting force reaches around 180 N. When the fiber orientation angle is 135°, at a cutting depth of 20 mm, the interaction between the tool and the fiber results in relatively low initial cutting resistance and a stable cutting force of around 50 N. When the cutting depth is 40 mm, the difficulty of coordinating cutting between the fiber and the matrix increases, and the stable cutting force rises to 70 N. When the cutting depth is 60 mm, the combined effect of interlaminar stress and fiber cutting causes the stable cutting force to reach around 130 N.

[0193] Figure 18 This study demonstrates the temperature response of CFRP materials with different fiber orientation angles under varying cutting speeds when the cutting depth is fixed at 40 mm. Cutting speed directly affects the rate of heat generation during cutting; cutting heat is positively correlated with cutting speed and has a shorter heat diffusion time. That is, the higher the speed, the shorter the heat diffusion time, thus temperature changes are more sensitive to speed.

[0194] When the fiber orientation angle is 0°, the highest temperatures corresponding to cutting speeds of 100 mm / min, 150 mm / min, and 200 mm / min are 28.3℃ and 27.9℃, respectively. At 0°, the cutting speed has a relatively small impact on temperature because the fiber axis conducts heat and dissipates heat quickly. Even as the speed increases, the amount of heat generated during cutting increases, but the heat diffusion efficiency also increases, maintaining the temperature at a low level of approximately 28℃, demonstrating the good thermal stability at 0° fiber orientation.

[0195] When the fiber orientation angle is 45°, the highest temperatures at different cutting speeds reach 59.5℃, 65.4℃, and 64.2℃, respectively, representing an increase of over 133% compared to the 0° operating temperature. At 45°, the increased cutting speed leads to a higher frequency of interaction between the tool and the material, accelerating the energy consumption rate of fiber shearing and fracture, and matrix plastic deformation, resulting in a significant increase in cutting heat generation. Simultaneously, the shortened heat diffusion time at high-speed cutting makes it easier for heat to accumulate in the cutting zone, causing the temperature to rise with increasing speed. At a speed of 200 mm / min, the temperature decreases slightly, possibly due to increased tool wear altering the contact state in the cutting zone and changing the heat transfer path, allowing some heat to be dissipated through the worn tool.

[0196] When the fiber orientation angle is 90°, the highest temperatures corresponding to the changes in cutting speed are 58.9℃, 55.4℃, and 50.9℃. At 90°, the tool cuts the fiber perpendicularly; increasing the cutting speed increases the fiber breakage frequency and the amount of cutting heat generated. However, at high-speed cutting, the contact time between the tool and the fiber fracture surface is shortened, resulting in a slight decrease in frictional heat. Simultaneously, the insulating effect of the interlayer resin makes heat dissipation difficult, and the temperature change shows a trend of first rising and then falling, reflecting the combined effect of cutting heat generation, tool wear, and heat diffusion.

[0197] When the fiber orientation angle is 135°, the highest temperatures at the cutting speeds are 79.3℃, 78.2℃, and 75.8℃. The large-angle cutting at 135° results in the most complex deformation mechanism between the fiber and the matrix, and the largest amount of cutting heat generation. As the cutting speed increases, the heat diffusion time shortens, and the temperature rises significantly; however, at excessively high speeds, tool wear and material breakage intensify, altering the energy consumption pattern in the cutting zone. Some energy is used for material breakage rather than heat generation, leading to a slight decrease in temperature, demonstrating a complex thermo-mechanical coupling mechanism.

[0198] Figure 19 The temperature evolution of CFRP materials with different fiber orientation angles under varying cutting depths is presented when the cutting speed is constant at 150 mm / min. During the cutting process, the cutting heat mainly originates from fiber shearing and fracture, matrix plastic deformation, and tool-workpiece friction. The temperature change exhibits a "rising-stabilizing" characteristic, which is essentially the result of a dynamic equilibrium between cutting heat generation and heat diffusion.

[0199] When the fiber orientation angle is 0° and the cutting depth is 20mm, 40mm, and 60mm, the highest temperatures are 27.3℃, 27.9℃, and 28.6℃, respectively. At 0° fiber orientation, the tool cuts parallel to the fiber, resulting in high axial fiber strength, low energy required for shear fracture, and rapid diffusion of cutting heat along the fiber axis. Therefore, the temperature rise is gradual and remains at a low level overall. As the cutting depth increases, the contact area between the cutting edge and the material increases, slightly increasing the amount of cutting heat generated. However, due to the efficient thermal conductivity of the fiber, the temperature only increases slightly.

[0200] When the fiber orientation angle is 45°, the highest temperatures corresponding to cutting depths of 20mm, 40mm, and 60mm are 62.3℃, 65.4℃, and 58.2℃, respectively. At this angle, the tool obliquely cuts into the fiber-matrix interface, requiring the fiber to withstand combined shear and tensile loads, increasing the difficulty of fracture. Simultaneously, significant plastic deformation occurs in the matrix during cutting due to tool compression, leading to a dramatic increase in cutting heat generation. Compared to the 0° operating condition, the temperature increases by over 120%. When the cutting depth is 60mm, the temperature decreases slightly. This is because at a large cutting depth, the increased cutting force leads to accelerated tool wear, alters the tool-workpiece contact state, reduces heat transfer efficiency, and allows some heat to dissipate through the tool, causing a drop in the cutting zone temperature.

[0201] When the fiber orientation angle is 90°, the highest temperatures corresponding to cutting depths of 20mm, 40mm, and 60mm are 53.6℃, ​​55.4℃, and 58.3℃, respectively. At a 90° angle, the tool cuts the fiber perpendicularly, resulting in high energy consumption during fiber breakage and a large contact area between the fracture surface and the tool, leading to significant frictional heat. As the cutting depth increases, the number of fiber layers cut increases, causing continuous accumulation of cutting heat and a gradual increase in temperature. However, when the fiber breaks perpendicularly, the heat diffusion path is blocked by the interlayer resin due to its low interlayer thermal conductivity, resulting in a lower temperature increase rate than under the 45°C condition.

[0202] When the fiber orientation angle is 135°, the highest temperatures corresponding to cutting depths of 20mm, 40mm, and 60mm reach 70.8℃, 78.2℃, and 78.9℃, respectively. In this direction, the tool cuts the fiber at a large angle, causing complex bending-fracture deformation of the fiber under cutting force, while the matrix experiences intense compression-shearing. The cutting heat generation mechanism is the most complex at this angle. Simultaneously, the interlaminar stress concentration effect at 135° exacerbates internal material damage, converting energy consumption into more heat, resulting in a significantly higher temperature than in other directions. Furthermore, the temperature tends to stabilize at around 78℃ with increasing cutting depth, reflecting a dynamic equilibrium between cutting heat generation and diffusion.< / x>

Claims

1. A CFRP thermal-mechanical coupling cutting modeling method based on micro-failure theory, characterized in that, The method comprises the following steps: Step S1) establishing a carbon fiber three-dimensional geometric model, a matrix three-dimensional geometric model and a tool three-dimensional geometric model in a 3D modeling software, and obtaining a CFRP three-dimensional grid model after meshing and assembling; The carbon fiber three-dimensional geometric model adopts a representative volume element model; Step S2) setting a multi-phase three-dimensional damage constitutive relation for the CFRP three-dimensional grid model to obtain a mesoscopic simulation material model; The multi-phase three-dimensional damage constitutive relation comprises three-dimensional damage constitutive relations of fiber phase, matrix phase and interface phase; Step S3) setting a heat conduction equation, an initial environmental temperature and an adiabatic boundary condition for the mesoscopic simulation material model, inputting a heat source equation comprising a main shear surface deformation heat, a tool-chip interface friction heat and a tool-workpiece interface friction heat, and inputting a thermal strain equation, and then obtaining a thermal-mechanical coupling finite element model; Step S4) using the thermal-mechanical coupling finite element model to perform thermal-mechanical coupling analysis on a cutting process of the structure to be cut according to preset parameters and a preset time step, to realize thermal-mechanical coupling dynamic cutting simulation, and to obtain a simulation result.

2. The microcosmic failure theory based CFRP coupled thermo-mechanical cutting modeling method according to claim 1, characterized in that: In the carbon fiber three-dimensional geometric model, the carbon fiber three-dimensional geometric units are arranged in a staggered manner in a rectangular region.

3. The microcosmic failure theory based CFRP coupled thermo-mechanical cutting modeling method according to claim 1, characterized in that: The three-dimensional damage constitutive relation of the fiber phase comprises: adopting a transverse isotropic constitutive model, setting a stress-strain equation before failure according to a generalized Hooke's law, determining damage initiation by adopting a Tsai-Wu failure model, calculating damage variables in axial and transverse directions by adopting an exponential mode, calculating a damage variable in a shear direction by adopting a linear mode, and determining failure by adopting a maximum stress criterion.

4. The microcosmic failure theory based CFRP coupled thermo-mechanical cutting modeling method according to claim 1, characterized in that: The three-dimensional damage constitutive relation of the matrix phase adopts a Johnson-Cook constitutive model to describe mechanical properties and fracture behavior.

5. The microcosmic failure theory based CFRP coupled thermo-mechanical cutting modeling method according to claim 1, characterized in that: The three-dimensional damage constitutive relation of the interface phase comprises: adopting a cohesive element constitutive model, determining damage initiation and calculating a damage variable by adopting a Quads model, and determining failure or cracking by adopting a Power-Law energy dispersion model.

6. The microcosmic failure theory based CFRP coupled thermo-mechanical cutting modeling method according to claim 1, characterized in that: The structure to be cut adopts a carbon fiber reinforced composite material.

7. The microcosmic failure theory based CFRP coupled thermo-mechanical cutting modeling method according to claim 1, characterized in that: In step S4), the preset parameters comprise the following parameters: physical property parameters of the structure to be cut, a fiber direction angle, a cutting direction, a cutting speed, a cutting depth, a feed amount, a tool rake angle, a tool relief angle and environmental physical quantities.

8. The microcosmic failure theory based CFRP coupled thermo-mechanical cutting modeling method according to claim 1, characterized in that: The CFRP thermal-mechanical coupling cutting modeling method further comprises: performing a cutting experiment by using an orthogonal cutting comprehensive experiment platform to obtain an experimental result; and comparing and verifying the simulation result with the experimental result to verify the accuracy of the simulation result.

9. A comprehensive orthogonal cutting experiment platform applied to the CFRP thermal coupling cutting modeling method of claim 8, characterized in that, It comprises: A material cutting unit for cutting a structure to be cut; A data acquisition unit comprising a dynamometer, an acoustic emission sensor and a temperature measuring instrument; respectively for measuring cutting force, damage and / or failure of the structure to be cut and cutting temperature during the cutting process. A data processing unit for accepting and processing data obtained by the data acquisition unit to obtain an experimental result.

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