Method for establishing cutting model of carbon fiber reinforced thermoplastic resin-based composite material

Abstract

The invention relates to a method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material, and belongs to the field of cutting processing research. The elastic-plastic characteristic of the matrix is fully considered, and in the direction perpendicular to the fibers, the Saint-Venant body-mechanical spring is adopted to describe the coupling constraint relation between the elastic-plastic matrix and the elastic fibers; on this basis, based on the minimum potential energy principle and the two-parameter elastic foundation beam theory, the influence of elastic-plastic transformation of the matrix on the constraint stiffness is quantified, and a single-fiber variable-stiffness constraint cutting model considering the elastic-plastic characteristic of the resin is established; then, a contact model of the cutter and the fibers is established, when the fibers are broken is determined, and finally accurate solving of deformation and damage in the single fiber cutting process is achieved. The method is wide in applicability, suitable for any one-way carbon fiber composite material with elastic-plastic matrix characteristics, simple in form and practical in function, further enriches the understanding of the cutting mechanism of the composite material, and lays a foundation for subsequent research on damage inhibition of the thermoplastic composite material.

Description

Technical Field

[0001] The invention belongs to the field of cutting processing research and relates to a method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material. Background Art

[0002] Carbon fiber reinforced thermoplastic resin-based composite materials (referred to as "thermoplastic composites") have attracted widespread attention in key fields such as aerospace due to their excellent mechanical properties, better interlaminar / intralaminar fracture toughness, and long-term service at high temperatures. Large components usually adopt near-net shaping, but in order to meet the connection and assembly requirements, a large amount of mechanical processing such as milling, window opening, and hole making is still required. However, thermoplastic composites are a typical difficult-to-process material with non-uniform and anisotropic properties and extremely strong plasticity in its matrix. The material is prone to large deformation during processing, and defects such as flash, fiber pullout, and fiber-matrix debonding will occur during the cutting process, which seriously affects the matching accuracy and load-bearing performance between components. At present, most of the processing of thermoplastic composites in engineering adopts a trial-and-error strategy or uses the more mature processing experience of carbon fiber reinforced thermosetting resin-based composite materials (referred to as "thermosetting composites") as a guide to select tools and processing technology. However, the difference in the mechanical properties of the matrix leads to significant differences in the removal behavior and damage forms of the two materials, making the tool and process modified by the above method poorly matched for the processing of thermoplastic composite components. To solve this problem, it is necessary to accurately describe the removal process of thermoplastic composites based on basic theory, and then clarify its removal mechanism and damage formation mechanism, and finally guide the design of highly applicable special tools and the formulation of process parameters, so as to suppress damage from the root and achieve high-quality and efficient processing of thermoplastic composites.

[0003] The existing composite material basic cutting theory is mainly aimed at thermosetting composites. Xu W published "Mechanics of fiber deformation and fracture in vibration-assisted cutting of unidirectional fiber-reinforced polymer composites" in the International Journal of Machine Tools & Manufacture, 2016, 103:40-52. Based on the foundation beam theory, the fiber is equivalent to a beam. When the fiber is cut, it is subject to the normal constraint of the unprocessed side and the bonding effect of the processed side resin. This theory equates the unprocessed side material to an elastic foundation, which better reveals the removal mechanism and damage formation mechanism of thermosetting composites. Jia Zhenyuan et al.'s invention patent "A method for establishing a cutting model of carbon fiber composite materials", application number 201610446046.5, established a bidirectionally constrained single fiber cutting model, which well considered the constraint effect of the surrounding materials on the fiber. Jia Zhenyuan et al. published "Research on Cutting Mechanism of Carbon Fiber Reinforced Resin-based Composite Materials" in the Journal of Mechanical Engineering, 2018, 54(23): 199-208. Based on the dual-parameter elastic foundation beam theory, a single fiber cutting model was established that takes into account the normal and tangential constraints on the fiber, and the temperature variation characteristics of the resin and the interface, and the fiber fracture process was accurately solved. The above research provides a certain reference for the theoretical research on thermoplastic composite cutting, but the existing basic theoretical research on composite materials is basically based on the pure elastic assumption, which equates the resin matrix to pure elasticity, but the resin itself is an elastic-plastic material, especially for some thermoplastic resins with strong ductility. If it is still equivalent to pure elasticity, it is impossible to accurately describe the removal mechanism of this type of material. However, there is no micro-basic cutting theory of carbon fiber composites that takes into account the elastic-plastic properties of the resin. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material. First, a St. Venant body-mechanical spring is introduced to describe the coupling constraint relationship between the elastic-plastic matrix and the elastic fiber, and the relationship between the elastic-plastic transformation of the matrix and the constraint stiffness is quantitatively analyzed based on the minimum potential energy principle and the dual-parameter elastic foundation beam theory, and then a single fiber variable stiffness constraint cutting model is established, and then a contact model between the tool and the fiber is established, and finally the fiber deformation and damage are accurately solved.

[0005] The technical solution of the present invention is:

[0006] A method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material fully considers the elastic-plastic characteristics of the matrix, and uses a St. Venant body-mechanical spring to describe the coupling constraint relationship between the elastic-plastic matrix and the elastic carbon fiber in the direction perpendicular to the fiber; on this basis, based on the minimum potential energy principle and the dual-parameter elastic foundation beam theory, the influence of the elastic-plastic transformation of the matrix on the constraint stiffness is quantified, and a single fiber variable stiffness constraint cutting model considering the elastic-plastic characteristics of the matrix is ​​established; then a contact model between the tool and the fiber is established to determine when the fiber breaks, and finally the deformation and damage of a single fiber in the cutting process are accurately solved; the specific steps of the establishment method are as follows:

[0007] In the first step, St. Venant body-mechanical spring is used to describe the coupling constraint relationship between the matrix and the carbon fiber:

[0008] The carbon fiber is equivalent to a linear elastic body, and the matrix is ​​simplified to be equivalent to an ideal elastic-plastic body. Before the matrix reaches the yield strain, it is in the elastic stage, and when it reaches the yield strain, it enters the plastic stage. During this stage, the matrix strain continues to increase, and the matrix stress remains unchanged. When the matrix strain reaches the fracture strain, the matrix fails. Thermoplastic composites are composed of carbon fibers and matrices, in which the stress between carbon fibers is transmitted by the matrix. When the matrix properties change, the stress transmission between carbon fibers is also affected. Therefore, thermoplastic composites also have three stages: Stage 1: The matrix is ​​in the elastic stage; Stage 2: The matrix is ​​in the plastic stage; Stage 3: The matrix reaches the fracture strain of the material, and the bearing capacity reaches the limit and fails.

[0009] Since carbon fiber is considered to be purely elastic, a mechanical spring is used to describe it, and the matrix is ​​regarded as an ideal elastic-plastic body, so a St. Venant body (composed of a mechanical spring and a friction block in series) is used to describe it. In the direction perpendicular to the carbon fiber, the thermoplastic composite is approximately equivalent to a series model of the matrix and the carbon fiber. Therefore, a mechanical spring and a mechanical model of a St. Venant body in series are used to describe the three stages of the thermoplastic composite, in which the friction block plays the role of transferring stress.

[0010] In the second step, based on the minimum potential energy principle and dual-parameter elastic foundation beam theory, the influence of the elastic-plastic transformation of the matrix on the constraint stiffness is quantitatively analyzed, and a single fiber variable stiffness constraint cutting model considering the elastic-plastic characteristics of the matrix is ​​established:

[0011] The two-parameter elastic foundation beam model is used to describe the fiber cutting process, and the carbon fiber is considered to be in a plane strain state. The part that supports the carbon fiber, that is, the supporting material, is regarded as an equivalent homogeneous material (EHM). The x direction is defined as the carbon fiber direction, the z direction is the transverse direction of the carbon fiber, and the y direction is perpendicular to the xoz direction. The total potential energy of the system composed of the cut fiber and its supporting material at a certain moment is approximately expressed as formula (1):

[0012]

[0013] Among them, π(x,z) is the total potential energy, τ zx and ε zz are the shear strain and normal strain in the xoz plane, l is the length of the cut fiber, d is the fiber diameter, E b is the axial Young's modulus of carbon fiber, I b (=πd 4 / 64) is the fiber section inertia moment, w(x) is the fiber deflection, q(x) is the force applied by the tool to the fiber, E is the transverse modulus of the support material, and G is the shear modulus of the support material, where E and G are calculated using the modified Chamis method:

[0014]

[0015] In the formula, E1, E m are the transverse Young's modulus of carbon fiber and the Young's modulus of matrix, G1, G m are the shear modulus of carbon fiber and matrix, V f is the fiber volume fraction.

[0016] The displacement field of the support material usually depends on the displacement perpendicular to the carbon fiber direction, and the displacement along the carbon fiber direction can be approximately ignored. Therefore, the displacement field of the support material is expressed as:

[0017] u(x,z)=0,w(x,z)=w(x)η(z) (4)

[0018] Where u(x, z) is the displacement field of the supporting material along the carbon fiber direction, w(x, z) is the displacement field of the supporting material perpendicular to the carbon fiber direction, η(z) is the displacement attenuation function perpendicular to the carbon fiber direction, and η(z) takes the form of a linear attenuation function:

[0019]

[0020] Where H is the thickness of the equivalent foundation compression layer, H = k h d, k h is the foundation constant, a dimensionless number that characterizes the thickness of the foundation compression layer, and is taken as k h=3.414, and η(0)=1, η(H)=0; so the potential energy function, that is, formula (1), can be expressed as:

[0021]

[0022] Based on the principle of minimum potential energy, by applying the principle of variational calculus to the change of π(x,z) caused by the change of w(x) and η(z), we can obtain:

[0023]

[0024] In the formula, δπ(x,z) is the change in potential energy, δ(w(x)) is the change in deflection, is the change of the first-order derivative of deflection, k1 and k e They represent the tangential and normal constraints of the support material on the carbon fibers, respectively.

[0025] The carbon fiber deformation control equation is:

[0026]

[0027] The boundary conditions of the free end of the carbon fiber meet the following requirements:

[0028]

[0029] in,

[0030]

[0031] The strain of the support material is described by the series model of the matrix and carbon fibers in the first step:

[0032]

[0033] Where ε represents the strain of the support material, ε1 and ε m are the strains contributed by carbon fiber and matrix respectively.

[0034] In formula (10), k e It can only represent the normal constraint stiffness of the support material on the fiber when the matrix is ​​in the elastic stage. The matrix described in the first step has three stages, so the constraint stiffness of the support material on the carbon fiber in different stages needs to be solved separately:

[0035] Phase 1:

[0036] When the strain of the matrix at a certain point under the cut carbon fiber does not reach the yield strain ε s , that is, ε m <ε s, the matrix is ​​in the elastic stage. At this time, the point can be approximately regarded as pure elastic deformation. The matrix material has not reached the yield strain. At this time, the Saint-Venant body is in the elastic stage. At the same time, according to the dual-parameter elastic foundation beam theory, the reaction force p at this point can be obtained:

[0037]

[0038] In addition, at the end of stage 1, the matrix has yield strain, and the support material must have corresponding yield strain. Equation (11) also applies, so the yield strain ε corresponding to the support material is s1 for:

[0039]

[0040] According to formula (4), the yield deflection is obtained:

[0041]

[0042] Phase 2:

[0043] When the strain of the matrix at a certain point under the cut carbon fiber exceeds the yield strain but does not exceed the fracture strain ε f , that is, ε s <ε m <ε f , at this time the matrix is ​​in the plastic stage.

[0044] As the tool continues to move, the matrix reaches the plastic stage, and the supporting effect of the supporting material on the carbon fiber decays. From the relationship between matrix stress and strain, as the matrix strain continues to increase, the matrix stress remains unchanged, and the matrix can no longer bear the role of transmitting stress. From this, the reaction force p and the equivalent constraint stiffness k at this point in this stage can be obtained. p They are:

[0045]

[0046] In the formula, E p and E m * are the equivalent moduli of the support material and the matrix when the matrix is ​​in the plastic stage.

[0047] At the end of stage 2, the matrix has a fracture strain, and the support material must have a corresponding fracture strain ε f1 , which is calculated as follows:

[0048]

[0049] The corresponding fracture deflection is:

[0050]

[0051] Phase 3:

[0052] As the strain of the matrix increases, when the matrix strain at a certain point under the cut carbon fiber exceeds the fracture strain of the matrix, that is, ε m >ε f At this point, the matrix is ​​considered to have failed, and the supporting material can be approximately equivalent to direct contact between carbon fibers. This point is in the third stage, and the support of the supporting material on the carbon fibers begins to gradually become stronger. The reaction force p and the equivalent constraint stiffness k at this stage can be obtained. f for:

[0053]

[0054] From equations (12) to (21), the reaction forces corresponding to different stages are obtained as follows:

[0055]

[0056] The corresponding equivalent spring stiffness coefficients at different stages are:

[0057]

[0058] Thus, the single fiber variable stiffness constraint cutting model is established.

[0059] The third step is to establish a contact model between the tool and the carbon fiber to determine when the fiber breaks, and finally to accurately solve the deformation and damage of a single carbon fiber during cutting:

[0060] The second step can solve the fiber deformation, but it is also necessary to determine when the fiber breaks in order to accurately describe the entire process from the initial deformation to the final breakage of the fiber.

[0061] Carbon fiber is a typical brittle material, so the maximum tensile stress criterion is selected as the condition for judging the fracture of carbon fiber. The tool edge circle and carbon fiber are usually of the same order of magnitude. The contact between the cutting edge and the carbon fiber is approximately regarded as the contact between two axially perpendicular cylinders subjected to normal pressure and tangential friction. The maximum tensile stress in the contact area is calculated using the Hertz contact theory. When the maximum tensile stress in the contact area reaches the maximum tensile strength of the carbon fiber, the carbon fiber fails. Specifically:

[0062] The projection surface of the intersection of the two cylinders is approximately equivalent to an ellipse, and the normal compressive stress and tangential stress distribution in the contact area are calculated by the following formula:

[0063]

[0064] Where p(y,z) is the normal compressive stress distribution in the contact area, q(y,z) is the tangential stress distribution in the contact area, p0 is the maximum compressive stress in the contact area, μ1 is the friction coefficient between the tool and the fiber, and fz1 is the normal force in the contact area, e is the eccentricity of the ellipse, [F1(e)] -2 / 3 is the correction factor of the ellipse eccentricity, obtained by looking up the table, R is the equivalent radius, which is related to the blade arc radius and the fiber radius, a and b are the semi-axes of the contact area, respectively, and E ft * is the equivalent modulus of the tool and fiber, and its calculation method is as follows:

[0065]

[0066] In the formula, E t is the Young's modulus of the tool, v t is the Poisson's ratio of the tool, v f is the Poisson's ratio of carbon fiber.

[0067] Analyze the stress field in the contact area and calculate the maximum tensile stress σ T Solve, σ T Approximately equal to 2μ1p0; when the maximum tensile stress in the contact area σ T When the tensile strength is greater than the corresponding maximum tensile strength of the carbon fiber (such as the maximum tensile strength of T700 carbon fiber is 4.9GPa), the fiber fails. Finally, the entire process from the beginning of deformation to fracture of the fiber is accurately described.

[0068] The beneficial effects of the present invention are as follows: the method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material proposed in the present invention can better consider the influence of the matrix on the cutting process. Compared with existing methods, the present invention introduces the elastic-plastic properties of the matrix into the theoretical research on thermoplastic composite cutting for the first time, and the method involved has a wider applicability, and can predict the fiber deformation and subsurface damage during the cutting process of any unidirectional carbon fiber composite material with elastic-plastic matrix properties, and better consider the influence of the mechanical properties of the matrix itself on the damage and removal during composite cutting. The present invention is simple in form and practical in function, which further enriches the understanding of the cutting mechanism of composite materials and lays the foundation for subsequent research on damage inhibition of thermoplastic composites. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a schematic diagram of the ideal elastic-plastic model of the resin matrix. In the figure, ε s is the matrix yield strain, ε f is the matrix fracture strain;

[0070] Figure 2 It is a schematic diagram of the series model of matrix and carbon fiber;

[0071] Figure 3 is a schematic diagram of equivalent modulus. In the figure, E m is the Young's modulus of the matrix, E m* is the equivalent modulus of the matrix when it is in the plastic stage, ε s is the matrix yield strain, ε f is the matrix fracture strain;

[0072] Figure 4 is the schematic diagram of tool-fiber contact;

[0073] Figure 5 Graphs of fiber deformation deflection with a cutting depth of 50 μm in the embodiments, wherein (a) is a graph of CF / PEEK fiber deformation deflection with a cutting depth of 50 μm, and (b) is a schematic diagram of CF / epoxy fiber deformation deflection with a cutting depth of 50 μm;

[0074] Figure 6 It is a comparative diagram of the relationship between the damage depth and cutting time of CF / PEEK and CF / epoxy with a cutting depth of 50 μm;

[0075] Figure 7 The following are the fiber subsurface damage diagrams at different cutting depths, where (a) is the CF / PEEK subsurface damage diagram with a cutting depth of 50 μm, (b) is the CF / PEEK subsurface damage diagram with a cutting depth of 90 μm, (c) is the CF / epoxy subsurface damage diagram with a cutting depth of 50 μm, and (d) is the CF / epoxy subsurface damage diagram with a cutting depth of 90 μm. DETAILED DESCRIPTION

[0076] The implementation of the present invention will be further described below with reference to the accompanying drawings and specific examples.

[0077] A method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material, the specific steps are as follows:

[0078] In the first step, St. Venant body-mechanical spring is used to describe the coupling constraint relationship between the matrix and the carbon fiber:

[0079] The carbon fiber is equivalent to a linear elastic body, and the matrix is ​​simplified to be equivalent to an ideal elastic-plastic body. Before the matrix reaches the yield strain, it is in the elastic stage, and when it reaches the yield strain, it enters the plastic stage. During this stage, the matrix strain continues to increase, and the matrix stress remains unchanged. When the matrix strain reaches the fracture strain, the matrix fails. Thermoplastic composites are composed of carbon fibers and matrices, in which the stress between carbon fibers is transmitted by the matrix. When the matrix properties change, the stress transmission between carbon fibers is also affected. Therefore, thermoplastic composites also have three stages: Stage 1: The matrix is ​​in the elastic stage; Stage 2: The matrix is ​​in the plastic stage; Stage 3: The matrix reaches the fracture strain of the material, and the bearing capacity reaches the limit and fails, such as Figure 1 shown.

[0080] Since carbon fiber is considered to be purely elastic, a mechanical spring is used to describe it, and the matrix is ​​regarded as an ideal elastic-plastic body, so a St. Venant body (composed of a mechanical spring and a friction block in series) is used to describe it. In the direction perpendicular to the carbon fiber, the thermoplastic composite is approximately equivalent to a series model of the matrix and the carbon fiber. Therefore, a mechanical spring and a mechanical model of a St. Venant body in series are used to describe the three stages of the thermoplastic composite, in which the friction block plays the role of transferring stress, such as Figure 2 shown.

[0081] In the second step, based on the minimum potential energy principle and dual-parameter elastic foundation beam theory, the influence of the elastic-plastic transformation of the matrix on the constraint stiffness is quantitatively analyzed, and a single fiber variable stiffness constraint cutting model considering the elastic-plastic properties of the resin is established:

[0082] The dual-parameter elastic foundation beam model proposed by Vlazov is used to describe the fiber cutting process, and the carbon fiber is considered to be in a plane strain state. The part supporting the carbon fiber, that is, the supporting material, is regarded as an equivalent homogeneous material. The x direction is defined as the carbon fiber direction, the z direction is the transverse direction of the carbon fiber, and the y direction is perpendicular to the xoz direction. The total potential energy of the system composed of the cut fiber and its supporting material at a certain moment is approximately expressed as formula (1), where E and G are calculated using the modified Chamis method, as shown in formulas (2) and (3).

[0083] The displacement field of the support material usually depends on the displacement perpendicular to the direction of the carbon fiber, and the displacement along the direction of the carbon fiber can be approximately ignored. Therefore, the displacement field of the back support material is as shown in formula (4), wherein η(z) takes the form of a linear attenuation function, such as formula (5), and η(0) = 1, η(H) = 0; so the potential energy function, that is, formula (1) can be expressed as formula (6); based on the principle of minimum potential energy, by applying the principle of variational calculus to the change of π(x, z) caused by the change of w(x) and η(z), formula (7) can be obtained.

[0084] The carbon fiber deformation control equation is equation (8), the boundary conditions of the free end of the carbon fiber satisfy equations (9) and (10), and the strain of the support material is described by the series model of the matrix and the carbon fiber in step 1, as shown in equation (11).

[0085] In formula (10), k e It can only represent the normal constraint stiffness of the support material on the fiber when the matrix is ​​in the elastic stage. The matrix described in the first step has three stages, so the constraint stiffness of the support material on the carbon fiber in different stages needs to be solved separately:

[0086] Phase 1:

[0087] When the strain of the matrix at a certain point under the cut carbon fiber does not reach the yield strain ε s , that is, εm <ε s , the matrix is ​​in the elastic stage. At this time, this point can be approximately regarded as pure elastic deformation. The matrix material has not reached the yield strain. At this time, the Saint-Venant body is in the elastic stage. At the same time, according to the dual-parameter elastic foundation beam theory, the reaction force p at this point can be obtained as shown in formula (12).

[0088] In addition, at the end of stage 1, the matrix has yield strain, and the support material must have corresponding yield strain. Equation (11) also applies, so the yield strain ε corresponding to the support material is s1 As shown in formula (13), the yield deflection is obtained according to formula (4) as shown in formula (14).

[0089] Phase 2:

[0090] When the strain of the matrix at a certain point under the cut carbon fiber exceeds the yield strain but does not exceed the fracture strain ε f , that is, ε s <ε m <ε f , at this time the matrix is ​​in the plastic stage.

[0091] As the tool continues to move, the matrix reaches the plastic stage, and the supporting effect of the supporting material on the carbon fiber decays. From the relationship between matrix stress and strain, as the matrix strain continues to increase, the matrix stress remains unchanged, and the matrix can no longer bear the role of transmitting stress. From this, the reaction force p and the equivalent constraint stiffness k at this point in this stage can be obtained. p Such as equation (15) to equation (17).

[0092] At the end of stage 2, the matrix has a fracture strain, and the support material must have a corresponding fracture strain ε f1 As shown in formula (18), the corresponding fracture deflection is as shown in formula (19).

[0093] Phase 3:

[0094] As the strain of the matrix continues to increase, when the matrix strain at a certain point under the cut carbon fiber exceeds the fracture strain of the matrix, the matrix is ​​considered to have failed, and the supporting material can be approximately equivalent to direct contact between carbon fibers. This point begins to be in the third stage, and the support of the supporting material on the carbon fiber begins to gradually become stronger. The reaction force p and the equivalent constraint stiffness k at this point in this stage can be obtained. f Such as formula (20) and formula (21).

[0095] From equations (12) to (21), the reaction forces corresponding to different stages are obtained as shown in equation (22), and the corresponding equivalent spring stiffness coefficients of different stages are obtained as shown in equation (23).

[0096] Thus, the single fiber variable stiffness constraint cutting model is established, as shown in Figure 3 shown.

[0097] The third step is to establish a contact model between the tool and the carbon fiber to determine when the fiber breaks, and finally to accurately solve the deformation and damage of a single carbon fiber during cutting:

[0098] The second step can solve the fiber deformation, but it is also necessary to determine when the fiber breaks in order to accurately describe the entire process from the initial deformation to the final breakage of the fiber.

[0099] Carbon fiber is a typical brittle material, so the maximum tensile stress criterion is selected as the condition for judging the fracture of carbon fiber. The tool edge circle and carbon fiber are usually of the same order of magnitude. The contact between the cutting edge and the carbon fiber is approximately regarded as the contact between two axially perpendicular cylinders subjected to normal pressure and tangential friction (such as Figure 4 As shown in Figure 2, the maximum tensile stress in the contact area is calculated using the Hertz contact theory. When the maximum tensile stress in the contact area reaches the maximum tensile strength of the carbon fiber, the carbon fiber fails. Specifically:

[0100] The projection surface of the intersection of the two cylinders is approximately equivalent to an ellipse, and the normal compressive stress and tangential stress distribution in the contact area are as shown in formula (24), where E ft * The calculation method is as shown in formula (25).

[0101] Analyze the stress field in the contact area and calculate the maximum tensile stress σ T Solve, σ T Approximately equal to 2μ1p0; when the maximum tensile stress in the contact area σ T When the tensile strength is greater than the maximum tensile strength of the carbon fiber, the fiber fails. Ultimately, the entire process from the initial deformation to the fracture of the fiber is accurately described.

[0102] In this embodiment, thermoplastic CF / PEEK and thermosetting CF / epoxy are used as examples to verify the applicability of the proposed model. The carbon fibers of the two composite materials are both T700 grade carbon fibers with a maximum tensile strength of 4.9 GPa. The specific material parameters of the tool and the specific material parameters of the fiber resin are shown in Table 1 and Table 2, respectively. At the same time, it is believed that after the blade cuts off, the carbon fiber will be further squeezed by the lower half of the blade circle of the tool to cause secondary fracture. Among them, the differential equations controlling the deformation of the carbon fiber, the boundary condition settings, and the solution of the damage depth are detailed in the invention patent "A method for establishing a cutting model of carbon fiber composite materials", application number 201610446046.5.

[0103] Table 1 Tools and cutting parameters

[0104]

[0105]

[0106] Table 2 Fiber and resin properties

[0107]

[0108] According to the first to third steps above, the performance parameters of CF / PEEK and CF / epoxy materials are respectively entered into the calculation to obtain the fiber deformation and damage of the two materials when the cutting depth is 50μm. Figure 5 For the comparison of fiber deformation, Figure 6 The damage depth comparison of the two is shown in Figure 2. It can be seen that the fiber deformation of CF / PEEK is greater than that of CF / epoxy, and the subsurface damage depth of CF / PEEK is greater than that of CF / epoxy. This is mainly because the PEEK matrix itself has strong ductility. During the fiber cutting process, the matrix has weak constraints on the fiber, resulting in greater subsurface deformation, which in turn leads to a greater probability of subsurface damage and more serious damage. Figure 7 The subsurface damage of CF / PEEK and CF / epoxy is compared at a cutting depth of 50 μm and 90 μm respectively. The results show that the present invention can accurately describe the cutting mechanism of unidirectional carbon fiber composites with different matrices and has a high accuracy in damage prediction.

Claims

1. A method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material, characterized in that: The establishment method comprises: using Saint-Venant body-mechanical spring to describe the coupling constraint relationship between the matrix and the carbon fiber in the direction perpendicular to the fiber; quantifying the influence of the elastic-plastic transformation of the matrix on the constraint stiffness based on the minimum potential energy principle and the dual-parameter elastic foundation beam theory, and establishing a single fiber variable stiffness constraint cutting model considering the elastic-plastic characteristics of the matrix; establishing a contact model between the tool and the fiber to determine when the fiber breaks, and finally realizing the solution of deformation and damage in the cutting process of a single fiber.

2. The method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material according to claim 1, characterized in that: The specific steps of the establishment method are as follows: In the first step, Saint-Venant body-mechanical spring is used to describe the coupling constraint relationship between the matrix and the carbon fiber: If carbon fiber is equivalent to a linear elastic body and the matrix is ​​equivalent to an ideal elastic-plastic body, the thermoplastic composite has three stages: stage 1: the matrix is ​​in the elastic stage; stage 2: the matrix is ​​in the plastic stage; stage 3: the matrix fails; A mechanical spring is used to equate the carbon fiber, and a Saint-Venant body is used to describe the matrix. In the direction perpendicular to the carbon fiber, the thermoplastic composite is equivalent to a series model of the matrix and the carbon fiber, that is, a mechanical spring and a Saint-Venant body are used in series to describe the three stages of the thermoplastic composite. In the second step, based on the minimum potential energy principle and dual-parameter elastic foundation beam theory, the influence of the elastic-plastic transformation of the matrix on the constraint stiffness is quantitatively analyzed, and a single fiber variable stiffness constraint cutting model considering the elastic-plastic characteristics of the matrix is ​​established: The dual-parameter elastic foundation beam model is used to describe the fiber cutting process, and the carbon fiber is considered to be in a plane strain state. The part supporting the carbon fiber, that is, the supporting material, is considered to be an equivalent homogeneous material. The x direction is defined as the carbon fiber direction, the z direction is the transverse direction of the carbon fiber, and the y direction is perpendicular to the xoz direction. The total potential energy of the system composed of the cut fiber and its supporting material at a certain moment is expressed as formula (1): Among them, π(x,z) is the total potential energy, τ zx and ε zz are the shear strain and normal strain in the xoz plane, l is the length of the cut fiber, d is the fiber diameter, E b is the axial Young's modulus of carbon fiber, I b is the fiber section inertia moment, w(x) is the fiber deflection, q(x) is the force applied by the tool to the fiber, E is the transverse modulus of the support material, and G is the shear modulus of the support material. The calculation formulas of E and G are as follows: In the formula, E1, E m are the transverse Young's modulus of carbon fiber and the Young's modulus of matrix, G1, G m are the shear modulus of carbon fiber and matrix, V f is the fiber volume fraction; The displacement field of the support material depends on the displacement perpendicular to the carbon fiber direction, and the displacement along the carbon fiber direction is ignored. Therefore, the displacement field of the support material is expressed as: u(x,z)=0,w(x,z)=w(x)η(z) (4) Where u(x, z) is the displacement field of the supporting material along the carbon fiber direction, w(x, z) is the displacement field of the supporting material perpendicular to the carbon fiber direction, η(z) is the displacement attenuation function perpendicular to the carbon fiber direction, and η(z) takes the form of a linear attenuation function: Where H is the thickness of the equivalent foundation compression layer, and η(0) = 1, η(H) = 0; so formula (1) is expressed as: Based on the principle of minimum potential energy, by applying the principle of variational calculus to the change of π(x,z) caused by the change of w(x) and η(z), we get: In the formula, δπ(x,z) is the change in potential energy, δ(w(x)) is the change in deflection, is the change of the first-order derivative of deflection, k1 and k e They represent the tangential and normal constraints of the support material on the carbon fiber, respectively; The carbon fiber deformation control equation is: The boundary conditions of the free end of the carbon fiber meet the following requirements: in, The strain of the support material is described by the series model of the matrix and carbon fibers in the first step: Where ε represents the strain of the support material, ε1 and ε m are the strains contributed by carbon fiber and matrix respectively; The constraint stiffness of the supporting material on the carbon fiber at different stages of the thermoplastic composite is solved separately: Phase 1: When the strain of the matrix at a certain point under the cut carbon fiber does not reach the yield strain ε s , the matrix is ​​in the elastic stage. According to the dual-parameter elastic foundation beam theory, the reaction force p at this point is obtained: The yield strain ε corresponding to the support material s1 for: According to formula (4), the yield deflection is: Phase 2: When the strain of the matrix at a certain point under the cut carbon fiber exceeds the yield strain but does not exceed the fracture strain ε f , the matrix is ​​in the plastic stage; at this stage, the reaction force p and the equivalent constraint stiffness k of the point p They are: In the formula, E p and E m * are the equivalent moduli of the support material and the matrix when the matrix is ​​in the plastic stage; The fracture strain ε of the support material at the end of stage 2 f1 Calculate according to the following formula: The corresponding fracture deflection is: Phase 3: When the matrix strain at a certain point under the cut carbon fiber exceeds the fracture strain, the matrix fails and the supporting material is equivalent to direct contact between carbon fibers. At this stage, the reaction force p at this point and the equivalent constraint stiffness k f for: From equations (12) to (21), the reaction forces corresponding to different stages are obtained as follows: The corresponding equivalent spring stiffness coefficients at different stages are: Thus, the single fiber variable stiffness constraint cutting model was established; The third step is to establish a contact model between the tool and the carbon fiber to determine when the fiber breaks, and finally to accurately solve the deformation and damage of a single carbon fiber during cutting: The maximum tensile stress criterion is selected as the condition for judging the fracture of carbon fiber. The contact between the cutting edge and the carbon fiber is regarded as the contact between two axially perpendicular cylinders subjected to normal pressure and tangential friction. The maximum tensile stress in the contact area is calculated using the Hertz contact theory. When the maximum tensile stress in the contact area reaches the maximum tensile strength of the carbon fiber, the carbon fiber fails. Specifically: The projection surface where the two cylinders intersect is equivalent to an ellipse, and the normal compressive stress and tangential stress distribution in the contact area are calculated by the following formula: Where p(y,z) is the normal compressive stress distribution in the contact area, q(y,z) is the tangential stress distribution in the contact area, p0 is the maximum compressive stress in the contact area, μ1 is the friction coefficient between the tool and the fiber, and f z1 is the normal force in the contact area, e is the eccentricity of the ellipse, [F1(e)] -2 / 3 is the correction factor of the ellipse eccentricity, R is the equivalent radius, a and b are the semi-axes of the contact area, E ft * is the equivalent modulus of the tool and fiber, which is calculated as follows: In the formula, E t is the Young's modulus of the tool, v t is the Poisson's ratio of the tool, v f is the Poisson's ratio of carbon fiber; Analyze the stress field in the contact area and calculate the maximum tensile stress σ T Solve; when the maximum tensile stress σ in the contact area T When the tensile strength is greater than the maximum tensile strength of the carbon fiber, the fiber fails, ultimately achieving an accurate description of the entire process from the initial deformation to the fracture of the fiber.

3. The method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material according to claim 2, characterized in that: In the formula (1), I b =πd 4 / 64.

4. The method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material according to claim 2, characterized in that: In the formula (5), H = k h d, k h It is a dimensionless number that characterizes the thickness of the foundation compression layer.

5. The method for establishing a cutting model of a carbon fiber reinforced thermoplastic resin-based composite material according to claim 2, characterized in that: In the third step, the maximum tensile stress σ in the contact area T Equal to 2μ1p0.

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