Effects of delamination in drilling glass/polyester composite

Abstract

Considering failures during machinery processes such as drilling, a precautionary analysis involving delamination and the corresponding dissipated energy is required, especially for composite structures. In this context, because of the complexity of both the analysis procedure and experimental test setup, most studies prefer to represent mode I and III interlaminar crack propagation instead of that involving mode II. Therefore, in this study, the effect of mode II delamination and corresponding interlaminar crack propagation was considered during the drilling process of multilayered glass/polyester composites using both numerical and experimental approaches. In the experimental procedure, the mechanical properties of the glass/polyester specimens were obtained according to ASTM D3039. In addition, the interlaminar mixed-mode (I/II) loadings were determined using an ARCAN test fixture so that the fracture toughness of glass/polyester could then be identified. The mode II critical strain energy release rate (CSERR) was then obtained using an experimental test performed using an ARCAN fixture and the virtual crack closure technique (VCCT). It was determined that the numerical approach was in accordance with the experiments, and more than 95% of crack propagation could be attributed to mode II compared to the two other modes.

Graphical abstract

Keywords

delamination / VCCT / ARCAN specimen / drilling / mode II

Introduction

In various engineering applications, there is no possibility of using a certain type of material that satisfies all mechanical properties. In such cases, combining two or more materials as composites can be more advantageous because they are not only easy to obtain but can also have convenient mechanical properties such as high specific strength/stiffness, superior corrosion resistance, lightweight construction, low thermal conductivity, high fatigue strength, fire resistance, and resistance to chemical attacks. Glass fiber reinforced plastics (GFRPs) are the most common composite structures found in industry, and the machining of these materials has become a very important research subject. Several non-traditional machining processes such as laser cutting, water-jet cutting, ultrasonic cutting, and electro discharge machining have been developed to machine holes in fiber reinforced plastics (FRPs) [1]. Owing to the inhomogeneous nature of FRP, some problems such as delamination occur in composite plies, which leads to a lowering of the bearing strength and can be detrimental to durability by reducing the in-service life under fatigue loads [2]. Delamination can often become a limiting factor in the use of FRPs for structural applications [2–4]. Considering the failure prediction of FRPs, several experimental and theoretical studies have been conducted to investigate the hole surface quality, life of a joint, and damage evaluation resulting from any type of drilling operation, such as conventional, high-speed, and vibration-assisted drilling. The vibration drilling technique has attracted attention in both theoretical and experimental investigations because of the achievable hole quality and reduction of thrust force [5–8] and delamination [6,9]. For conventional drilling [10], peel-up at the entrance [11], push-out at the exit [12] and cutting parameters [13] are the three main delamination factors associated with FRP composites. Kilickap [14] studied the effect of the cutting parameters on GFRP composite delamination by observing both the entrance and exit drilling results. Rajamurugan et al. [15] investigated the thrust force and drilling parameters such as tool feed rate, rotational speed, and fiber orientation angle through experimental evaluation of GFRP specimens. Because the quality of a drilled hole depends on delamination, Reddy et al. [16] compared the performance of drilling with carbide and high-speed steel (HHS) tools. Khashaba et al. [17] determined that the thrust force during the drilling process is greatly affected by the drill pre-wear by conducting an experimental study of the drilling parameters (i.e., feed, speed, and drill pre-wear) on the machinability parameters when drilling glass fiber reinforced epoxy (GFRE) composites. Venkateshwaran and ElayaPerumal [18] analyzed the delamination behavior as a function of the drilling process parameters. Ramkumar et al. [19] investigated the effect of workpiece vibration when drilling glass/epoxy laminates by applying three types of drills: tipped WC, 2-flute solid carbide, and 3-flute solid carbide. Wang et al. [7] utilized a carbide drill and an HSS drill, and proved that the thrust of vibration drilling is less than that of conventional drilling conducted on GFRP. Sadek et al. [20] determined the characterization and optimization of vibration-assisted drilling related to GFRE laminates. High-speed drilling of GFRP as a high-speed machining technology has been applied by Rubio et al. [21]. The experimental results indicated that higher spindle speeds should be used for drilling GFRP when large material removal rates with minimal delamination are needed. However, several studies have reported the presence of mode I and III crack propagation in composite materials, and analysis often involves only the mode I crack propagation (e.g., experimental observations by Hocheng and Tsao [22–26], whereas in many cases, the composite material is subjected to either pure mode or mixed-mode (I and II) analysis, which must be investigated more accurately). In this regard, some studies have been conducted to evaluate the effects of some parameters such as the delaminating interface, specimen geometry, stacking sequence, loading rate, and moisture by evaluating the mode II critical strain energy release rate (CSERR). By detecting the effect of loading rate on mode II delamination in carbon/epoxy laminated composites, Zabala et al. [27] demonstrated that the mode II CSERR values are not dependent on the loading rate. Msekh et al. [28] investigated the dissipation energy due to fracture in polymeric nanocomposites (PNCs) with a polymer matrix of silicate clay by considering the interphase zone thickness and fracture toughness. Talebi et al. [29] proposed an open-source software framework called PERMIX for modeling fractures on the continuum level by considering the extended finite element method (XFEM) coupling for dynamic crack propagation. In addition, Machado et al. [30] investigated the effect of strain rate and temperature on the mode II CSERR of carbon/epoxy composite materials. The results demonstrated that not only is the mode II CSERR affected by temperature, but also increases as the temperature increases. Another experimental study was performed by Fernandes et al. [31] in which the mode II CSERR of a carbon/epoxy composite was determined to be significantly affected by moisture. Finally, several studies have demonstrated the dependency of the mode II CSERR on the curing pressure [32], fiber stacking sequence [33], fiber volume fraction [34] and pre-crack length [35].

As mentioned previously, although several drilling techniques such as conventional, high-speed, and vibration-assisted drilling have been considered for composite structures, they are limited to modes I and III or to pure experimental investigation of mode II. Therefore, in the present research, a numerical FE analysis, in addition to some experimental investigations, have been carried to study induced delamination and mode II crack propagation created by the drilling process on a glass/polyester composite. In this study, the virtual crack closure technique (VCCT) was employed to evaluate the crack propagation in mode II, which was then modeled using the ABAQUS industrial software suite. Moreover, the mode II CSERR was calculated and compared with its critical value.

Theoretical concepts

Delamination is the most commonly encountered problem during the machining of composite plies. This phenomenon causes a rupture between the matrix and the reinforcement of the composite, which is well known as delamination. If the drill is close to the end of the specimen, the outer plies will resist the drill’s forward force, and the forward speed will be lower than the nominal value. In this case, the drilling procedure will not to be able to penetrate smoothly into the material and causes separation of the plies. In general, delamination occurs in the input and output of the specimen surface when a hole is drilled, which are respectively referred to as “push-out” and “peel-up”.

Considering the Hocheng model [22,23], the uncut plies under the tool are drawn downward by the thrust force as the tool moves forward. For orthotropic materials, considering the virtual work theorem, the expression of the delamination critical force is as follows based on the Hocheng model [37]:

(1)F_z=\mathrm{8}\mathrm{\pi }{\left({\displaystyle \frac{G_{\mathrm{Ic}}·D}{{\displaystyle \frac{\mathrm{1}}{\mathrm{3}}}-{\displaystyle \frac{D\text{'}}{\mathrm{8}D}}}}\right)}^{\frac{\mathrm{1}}{\mathrm{2}}},

where G_Ic is the critical energy release rate in mode I. Moreover, D and D′ are defined as follows:

D={\displaystyle \frac{\mathrm{1}}{\mathrm{8}}}\left(\mathrm{3}{D}_{\mathrm{11}}+\mathrm{2}{D}_{\mathrm{12}}+\mathrm{4}{D}_{\mathrm{66}}+\mathrm{3}{D}_{\mathrm{22}}\right),

(2)D\text{'}={\displaystyle \frac{D_{\mathrm{11}}+D_{\mathrm{22}}}{\mathrm{2}}}+{\displaystyle \frac{D_{\mathrm{12}}+D_{\mathrm{66}}}{\mathrm{3}}},

where D_ij (i,€j = 1,€2,€6) are coefficients that constitute the bending plate.

Virtual crack closure technique

In VCCT, it is assumed that with the propagation of the crack from a+Da (node i) to a +2Da (node k), the tip of the crack does not change significantly. Therefore, when the crack tip is at node k, the amount of displacement behind the crack tip at node i is approximately equal to the amount of displacement at node l when the tip is in the node i position. With this assumption in the two-dimensional 4-node element, the amount of work (DE) required to close the crack in an element is computed as follows:

(3)\mathrm{\Delta }E={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\left[X_i\mathrm{\Delta }{u}_l+Z_i\mathrm{\Delta }{w}_l\right],

where X_i and Z_i are the shear and opening forces, and \mathrm{\Delta }{u}_l and \mathrm{\Delta }{w}_l are represented as the horizontal and vertical displacements at node i, respectively. The amounts of these forces and displacements are determined by performing a one-step finite element analysis. The value of G, which is the energy release rate during crack propagation, is defined as \mathrm{\Delta }E/\mathrm{\Delta }A. The values of the strain energy release rate in modes I (G_{\mathrm{I}}) and II (G_{\mathrm{II}}) are defined as

(4)G_{\mathrm{I}}=-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}\mathrm{\Delta }a}}{Z}_i\left(w_l-w_{l*}\right),

(5)G_{\mathrm{II}}=-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}\mathrm{\Delta }a}}{X}_i\left(u_l-u_{l*}\right).

Therefore, the total strain energy release rate in modes I (G_{\mathrm{I}}) and II (G_{\mathrm{II}}) is defined as

(6)G_{\mathrm{T}}=G_{\mathrm{I}}+G_{\mathrm{II}}+G_{\mathrm{III}},

where, for a 2D dimensional analysis, G_{\mathrm{III}}=\mathrm{0}, and thus, the total release rate is G_{\mathrm{T}}=G_{\mathrm{I}}+G_{\mathrm{II}}.

Materials and methods

Composite specimens were prepared using the hand layup method based on an approximation volume of 50% for 30 plies. The thickness of each ply is approximately 0.25 mm. Curing and post curing took place at room ambient conditions for one week. The geometries and number of samples were prepared according to ASTM D3039 by applying an extensometer (Fig. 1), and the mechanical properties of the composite specimens were evaluated and are listed in Table 1.

Moreover, to obtain the fracture properties, each composite was prepared from glass/polyester (using glass fibers (200 gr/m²)), and a cut-off sample was observed (Fig. 2).

To investigate the composite properties, an ARCAN fixture was used. The Uhu 2-K-Epoxidkleber industrial adhesive was used to connect the specimens to the fixture, and the adhesive’s mechanical properties reached 30 MPa after curing. All specimens were attached to metal parts and were then heated in a furnace at 180°C for 5 min to obtain maximum adhesion. Specimens with dimensions of 30 mm × 10 mm × 6 mm were prepared and placed inside the fixture (Fig. 3).

To avoid dynamic effects at 0°, 45°, and 90° (Fig. 4), specimens were loaded at a rate of 2 mm/s. Therefore, the critical load leading to fracture of every specimen was evaluated, and the results are presented in Table 2.

Numerical analysis

Simulation of drilling process

The purpose of this section is to obtain the values of G_I and G_II created during the composite drilling process. Because the analysis is in the 3D state, there is no single value for G_I and G_II, that is, there is a distribution of these two quantities, which is assumed to be circular along the crack tip. The model presented in this study has some advantages in comparison with other analytical and numerical models previously proposed.

1)‚The corresponding shear stresses can be investigated.

2)‚The complexity of the drill geometry, especially at the tip, is not disregarded, and the true geometry is considered.

3)‚The model is sensitive to crack initiation in such a manner that the crack length can be changed according to the number of remaining plies during drilling.

The type of modeled composite is a quasi-isotropic stacking sequence featuring 16 plies with a layup of (90°/+45°/0°/–45°)_2s. The approximate thickness of each layer is 0.25 mm and the number of remaining plies under the impact drill is three plies. This means that the hypothetical leave in the interface is between the 0° and –45° plies. As shown in Fig. 5, the force input by the tool to specimen F_z is divided into two parts: one part is applied by the chisel edge (F_z2) and the other (F_z1) is applied by the cutting lip on the specimen (F_z= F_z1+ F_z2).

The drilled structure is modeled as a volume with circular geometry having an external radius R_e and interior radius R_t (i.e., the nominal drilled hole radius). A schematic of the (YZ) section of the model is shown in Fig. 6.

In addition, R_a and e represent the chisel edge radius and thickness of the non-machined plies, respectively. According to a study conducted by Zitoune and Collombet [38], it is estimated that approximately 40% of the force is applied by the chisel edge and the remainder is applied to the workpiece by the cutting tip. When the energy release rate G reaches its critical level, crack propagation will occur. One of the criteria for crack expansion is the “Power Law” defined as follows [39]:

(7){\left({\displaystyle \frac{G_{\mathrm{I}}}{G_{\mathrm{Ic}}}}\right)}^{{\alpha }_{\mathrm{1}}}+{\left({\displaystyle \frac{G_{\mathrm{II}}}{G_{\mathrm{IIc}}}}\right)}^{{\alpha }_{\mathrm{2}}}+{\left({\displaystyle \frac{G_{\mathrm{III}}}{G_{\mathrm{IIIc}}}}\right)}^{{\alpha }_{\mathrm{3}}}=\mathrm{1},

where {\alpha }_{\mathrm{1}}, {\alpha }_{\mathrm{2}}, and {\alpha }_{\mathrm{3}} are coefficients related to the materials between layers 1 and 2. For the present material, these coefficients are selected as {\alpha }_{\mathrm{1}}={\alpha }_{\mathrm{2}}={\alpha }_{\mathrm{3}}=\mathrm{1.6}. The specimen mesh size and crack tip mesh concentration are depicted in Fig. 7.

As mentioned previously, the modeled composite is a quasi-isotropic stacking sequence featuring 16 plies with a layup of (90°/+45°/0°/−45°)_2s. The approximate thickness of each layer is 0.25 mm, and three plies under the impact drill are considered. This implies that there is a hypothetical leave in the interface between the 0° and –45° plies. In the following, the settings for crack propagation were performed using the VCCT method in the software, and the composite failure properties (G_Ic and G_IIc) and other related coefficients in the corresponding sections were introduced to complete the problem-solving process. The drilling diameter and chisel length used were 4.8 and 1.3 mm, respectively. In this study, a specimen having a depth of 8 mm and a chisel diameter of 2 mm was initially made and then drilled using a 16 mm-diameter drill bit to the end of the specimen.

According to experimental studies, the outer diameter of the model should be chosen so that the bending momentum is insignificant and the critical thrust force is increased [40]. To define the crack, the VCCT method was used. The node to surface method for partitioning interactions between two surfaces was applied, and the sliding formulation considered small sliding. Then, nodes from the lower surface that were connected at the beginning of the analysis were used to create the desired cracks. An alternate method is the surface to surface method, which can achieve higher accuracy than the node to surface method. However, owing to the small size of the elements along the interfacial surfaces, the difference between the two methods is insignificant and solutions based on the node to surface method were used. The properties of fracture mechanics are thus G_Ic, G_IIc, and G_III, and the criterion for crack propagation is also considered as a power law. To obtain higher precision in the results, the size of the elements around the crack tip was smaller than in the other zones. For this purpose, the size of the elements around the crack tip was selected as 0.035 mm. Convergence was achieved by changing the size of the elements around the crack tip compared to other zones. In the VCCT method, the size of the elements before and after the crack (i.e., where the crack propagates) should be the same. In this context, a circular zone was considered with a thickness of 0.2 mm around the crack tip (element size of 0.035 mm). The element distributions in the proposed model and mesh convergence are defined in Fig. 8 and the resulting critical thrust force versus element size is shown in Fig. 9.

The boundary conditions are defined at the bounded outer surface nodes such that the displacements in the x, y, and z directions are considered to be zero, that is, the outer nodes have zero degrees of freedom (see Fig. 10).

Composite cracked body simulation

The ARCAN geometry model and composite specimen were prepared in two-dimensional format in the ABAQUS software. The analysis is also two-dimensional and the plane strain condition is assumed (Fig. 11).

The properties of the material were defined, and the type of fixture and specimen were considered as ST37 structural steel and composite glass/polyester, respectively. Owing to the orthotropic nature of the composite specimen, the main direction of a specimen should be determined. In this context, the y direction was aligned with the fiber, the direction of z was orthogonal to y axis, and the layup direction was aligned with the x axis. In the next step, a crack with a length of 15 mm was created on the specimen, which is the initial crack. The crack tip zone elements are shown in Fig. 12.

After meshing, the concept of contour integrals was applied. The crack front, crack tip, and direction of crack propagation were considered. As is well known, the concept of the contour integral J is one of the most accurate methodologies applicable to crack modeling. In this analysis, the parameters play a role in linear elastic fracture mechanics. Available methods for extracting stress intensity factors (SIFs) include singular integral equations [41–43], weight functions [44–47], boundary collocation [48,49], finite element [50–53], boundary element [54,55], XFEM, and combination methods [56,57]. Numerical solutions of singular integral equations are popular in the calculation of SIFs in finite elastic domains. In this study, a J-integral-based method built in the ABAQUS software was employed to obtain SIFs. To achieve higher precision in the SIFs and J integral, seven contours were considered. Owing to the fact that achieving greater precision in the SIFs and J integral requires higher accuracy in the loading condition at the crack tip vicinity, in the present study, an RCAN fixture was employed, in which accurate mixed-mode loading can be applied and every direction of loading and corresponding boundary condition can be considered. For every direction, the boundary condition and load were considered. It was observed that if the middle nodes are approximately 1/4 of all nodes in the crack tip, the tensile field singularity in the crack tip is better represented. Mode I loading was first considered (Fig. 13).

As shown in the figure, the x direction was located at the center of the model and the displacement boundary condition was applied along the y direction. In addition, mesh refinement around the crack tip is shown in Fig. 14.

Results and discussion

It is well known that most machining procedures performed on composite structures involve drilling, which leads to crack propagation. Delamination is one of the most important factors that can reduce the strength of a composite structure. Many researchers have studied delamination in the drilling of composite materials and have attempted to define this phenomenon by developing analytical, numerical, and experimental models. In most studies, only the effects of mode I and mode III crack propagation are considered, whereas the effect of mode II can be more critical. In other words, although mode I is the dominant mode of failure, our study confirmed that mode II can play a significant role in the propagation of interlaminar cracks during drilling. Therefore, the goal of this research is to determine the mode II effects on the propagation of interlaminar crack propagation during drilling of multi-layer composites, which requires various experimental and numerical results. The following experimental procedures were employed.

1)‚Mechanical properties of glass/polyester specimens were obtained based on the ASTM D3039 standard.

2)‚The interlaminar mixed-mode (I/II) loadings were determined using an ARCAN test fixture so that the fracture toughness of the glass/polyester could then be determined.

In order to validate the results [38], was considered, and G_{\mathrm{Ic}} and G_{\mathrm{IIc}} were obtained as 0.44 and 1.4 N/mm for T800/M21, respectively. Then, the fracture and mechanical properties of T800/M21 in addition to the energy release rate in modes I and II were obtained, as listed in Table 3.

Energy release rate

The proposed numerical model has the advantage that it considers the use of an adapted finite element available in the software library of the SAMCEF FE code. The contour distributions of G_I and G_II along the crack length are illustrated in Figs. 15 and 16. As mentioned previously, based on experimental and numerical results, the mode II energy release rate has a more critical value than mode I. This can be observed in Figs. 15 and 16, in which the contour distribution of the mode II energy release rate (G_II) reaches a maximum of 5.932e-001 in comparison with the mode I energy release rate (G_I) maximum of 3.873e−001.

Therefore, based on several investigations (i.e., the present literature review), the maximum value of the energy release rate is different for mode II and mode I crack propagation, indicating that the mode II parameters are suitable for failure analysis.

As shown, the locations of the maximum energy release rates are different. This can be observed in Fig. 17, where the variation in the energy release rate of mode I (G_{\mathrm{I}}) and mode II (G_{\mathrm{II}}) are compared.

Figure 18 presents the distribution of the power crack propagation criterion along the crack under quasi-static conditions.

As shown in Figs. 19 and 20, G_{\mathrm{II},\max } is much greater than G_{\mathrm{I},\max }, indicating that crack propagation and delamination takes place more easily in mode I in comparison to mode II. Therefore, owing to the energy reduction corresponding to mode I, crack propagation can occur more easily in this mode. Moreover, it was shown that the critical thrust force (PC) not only depends on mode I but can also be affected by mode II. On the other hand, the polymer matrix composite strength in mode II is greater than that in mode I, and its effects are more critical. Therefore, analysis was considered for 1, 2, 3, and 4 plies under the drilling thrust force comparing our model with the results obtained in Ref. [38] (numerical model), and our experimental results (Fig. 19).

The experimental, numerical, and proposed model results were compared, as shown in Fig. 19. In addition, the horizontal ordinates (Figs. 19, 21, and 26) indicate the various loading angles applied by the ARCAN fixture. Therefore, for glass/polyester, the SIFs can be plotted for various loading angles (Fig. 20).

As shown in the figure, by increasing the angle of loading from 0° to 90°, the f₁ and f₂ values decrease and increase, respectively. This indicates that the mode II SIF plays a significant role in the drilling process involving glass/polyester composites, especially as the loading angle increases up to 65°. Beyond this angle, f₂ becomes greater than f₁.

Using the elastic modulus and critical loading, the mode I and II fracture toughness (K_{\mathrm{Ic}}, K_{\mathrm{IIc}}) and corresponding energy release rate (G_{\mathrm{Ic}}, G_{\mathrm{IIc}}) can be obtained and values are reported in Tables 4 and 5, respectively. The variation in the energy release rate is illustrated in Fig. 21.

As shown in Fig. 21, by increasing the loading angle, the crack propagation resistance in mode II will be increased. In the previous section, the mechanical and fracture properties of glass/polyester were obtained and validated with the data presented. In the following sections, the mode I and mode II contributions will be investigated.

Crack propagation under drilling

The critical thrust force was evaluated as 102 N considering the mode I and II energy release rates. In Fig. 22, the von Mises stress is illustrated along the crack length in which the stress field in the vicinity of the inner part of the crack tip has been neglected.

As shown, the maximum stress occurred at the crack tip with a 0° fiber direction. Although the maximum amount of G_{\mathrm{I}} is affected by crack initiation and corresponding delamination, there is little effect on G_{\mathrm{II}}. This result can be generalized to the critical layer remaining below the drill press (Fig. 23).

As shown in the Fig. 23, the loading angle is presented as a normalized amount instead of other possible forms for simplicity. Furthermore, in the case of two, three, and four plies remaining under the drill bit, the critical thrust force can be obtained versus the number of plies (Fig. 24).

In Fig. 25, the von Mises stress is illustrated along the crack length for one layer remaining below the drill bit.

The corresponding energy release rate along the crack is demonstrated for mode I and mode II, respectively in Fig. 25. Moreover, the normalized loading angle is shown in addition to the load applied by the ARCAN fixture.

Based on Fig. 26, the dominant mode for crack propagation and initiation of delamination is mode I, as the peak value in mode I is greater than that in mode II, and the fracture strength of plies for mode I is less than that corresponding to mode II. By performing the analysis for two, three, and four layers under the drill bit, it was determined that the last layer is the critical one (Fig. 27).

Effect of layup and angle of plies

To determine the effect of the layup and the angle of the plies on the obtained results, the last layer of the composite was evaluated at 30°, 45°, 60°, and 90° under the same force (the vertical critical force at 0° (102 N)). The distributions of G_{\mathrm{I}} and G_{\mathrm{II}} versus fiber angle are plotted along the crack length in Figs. 28 and 29, respectively.

As shown in the figures, the maximum value of G_{\mathrm{I}} and G_{\mathrm{II}} changes when considering the orientation of the fiber in the last ply. Despite the small differences between G_{\mathrm{I}} and G_{\mathrm{I}\mathrm{c}}, G_{\mathrm{II}} has a significant difference compared to G_{\mathrm{II}\mathrm{c}}. Therefore, there is a tendency for crack propagation to occur in the mode II direction. Moreover, the mixed-mode energy release rate (G_{\mathrm{II}}/\left(G_{\mathrm{I}}+G_{\mathrm{II}}\right)) is plotted in Fig. 30.

As shown in this figure, the maximum G_{\mathrm{I}} occurs at the same position, and consequently, the delamination is the same. Here, G_{\mathrm{II}}/\left(G_{\mathrm{I}}+G_{\mathrm{II}}\right) and G_{\mathrm{I}}/\left(G_{\mathrm{I}}+G_{\mathrm{II}}\right) are the minimum and maximum values, respectively. Therefore, it can be determined that the crack propagates where mode I is dominant. Similar results have been reported by previous studies that have evaluated crack propagation under the cutting tip (Figs. 31, 32 and 33).

As shown in these figures, although the maximum G_{\mathrm{I}} and G_{\mathrm{II}}/\left(G_{\mathrm{I}}+G_{\mathrm{II}}\right) is increased by increasing the angle of the last ply, the maximum G_{\mathrm{II}} decreases. Therefore, it can be determined that the crack propagates where mode I is dominant.

Conclusions

Based on the mode II complexity, a numerical FE analysis was carried out to investigate the effect of induced delamination created by the drilling process in the pure mode II loading condition. In this context, the VCCT was employed to evaluate the crack propagation in mode II using the ABAQUS software suite. Moreover, the mode II strain energy release rate (CSERR) was obtained and compared with its critical value. In the present research, by determining the strain energy release rates in mode  and mode  and comparing them with their corresponding critical values G_{\mathrm{I}\mathrm{c}} and G_{\mathrm{I}\mathrm{I}}, the critical thrust force that causes delamination in T800/M21 composite was determined.

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