Finite element study into the effects of fiber orientations and stacking sequence on drilling induced delamination in CFRP/Al stack

1 Introduction

Carbon fiber reinforced polymer (CFRP) is at the forefront of replacing conventional materials like aluminum and steel in the construction of aircraft structural components [1]. The highly favorable combination of material properties of CFRP including high stiffness, high tensile strength, low weight, high chemical resistance, high temperature tolerance and low thermal expansion have made them perfect candidates for use in the aerospace and other technological applications requiring high strength and low weight [2].

Machining is an inevitable process in aerospace industry to facilitate assembly of individual components [3]. Several thousand holes are required for riveting and bolting of the components. In an Airbus A350 aircraft, for example, up to 55,000 holes are required for a complete single-unit production [4]. There are several factors that influence the quality of the drilled hole. These factors have been studied extensively by researchers both experimentally and by simulation. The factors can be categorized as work piece, drilling tool or drilling parameters related. Ozden et al. [5] did a numerical model to investigate the effects of drill geometry on drilling induced delamination of carbon fiber reinforced composites. They found a reduced torque and trust force for step drill in comparison to twist drill at similar drilling parameters, which could result in reduced damage. Zitoune et al. [6] did experimental studies on the effects of drilling parameters on thrust force, torque and hole quality of composites/Al stack. Their results showed that quality of holes can be improved by proper selection of cutting parameters.

Experimental damage measurement, as has been used by most researchers, is costly and time consuming, and most of the times, it involves destructive techniques to analyze the component. This is where finite element comes in, apart from saving on time required for experimental set ups and runs; it also saves on costs for buying materials and equipments. On top of this, it provides accurate results regardless of complexities in geometry, material properties, boundary conditions and loading. Riccio et al. [7] used a finite element model to study the effects of orientations and stacking sequence to delamination when a composite plate is subjected to low velocity impact. Several other researchers [8], [9], [10], [11], [12], [13], [14] have used finite element method to predict damage on composites under low velocity impact and have come up with conclusive results.

In summary, delamination has been recognized as the most common and serious defect in the drilling of composites. A larger percentage of components is rejected during final assembly due to delamination alone, and it accounts for up to 60% of all parts rejection [15], [16]. Much work has been done on the effects of drill geometry and process parameters. Some work also has been done about orientations and stacking, but all are dealing with the impact of low velocity. This work, therefore, is attempting to study the influence of orientations and stacking to delamination in CFRP/Al stacks during drilling process.

The work begins with understanding the mathematical damage models of both CFRP and aluminum. Chapter 3 deals with the finite element model and the simulation runs. The discussion of the results and conclusions follow in Chapters 4 and 5, respectively.

2 Damage modeling

2.1 Composite damage

The analysis of fiber reinforced composite materials calls for a good understanding of their damage. Much has been done by pioneering researchers in this field, and therefore, composite damage is a fairly understood phenomenon. Much fiber reinforced composite materials exhibit elastic-brittle behavior, meaning that damage in these materials is initiated without significant plastic deformation [2]. The damage behavior of composite laminates can be divided into two types: intra-laminar and inter-laminar damage.

2.1.1 Intra-laminar damage

The intra-laminar damage consists of fiber and matrix damage [8]. There are several well-known theories to explain this kind of damage including Hashin, Tsai-Wu, and Tsai-Hill failure criteria [17]. The Hashin criterion, which was postulated by Zvi Hashin, a mechanical engineer and a retired professor of solid mechanics at Tel Aviv University, in 1980, is a widely used criterion in the industry. It is also included in the finite element code ABAQUS as a failure criterion for fiber reinforced composites.

The Hashin criterion considers four different modes of failure for composites, namely, fiber tension, fiber compression, matrix tension, and matrix compression [18]. Equations (1)–(4) express these four kinds of Hashin failure criterion.

1. Tensile fiber failure for σ₁₁≥0

   (1)(σ11XT)2+σ122+σ132S122={≥1 failure    <1 no failure

2. Compressive fiber failure for σ₁₁<0

   (2)(σ11XC)2={≥1 failure    <1 no failure

3. Tensile matrix failure for σ₂₂+σ₃₃>0

   (3)(σ22+σ33)2YT2+σ232−σ22σ33S232+σ122+σ132S122={≥1 failure    <1 no failure

4. Compressive matrix failure for σ₂₂+σ₃₃<0

   (4)[(YC2S23)2−1](σ22+σ33YC)+(σ22+σ33)24S232+σ232−σ22σ33S232 +σ122+σ132S122={≥1 failure    <1 no failure

In the above equations,

σ_ij is the stress component.

Subscripts T and C denote tensile and compressive strengths of the laminate, respectively.

X_T and Y_T denote the allowable tensile strengths.

X_C and Y, denote the allowable compressive strengths.

S₁₂, S₁₃ and S₂₃ denote allowable shear strengths.

2.1.2 Inter-laminar damage

Inter-laminar damage in composites is mainly contributed by delamination [8]. This is the main focus of this study. Several researchers have explained two types of damage associated with delamination. The recent works by Antonio et al. [19] explain this very well. The two types are pill-up and push down delamination. Peel-up delamination is a consequence of the cutting force pushing the abraded and cut materials to the flute surface. The material spirals up the drill flute before it is completely machined. Push-out delamination is a damage that occurs in inter-laminar regions. This damage is a consequence of the compressive thrust force that the drill tip always exerts on the uncut laminate plies [19]. Figure 1 demonstrates these two types of delamination.

Figure 1:

Classification of delamination [4].

2.1.2.1 Modeling delamination

Cohesive behavior is used to simulate delamination. There are two types of cohesive behavior mostly used by researchers: element-based and surface-based behavior [20]. In this study, surface-based cohesive behavior is used. It is a simplified way to model cohesive connections with negligible small interface thicknesses using the traction separation model.

The formula and laws that govern the surface-based cohesive behavior are very similar to those used for cohesive elements with traction-separation behavior. The difference between the two is that, for cohesive surfaces, damage is specified as part of contact interaction property. Normal stress, σ_n, and shear stresses, σ_s (first shear direction) and σ_t (second shear direction), are defined for surface-based cohesive behavior using the following governing equation (5). The equation has been obtained from literature [5].

(5)σi={kiδiD<1kiδi(1−d)D≥1 i=n, s, t

where k=traction separation stiffness modulus, δ=separation for normal and shear directions, and D=damage variable.

2.1.2.2 Damage evolution

For surface-based cohesive behavior, damage evolution describes the degradation of the cohesive stiffness. In contrast, for element-based behavior, it describes the degradation of material stiffness. Once the damage criterion is satisfied, cohesive stiffness of the damaged element will degrade gradually based on a linear-softening law [21]. Same as cohesive element-based, surface-based damage evolution can be based on energy or separation [20]. The total fracture energy or the post damage-initiation effectiveness separation at failure can be specified. Figure 2 shows the energy-based damage evolution model.

Figure 2:

Energy based damage evolution [20]. t_n = normal contact stress in the pure normal mode, t_s = shear contact stress along the first shear direction, t_t = shear contact stress along the second shear direction, δ_n = separation in pure normal mode, δ_s = separation in the first shear direction, δ_t = separation in the second shear direction.

The criterion can be defined as a function of mode mix using either a tabular form or power law or Benzeggagh-Kenane (BK). In this study, BK was used and the formula is shown in equation (6):

(6)GIC+(GIIC−GIC)(GshearGT)η=GTC

where Gshear=GIC+GIICGT=GIC+Gshear,G_IC=normal fracture energy, G_IIC=first shear fracture energy, and G_IIIC=second shear fracture energy.

3 Finite element model

Boundary conditions

Same drilling parameters were subjected to the sequences studied so that the main purpose of this study could be achieved. A spindle speed of 2500 RPM and a feed rate of 0.12 mm/rev were used. All the faces of the CFRP/Al stack were fixed in Encastre conditions, and the tool, given angular and linear velocity in the Z direction. Figure 3 shows the assembly of the CFRP/Al stack, whereas Figure 4 shows the boundary conditions applied.

Figure 3:

Assembly of CFRP/Al stack.

Figure 4:

Boundary conditions.

4 Results and discussion

This chapter presents the results obtained from simulations. Various forms of results are available in Abaqus’ visualization module including stresses, energy, forces, intra-laminar damage, and inter-laminar damage. Intra-laminar damage results include Hashin’s fiber compression, fiber tension, matrix compression, and matrix tension. The inter-laminar damage (delamination), which was modeled using cohesive-based contact surfaces, is the main focus in this chapter. Through the “create display group” option available in Abaqus’ visualization module, we can study the result of each individual layer involved in the analysis.

Delamination mechanisms, as already mentioned, have been known to happen in two main ways: peel-up and push-down delamination. The former happens at drill entry, while the latter, at drill exit. We could capture each and every layer delamination result in this report, but the 24 layers in each sequence and the four sequences could mean a lot of space. Therefore, for each sequence, we will capture the first two layers (for peel-up delamination) and the last two layers (for push-down delamination).

The delamination area around the drilled hole provides an insight into the extent of damage in each layer. In this study, comparisons of delamination in each layer, therefore, have been done using the delamination area around the drilled hole. In order to distinguish the extent of damage in each sequence, delamination was quantified using the ratio between the maximum delaminated diameter and the nominal diameter of the hole as shown in equation (10). This is called delamination factor expressed as F_d. Figure 5 illustrates the nominal and maximum delaminated diameter used to calculate delamination factor. The values D_max and D₀ were obtained by exporting the drilled laminates from Abaqus/CAE to 3D modeling software CATIA and measuring the diameters. Figure 6 shows the graphical representation of the entry and interface delamination factors of the sequences studied.

Figure 5:

Delaminated and nominal diameter.

Figure 6:

Delamination factor.

Figures 7 and 8 show the delamination on the first two layers and the last two layers in each sequence studied. The sequence with all the laminates being 0° degree orientation distinguishes itself as the most affected by delamination. Display group manager available in Abaqus/CAE enables us to access the damage in each layer. From Figures 5 and 7 the sequence [−45°/90°₄/45°₂/−45°]_3s is seen to have the least delamination factor both at entry and interface. This shows a better resistance to this kind of damage than the rest of the sequences studied. It is also clear from the figures that delamination at exit is a slightly higher than at entry for all the sequences studied.

Figure 7:

Delamination on the first two layers.

Figure 8:

Delamination on the last two layers.

Figures 9 and 10 depict the thrust forces and torques, respectively, all at 2500 RPM and 0.12 mm/r. Reference point was created on the drill tool model to record the thrust forces during the simulation. Once the thrust forces were obtained courtesy of the reference point, these forces were multiplied with the radius of the drilling tool in order to get the torques. These are two important parameters in any drilling exercise. Researchers have shown a linear relationship between thrust force and delamination and therefore the need to capture this force in any delamination analysis work. The sequence [−45°/90°₄/45°₂/−45°]_3s records the lowest force (also has the least delamination) of the three sequences.

Figure 9:

Thrust forces.

Figure 10:

The torques.

5 Conclusions

Inter-laminar damage during drilling, well known as delamination in composites damage, has been studied in this paper. It is considered as one of the most critical mode of failures in CFRP. This paper has explored the effects of different fiber orientations in the composite and different stacking sequences in the drilling induced delamination. A 3D finite element model of drilling considering both intra-laminar and inter-laminar damages was developed using Abaqus/CAE. Intra-laminar damage was modeled using the Hashin damage criterion available in Abaqus, while inter-laminar damage was modeled using a contact property, cohesive-based contact surfaces. The following conclusions have been deducted from this study:

1. In order to capture peel-up and push-down delamination, otherwise known as entry and exit delamination, the results of the first two layers and the last two layers at CFRP/Al interface have been presented. Figures 7 and 8 show the delamination of the said layers at entry and interface, respectively. Of the three sequences considered, the finite element model predicted that the [0]₂₄ is most vulnerable to delamination. The sequence [−45/90₄/45₂/−45]_6s is found to better resist this kind of damage. In all cases, the exit delamination (CFRP/Al) interface is found to be more than at the entry. The entry and exit delamination factors have been compared clearly in Figure 6. Considering the delamination factors for the current study, we can confidently conclude that the best stacking sequence for better resistance is [−45/90₄/45₂/−45]_3s.

2. Although delamination has been the major focus of this paper, thrust forces have also been captured. A reference point created on the tool was made to record forces involved in drilling. Various researchers have reported direct linear relationships between thrust force and delamination. This has been proven in Figures 9 where thrust force for each sequence is recorded. The sequence with the least delamination is seen to have the least forces as well. From the thrust forces recorded in simulations, the torques have been calculated and presented in Figure 10.

3. Delamination resistance of the [−45°/90°₄/45°₂/−45°]_3s sequence can be attributed to the various fiber directions; hence, balanced shear strength contrary to [0]₂₄ has all the fibers in one direction, making it susceptible to damage by delamination.

This study focused only on the inter-laminar damage. All the damages should be accessed to confidently conclude the best sequence to use in manufacturing parts. The fiber orientations considered in this study were limited to 0, 90, 45, and −45. Future studies should consider other angles like 15, 30, or 60, as they may show better results.