Investigation on cutting damage mechanism of carbon fiber reinforced polymer based on macro/microscopic simulation

Carbon fiber reinforced polymer (CFRP) is widely used in the aerospace field due to its excellent physical and mechanical properties such as high specific strength, high specific modulus, and good corrosion resistance. However, it is prone to bring burrs, tears, matrix, and fiber debonding during the cutting process due to its non-homogeneity and anisotropy, which seriously affects the service life of the material. To explore the damage failure mechanism of the CFRP cutting process, 2D and 3D finite element simulation models were established based on Abaqus in this paper. Furthermore, the influence law of fiber direction on cutting damage failure and chip forming was analyzed from micro and macro levels. Finally, the effectiveness of the simulation model was verified by experiments. The results show that the cutting surface of CFRP with a 45° fiber angle is serrated, and the local failure is not obvious; the main defect of CFRP with 90° fiber angle cutting is a matrix and fiber debonding, and some fibers will be crushed and off. Serious degumming phenomenon occurred in the cutting process of CFRP with 135° fiber angle, and the bending and fracture of fiber also occur below the cutting depth. It is noteworthy that the stress distribution diverges along the fiber direction.


Introduction
Carbon fiber reinforced polymer (CFRP) is an advanced material made of carbon fiber as the reinforcing phase and resin as the matrix, and it is widely used in the aerospace field due to its excellent physical and mechanical properties such as high specific strength, high specific modulus, and good corrosion resistance [1][2][3][4]. What is more, due to its non-homogeneity and anisotropy, it is susceptible to the influence of fiber and matrix properties, fiber direction, and interlayer layup, resulting in burr, fiber tearing, matrix and fiber debonding, and other processing damage phenomena, which seriously affect the workpiece processing quality and service performance [5][6][7][8]. Therefore, revealing the mechanism of CFRP cutting and improving the machining quality of workpiece have become the research focus of many scholars in recent years.
Scholars at home and abroad have mainly studied the damage mechanism of CFRP cutting from the micro and macro aspects and have achieved fruitful results. In terms of microscopic perspective, Dankekar et al. [9] established the FRP meso-finite element cutting simulation model to analyze the material removal process at different fiber angles, and the results showed that the degree of resin cracking and matrix damage increased with the increase of fiber angles. Santiuste et al. [10] proposed GFRP and CFRP finite element models to explore chip formation, matrix damage, and subplane damage. The results showed that the fiber direction affects the chip formation and matrix damage, and it is worth noting that the fiber direction at 135° has the most serious matrix damage. Gao et al. [11] proposed an FRP three-dimensional finite element cutting model and analyzed the fiber damage, matrix, and boundary phases under different fiber angles, and they found that the surface contours are different under different working conditions. The machining surface at 45° fiber angle is relatively smooth, while it is rough at 135°. In Wang's research [12], they proposed a 2D CFRP cutting simulation model, and they found that as the fiber direction is 0° or 45°, the interface crack is the main cause of chip generation; while as the fiber direction angle 1 3 is 90° and 135°, the chip generation is caused by interface crack and fiber fracture. Gao et al. [13] established a CFRP microscopic cutting finite element model, which contains the constituent phases of fiber, matrix, and interface and elucidates the fiber/matrix fracture, interface cracking, and evolution process during CFRP cutting at different fiber angles. In the macroscopic aspect, Rameshs et al. [14] applied anisotropic plasticity theory to explore the cutting process of four different fiber direction angles and determined the minimum load required for the crack to appear at 135° fiber direction angle. Ali Mkaddem et al. [15] characterized the failure behavior and anisotropy of unidirectional glass fiber composite plane stress conditions based on the Tsai-Hill criterion, which investigated the effect of different cutting parameters on cutting force, but the model was unable to achieve chip generation. Zenia et al. [16] used the combined elastic-plastic damage model to study the chip formation process, which failed to consider the interface between the composite layers.
In general, there are a lot of studies on the micro or macro simulation models of CFRP by domestic and foreign researchers, but there are relatively few studies on the cutting damage mechanism of CFRP at both macro and microcosmic levels. Therefore, we established a 2D CFRP multiphase microcosmic cutting model by defining material properties, damage failure model, and different fiber directions. In addition, a three-dimensional CFRP solid element macro cutting model was established by VUMAT subroutine. Through the above two models, the influence of different fiber angles on the surface failure damage mechanism, stress distribution, and chip forming in CFRP cutting process was explored across scales, and the validity of the two models was verified by experiments.

Finite element modeling
The material failure criterion is crucial to the accuracy of the simulation results. In this paper, Hashin failure criterion is used in 2D CFRP multiphase cutting model and 3D CFRP simulation model. Since Abaqus software itself does not have the required constitutive relation, damage criterion, and its evolution procedure for 3D CFRP cutting model, this paper establishes the material constitutive relation model, damage criterion, and evolution by writing VUMAT subroutine and decides the unit deletion by the failure criterion.

Establishing Hashin failure criteria
Hashin failure criterion [17] divides the failure into four modes, namely, tensile and compressive failure in the fiber direction and tensile and compressive failure perpendicular to the fiber direction, which is simplified and can be integrated in Abaqus. The formula of 2D-Hashin failure criterion is shown in Table 1.
X T ,X C , Y T , and Y C represent the longitudinal tensile, longitudinal compression, transverse tensile, and transverse compression strengths, respectively. S L and S T represent the longitudinal strength and transverse shear strength. Since the 2D Hashin theory can be used for failure analysis of single-phase carbon fibers, the fiber-phase material properties of the 2D CFRP multiphase cutting model are defined as Hashin damage.
In addition, since the Hashin theory is used to predict the failure problem of CFRP laminates under various operating conditions and can guarantee high solution accuracy, this damage theory is also used as the core of the VUMAT subroutine used in the 3D macro cutting simulation in this paper. The formula of 3D Hashin failure criterion can be expressed as Fiber stretch failure (σ 11 ≥ 0).
Of the four modes, X T is the axial tensile strength, Y T is the transverse tensile strength, X C is the axial compression strength, Y C is the transverse compression strength, S 12 is axial shear strength, S 23 is the transverse shear strength, and σ 11 , σ 22 , σ 33 , σ 12 , σ 23 , and σ 31 are the components of effective stress σ. σ 11 , σ 22 , and σ 33 are the initial value of the assessed damage.

Geometric modeling
The fiber diameter is set to 7 μm, the matrix size between adjacent fibers is set to 4 μm, and the interface phase between fibers and matrix is set to 1 μm. The tool is defined as a discrete rigid body, the front and rear angles are 10°, and the radius of the tool filet is set to 0.01 mm. The equivalent homogeneous phase size of the model is set to 1 mm × 0.6 mm, and the 0.1 mm × 0.1 mm area in the upper right corner of the equivalent homogeneous phase is used to establish the fine cutting area, which is shown in Fig. 1. In the mesh division, the mesh size of the equivalent homogeneous area is 0.01 mm, and the cutting area in the upper right corner is refined to 0.001 mm. The cutting speed of the tool is set to 13 mm/s, and the friction coefficient is set to 0.3.

Fiber phase definition
Since carbon fiber is a brittle material, only the linear elastic constitutive model needs to be established without considering the plastic deformation, but the influence brought by the damage should be taken into account, so the linear elastic constitutive model of CFRP fiber phase is shown in equation (5), where d s , d m , and d f represent the damage factors of shear damage, matrix damage, and fiber damage, respectively. E 1 and E 2 are the modulus of elasticity in the fiber direction and the modulus of elasticity perpendicular to the fiber direction, respectively. G 12 is the shear modulus, ϑ 12 is the Poisson's ratio, and σ 1 , σ 2 , and σ 12 are the fiber direction stress, perpendicular to fiber direction stress, and shear stress, respectively. The physical and mechanical properties of carbon fibers are shown in Table 2 [18].

Matrix phase definition
The material of the matrix phase is resin, whose constitutive behaves isotropically and elastoplastically, and its elastic constitutive model is shown in equation 6, and the stress-strain curve changes as shown in Fig. 2, which are divided into three stages: AM, MB, and BC. And the plastic behavior uses each isotropic plastic hardening model.
The AM stage is the linear elastic stage, because it is an isotropic material, only the elastic modulus E and Poisson's ratio υ need to be determined. M point is the yield point, beyond which the plastic stage is entered. When the B point is reached, the material is judged to be damaged and finally enters the damage evolution stage. The damage determination formula as follows [19].  where the equivalent plastic strain is pl , the equivalent plastic strain rate is ṗl , the strain rate and shear stress ratio as a function of pl s , the shear stress ratio is. The calculation formula of θ s is where the compressive stress is p, the maximum value of shear stress is τ max , the material correlation coefficient is k s , and the Mises equivalent stress is q. The parameters of the physical and mechanical properties of the matrix phase are shown in Table 3.

Interface phase definition
Cohesive element is often used in Abaqus to simulate the bonding state between fiber and matrix. traction-separation law is the basis for the establishment of the intrinsic model of the cohesive element, as shown in Fig. 3. AB represents the linear elastic stage of the cohesive element, and the intrinsic model of this stage is shown in equation 9, where n, s, and t represent the open type, slip type, and tear type damage, respectively. When reaching point B, damage is judged to occur, and this paper adopts the quadratic nominal stress criterion, and its damage determination is shown in equation 10 [13]. The BC section is the damage evolution stage, and at point C, it fails completely and the Cohesive unit is deleted. The interface phase physical and mechanical properties parameters are shown in Table 4.

Geometric modeling
The macroscopic CFRP model does not distinguish between fibers and matrix and models the whole monolayer as an equivalent homogeneous material with orthogonal anisotropy, assigning the material orientation by establishing a coordinate system. The fiber direction is defined as the 1 direction of the coordinate system, while the direction perpendicular to the fiber and the normal direction of the monolayer are defined as the 2 and 3 directions, respectively. Therefore, CFRP monolayers with different fiber angles can be built by changing only the direction of the coordinate system. T h e s i z e o f t h e s i n g l e -l a y e r p l a t e i s 1 mm × 0.9 mm × 0.05 mm, the cutting depth is 0.1 mm, and the 1 mm × 0.03 mm above is set as the cutting area. The bottom of the single-layer plate is completely fixed, that is, the six degrees of freedom are all 0. The left end constraint is set to U1 = 0 in order to set the freedom of cutting direction to 0. Because of the large computational volume of three-dimensional cutting, the mesh of the cutting area is refined to minimize the non-essential computational volume under the premise of ensuring the simulation accuracy. As the mesh is refined to a cell size of 0.007 mm or less, the accuracy is not significantly improved. Therefore, the cell size of the cutting area is set to 0.007 mm, the cell size of other areas is set to 0.1 mm, and the established mesh is shown in Fig. 4. The front and rear angles of the tool are 10°, the rounding angle is 0.01 mm, and the cutting speed is 100 mm/s. Without considering the deformation of the tool, the tool is set as a discrete rigid body, and the cells near the rounding angle of the tool are refined to improve the accuracy of the cutting simulation. The tool filet refinement unit size is 0.003 mm, and the non-contact area size is 0.02 mm.

Material modeling
Since the Abaqus itself does not have the procedures for the constitutive relation, damage criterion, and its evolution required in the 3D solid unit establishment CFRP model, if the CFRP 3D cutting simulation is required, the user is required to establish the VUMAT subroutine for the corresponding model for secondary development.
CFRP monolayers can be viewed as homogeneous orthotropic anisotropic materials on a macroscopic scale, using the following linear elastic constitutive model of equation 11. The present constitutive model represents the material stress-strain relationship, while the damage determination in this paper is based on the simplified three-dimensional Hashin failure criterion with four failure criterion formulas as follows.
Matrix compression failure (σ 22 + σ 33 < 0). Since the failure judgment of 3D Hashin in the matrix direction is not accurate, this paper uses a simplified 3D Puck failure theory in the matrix direction [21]. The specific formula is as follows.
When the material unit meets the failure criterion, that is, the material fails completely, at this time, this one unit is deleted. The physical and mechanical properties of the CFRP monolayer are shown in Table 5.

Analysis of mesoscopic failure phenomena
Three typical fiber angles (45°, 90°, and 135°) were selected to analyze the failure damage phenomena of the 2D CFRP mesoscopic cutting models with different fiber angles during the cutting process. Figure 5 depicts the compression and tensile damage to the fiber in the transverse and longitudinal directions when the fiber angle is 45°. It can be seen from the figure that the matrix is crushed by the tool, and the unit is deleted before the tool comes into contact with the fiber. At the same time, the fibers are subjected to transverse tensile damage symmetrically with the tool tip due to the action of the matrix on the fibers, as shown in Fig. 5(a) and (b). The longitudinal compressive stress is located above the fiber, and the longitudinal tensile stress is located below the fiber, as shown in Fig. 5(c) and (d). As can be seen from Fig. 6, since Hashin failure factor greater than 1 appears first under the HSNMCCRT mode (which represents the maximum of matrix fracture initiation criteria), the earliest form of damage that occurs from tool contact with the fiber is transverse compressive damage, which leads to fiber breakage. As the tool advances and contacts the tip, the fibers are mainly subjected to transverse compressive stress and are gradually crushed, and the tool continues to advance, which eventually causes the fibers to be broken, as shown in Fig. 6(b). It can be observed from Fig. 6(c) that the machined surface is serrated and degummed. When the fiber angle is 90°, cutting is mainly based on crushing. The tool first makes contact with the matrix, which is cut off in a crumbly form. In addition, the fiber is squeezed by the matrix and suffers a transverse tensile and compressive damage symmetrically with the tool, as shown in Fig. 7. As the tool is in contact with the fiber, the transverse tensile and compressive damage occur almost simultaneously, and the fiber is crushed along the outer surface of the tool, while the matrix and the fiber are deboned and the damage phenomenon occurs, as shown in Fig. 8. With the cutting tool feed, the fiber and matrix are broken, and serious degumming of the cutting surface can be observed.
As shown in Fig. 9, when cutting CFRP with fiber angle of 135°, the matrix and fiber degummed, and the fiber behind the matrix appeared transverse tensile and compressive damage failure. With the contact between the tool and the upper end of the fiber, the upper end of the fiber was crushed, while the whole fiber experienced tensile and compression damage failure due to bending by compression, as shown in Fig. 9(a). As the tool continues to advance, the fibers break at the depth of cut position and the rear end of the fiber is crushed by the front end of the fiber, as shown in Fig. 9(b). Severe fiber and matrix debonding occurred on the cutting surface, fiber fracture and bending occurred below the depth of cut, and the cutting effect was significantly worse than the first two fiber angles, as shown in Fig. 9(c).
In summary, it can be concluded that in the 2D fine view failure damage simulation analysis, with the increase of fiber angle, the more obvious the burr in the already cut area, the more serious the debonding phenomenon on the cut surface. Poisson's ratio υ 13 0.29 1 3

Analysis of macroscopic failure
The chip forming process of CFRP with 45° fiber angle is shown in Fig. 10. In the stress cloud diagram, it is obvious that the main stresses are divided into two parts: the compressive stress perpendicular to the fiber direction at the lower right of the tool tip and the shear stress in line with the fiber direction, as shown in Fig. 10(a). When the tool tip first touches the material, the tip squeezes the fibers causing the material below and directly in front of it to be crushed, as shown in Fig. 10(b). As the tool continues to advance, a crack appears along the material at 45°, as shown in Fig. 10(c), and this crack continues to extend as the tool continues to move forward, reaching the upper surface of the material and extending faster, and eventually a chip sliding out along the 45° fiber direction is created when the front face of the tool pushes, as shown in Fig. 10(d).
The chip forming process of CFRP with 90° fiber angle is shown in Fig. 11. From the stress cloud diagram, the stress is mainly divided into two parts: compressive stress The chip forming process of CFRP with 135° fiber angle is shown in Fig. 12. At the initial stage when the tool touches the material, the material is mainly subjected to the extrusion effect of the tool tip and the front tool face, as shown in Fig. 12(a) and (b). As the tool advances, a crack appears in the direction approximately perpendicular to the front tool face, and this crack expands as the tool advances, and eventually, chips are generated, as shown in Fig. 12(c). Thereafter, the material unit in contact with the front tool face is also continuously crushed to form chips and the crack is generated again, but this time, it does not expand in one direction and the crack shape shows a certain randomness, as shown in Fig. 12(d). In the stress cloud diagram, a more obvious distribution of stresses along the 135° direction appears, as shown in Fig. 12(e). It is known from the 135° fine view cutting that the fibers start to be in contact with the tool tip due to the 135° cutting process, and the contact gradually extends to the whole front tool face as the tool advances. In the process of continuously squeezing the material at the front tool face, the fibers bend, and when the bending reaches a certain level, the fibers fracture. This is why it is clear from the stress cloud diagram that there is a significant stress distribution in the 135° direction during the cutting process and that the front tool face is under greater stress. However, the location of the fractured fibers is not exactly along a straight line, but has a certain randomness, so it can be seen that the cracks generated by cutting shows this characteristic. In summary, it can be concluded that in the 3D macroscopic failure damage simulation analysis, the stress direction is always distributed along the fiber direction, and the stress magnitude follows the law of 135° > 90° > 45°; the same as the 2D fine simulation analysis, with the increase of fiber direction, the roughness of the cut surface is larger.

Test verification and cutting test platform
The test material used in this paper is T300 carbon fiber composite one-way laminate produced by Texas Blue Label Composites Technology Co., Ltd. with the dimensions of 400 mm × 100 mm × 5 mm; it is made of 25 fiber monolayers with a thickness of 0.2 mm bonded together. The tool used for the test was a three-flute carbide milling cutter with the specific parameters shown in Table 6. The cutting test platform was a Mazak VARIAXIS 500-5X II vertical 5-axis machining center, as shown in Fig. 13, for milling CFRP with a spindle speed of 2000 r/min, a feed rate of 100 mm/min, and a cutting depth of 1 mm.

Surface damage analysis
The milling test is performed on the unidirectional laminates from three fiber angles. The cutting surfaces of CFRP with 45° and 90° fiber angles under the microscope are shown in Fig. 14(a) and (b). As can be seen from the figure, these two directions are better, and the machined surface is smoother and does not show significant damage. However, the milling surface in the 135° direction as shown in Fig. 14(c) showed a large number of pits on the cutting surface. It has been known through the previous simulation that 135° is reverse milling, which will lead to a large number of pits on the cutting surface. This is due to the fracture of the fiber below the depth of cut after being lifted by the tool, and then the fiber is carried away.

Conclusion
This paper establishes a 2D multiphase cutting simulation model and a 3D equivalent homogeneous state cutting simulation model for CFRP to reveal the removal mechanism from mesoscopic local damage to macroscopic chip formation during CFRP cutting and verifies the simulation model by experiments.
(1) The 2D multiphase cutting simulation model analyzes the influence of different fiber angles on the mesoscopic damage of CFRP. It finds that the cutting surface of CFRP with 45° fiber angle is serrated with mild local failure; the main defect of CFRP with 90° fiber angle cutting is matrix and fiber debonding, and CFRP is mainly crushed and cut off during the cutting process. The local damage of CFRP with 135° fiber angle is the most severe, with serious degumming phenomenon and fiber bending and breaking below the cutting depth. It concludes that with the increase of fiber angle, the burr in the cut area becomes more obvious, and the degumming phenomenon of the cutting surface becomes more serious (2) The 3D equivalent homogeneous cutting simulation model analyzes the influence of different fiber angles on the cutting stress distribution. It finds that the stress direction always diverges along the fiber direction, and the stress increases with the increase of fiber angle (3) The experimental results show that the surface failure of CFRP with fiber angle of 45° and 90° is not serious, but there are many pits on the machined surface as the fiber angle is 135° due to the fracture of the fiber below the cutting depth during milling. The simulation results are consistent with the experimental results Author contribution Zhaoju Zhu worked on conceptualization, methodology, formal analysis, and preparation of the original draft with input from all authors. Rongqing Kang and Jianwei Huang developed the computational modal, design optimization, and conducted the experiments. Yunqi Zhu and Xinghui Sun worked on data collection, processing, and segmentation. Zhaoju Zhu supervised the project.
Funding This work was supported by Natural and Science Foundation of China (52205455), Natural and Science Foundation of Fujian Province (2021J01560), and Education and scientific research foundation for young teachers in Fujian Province (JAT190006).

Data availability
The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
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Conflict of interest
The authors declare no competing interests.