*Delamination Modelling*

Delamination has long been viewed from a fracture mechanics perspective as a crack propagation phenomenon and the critical force at its onset (*CF*) can be calculated according to Equation (4), proposed by Cheng et al. [15], assuming a point load applied on an isotropic-circular-clamped plate, where *GIC* corresponds to the mode I fracture energy associated to the material interface delamination, *E* is the Young's modulus, *ν* is the Poisson coefficient and *h* is the depth of uncut material under the drill tool.

$$\mathcal{C}\_{\rm F} = \pi \left[ \frac{8 G\_{\rm I\mathcal{C}} E h^3}{3(1 - \nu^2)} \right]^{1/2} \tag{4}$$

In order to estimate the fracture energy of the CFRP-AA interface, asymmetric double cantilever beam (ADCB) tests were performed. In this type of test, a traction load is applied to the specimen arms, inducing the propagation of an existent pre-crack at a specified specimen plane, with a length and thickness of *a*<sup>0</sup> and *t* (refer to Figure 2a). A specially built testing machine coupled with a 50N capacity load cell (Tedea-Huntleigh Model 1042), intended for fracture characterization, was employed (refer to Figure 2b). The specimens arms were bonded (Araldite 2052-1 structural adhesive) to aluminium blocks with a 6 mm hole to allow for ADCB specimen gripping in the testing machine. The challenging realtime monitoring of crack propagation can be avoided using an equivalent crack length (*ae*) procedure [30,31]. A relationship between *ae* and specimen compliance (defined as the ratio between the applied displacement, *δ*, and load, *P*), can be obtained considering the strain energy (*U*) of the specimen due to bending and shear effects (Timoshenko beam theory) and applying the Castigliano theorem (*δ* = *dU*/*dP*). In this context, specimen current compliance can be defined as shown in Equation (5), where *B*, *hu* and *hl* correspond to specimen dimensions, *Du* and *Dl* are the bending stiffness of upper and lower arms. Although critical load estimation relies exclusively on mode I fracture, in this work the ADCB specimens were selected given the relative difficulty in inducing a pre-crack in middle layer when compared to layer interfaces. Moreover, the fracture mechanism in drilling is consistent with the representation of mixed mode fracture with predominant mode I [32].

$$C = \frac{a\_\varepsilon^3}{3} \left( \frac{1}{D\_\mathrm{u}} + \frac{1}{D\_\mathrm{l}} \right) + \frac{6a\_\varepsilon}{5BG\_{13}} \left( \frac{1}{h\_\mathrm{u}} + \frac{1}{h\_\mathrm{l}} \right) \tag{5}$$

Combining Equation (5) with the Irwin–Kies relation, Equation (6) can be derived, providing the total strain energy release under mixed mode I + II (with predominant mode I) as a function of *ae*. Other approaches could be applied, namely within the scope of the linear-elastic fracture mechanics, such as that described in [33,34].

$$G\_T = \frac{P^2}{2B} \left[ a\_\varepsilon^2 \left( \frac{1}{D\_\mu} + \frac{1}{D\_l} \right) + \frac{6}{5B G\_{13}} \left( \frac{1}{h\_\mu} + \frac{1}{h\_l} \right) \right] \tag{6}$$

**Figure 2.** Experimental details of delamination fracture energy evaluation procedure: (**a**) Scheme of ADCB specimens loading, showing pre-crack location. (**b**) Fracture testing machine equipped with load cell. (**c**) ADCB specimen with bonded aluminium blocks on both upper and lower arms. (**d**) Detail A of **Figure 2b**, showing ADCB specimen with aluminium blocks assembled to testing machine.

#### **3. Results and Discussion**

The thrust force (*Ft*) evolution of each tested tool geometry and its association with current drill point position is exhibited in Figure 3. A specific load signature can be identified and significant correspondence can be made with each layer of the laminate material. Common to all drill geometries, a rise in *Ft* is observed due to the contact increase (between the drill's primary cutting edge and the laminate material), from the start of the drilling operation up to instant B. A steeper increase of the force is noticed from instants B to C, corresponding to the CFRP material layer, evidencing the higher cutting resistance of this material as compared to the AA. This effect is further highlighted by the subsequent *Ft* decrease in the C to D path. Load curve tends to another maximum as the drill exits the laminate material (E). Up to this instant, *Ft* signature is rather indistinct of drill geometry, which is coherent with the identical point and helix angles of the three tested drills.

**Figure 3.** Maximum thrust force evolution in function of drill displacement. (**a**) CNV drill geometry. (**b**) CBR drill geometry. (**c**) 2PA drill geometry.

Instant X, in Figure 3a, indicates the moment the CNV drill's secondary cutting edge engages the first layer of the laminate material. A slight transition (increase) in the curve's slope is noticed. Similarly, and referring to Figure 3c, the instant Z corresponds to the moment the second point angle of the 2PA drill engages the laminate material. It is interesting to note that with the addition of a second (smaller) point angle, *Ft* conveniently decreases more rapidly. In contrast, as the chip-breaking groove of CBR drill engages the laminate material (instant Y of Figure 3b) a very significant load increase is noticed, peaking at approximate double *Ft* values of the A-Y drill tip path. Given the assumption that higher loads may contribute to higher delamination, the CBR drill might be inadequate. The load signature differences between drilling operations with and without back support are illustrated in Figure 3. It is possible to note that the overall thrust force signature does not significantly change. Still, the maximum values (peak of the *Ft* curves) are consistently higher for all drill geometries, promoted by the stiffness increase of the clamping system. Moreover, at the end of the drilling operation, a load plateau is maintained, corresponding to the cutting of the PTFE disk (back support provider).

The analysis of variance (ANOVA) conducted for the maximum thrust force revealed significant impact of drill geometry, feed as well as the usage of back support. Such is illustrated by the <0.05 *p*-values respective of those variables, in Table 3. Moreover, despite the slight increase of maximum *Ft* with cutting speed, it did not present a relevant influence, especially when compared with the other considered variables, as shown in Figure 4. Drill geometry CBR seems to develop much higher thrust forces (approximately two-times higher), when compared with the other two drill configurations, which show identical results (slightly lower axial force with the CNV), as illustrated in Figure 4c. Therefore, as thrust force magnitude may be an indicator of delamination severity, the CBR drill may not perform adequately.

**Figure 4.** ANOVA results for axial force variability in function of: (**a**) Cutting speed. (**b**) Feed. (**c**) Drill geometry. (**d**) Back support.



Figure 5a–c illustrate some representative examples of delamination occurrence on the machined holes using each drill geometry. The X-ray analysis has enabled the observation of the otherwise indiscernible defects. Figure 5a shows the delamination type mostly associated with the usage of CNV drill. The high directionality of damage occurrence (aligned with fibre orientation) is coherent with the push-out delamination mechanism resultant from AA-CFRP material de-bonding caused by the drill thrust. Since this interface debonding is predominantly mode I fracture, the developed modelling towards delamination prediction using ADCB is in accordance with the obtained results.

Alternatively, uniformly distributed delamination (as illustrated in Figure 5b) was more prone to occur with the CBR drill. The damage around the hole contour may be associated with the chip-breaking v-grooves on the principal cutting edge of the drill. These structures have seemingly failed to control chip morphology, which was identical regardless of the employed tool as well as operative conditions: continuous (ribbon) chips constituted of an aluminium core and with discontinuous bonded CFRP, as illustrated in Figure 5d. Unable to improve chip segmentation or breakage (comparatively to CNV and 2PA drills), the v-shaped grooves on the CBR drill seem to have caused internal delamination due to chip imprisonment. Repositioning of the groove towards a more central position of the drill's cutting edge or increasing the number of grooves along the

cutting edge may promote better chip splitting. Further research on the identification of suitable drill morphologies towards effective chip partition in fibre metal laminates is required, which may be supported using more advanced numerical methods. Constitutive and damage modelling may be convenient towards accurate portrayal of chip flow. Apart from the delamination effects, an example of a delamination-free drilled hole (using 2PA drill) is shown in Figure 5c.

**Figure 5.** X-ray images of representative delamination defects on drilled holes using: (**a**) CNV drill geometry and (**b**) CBR drill geometry. (**c**) Example of delamination-free drilled hole using 2PA drill geometry. (**d**) Typical chip morphology obtained from drilling operations of FML, regardless of the employed drill.

The influence of the tested variables on the considered delamination factors results is shown in Figure 6. In addition, Tables 4–6 present the analysis of variance details. Despite having a negative impact on maximum thrust force (refer to Figure 4d), back support is commonly employed with the goal of increasing the fixture stiffness and minimizing delamination (preventing displacement of FML layers up to fracture initiation and propagation). Figure 6 shows the influence of the tested variables on the calculated delamination factors (*Fa*, *Fd*, *Fad*) for each used drill tool. Although it is not expressive for the *Fd* and *Fda* delamination factors, a significant correlation between back support employment and delamination factor minimization (*Fa*) is observed in Figure 6d, illustrating its decreasing tendency with back support usage. Cutting speed and feed did not show accountable statistical impact (*p*-value higher than 0.05), as illustrated in Figure 6a,b. Drill geometry is the most influential variable on delamination results. The CBR drill yields the worst case scenario regarding delamination values for all calculated factors (up to three-times higher than CNV). In addition, 2PA seems to slightly outperform the CNV drill geometry. It is important to note the consistency of delamination results with the previous maximum load measurements, illustrating the importance of load prediction in metal cutting operations.


**Table 4.** ANOVA results on *Fa* delamination factor of the conducted experimental campaign.


**Table 5.** ANOVA results on *Fd* delamination factor of the conducted experimental campaign.

**Table 6.** ANOVA results on *Fda* delamination factor of the conducted experimental campaign.


**Figure 6.** ANOVA results on delamination factors in function of: (**a**) Cutting speed. (**b**) Feed. (**c**) Drill geometry. (**d**) Back support.

The arithmetical mean height roughness (*Ra*) has been estimated on a 5 mm length profile of the generated hole surface. Three measurement repetitions were performed for each hole and the average values were taken into consideration for ANOVA. The ANOVA statistical results show that drill geometry is the only relevant variable with regard to roughness (*Ra*) values (refer to Figure 7). Still, both cutting speed and feed p-values range relatively close to the 0.05 limit, from which significant impact can be inferred, thus showing slight tendencies for smaller roughness values when higher cutting speed and smaller feed operative conditions are applied. With regard to drill geometry, an identical trend to the tested variables has been identified, meaning that lower surface quality holes have resulted from hole making with the CBR drill. Moreover, from all machined holes, only 20% were above the 3.2 μm surface roughness limit (*Ra*). The majority of those were performed using the CBR drill (87%) with the remainder using the CNV drill. Only the 2PA drill was capable of attaining *Ra* < 3.2 μm in all machined holes. This criterion has been a useful indicator of the *Ra* quality in industrial conditions, with special relevance to the aeronautics sector [35].

The arithmetical mean height roughness (*Ra*) has been estimated on a 5 mm length profile of the generated hole surface. Three measurement repetitions were performed for each hole and the average values were taken into consideration for ANOVA. The ANOVA statistical results show that drill geometry is the only relevant variable with regard to roughness (*Ra*) values (refer to Figure 7). Still, as can be seen from 7, both cutting speed and feed p-values range relatively close to the 0.05 limit, from which significant impact can be inferred, thus showing slight tendencies for smaller roughness values when higher cutting speed and smaller feed operative conditions are applied. With regard to drill geometry, an identical trend to the tested variables has been identified, meaning that lower surface quality holes have resulted from hole making with the CBR drill. Moreover, from all machined holes, only 20% were above the 3.2 μm surface roughness limit (*Ra*). The majority of those were performed using the CBR drill (87%) with the remainder using the CNV drill. Only the 2PA drill was capable of attaining *Ra* < 3.2 μm in all machined holes. This criterion has been a useful indicator of the *Ra* quality in industrial conditions, with special relevance to the aeronautics sector [35].

**Figure 7.** ANOVA results on measured surface roughness (*Ra*) in function of: (**a**) Cutting speed. (**b**) Feed. (**c**) Drill geometry. (**d**) Back support.


Feed 0.0126 1 0.0126 1.10 0.2979 Drill geom. 0.8245 2 0.4122 36.06 <0.0001 Back support 0.0016 1 0.0016 0.1408 0.7086 Residual 0.8002 70 0.0114 - -

**Table 7.** ANOVA results on *Ra* surface roughness conducted during the experimental campaign.

The load–displacement results of the ADCB fracture tests are shown in Figure 8a. The resistance curves (refer to Figure 8b) were obtained to determine the energy release rate, needed to estimate a delamination critical force (*CF*) through Equation (5). From the analysis of Figure 8b, an energy value plateau of approximately 0.249 N/mm with upper and lower boundaries of 0.29 and 0.20, respectively, is identified. Although delamination is more likely to occur as the drill approaches material exit (commonly known as exit delamination and promoted by the lack of subsequent material layers), the critical force, *CF* (or delamination onset load) has been calculated for three distinct interfaces as the tool advances on the laminate. These are labelled and highlighted in Figure 8c. Since the ADCB fracture tests were conducted at an AA-CFRP interface, delamination prediction is limited to those interfaces within the considered laminate. It is important to note that the critical force value obtained by Equation (5) refers to a single point at the drill tool path. This point is defined by the distance between the drill point and the bottom surface of the laminate (also called depth of uncut material, *h*).

**Figure 8.** Load–displacement and energy release rate results obtained from ADCB fracture tests: (**a**) Load–displacement curves. (**b**) Resistance curves. (**c**) Interfaces where delamination occurrence has been analysed.

Table 8 presents the range of critical forces for each identified interface of Figure 8c, based on the upper and lower boundaries energy values. Elastic modulus has been calculated based on weighted average of metal volume fraction (MVF) of the uncut material, which in the case of interface 3 corresponds exclusively to CFRP material. A Poisson ratio of 0.4 was considered for the *CF* estimation.

**Table 8.** Estimation of critical force range for each respective interface, based on ADCB fracture tests critical energies.


The estimated critical force *CF* range can be seen as a threshold of values from which delamination is likely to occur. This range has been compared with several drilling operation thrust force signatures and the X-ray images of drilled holes showing delamination occurrence (or the absence thereof). It is important to note that the usage of back support hinders delamination by bending prevention (and thus interface de-bonding) of the laminate layers. For this reason, the tests conducted with sacrificial back support were not considered in this part of the study. In adition, the model proposed by Cheng et al. [15], is not valid for such support conditions.

Figure 9a shows the critical force range thresholds comparison with the thrust force loading signature of the CNV drill using a cutting speed of 120 m/min and 0.03 mm/rev feed. Since maximum thrust force was consistently below the drill point path corresponding threshold, delamination is not predicted, which is coherent with its absence in the X-ray image of the corresponding hole. Figure 9b shows a similar example for a CNV drill with a cutting speed of 100 m/min and 0.07 mm/rev of feed, where maximum thrust force surpasses the minimum delamination threshold at "interface 3" (refer to Figure 8c for interface relative position) resulting in delamination occurrence, as verified in the corresponding X-ray image of the drilled hole.

One of the shortcomings of the presented methodology is illustrated by Figure 9c. Although the critical force limit is not attained within the considered tool path, it may have been surpassed by the action of the drill's chip grooves. Such a possibility is consistent with the delamination morphology and its occurrence at an internal interface (contrary to the exit delamination of the previous examples in Figure 9a,b). The estimated critical force of Equation (4) relies on the assumption of a point load (associated with the cutting phenomenon) and thus, in the current case, its applicability is compromised since it is

only valid to drill features that are effectively cutting (principal cutting edge). Still, when considering a critical load value that is independent of drill position, the developed model would correctly predict delamination occurrence.

Given that the load has not surpassed the critical force threshold, Figure 9d shows an example of unexpected defects. It is, however, noticeable that the pattern of damage occurrence (indicated by red arrows) is compatible with the delamination type of chip formation in fibre-reinforced polymers [32,36], suggesting fibre-matrix interface failure (and crack propagation) within the composite material. In drilling, the relative position constantly changes with each rotation and when the cutting direction and fibre direction are the same (occurring in two distinct instants) mixed mode fracture occurs. Thus, predominant type I or II, depending on rake angle, develops within fibre-composite material, promoting crack initiation and its propagation along the fibre-reinforcement interface. This observation explains the non-compliance of the developed criterion (only valid for AA-CFRP interfaces).
