Effect Mechanism of Plain Woven Structure of Carbon Fiber on CFRP Cutting

Carbon ber-reinforced plastic (CFRP) is increasingly employed as structural components for aircrafts in aerospace. The plain woven CFRP is more commonly used than the UD-CFRP. The machining-induced damages are easy to occur. The inuence of the plain-woven structure on the cutting mechanism and the defects occurrence mechanism are seldom studied in detail. In this paper, the three-dimensional FEM model of plain woven CFRP is established. The occurrence and propagation of the delamination are investigated. The results indicate that the stress concentrations are easy to occur at the junction of warp and ll bundles near the cutting position. The plain-woven structure can block the transfer of stress and the crack propagation. When θ=90°, the damages of the ll bers and the crack of the interface are easy to occur. When θ=45°, the step-like fracture is formed in both of the warp and the ll bundles, especially in the ll bundles. Under the same cutting conditions, the exit delamination of the plain-woven CFRP is obviously less than that of the UD-CFRP. The delamination greatly increases with the increase of the feed speed. The delamination decreases with the increase of the cutting speed. The delamination is closely related to the instantaneous cutting position of the cutter.


Introduction
Carbon ber-reinforced plastic (CFRP) is increasingly employed as structural components for aircrafts in aerospace due to the good properties, such as high speci c strength, high speci c stiffness and high modulus [1][2][3][4][5]. Speci cally, the plain woven CFRP is more commonly used than the UD-CFRP. In reality, subsequent machining operations, such as milling, drilling, are necessary to be required for the removal of excess material to meet tolerances or for assembling [6]. However, the presence of the machininginduced damages, for example, delamination, cracking, ber pull-out, etc., let to the poor quality of the machined surface.
Numerous existing studies have investigated the cutting mechanism of CFRP. Alessandro et al. [7][8] pointed out that the cutting mechanism was highly dependent on the ber orientation and the damage area was orthogonal to the ber orientation when θ = 135° by the FE cutting model. Su et al. [9] also established a three-dimensional nite element model and characterized the ber fracture evolution processes of ber and resin. Meng et al. [10] indicated that the machined surface roughness and the subdamage could be affected by the ber orientation by the three-dimension micro-scale cutting simulation model. Cepero-Mejias et al. [11] investigated the in uence of cutting parameters on the machininginduced damage of unidirectional (UD) CFRP by establishing the nite element model. Li et al. [12] discussed the damage behaviors of UD-CFRP in single-and multiple-pass strategies orthogonal cutting by combining the FE models and the experiments. Liu et al. [13] proposed a novel three-phase nite element model of CFRP to simulate the machining damages. Cheng et al. [14] revealed the deformation mechanism of UD-CFRP by building the micro-scale thermal-mechanical coupling numerical simulation model. Most of the above researches had only studied the cutting mechanism of the UD-CFRP.
Kishore et al. [15] conducted the drilling experiments for plain weave CFRP. They pointed out that the modulation-assisted drilling technique produces better quality holes than conventional drilling under identical conditions. Voss et al. [16] investigated the occurrence of top layer delamination for the unidirectional CFRP. Hintze et al. [17][18] also studied the occurrence and propagation of the UD-CFRP top ply delamination. An analytical model of maximum ber protrusion lengths of curved contours was derived. They con rmed that the ber protrusions could be avoided if the cutting velocity and the cutting edge were appropriately employed. He et al. [19] conducted the slot milling of the UD-CFRP tests. The patterns of cutting force and defects were investigated. They reported that the occurrence of the delamination of UD-CFRP was closely related to ber cutting angle. In order to deeply investigate the forming mechanism of the delamination, the corrections between weave induced ber undulation and delamination were investigated. Hintze et al. [20] established a theoretical model for maximum ber protrusion. They validated that combination of ber undulation angle and thicknesses of top matrix layer were responsible for different occurrences of delamination. Ghafarizadeh et al. [21] claimed that the machining damage around the cutting area were caused by the ber compression damage and matrix cracking. Li et al. [22] expounded the occurrence and propagation of ber burrs and surface cavities for plain woven CFRP. They highlighted that various surface defects predominantly occurred owing to the cutting conditions and ber con gurations, and the defects were mainly located in the layers with bers orientated at 45°/135°.
Most of the previous researches focus their attention on the cutting mechanism and the delamination of UD-CFRP. However, the cutting mechanism and the defects occurrence mechanism of plain woven CFRP are seldom studied in detail. Especially, the three-dimensional FEM model for plain woven CFRP is extremely rare. In this paper, the three-dimensional FEM model of plain woven CFRP was established.
Then, the in uence of the plain woven structure on the cutting mechanism was analyzed. The occurrence and propagation of the top layer defects were investigated.
2 Plain-woven Structure And Fe Modelling 2.1 Plain-woven structure and 3D geometrical model A warp or a ll bundle contains a lot of carbon bers, as shown in Fig. 1. The ber bundles have the geometric characteristics of plain-woven structure. To obtain the geometric characteristics of plain-woven CFRP, the necessary assumptions are required. The periodic bending of a bundle is assumed as the cosine curve. The cross-section shape of the bundle is like a convex lens shape and keeps the shape in direction of the bundle. The bundle is the continuum and the volume fraction is basically equal to that of the whole CFRP plate. The warp bundle and the ll bundle have the same bending and cross-section shapes. Taking the ll bundle as the example, the coordinate system oxy is established. Then, the twodimensional contour curves characteristics of a warp bundle can be written by Eq. (1) [23].
Where, P 1 = a/2 is the amplitude of the bending curve in y direction, a is the thickness of the bundle crosssection center, P 2 = π/b, b is the distance between two adjacent warp bundles, P 3 is the offset distance of the bending curve in y direction. A straight segment of a warp bundle can be determined by Eq. (2) [23].
Where, the range value of x can be determined by the distance b and the width of the cross-section c. P 4 = d is the thickness of the cross-section edge. The relevant characteristic parameters of the geometric shapes can be obtained by observing the plain-woven CFRP. Namely, a = 0.5 mm, b = 2.5 mm, c = 2.5 mm, d = 0.626 mm. the warp and the ll bundle can be assumed as a homogeneous equivalent ber based on the volume fraction, according to the principle of homogenization, the geometric shape characteristic parameters and bending shape function. Then, according to the mechanical mixing law of composite materials, the mechanical properties of a bundle can be expressed as Eq. (3). The 3-dimensional (3D) geometric model of the plain-woven CFRP is established by assembling the warp and ll bundles into a plain-woven model. Simultaneously, in order to approximately simulate the cutting process of plainwoven CFRP as much as possible, a layer of resin matrix is attached to the upper and the lower surface respectively, as illustrated in Fig. 1.
Where, E f , E m , c f , c m , G f , G m , ν f , ν m , E 1 , E 2 , G 12 , ν 12 , ν 21 are the Young's elastic modulus of the ber, the Young's elastic modulus of the matrix, the ber volume fraction, the matrix volume fraction, the ber shear modulus, the matrix shear modulus, the ber Poisson's ratio, the matrix Poisson's ratio, the equivalent elastic modulus in 1-direction (viz. the ber axial direction), the equivalent elastic modulus in 2-direction (viz. vertical the ber axial direction), the in-plane shear modulus, the equivalent Poisson's ratio for the deformation in 2-direction causing by the stress in 1-direction, the equivalent Poisson's ratio for the deformation in 1-direction causing by the stress in 2-direction, respectively.

Cutting nite element modeling of plain-woven CFRP
In order to analyze and compare the plain-woven bers cutting process, the micro-scale orthogonal cutting simulations with two warp ber orientation, i.e. θ = 45° and θ = 90°, are established. When the bundle of bers is perpendicular to the cutting direction, the bundle of bers can be de ned as the warp.
The warp ber orientation θ is the angle between the warp and the cutting direction, as illustrated in Fig.  2.
Based on the single 3D geometric model of the plain-woven CFRP, the upper and lower layers of resin matrix are regarded as a whole, respectively. The zero thickness elements are built between the resin matrix and the ber bundle as well as between each bundles of warp and ll. The relevant de nitions for various materials for cutting model are listed as follows. 1) The constitutive relation of carbon ber bundle is implemented into the nite element code through VUMAT to predict the character and the extent of damage. The maximum stress failure criterion is employed to evaluate the removing of the carbon ber bundle. During the nite element calculation process, if the axial maximum principal stress meets the ultimate tensile strength (X t ) or the minimum principal stress reaches the ultimate compressive strength (X c ), the carbon ber bundle elements will be deleted, the stress-strain relationship of the carbon ber bundle is illustrated in Fig. 2. 2) The epoxy matrix in the plain-woven CFRP model is modeled as an isotropic material. The constitutive model is depicted in Fig. 2. The segment AB is the response curve of the material without failure. Once the stress reaches the ultimate tensile or compressive strength at point B, the initial damage is assumed to take place. Point B is the initial failure point. Segment BC is damage evolution curve. The shear failure criterion is used as initial failure criterion.
3) The states of bonding between ber bundle and epoxy matrix as well as between ber bundles are assumed as the interface material, namely, the zero thickness elements. To resolve the issue of excessive distortion and stress transfer within a zero thickness element, the cohesion elements are applied. The constitutive response is presented in Fig. 2.
Additionally, the underside and back side of the plain-woven CFRP plate are completely xed. The contact type between ber and matrix is considered as the general contact with a friction coe cient of 0.3. A surface-to-surface kinematic contact algorithm is de ned to model the interaction between the cutter and the matrix as well the ber bundle. The normal behavior is de ned as hard contact, the tangential behavior is simulated by penalty function, with the friction coe cients of 0.3 and 0.8, respectively. The cutter is modeled as a rigid body and 3-node triangular facet rigid body elements are applied. The ber bundles are meshed as the hexahedral units (C3D8R) along the ber axis by using an advanced algorithm. The matrix is meshed as the tetrahedral units (C3D4). The junction or boundary of warp and ll bundles is marked as the symbol of W, as shown in Fig. 2. Thus, a three-dimensional orthogonal cutting model of plain-woven CFRP is established.

Experimental details
To validate the nite element simulation model established in the previous sections and analyze the formation mechanisms of the machined surface and delamination, a series of drilling tests were carried out on KVC1050M vertical machining center with coolant, by the novel drill made of YG6X carbide without coating, with 2 utes and a diameter 6 mm. The drilling parameters of 2000 ~ 5000 rpm in spindle speed and 105 ~ 420 mm/min in feed speed were applied. All the experimental setups were depicted in Fig. 3. After the tests, the microstructures of hole wall were observed and analyzed by scanning electron microscope (SEM). The hole exit were observed and the exit delamination was investigated by ultra-eld microsystem. The exit delaminations with different warp ber orientation were measured, as illustrated in Fig. 4.
The plain woven carbon ber reinforced plastics (CFRP) with about 10 ~ 15 mm thickness were employed in all these experiments. The bre diameter was about 7 ~ 8 µm. The ber volume content was about 60 70%. Each ply had a thickness of 0.25 mm. The width of a bers bundle was 2.5 mm. The material properties of CFRP and tool were listed in Table 1.

In uence of plain-woven structure on material removal mechanism
The cutting process of the plain-woven bers with speci ed ber orientations (θ = 90°, 45°, etc.) is analyzed, as presented in Fig. 5 (a) (b). And the formation mechanisms of cutting surface are studied, as displayed in Fig. 6 (a) (b).
In Fig. 5 (a) The cutting stress zone is mainly concentrated on the front cutter during the cutting of the plain-woven CFRP, as depicted in Figs. 6 (a) (b). Under the same cutting conditions, the cutting stress zone when θ = 45° is larger than that when θ = 90°. The bers bundles at the front cutter and the rake face of the cutter are crushed serious. The bers and the matrix are all crushed. When θ = 90°, the warp bers are damaged to some extent. However, the signi cant stress concentration can be observed on the sides of the ll bundles and the interface between the ll bundle and the matrix. The damages of the ll bers and the crack of the interface can be obviously observed by the SEM observation. The warp bers fractures are neat, but the bers roots are broken. When θ = 45°, the step-like fracture is formed in both of the warp and the ll bundles, especially in the ll bundles. These results are basically consistent with the experimental results. In

In uence of plain-woven structure on machining defects
Actually, the basic morphology and the formation mechanism of the delamination of the exit hole can be re ected by the cutting simulation of the plain-woven CFRP. As mentioned above, under the same cutting conditions, the cutting stress zone when θ = 45° is larger than that when θ = 90°. Then, the cutting damage when θ = 90° is less than that when θ = 45°. Therefore, in most cases, the exit delamination when θ = 45° is more serious, as presented in Fig. 7 (a). Furthermore, under the same cutting conditions, the exit delamination of the plain-woven CFRP is obviously less than that of the UD-CFRP due to the blocking effect of the plain-woven structure on the transfer of stress and the crack propagation. Generally, the exit delamination of the UD-CFRP extends along the axial direction of the ber, as depicted in Fig. 7 (b).

In uence of processing parameters on effect of plainwoven structure
In order to further investigate the formation and evolution of the exit delamination, according to the nite element cutting model, the in uences of the cutting speed and the cutting position on the cutting damages and the exit delamination, as illustrated in Figs. 8 (a) (b). The cutting damage decreases gradually with the increase of the cutting speed, according to the observation of the cutting damage evolution process when θ = 90° and θ = 45°. When θ = 90°, the cutting damage decreases from 1.8 mm to 0.8 mm as the cutting speed V c increases from 56.59 mm/min to 69.85 mm/min. And when θ = 45°, the cutting damage decreases from 3.1 mm to 2.2 mm. During the cutting of the plain-woven CFRP, the cutting position can be divided into two cases. The rst case is that the cutter cuts plain-woven CFRP along the middle of a single ll bundle. The other case is that the cutter cuts along the boundary of warp and ll bundles. As revealed above, the stress concentrations are easy to occur at the junction of warp and ll bundles near the cutting position. Then, the plain-woven structure can block the transfer of stress and the crack propagation. Therefore, when the cutting position is at the junction of warp and ll bundles, the cutting damages propagation can be prevented at the junction of warp and ll bundles, and then the cutting damages can be decreased obviously. However, the cutting position is in the middle of a single ll bundle, the cutting damages can't be blocked, but the damages extend to the boundary of warp and ll bundles. When θ = 90°, the cutting damage of warp bundle is less than that of ll bundle. Additionally, the size of the cutting damage is basically equal to the width of the uncut part of the ll bundle. When θ = 45°, the cutting damage of warp bundle is a little less than that of ll bundle. The cutting damage size is approximately equal to the distance between the uncut part of the ll bundle and the junction of warp and ll. Therefore, the larger the width of the uncut parts of the ll bundle, the greater the cutting damage. Namely, the farther the cutting position is from the junction of warp and ll bundle, the greater the cutting damage.
The exit delamination increases with the increase of the feed speed. When spindle speed n = 4000 rpm, the feed speed V f increases from 105 mm/min to 420 mm/min, the average value of exit delamination increases from 3.06 mm to 3.43 mm as θ = 90°, and the average value of exit delamination increases from 3.19 mm to 3.32 mm as θ = 45°. Conversely, the exit delamination slightly reduces with the increase of the spindle speed (or the cutting speed). When the feed speed V f =315 mm/min, the spindle speed n increases from 2000 rpm to 5000 rpm, the average value of exit delamination decreases from 3.30 mm to 3.22 mm as θ = 90°, and the average value of exit delamination increases from 3.23 mm to 3.13 mm as θ = 45°.
Additionally, the exit delamination size is also closely related to the cutting position of the cutter, as shown in Fig. 10. The tool drills the CFRP. Then, the cutter cuts the CFRP counterclockwise. When the cutter cuts the CFRP from θ = 90° to θ = 45°, namely the A 1 stage, the cutting position of the cutter is in the middle of a ll bundle. As reported above, under the same cutting condition, the cutting damages when θ = 45° are slightly larger than that when θ = 90°. Thus, the cutting position is far away from the junction of warp and ll bundle when the cutter cuts plain-woven CFRP from θ = 90° to θ = 45°. The plainwoven structure is less able to prevent delamination. Therefore, the delamination increases when the cutter cuts plain-woven CFRP from θ = 90° to θ = 45°. Nevertheless, when the cutting position is close to the junction of warp and ll bundle, the extension of the delamination is inhibited and the delamination gradually decreases, as C 1 and E 1 stages. However, when the cutter cuts plain-woven CFRP from θ = 45°t o θ = 90°, the delamination decreases. Especially, when the cutting position is close to the junction of warp and ll bundle, the propagation of delamination is greatly inhibited due to the plain-woven structure and the delamination is well restrained. Conversely, when the cutting position is far away to the junction of warp and ll bundle, the propagation of delamination can't be prevented until the delamination extends to the warp and ll junction. The further the cutting position is from the junction, the greater the delamination, as B 1 , D 1 and F 1 stages.
In summary, both of cutting speed and feed speed has signi cant in uence on delamination. The delamination greatly increases with the increase of the feed speed. And the delamination decreases with the increase of the cutting speed. Additionally, the delamination is closely related to the instantaneous cutting position of the cutter. When the cutter cuts plain-woven CFRP from θ = 90° to θ = 45°, the delamination increases because the cutting position is in the middle of a ll bundle. But the delamination can be restrained at the junction of warp and ll bundle. When the cutter cuts plain-woven CFRP from θ = 45° to θ = 90°, the farther the cutting position is from the warp and ll junction, the greater the delamination is. The delamination maximum value is almost equal to the width of the uncut part of the ll bundle.

Conclusions
In this paper, the three-dimensional FEM model of plain-woven CFRP is established. Then, the in uence of the plain-woven structure on the cutting mechanism is analyzed. The occurrence and propagation of the top layer delamination are investigated. Some key conclusions are drawn from the results presented in this research as follows: (1) When θ = 90°, the tensile fracture occurs on the near the cutting position side of the warp bundle and compression fracture appears on the other side of the warp bundle. The damages of the ll bers and the crack of the interface are easy to occur. When θ = 45°, the failure of the warp bundles is mainly compression fracture, the failure of the near the cutting position side of the ll bundle is the tensile fracture and the other side is the compression fracture. The step-like fracture is formed in both of the warp and the ll bundles, especially in the ll bundles.
(2) The stress concentrations are easy to occur at the junction of warp and ll bundles near the cutting position. Then, the plain-woven structure can block the transfer of stress and the crack propagation.
(3) The exit delamination when θ = 90° is less than that when θ = 45°. Under the same cutting conditions, the exit delamination of the plain-woven CFRP is obviously less than that of the UD-CFRP.
(4) The delamination greatly increases with the increase of the feed speed. The delamination decreases with the increase of the cutting speed. The delamination is closely related to the instantaneous cutting position of the cutter.
(5) When the cutter cuts plain-woven CFRP from θ = 90° to θ = 45°, the delamination increases. And the delamination can be restrained at the junction of warp and ll bundle. When the cutter cuts plain-woven CFRP from θ = 45° to θ = 90°, the farther the cutting position is from the warp and ll junction, the greater the delamination is. The delamination maximum value is almost equal to the width of the uncut part of the ll bundle.  Plain-woven ber bundles cutting processes with different ber orientation  In uences of cutting speed and cutting point on damages Figure 9 In uences of cutting parameters on delamination Figure 10 Evolutionary mechanism of plain-woven CFRP delaminations