Influence of skin wrinkles and resin insertions in maximum stress of transitions of pure bending sandwich beams

1 Introduction

Sandwich beams are made up of unidirectional glass-fiber-reinforced polymer (GFRP) or carbon-fiber-reinforced polymer (CFRP) skins and low-density foam cores, thereby offering high mechanical properties/weight ratio under pure bending loads. This type of structure is also appropriate in order to achieve large deflections.

There are many types of manufacturing defects such as delamination within the skins, porosity, or interfacial cracks between the skin and the core. These defects can generate a stress concentration that reduces the maximum change of curvature and the stress level that the beam is able to reach. The crack of the structure depends on the size and the locations of the defect. There are specific locations sensitive to their presence. This study analyzes two specific types of defects – skin wrinkles and resin insertions.

Resin insertions can be caused by resin-starved areas or resin-remaining areas. It can be caused due to poor resin application, inadequate wetting out of fibers/fiber preforms, or poor resin flow (incorrect cure process). This study analyzes the resin-remaining areas or resin insert in the interlaminal sandwich panel.

Fiber wrinkling or kinking or in general a defect can be formed when producing pre-forms, that is, tight radii corners, inability of the material to drape. This type of defect caused by a material arises during the manufacture of laminate composites. It can be caused by an excess of reinforcement in one or more plies. It is actually very common in CFRP ship production. Typical characterization of a wrinkle is evident on its width and height. Some other authors [1] also defined other parameters to explain the wrinkle geometry as different plies angle and radius.

The classic analyses of these types of defects result in establishing a strength reduction factor which is defined as the ratio of the strength of a structural element with and without the defect [2]. Hayman [1] established this factor for sandwich beams and beams having wrinkle defects with a range of geometries. It was tested with sandwich beams in four-point bending and sandwich beams with in-plane compression.

Just-Agosto [3] considered two vibration (mode shape curvature and damping matrix identification) and two transient temperature response techniques to analyze minor impacts, perforations, and deboning damage in sandwich composites. According to Just-Agosto, a strategic combination of both the techniques is the best approach to detect the damage.

Theotokoglou [4] studied the initiation and propagation of a fatigue crack in the foam core of a sandwich composite under flexural loading. A static two-dimension finite element analysis (FEA) has been used to evaluate stress intensity factors and crack behavior. Quintana-Alonso [5] explored the fracture of a sandwich panel with an elastic-brittle square lattice core with finite elements simulations and analytical models. The author assumed that the sandwich fails when the local stress in the skin attains the solid strength or when the local buckling occurs. So failure maps were constructed for a cracked sandwich panel.

Skin-core interlaminate gap is the other typical sandwich composite manufacturing defect that had been analyzed by several authors. Thomson [6] investigated the effects of interfacial crack size and impact damage size on the shear properties and failure mechanisms in a GRP skin and polyvinyl chloride (PVC) foam core sandwich composite. Mouritz [7] studied the mechanical properties of a GFRP-PVC sandwich composite which contains interfacial cracks and compared them when loaded in an edgewise compression, flexure, or shear. The properties reduced with the increasing interfacial crack but only when the defect causes a change in the failure mode which is dependent on the load state. The properties are also dependent on the severity of the impact damage, with the low-energy damage to the skin having a smaller effect on stiffness and strength than the high-energy impact that damage both the skin and the foam core. As a result, the author says that the strength (but not the stiffness) decreases rapidly with increasing crack length above 30 mm. However, the properties are not affected under flexural loading because the failure mechanism remains unchanged.

Russo [8] studied sandwich structures with PVC and polyester foam cores. The work showed that there is a skin-core delamination in the PVC foam core, whereas the failure in the polyester composites is basically a shear cohesive failure.

Other authors like Leong et al. [9] analyzed specific applications such as sandwich structures used for wind turbine blades with sheet wrinkle defects. They have developed failure criteria which are applied to predict failure initiation with a good correlation with experimental observations.

2 Design of sandwich beam: no defects model

Sandwich beams with unidirectional GFRP skins and low-density foam core can be used when large deflections and changes of curvature are required. These types of structures can be modeled as pure bending beams [10]. The base beam with no defects was designed using the materials shown in Table 1. The GFRP in this case consists of fiberglass VS2 and epoxy resin Gairesa 14 (University in Madrid, Spain). Fiber volume content of the skins is theoretically defined to be 40%.

The cross section of the sandwich is appropriate for the central section of the beam, which is subjected to pure bending loads, but not for its ends. Pure bending is achieved by the introduction of a bending moment at both the ends of the beam, therefore, shear and other loads, different from those induced by pure bending, could appear in this zone of the beam. Due to these reasons, the design of the ends is a monolithic zone made up with the same material as that of the skins. It is also necessary to design a transition zone between the sandwich cross section and the monolithic part in order to guarantee the appropriate adhesion and to avoid high changes in the bending stiffness.

To simplify the model and to reduce the computer process time, the thickness of the central beam and the monolithic end are kept the same. So the beam thickness is constant all along its length.

The main dimensions of the base beam are as follows: traction skin thickness 1.5 mm, compression skin thickness 1.5 mm, foam thickness 27 mm, central beam length 200 mm, monolithic section thickness 30 mm, and monolithic section length 100 mm. The transition between the central and the monolithic section is a central chamfer of a 20° angle and 70 mm length. This specific chamfer has been designed to avoid abrupt changes in the stiffness [11].

The FEA simulations have been made using the Abaqus computer-aided engineering (CAE) program (Figure 1). The model developed consists of a cantilever beam with a bending moment applied on the free side. However, the experimental set up consists of a beam with the bending moments applied at both the ends by a test rig specially designed to introduce pure bending loads in the test samples [12]. The FEA model is equivalent to the experimental test because beam length in the FEA model is half of the beam length in the experimental test [13]; beam thickness and height are the same in both the cases. Although a two-dimensional model could be used, as this work deals with pure bending loads (only stresses in the XY plane), building a three-dimensional model needs approximately the same time and it could alert us of the appearance of any stress in the Z direction due to the defects in the model.

Figure 1

FEA detail of Abaqus CAE simulation.

The pure bending loads can cause large deflections in the beam. The FEA option “Nlgeom” is used to account for geometric nonlinearity. The model developed distinguishes between traction and compression skins and monolithic ends (GFRP) and the core (foam). GFRP parts are considered as laminated composite plates and foam as a homogeneous element. Each of them has been meshed independently and constrains have been defined among them. The element type used for both, skins and core, is a solid element; its size has been chosen in order to prevent differences >0.5% between FEA simulations and experimental results. The elements of the mesh in the transition zone between the foam core and the GFRP monolithic end are smaller than the other areas of the beam in order to provide a better accuracy. To simplify the model, a frictional and softened contact has been defined in the skin-foam interface instead of modeling the adhesive between these two parts.

As stated previously, this work analyzes three types of defects (Figure 2):

Figure 2

Model of cantilever beam with a bending moment in the free side and also with different types of manufacturing defects analyzed.

1. Wrinkle in traction or compression skin. It is characterized by its position to monolithic end and its height.

2. Resin insert in traction or compression skin. It is characterized by its position and its height.

3. Foam defect that can be defined as a defect in the foam geometry that can generate a resin insert. It is characterized by its length.

A special element has not been developed for the mesh at the defects area. However, the element size is smaller in the defect area than in the rest of the beam.

3 Analysis of the influence of a wrinkle defect in maximum stress

A wrinkle is a typical defect caused during the manufacturing procedure. The wrinkle can be found in traction or in compression skin. The FEA model analyzes the interference between the skin (traction or compression depending on the study case) and the monolithic end.

3.1 Wrinkle in traction skin

A wrinkle in traction GFRP skin was the first case to be studied. This defect is located in the traction skin close to the transition zone. The FEA simulations show that the maximum stress in the skin appears on the edge of the transition region, close to the beginning of the chamfer of the core (see red region in Figure 3B). Figure 3A shows how this maximum axial stress varies with the height of the defect and the distance between the wrinkle and the end of the monolithic section. The increase in the defect height implies a reduction of the maximum axial stress. It can also be observed that there is no significant influence of the wrinkle-monolithic end distance in the maximum stress. The mesh size in the defect is smaller than in the rest of the beam (8 vs. 2 mm in its principal dimension; Figure 3B) in order to obtain better accuracy in the results.

Figure 3

(A) Influence of wrinkle in traction skin dimensions in maximum axial stress. (B) Detail of defect and beam mesh.

3.2 Wrinkle in compression skin

The second case studied is a wrinkle in compression GFRP skin. The position of the defect is symmetric with respect to the one analyzed in the traction skin. Only the behavior of a 2 mm height wrinkle is studied. An increase in maximum axial stress (in absolute value) is observed when the distance between the wrinkle and the beam end is higher than 165 mm (as stated in Figure 4).

Figure 4

Influence of distance wrinkle-monolithic section end in maximum stress.

Figure 5 shows the influence of the defect length in maximum stress in a defect of 1 mm of height and 5 mm of thickness. The maximum stress grows up with the increase of defect length. Between 5 and 20 mm, the maximum stress increases. For a length higher than 25 mm, the maximum stress is constant. The average stress with a defect height of 0.5 mm is 423 MPa and for a defect of 1.5 mm, it is 408 MPa. Figure 5 shows the influence of wrinkle-monolithic zone distance. For a distance <170 mm, it is mainly constant; 380 MPa for a defect height of 1.5 mm and 360 MPa for a defect height of 2 mm.

Figure 5

Influence of wrinkle dimensions in maximum stress in compression skin.

The position of the defect should be <165 mm to avoid a high increase in the maximum stress. However, this effect is higher when the defect is in the compression than in the traction skin. A similar study can be done when the position of the defect is in the central sandwich zone or in the transition zone.

As stated in Figure 5, there is no significant variation of the maximum stress calculated with the FEA model. The theoretical maximum axial stress in the skins is 380 MPa (traction) and -360 MPa (compression). Therefore, there is no significant influence of the distance of the defect in the maximum stress in the sandwich zone. These values correspond to the expected ones caused by pure bending loads.

4 Analysis of the influence of an epoxy resin insert in maximum stress

The other type of defect is a concentration of epoxy resin in the sandwich beam. Epoxy insert can be found both in the core and the skin, and in the interface between them.

4.1 Foam defect

Most of the epoxy resin inserts in the core are located at its end side, just in the chamfer made for the transition zone of the beam transition between the central and the monolithic section. Correct geometry of the chamfer is achieved by milling the foam. A defect in the geometry of the chamfer could lead to the appearance of a gap between the foam and the monolithic part which will be filled by epoxy resin all along the injection process. The insert of resin may cause the loss of maximum stress in this zone of the beam and the appearance of stress concentrators.

Figure 6A shows the FEA model and the influence of this type of defect among foam, skins, and the monolithic zone. Figure 6B shows the foam mesh with minor elements size in detail.

Figure 6

FEA of beam and foam with a manufacturing defect. The foam defect has a minor element size.

The defect does not have any influence on the maximum stress in the skin close to the transition zone and the monolithic zone. The stress in the resin insertion depends on its dimensions. As it can be seen in Figure 7, the maximum stress is achieved with a defect thickness of 3 mm and a height of 1 mm.

Figure 7

Influence of defect dimension on maximum stress (in absolute value).

The maximum axial stress in the resin insert could reach values from 7 to 12 MPa, very far from the ultimate axial stress of this resin epoxy (63 MPa); this, combined with the fact that the axial and transversal stresses are very close to zero implies that this type of defect does not have any influence in the range of use of this kind of sandwich beam. However, it is important to remember (as stated in Table 1) that the ultimate stress of the foam has a low value (6.8 MPa). Therefore, it is important to avoid the appearance of this type of defect in order to avoid the appearance of concentrators that can cause a crack in the foam.

4.2 Epoxy resin insert in the interface between foam monolithic ends in the transition zone of the beam

Figure 8A and B shows the FEA model of epoxy resin in the interface foam-monolithic zone. The element mesh size of the epoxy resin insert is also smaller (2 mm) than the other zones of the sandwich beam.

Figure 8

FEA of sandwich beam with resin epoxy in the foam-skin interface.

In this case, the maximum axial stress in the defect can be characterized by the distance from the resin insert to the end of chamber of the foam, or the size of the insert (Figure 9). Figure 9 shows the influence of the defect position (A) and defect height (B) in maximum end stress. An increase in maximum axial stress can be observed for distance values from 10 to 15 mm. There is a stress increase when the increment of the defect size.

Figure 9

Influence of defect position and dimensions in maximum end stress.

The ultimate stress of epoxy resin is 63 MPa. As shown in Figure 9, the resin insert in the monolithic zone-foam interface will be always subjected to higher values of axial stress. So there can be a crack in the epoxy resin insert which could affect foam and skins of the beam, inducing the failure of the structure.

4.3 Epoxy resin insert in the interface between foam core and traction or compression skin

Figure 10 shows the influence of the distance between the defect and the end of the sandwich beam in the maximum axial stress for a defect with a principal dimension of 10 mm. It can be observed that this type of defect does not cause large variations in the maximum axial stress of the skins.

Figure 10

Influence of distance defect – end beam in maximum stress.

Figure 11A and B analyzes the influence of defect size (thickness and height). In Figure 11B, the defect has a thickness of 10 mm, whereas in Figure 11A the defect height is 1 mm. Although there is a higher stress increase with defect thickness than with distance defect – beam end. However, the influence of the height defect is much higher, not in the compression skin (where the stress level is approximately constant), but in the traction skin. It can be observed how the maximum axial stress could reach 1000 MPa for a defect height of 2 mm. Therefore, although the variation of the distance to the end and the beam or the thickness do not have any influence on the axial stress level of the skins, an excessive height of the insertion could cause the failure of the structure.

Figure 11

Influence of defect height and thickness in maximum.

As stated in Figure 5, there is no significant variation of the maximum stress calculated by the FEA model. The theoretical maximum axial stress in the skins is 380 MPa (traction) and -360 MPa (compression). So, there is no significant influence of the distance of the defect in the maximum stress in the sandwich zone. These values correspond to the expected ones caused by pure bending loads.

5 Experimental validation

Experimental test has been made in order to verify the FEA simulation model. Long-established three- or four-point bending tests have some disadvantages for large deflection and curvature beams [13]. It is especially difficult with the sandwich beam because three- or four-point bending tests can produce a beam crack. For this reason, a pure bending test system, based on the Hill mechanism [14], has been developed to test beam samples with different kinds of defects [15]. Figure 12 shows the complete system.

Figure 12

Top view of the test ring [12].

The fabrication of the test samples was done using vacuum resin injection techniques. However, prior to that, the unidirectional glass fiber fabrics were carefully cut into the different lengths required to manufacture the sample with special attention paid to the layers that form the monolithic ends. The ends of the foam were machined so they would adapt to the specific geometry of the transition zone. A series of channels and holes were also made in the foam to help the resin run once the injection process had begun. When this process was completed, the GFRP fabrics and the foam were positioned to obtain the right shape for the sample. The vacuum bag was then prepared and the resin injection was started. Due to the presence of monolithic zones with a large accumulation of fiber, a low-viscosity resin was used that would facilitate all the layers being impregnated. Finally, while the vacuum pressure was maintained, the resin curing process was carried out by air dryers for 7 h at a temperature close to 60°C.

Although specific tests have not been done to check the influence of different kinds of defect in the maximum stress of the beam when it is subjected to pure bending loads, validation tests of the central zone of the beam (sandwich zone) [16, 17] have been done. One of the test samples had a wrinkle in the compression skin and also an epoxy resin insert in the interface between the compression skin and the foam (Figure 13). As it has been stated previously, the latter type of defect could cause the crack of the beam at its end side (Figure 11).

Figure 13

Crack in the foam and in compression skin and gap in the foam.

The resin insert has been measured, and its main dimension was 2 mm, and it was situated 280 mm from the end beam. So the maximum axial stress reached in the compression skin close to the transition zone should generate the beam failure. Two gauges had been installed in the traction and compression skin for the test (Figure 14). During the test, the failure in that zone was validated and the stress was 391 MPa in the traction skin and 358.2 MPa in the compression skin before the failure, as it was predicted by the FEA model (with an error of 8.39%). Another gauge was installed at the end of the beam in axial position close to the defect; however, no reliable measure was made by this gauge due to the technical failure of the acquisition system.

Figure 14

Gauge installed in the sandwich test beam.

So in conclusion, the FEA model is able to predict the failures caused by defects at the end of the beam but further investigations and more experimental tests must be done in order to completely validate the model.

6 Conclusions

The defects at the end of the sandwich beams with unidirectional GFRP skins and low-density foam core with pure bending loads and its influence in maximum stress are analyzed in this paper. Three different types of defects are analyzed: wrinkle in the skin, epoxy resin insertions in the skin, and foam defect. An FEM model has been developed using Abaqus software for composites materials. Only resin insert has a significant influence in the maximum stress at the end of the beam and is able to induce the beam crack. This has been proved by experimental tests. Further, experimental tests had to be conducted in order to completely validate the model and study the influence of different type of defects.