Key Engineering Materials Vol. 383 (2008) pp 35-52 online at http://www.scientific.net © (2008) Trans Tech Publications, Switzerland
Influence of Porosity on the Interlaminar Shear Strength of Fibre-Metal Laminates
Cláudio S. Lopes 1, a , Joris J.C. Remmers 2,b and Zafer Gürdal 1,c 1Faculty of Aerospace Engineering, Delft University of Technology, PO Box 5058, 2600 GB, Delft, The Netherlands 2Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands [email protected], [email protected], [email protected]
Keywords: Delaminations, Cohesive Elements, Fibre-Metal Laminates, Glare, Porosity, Fracture Toughness.
Abstract. Structures manufactured in fibre metal laminates (e.g. Glare) have been designed considering ideal mechanical properties determined by the Classical Lamination Theory. This means that among other assumptions, perfect bonding conditions between layers are assumed. However, more than often, perfect interfaces are not achieved or their quality is not guaranteed. When in laboratory, high quality fibre metal laminates are easily fabricated, but in the production line the complicated manufacturing process becomes difficult to control and the outcome products may not meet the quality expected. One of the consequences may be the poor adhesion of metal prepreg or prepreg prepreg as the result of porosity.
The interlaminar shear strength of fibre metal laminates decreases considerably, due to porosity, as the result of insufficient adhesion between layers. Small voids or delaminations lead to stress concentrations at the interfaces which may trigger delamination propagation at the aluminium prepreg and prepreg prepreg interfaces at load levels significantly lower than what is achievable for perfectly bonded interfaces. Mechanical experiments show a maximum drop of 30% on the interlaminar shear strength.
In the present work, the effects of manufacturing induced porosity on the interlaminar shear strength of fibre metal laminates are studied using a numerical approach. The individual layers are modelled by continuum elements, whereas the interfaces are modelled by cohesive elements which are equipped with a decohesion law to simulate debonding. Porosity is included in the geometry of the interface by setting some of these elements to a pre delaminated state.
Introduction Porosity is one of the most common manufacturing induced defects in composite laminates. Small porosities are formed due to the entrapment of air in the matrix due to the moisture absorbed during material storing, processing and application. Larger, elongated voids are formed at the ply interfaces due to inadequate curing cycles [1]. Moreover, in service conditions may contribute to the growth of these defects. Porosity has a detrimental effect on the loading response of laminates especially on the interlaminar shear strength (ILSS), compressive strength and bending strength that are associated with matrix dominated mechanical properties [2,3]. Since the larger voids are located at the ply interfaces, the larger influence is expected on the ILSS of laminates. The production of Fibre Metal Laminates (FML’s) follows methods similar to the ones employed in the production of traditional composite laminates. Hence, porosity is an issue with FML’s as well
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 132.229.212.106-23/05/08,16:47:04) 36 Progress in Fracture and Damage Mechanics
(Figure 1). Its effect on the ILSS of FML’s could be ascertained by carrying out mechanical tests and employing analytical methods. In the past, Gürdal et al. [4,5] studied the interlaminar tensile and bending strengths of AS4/3501 6 graphite/epoxy laminates by conducting an extensive experimental programme which included the characterization of the pores in terms of pore volume fraction, geometry, size and orientation. The porosity data were then used in an empirical model to predict the laminate strength as a function of porosity. Jeong [2] and Costa et al. [3] investigated the influence of porosity on the ILSS of graphite/epoxy systems by means of experimental and analytical approaches. In both works, a shear fracture criterion was used successfully to correlate the fracture strength of porous laminates. Although possible, it is difficult to exactly control the amount and configuration of porosity at the interfaces of the test specimens [4,5]. An in depth experimental investigation of the effects of porosity in multiple interfaces of FML’s is out of the scope of this programme. By relying on a few experimental data and observations, the influence of various degrees of interfacial porosity is studied by means of numerical methods developed in the framework of Damage and Fracture Mechanics and implemented in the Finite Element Method (FEM) package ABAQUS ® [6]. Nowadays, finite element (FE) analysis represents a relatively fast and inexpensive tool in the analysis of structurally loaded components. Over the past recent years a great effort has been made to implement fracture mechanics phenomena in the simulation of delamination growth in laminated materials on a mesoscopic level of observation [7 10]. This effort has led to the development of reliable numerical tools capable of dealing with delamination onset and propagation under a large variety of loading modes. In the present work these advanced tools are used to study the structural effects of interface porosity by actually including voids in the geometry of the interface. As opposed to the use of adhesion degradation parameters at a material level, this approach leads to the correct prediction of the location of delamination onset and a correct prediction of the ILSS.
Figure 1. SEM pictures of Glare. Left: specimen with no porosity. Right: Specimen with porosity due to inadequate curing cycle. Delamination growth in the different prepreg prepreg and aluminium prepreg interfaces is simulated by cohesive elements [8 10]. These are a numerical implementation of the cohesive zone approach [7] in which the energy involved in the delamination process is being dissipated in a small "process region" ahead of the crack tip. The opening of the cohesive zone is governed by a mixed mode delamination model [8 10], which accounts for both mode I (normal) and mode II (shear) delaminations and combinations thereof. The simulation of the ILSS test is exemplified by modelling a specimen of Glare 3 4/3 0.4 with and without porosities included. Porosity is modelled by pre delaminating a number of interface elements. Information about the size, position and distribution of porosities at the interfaces of an Key Engineering Materials Vol. 383 37
ILSS specimen was roughly obtained from a number of SEM pictures taken from actual test specimens (Figure 1).
Parameter Identification Besides the well known elastic and plastic properties of aluminium 2024 T3 and glass fibre prepregs, additional mechanical properties are needed to characterise the delamination process. These are the fracture toughness ( Gc) and ultimate tractions ( τu) of each interface at all possible loading modes. Specific standard tests were devised and are available in the literature to measure these properties for full composite laminates, namely de Double Cantilever Beam (DCB) test for mode I, the End Notch Flexure (ENF) test for mode II and the Mixed Mode Bending (MMB) test for mixed mode delamination propagation [12]. After a few adaptations, these fracture energy tests were conducted for FML’s as well [11]. The parameters of the constitutive model obtained from the experiments are checked against analytical calculations [13] and numerical simulations. In this way, trustable numerical tools and mechanical material properties are used to model the ILSS experiment. The most important value in the characterisation of delamination is the fracture toughness, due to its global influence in the fracture behaviour. The ultimate traction values have a minor influence in the delamination process (especially in mode I), since they influence only the delamination initiation load displacement point. Due to the difficulty in obtaining accurate measurements, approximate values of τu are taken ( τIu =75MPa and τIIu =90MPa), tuned in such a way to produce the best match between experiments, analytical and numerical calculations. In order to measure the mode I fracture energy of the interface, a DCB test procedure was followed [11]. As sketched in Figure 2, it consists of pulling the two tips of a 250x25x9.5mm pre cracked strip of laminate. This causes the crack to propagate. The specimen is previously cracked at a given interface in order to avoid the very high load peak, which otherwise would be necessary to initiate delamination. The high energy dissipation at delamination initiation would hinder the accurate evaluation of the fracture energy. The averaged fracture toughness is the energy dissipated per unit area of the new crack. This energy corresponds to the area underneath the traction displacement jump curve. In full composite specimens, virtually all the energy transferred is stored in elastic bending or delamination propagation. This is not the case with FML's, which can sustain plastic deformation in the metal layers. In such a case it would be very difficult to quantify the amount of energy actually spent on the fracture process. In order to maintain the whole specimen in the elastic regime, two 4mm thick plates of aluminium 7075 T6 were bonded to the Glare 3 2/1 0.4 strip.
Al 7075 T6
Pre Glare 3 2/1 0.4 crack Al 7075 T6
250mm Figure 2. Illustration of a DCB test. For this configuration a 50mm long pre crack is included at the prepreg prepreg interface. The mode II fracture energy was measured with the ENF test [11]. A similar, initially cracked specimen is used but now subjected to a 3 point bending load case where the loading point is 38 Progress in Fracture and Damage Mechanics located at 80mm of each support. In this case the delamination is not progressive, but rather catastrophic, i.e. once the delamination is started, the crack rapidly grows to the centre of the specimen. Such event produces a sudden decrease in bending stiffness, which results in a remarkable load drop. This makes the measurement of GIIc more delicate than GIc .
Figure 3. MMB test apparatus (after [10]). Mode I and mode II delaminations are particular examples of the wide range of loading situations a structural component may undergo from which mixed mode loading is the most common. Most real life delaminations initiate and propagate under the influence of combined normal and shear stresses. The mixed mode fracture propagation was investigated by means of the MMB test illustrated in Figure 3 [11]. Here the specimen is loaded by a combination of normal and shear forces, producing a specified ratio between the energies dissipated in mode I and mode II delamination, respectively. For the sake of brevity, only an even combination (50/50 ratio) of modes was considered in these experiments. This means that 50% of energy is consumed in mode I delamination and 50% in mode II delamination. The fracture toughness values measured for the three types of interfaces of Glare 3 2/1 0.4 are reported in Table 1. G G G Interface Ic IIc I/IIc [J/m 2] [J/m 2] [J/m 2]
Al L direction/fibres 0 ° 2960.8 1705.8 757.2 Fibre 90 °/fibres 0 ° 3545.5 1349.4 672.7 Al L direction/fibres 90 ° 3411.9 1623.1 622.7 Table 1. Mode I, mode II and mixed mode fracture energy values measured for the three types of interfaces in Glare 3 2/1 0.4 (after [11]). The fracture toughness values reported in Table 1 for the several interfaces of Glare 3 2/1 0.4 are somewhat different from what was expected. In general, for carbon fibre reinforced laminates, G Ic is lower than G IIc and the mixed mode fracture values fall in between these. Glare 3 shows lower fracture toughness values for mode II loading than for mode I and the values corresponding to mixed mode loading are even lower. This is counterintuitive since, when loaded under mixed mode, the energy dissipated by a crack corresponds to a specified ratio between the energies dissipated in mode I and mode II loading. Korjakins [14] found that for glass fibre reinforced plies, as the ones used in Glare 3, the results of the DCB test are highly dependent on the fibre surface treatment. If no surface treatment is applied to the fibres, the crack propagation is accompanied by extensive fibre bridging. This phenomenon opposes the crack propagation, hence “artificially” increasing the values of G Ic . On the other hand, the catastrophic failure of the ENF and MMB tests does not allow for stable crack propagation. The Four Point Bending experiment, described in [15], is an alternative test that Key Engineering Materials Vol. 383 39 allows the stable delamination propagation of mode II and mixed mode cracks and consequently the measurement of GIc and GI/IIc with higher accuracy. Nevertheless, the values reported in Table 1 are the ones used for the purpose of the present investigation.
Analytical and Numerical Analyses The experiments are simulated using two dimensional FEA models where the individual layers are modelled with standard geometrically nonlinear continuum elements. These elements can behave according to a plastic plane strain constitutive relation. Due to their geometrical simplicity, it is also possible to simulate the fracture energy tests analytically by using Beam Theory and Fracture Mechanics Theory [13]. In the FE models, the bond between each two layers is simulated by means of a cohesive zone [7]. In this approach, the fracture behaviour (delamination) is lumped into a single plane, which is represented by interface elements placed between two layers. These interface elements consist of two surfaces, which are attached to the adjacent continuum elements modelling the layers (Figure 4). The relative displacement of the two surfaces is a measure for the opening of the delamination crack. The opening is controlled by means of a cohesive constitutive relation that completely characterises the delamination process [8 10].
Figure 4. Illustration of the FE simulation of delamination in a multiply material. The individual layers of the specimen in the top left picture are modelled by continuum elements and the adhesive that bonds the layers is modelled by interface elements (the right hand side pictures). The relative displacement of the interface elements (bottom left) is a measure for the opening of the interface. As suggested by Camanho et al. [8 10], a bi linear cohesive relation is used here (Figure 5). This model is based on the input of four material parameters: mode I and mode II fracture toughness values ( GIc and GIIc ) and the corresponding ultimate traction values ( τIu and τIIu ) at which debonding is initiated. A fifth parameter, η, is necessary to completely define the mixed mode propagation criterion as function of GIc and GIIc only. This value must be extracted from the correlation of the test data for delamination in mode I, mode II and mixed mode loading. When loading an interface, the cohesive elements initially behave in a linear elastic way (point 1 in Figure 5). When the equivalent traction exceeds a limit value, based on the pure mode I and II ultimate tractions τIu /τIIu (Point 2 in Figure 5), damage is initiated. If the displacements are further increased, the stiffness is gradually reduced to zero and the delamination starts to propagate. A cohesive element becomes fully delaminated when it is unable to transfer any further load (points 4 and 5 in Figure 5). However, it is necessary to avoid interpenetration of the crack faces. The problem is addressed by reapplying the normal penalty stiffness when interpenetration is detected. 40 Progress in Fracture and Damage Mechanics
Figure 5. Pure mode constitutive equations: (a) Mode II The shear traction as a function of the shear opening for a zero normal opening. (b) Mode I Normal traction across the interface as a function of the normal displacement when the shear displacement is assumed to be zero (after [8]). Note that there is no softening in the case of a negative normal opening. This resembles self contact of two layers. The surface under the curves is the fracture toughness of the material.
DCB, ENF and MMB Test Simulations The DCB, ENF and MMB tests are simulated in the commercial FE code ABAQUS ® [6] by means of two dimensional, plane strain models. The aluminium and prepreg solid parts are modelled with 4 node solid elements. The interface is modelled by user developed cohesive elements [9,10]. The solid elements behave according to a linear elastic constitutive law. As explained previously, plastic behaviour was prevented by bonding two thick plates of strong aluminium to each side of the Glare 3 2/1 0.4 laminate specimen (Figure 2). For both aluminium alloys (Al 2024 T3 from the Glare laminate and Al 7075 T6 from the bonded plates) equal isotropic properties are defined, with properties: E=73GPa and ν=0.33. The orthotropic properties of the glass fibre prepreg were taken from [16] and are reported in Table 2.
E11 [MPa] 55000 ννν12 0.195 G12 [MPa] 5500 E22 [MPa] 9500 ννν13 0.195 G13 [MPa] 5500 E33 [MPa] 9500 ννν23 0.06 G23 [MPa] 3000 Table 2. Glass fibre prepreg properties (after [16]) In the DCB FE model, a minimum of two elements are required in thickness direction of the aluminium layers in order to avoid the phenomenon of shear locking. Alternatively, incompatible mode elements may be used but these require more computational resources than standard elements. In the longitudinal direction, the required number of elements is function of the length of the cohesive zone [17] defined by:
Gc lcz = E 2 . (1) τ u
In Equation 1, E is the Young's modulus, Gc is the fracture toughness and τu is the ultimate traction. When the cohesive zone is discretised by a coarse mesh, the fracture energy is not accurately represented and the model does not capture the continuum field of a cohesive crack. Experience shows that three elements along the cohesive zone are sufficient to predict the propagation of delamination in Mode I. This means that in the present case the length of the length of the interface elements should not exceed 0.5mm. In Mode II, a coarser mesh may be used. Key Engineering Materials Vol. 383 41
(a) Delamination initiation
(b) End of test simulation Figure 6. Illustration of the DCB test simulation. A pre crack exists between the 0◦ and the 90 ◦ prepreg layers. The crack propagates not only through the pre cracked interface but it "jumps" to the aluminium 0◦ prepreg interface. Two deformation plots for the DCB test simulations are shown in Figure 6. These correspond to two different loading stages: (a) delamination initiation and (b) the end of crack propagation. A displacement of 35mm is applied to the top adherent tip while maintaining the lower adherent tip constrained in the X and Y directions. The model includes a pre crack of 45mm in length between the 0◦ and the 90 ◦ prepreg layers. This crack starts to propagate when the tip displacement is about 5mm long (Figure 6(a)). At a certain load level, the interface between the top aluminium layer and the 0◦ prepreg layer starts to debond as well (Figure 6(b)). Although fibre bridging was observed during the experiments, this crack "jump" was not noticed. The computed longitudinal stress values in the 0 ◦ prepreg layer are in excess of 1200MPa. It is possible that this ply could fail at lower stress values, however the numerical models did not take into account intraply failure phenomenon such as fibre failure. The experimental and numerical results for tests with pre cracks at different interfaces show similar behaviour to the simulations described above. The crack initiation starts approximately at a load of 300N. Once the delamination starts to propagate, the load sustained by the specimen starts to decrease gradually. Both experiments and simulations were stopped at a prescribed tip displacement of 35mm, corresponding to a crack propagation of about 100mm. The load displacement behaviour for the DCB test is shown in Figure 7(a). The crack "jumping" phenomenon and the delamination at two interfaces justify the unstable crack propagation. The maximum computed load is around 690N, 25% higher than the 550N achieved in testing. A better agreement with the experiments is obtained if the crack is not allowed to "jump", i.e. only the pre cracked interface delaminates. This can be achieved by slightly reducing the mode I ultimate traction value of such interface. The result is not only a better match with the experimental load displacement curves but also a more accurate prediction of the maximum load: 614N; only 11% higher than the value obtained experimentally. It should be realised that perfect interfaces are being simulated while in laboratory these are virtually impossible to produce, i.e. there is always some degree imperfection that degrades the adhesive properties. Despite porosity being globally reflected in the experimental measurement of the fracture toughness, its local influence on the delamination initiation is unknown. Due to the occurrence of fibre bridging, a higher GIc than the real value may have been reported as well, as explained before. In such case, more energy is necessary to propagate the crack by the same length. 42 Progress in Fracture and Damage Mechanics
800 4000 1200 Numerical, del. 1 interface Numerical Results Numerical Results Fracture Mechanics Curve Fracture Mechanics Curve Fracture Mechanics Curve Beam Theory Curve Beam Theory Curve 1000 Experimental Results Beam Theory Curve 600 Numerical, del. 2 interfaces 3000 Experimental Results Experimental Results 800
400 2000 600 Load [N] Load [N] Load [N] 400 200 1000 200
0 0 0 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 0 2 4 6 8 Displacement [mm] Displacement [mm] Load Point Displacement [mm] (a) DCB (b) ENF (c) MMB Figure 7. Load displacement curve for the DCB, ENF and MMB tests simulations. Delamination onset is predicted by the analytical models at the point of intersection between the Beam Theory curve and the Fracture Mechanics curve [13]. Beam Theory predicts stiffer specimen behaviour as compared to experimental results and numerical calculations. For the sake of simplification, it is assumed that the pre cracked part of the DCB deflects as a beam built in at one of its tips (corresponding to the crack tip). This constitutes an over constraint because, in reality the pre cracked part of the DCB is continuum with the bonded part, i.e. it has a finite stiffness at the crack tip. The Fracture Mechanics Theory curve exactly matches the delamination propagation curve predicted by the FE simulation. However, because of the over stiff linear part, delamination onset is predicted at a higher load than experimented. Figure 7(b) depicts, as an example, the experimental, analytical and numerical load displacement plots for mode II delamination propagation between the aluminium and the 90 ◦ prepreg layers in Glare 3 2/1 0.4. The unstable and catastrophic nature of the crack propagation is correctly captured by the analytical 1 and numerical simulations, at very similar load and displacement values. The numerical model does not use the mixed mode delamination energy in a direct form but rather by means of a function which interpolates the fracture toughness values for mode I ( GI), mode II ( GII ) and mixed mode loading (GII /G T): η GII GGGIC+() IIC − IC , GGG T = I + II (2) GT In this function, proposed by Benzeggagh and Kenane [12], η should be tuned in such a way that the best interpolation of the experimental values is achieved. In the present case, η=0.1 produces the best results. The load displacement behaviour for the MMB test, for the propagation of delamination between the aluminium and the 0◦ prepreg layers in Glare 3 2/1 0.4, is shown in Figure 7(c). The maximum load point is predicted with remarkable accuracy, especially by the FE analysis.
ILSS Benchmark Test Simulation The interface properties, previously determined by means of the DCB, ENF and MMB tests were correlated with analytical and numerical models and may be used in independent simulations of the ILSS tests. The results may be directly compared to validate the model. 1 Notice the snap back behaviour of the Fracture Mechanics curve Key Engineering Materials Vol. 383 43
Figure 8. Left: ILSS Mechanical test set up. Right: load boundary conditions in the FE model. The geometry of the ILSS specimen is shown in Figure 8. It consists of a 50x10mm strip of Glare 3 4/3 0.4. The two supports, separated by a distance of 10mm, are modelled as constraints preventing displacements in the vertical direction. A single discrete nodal displacement replaces the die that loads the specimen at its centre line. In order to remove rigid body movement, the horizontal displacement of this node is prevented. Most material properties are the same as the ones used in the previously described models, except for the aluminium which is now simulated by a bilinear elasto plastic behaviour with yield strength of 325MPa and a hardening curve slope of 12%. The complete behaviour is modelled in a quasi static manner in the FE code ABAQUS® [6].
(a) Undeformed shape
(b) Deformed shape Figure 9. Finite element model of ILSS test specimen. The undeformed FE mesh of the ILSS specimen is shown in Figure 9(a). It consists of 100 elements in the length direction. In the thickness direction, one element per aluminium and prepreg layer is used. Experience shows that a higher number of elements in the vertical direction do not provide a more accurate global solution. Four nodded elements equipped with an incompatible modes constitutive behaviour are used in order to prevent shear locking. The deformed mesh of a perfectly bonded ILSS specimen, for a load point displacement of 0.3mm, is depicted in Figure 9 (b). A close up of one of the delaminated regions is provided in Figure 10. Cracks start at the shear loaded interfacial regions between the support points and the loading point and they propagate progressively to the specimen tips. The onset of delamination occurs at the inner prepreg prepreg interface, not only because the shear tractions are higher at the specimen midplane but also because the mode II fracture toughness (GIIc ) of this interface is the lowest of the three different types of interfaces. 44 Progress in Fracture and Damage Mechanics
Figure 10. Close up of the ILSS test specimen deformed mesh. Delaminations are visible at the inner prepreg prepreg interface. Figure 11 shows the shear stresses at interfaces 1 to 8 (counting from the lowest surface of the model), for a prescribed displacement slightly higher than needed to the onset of delamination. Shear stresses reach maximum values at the two regions between the loading and support points. Outside these regions they are maintained at negligible values. Shear stress values increase from the outer interfaces to the inner ones, e.g. from interfaces 1 to 3. The plots corresponding to the inner interfaces, specially interface 5, show inflection points. In these interfaces the shear stresses start to decrease after reaching the maximum shear traction values ( τIIu =90MPa). The regions where this phenomenon is observed are delaminating. Further load increase leads to delamination propagation away from the load point.
100 100 100 100 80 80 80 80 60 60 60 60 40 40 40 40 20 20 20 20 0 0 0 0 -20 0 10 20 30 40 50 -20 0 10 20 30 40 50 -20 0 10 20 30 40 50 -20 0 10 20 30 40 50 -40 -40 -40 -40 -60 -60 -60 -60 ShearStress [MPa] ShearStress [MPa] ShearStress [MPa] ShearStress [MPa] -80 -80 -80 -80 -100 -100 -100 -100 X [mm] X [mm] X [mm] X [mm] (a) Interface 1 (b) Interface 2 (c) Interface 3 (d) Interface 4
100 100 100 100 80 80 80 80 60 60 60 60 40 40 40 40 20 20 20 20 0 0 0 0 -20 0 10 20 30 40 50 -20 0 10 20 30 40 50 -20 0 10 20 30 40 50 -20 0 10 20 30 40 50 -40 -40 -40 -40 -60 -60 -60 -60 ShearStress [MPa] ShearStress [MPa] ShearStress [MPa] ShearStress [MPa] -80 -80 -80 -80 -100 -100 -100 -100 X [mm] X [mm] X [mm] X [mm] (a) Interface 5 (b) Interface 6 (c) Interface 7 (d) Interface 8 Figure 11. Shear stress values at specimen interfaces (numbered from lowest to upper layer). Prescribed displacement = 0.24mm, Load = 2000N
Numerical Analyses on the Influence of Porosity In this section, the model of the ILSS specimen described in the previous section is used to analyse the effect of porosity in Glare 3 4/3 0.4 interfaces. Porosity can be modelled by reducing the ultimate strength and/or the fracture toughness in a few elements at specific locations. Nevertheless, it is not obvious to what extent these parameters should be reduced. In order to be on the safe side, the worst case scenario is assumed. In this sense, the shear load carrying capability of the adhesive is locally reduced to zero as if entirely delaminated. In those interface elements, the original cohesive constitutive relation is replaced by a traction free relation. However, the normal compressive response is maintained in order to simulate crack closure effects. Key Engineering Materials Vol. 383 45
Three distinct cases have been considered. In the first two cases, the porosity is smeared evenly in a single and in all model interfaces. In the third case, porosity is randomly distributed along the interfaces. The final case approximates the real situation where the size of the porous and the distance between them is variable. Porosity in a Single Interface In these analyses, each interface contains a level of porosity of 25%. Nine simulations have been carried out, each to study the interlaminar shear strength reduction caused by porosity in each of the nine interfaces in the Glare 3 4/3 0.4 specimen. A smeared distribution of porosity is considered, i.e. one of each four equally sized, consecutive interface elements is a priori set to a delaminated state. This means that 25 out of the total 100 interface elements are pre delaminated. The load displacement curves corresponding to each of the nine single interface porosity cases are plotted in Figure 12(a). After an initial linear path, a non linear behaviour is observed in all of the cases. This is due to the delamination propagation in the porous interface. By increasing the load level even further, delaminations eventually start at other interfaces and the aluminium layers start to deform plastically, reducing the overall stiffness of the specimen. After a certain damage level, the specimen is unable to sustain a higher load. This means that the specimen maximum strength value is reached. From this point on the delaminations in the porous interface rapidly propagate to neighbouring elements away from the centre of the specimen, drastically reducing its strength. However, the specimens still retain part of their strength because this sudden delamination does not propagate through the entire interface span.
2500 2500
2000 2000
1500 1500 Porosity in: interface 1 interface 2 Load[N] Load[N] 1000 1000 interface 3 interface 4 interface 5 No porosity 500 interface 6 500 50% porosity interface 7 25% porosity interface 8 25% porosity in interface 5 interface 9 0 0 0 0.05 0.1 0.15 0.2 0.25 0 0.05 0.1 0.15 0.2 0.25 Displacement [mm] Displacement [mm] (a) Smeared porosity in discrete interfaces (level: 25%) (b) Several levels of smeared porosity in all interfaces Figure 12. Load displacement plots for several ILSS simulations including porosity. Interfaces with several degrees of porosity are characterised. By comparing the different load displacement curves and maximum strength points, it can be concluded that a 25% porosity level in the outer ILSS specimen interfaces does not lead to a significant interlaminar shear strength reduction as compared with the nominal case, whereas if the porous interface is one of the inner ones, a remarkable decrease in strength is observed. This is because this level of porosity in the outer interfaces does not trigger delamination propagation. Instead, as in the perfectly bonded case discussed in the previous section, delamination is triggered at the inner prepreg prepreg interface where the combination of the highest shear strain and the lowest fracture toughness occurs. When one of the three inner interfaces is porous, delamination occurs at a lower load level that could be achieved if the specimen was perfectly bonded. A maximum strength reduction of 15.2% is observed when porosity is located at the inner prepreg prepreg interface, again due to the combination of the highest shear strain and the lowest fracture toughness. Global Porosity In these simulations, global smeared porosity up to a level 50% of the total interfacial area is considered. This corresponds to specimen models where the interfacial stiffness of 46 Progress in Fracture and Damage Mechanics up to 50% of all the cohesive elements is ignored. These 0.5mm long pre delaminations are smeared along all the interfaces. The 50% porosity level case is considered the worst case scenario occurring in FML’s. The load displacement curves corresponding to perfectly bonded, 25% porous and 50% porous specimens are shown in Figure 12(b). The worst case scenario leads to an interlaminar shear strength reduction of 30.8%. The 50% porosity case shows a very gradual decrease in strength after the maximum load point while the cases corresponding to lower degrees of porosity are marked by sudden failure. This is correlated with the way delaminations propagate. As an example, considering the 25% porosity level case, the inner prepreg prepreg interface starts to delaminate at a load level around 1500N. The delamination propagates at this interface alone until the maximum shear strength level is reached. Then, another interface suddenly starts to delaminate and equilibrium is achieved at a lower load level. For the 50% porosity level case, the onset of delamination occurs at three interfaces barely at the same load level (1500N) followed by smooth propagation. It is interesting to notice that, for the 25% porosity level, the cases of global porosity and the porosity solely at the inner prepreg prepreg interface produce similar results; around 15% reduction in shear strength. This means that, for this porosity level the delamination of this interface dominates the shear failure process. Figure 13 is illustrative of the effect of porosity in all interfaces. The ILSS of FML’s seems to be linearly dependent on the overall level of porosity, for porosity levels ranging from 0% to 50%. The maximum load computed for the perfectly bonded ILSS is 2354N. On the other side, the worst case porosity scenario results in a failure load of 1630N.
2600
2200
1800 Maximum Load [N] Maximum
1400 0 10 20 30 40 50 Porosity Level [%] Figure 13. Effect of the interface porosity level in the maximum load supported by an ILSS specimen. Random Porosity In reality, the occurrence of porosity in a perfectly smeared fashion in one or all interfaces is rather unlikely. Most probably, there will be small and large voids and the distance between them will vary as well. The effects of this randomness on the interlaminar shear strength of FML’s may be quite significant and may deviate from the results obtained for the smeared porosity cases. Therefore, for a correct assessment of the effects of real life porosity on the ILSS of Glare, random porosity cases are considered. A total of 27 cases of global and single interface porosity (25% and 50% porosity levels) were generated by randomly choosing 25 or 50 of the interface elements, corresponding to pre delaminations. In the single interface scenario, porosity is included only in the inner prepreg prepreg interface (interface 5) since this represents the worst case scenario. Voids larger than the interface elements size (0.5mm) are obtained when two or more consecutive elements occur in the randomly generated list of element numbers. Similarly, if the difference between two consecutive members of that list is higher than average, it means that there will be a large perfectly bonded interface area. On average, the 25% porosity level case generated 18.9 voids at each interface with an average length of 0.668mm, while the 50% porosity level case generated, on average 25.7 voids with an average length of 0.98mm. The probability of the occurrence of two consecutive pre delaminated interface elements is obviously much higher in the 50% porosity set of cases than in the 25% set. Key Engineering Materials Vol. 383 47
The load displacement curves corresponding to random porosity in the inner prepreg prepreg interface are plotted in Figure 14(a) and 14(b), respectively for the 25% and 50% porosity levels. Similarly, the results for global porosity are depicted in Figure 14(c) and 14(d), respectively for the 25% and 50% porosity levels. The first important conclusion to draw from these plots is that there is a remarkable scatter in the ILSS produced by random porosity. This may be explained by the scatter in the number of pre delaminated elements in the region of the specimen between the two supports. As mentioned previously, this is a critical shear loaded area. The boundary and loading conditions here dominate the failure process of the whole specimen. As an example, in depth observation of the single interface (50% level porosity scenario) reveals that the specimen corresponding to the poorer results (1491.3N) contains 13 pre delaminated elements in this region, for an average probability of having only 10 of these elements. Part of these elements is grouped in two voids of 2mm and one of 1.5mm. The specimen showing the highest ILSS (1872.4N) contains only 6 pre delaminated elements in this region and most of them are dispersed, except for a single 1mm porous.
2000
2000 1600
1600
1200
1200 Load[N] Load[N] 800 800
400 400
0 0 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 Displacement [mm] Displacement [mm] (a) Porosity in interface 5 (level: 25%) (b) Porosity in interface 5 (level: 50%)
2100 1500
1800 1200 1500
1200 900
900 Load[N] Load[N] 600
600
300 300
0 0 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 Displacement [mm] Displacement [mm] (c) Global porosity (level: 25%) (d) Global porosity (level: 50%) Figure 14. Load displacement curves for 27 random porosity cases. The relations between the probability of failure of a specimen and the failure load values are plotted in Figure 15, for the four scenarios of random porosity studied. It is assumed that the results follow statistical normal distributions and there is a significant number of occurrences in the universe of possible results. It can be observed that, for porosity at the inner prepreg prepreg interface, 95% of the specimens fail at loads in the ranges 1631.6 2194.6N and 1473.2 1790.8N for the 25% and 50% porosity level scenarios, respectively. Similarly, for the global porosity scenario, 95% of the specimens have maximum interlaminar shear strength in the ranges 1532.1 1992.8N and 1052.4 1429.0N, respectively for the 25% and 50% porosity levels. Curiously, the scatter 48 Progress in Fracture and Damage Mechanics corresponding to the 50% porosity level cases is higher than for the 25% porosity level cases, either for the single interface or global porosity scenarios.
0.003 0.006
0.004 0.002 P(failure) P(failure)
0.002 0.001
0 0 1393.8 1473.2 1552.6 1632.0 1711.4 1790.8 1870.2 1490.9 1631.6 1772.4 1913.1 2053.8 2194.6 2335.3 Failure Load [N] Failure Load [N] (a) Porosity in interface 5 (level: 25%). Av. value = (b) Porosity in interface 5 (level: 50%). Av. value = 1913.1N. St. deviation = 140.7N. 95% of the 1632.0N. St. deviation = 79.4N. 95% of the specimens specimens fail at a load in the range 1631.6 2194.6N fail at a load in the range 1473.2 1790.8N
0.005 0.004
0.004 0.003
0.003
0.002 P(failure)
0.002 P(failure)
0.001 0.001
0 0 970.8 1062.4 1154.1 1245.7 1337.4 1429.0 1520.6 1416.9 1532.1 1647.3 1762.5 1877.6 1992.8 2108.0 Failure Load [N] Failure Load [N] (c) Global porosity (level: 25%). Av. value = (d) Global porosity (level: 50%). Av. value = 1245.7N. 1762.5N. St. deviation = 115.2N. 95% of the St. deviation = 91.6N. 95% of the specimens fail at a specimens fail at a load in the range 1532.1 1992.8N load in the range 1052.4 1429.0N Figure 15 Normal distributions of the ILSS of Glare 3 4/3 0.4 corresponding to several scenarios of porosity. The ILSS values for the configurations analysed, as well as the amount of strength reduction due to porosity, are reported in Table 3. For the random porosity scenarios, average results are shown. The worst case porosity configuration, corresponding to a level of 50% of random porosity, produces 46.5% reduction in the specimen shear strength. Without exception, the random porosity scenarios lead to lower ILSS results than the smeared porosity scenarios. Actually, for the global porosity scenarios the results corresponding to the smeared porosity cases do not even fall in the intervals of 95% probability of failure for the corresponding random porosity cases. This means that specimens with smeared porosity are a very particular case of all porosity cases and lead to failure results that highly surpass the average expected value. Unlike the smeared porosity scenario, random porosity does not produce similar ILSS values for the cases of porosity in the inner prepreg prepreg interface and global porosity. This may be due to the small number of specimens analysed. Key Engineering Materials Vol. 383 49
Specimen configuration ILSS [N] Strength reduction [%] Perfectly bonded 2354 25% smeared porosity in interface 5 1995 15.2 25% random porosity in interface 5 1913 18.7 25% global smeared porosity 2013 14.5 25% global random porosity 1762 (average) 25.1 (average) 50% random porosity in interface 5 1632 30.7 50% global smeared porosity 1630 30.8 50% global random porosity 1259 (average) 46.5 (average) Table 3. Average ILSS of Glare 3 4/3 0.4 and shear strength reduction due to several porosity scenarios.
Conclusions and Recommendations The existence of porosity triggers delaminations at the interfaces between different layers in FML’s causing them to fail at lower applied loads than otherwise achievable. The present report describes a study on the effects of such porosity on the interlaminar shear response of Glare. This work was performed by means of analytical and numerical simulations of laboratory tests. The objective was to replicate the ILSS experiments previously performed and quantify the decrease in Glare shear strength due to several degrees of porosity. Traditional FE methods were used in combination with a cohesive zone approach, developed by Camanho et al [9 10] to simulate delamination onset and propagation at material interfaces. However, its implementation in numerical models requires the input of nontrivial mechanical material properties such as the interface fracture toughness. Experiments were carried out to find these properties [11]. Then, FE simulations and simple analytical models based on Beam Theory and Fracture Mechanics Theory [13] were compared to these experiments, for the sake of model validation and fine tuning of the interfacial ultimate traction values. Remarkable agreement was found between the mode I loading delamination propagation test results and respective simulations. The catastrophic failure of the ENF and MMB tests does not allow for stable crack propagation. This unstable nature is correctly captured by the analytical and numerical simulations at remarkably similar load displacement points. Perfect interfacial bonding and several porosity scenarios were simulated with models of Glare 3 4/3 0.4 ILSS test specimens. The inner prepreg prepreg interface is the most prone to delaminate (hence the most sensitive to porosity), since it combines the highest shear strains with the lowest fracture toughness. A remarkable agreement in the load displacement behaviour was achieved between these simulations and experiments carried out previously, but not in the prediction of the maximum strength values. The tests reveal a failure load of 1650N for the specimens with the best interfacial quality, while the numerical models predict a 42% higher value (2354N). This could be explained by the fact that perfectly bonded interfaces, as simulated, are virtually impossible to manufacture, i.e. there is always some porosity that degrades the adhesive properties. Randomly generated porosity cases were simulated for a better agreement with reality. A significant drop in the ILSS is observed when comparing these cases with the smeared porosity cases because of the probable existence of larger voids located in the most critical specimen region for shear failure, i.e. between the supports. The worst case porosity scenario simulated resulted in a 46.5% reduction in the ILSS of Glare. Several recommendations should be given for future work. Firstly, intraply failure criteria should be incorporated in the models. This would result in a better match with reality since delaminations would be allowed to propagate at any of the Glare interfaces and the phenomenon of "crack jumping" could be analysed in more detail. Secondly, DCB tests should be repeated, this time avoiding fibre brigding. Also, the Four Point Bending tests [15] should be carried out in replacement of the three point bending ENF and MMB test. These would result in stable crack 50 Progress in Fracture and Damage Mechanics propagations in mode II and mixed mode loading, therefore allowing the measurement of accurate fracture toughness values, consequently better correlation with FE models. Thirdly, the development of three dimensional models for the investigation of porosity in test specimens and in critical structural components would better answer the needs of the industry. Three dimensional models would also allow the modelling of voids with better geometrical resemblance with reality. Finally, this investigation would benefit from more experimental data to which the numerical predictions could be compared. An extensive study onto the actual exact spatial distribution of voids in the porous layers, similar to the work conducted in [1 5] would improve the data available for the simulations. Having more experimental data available, it can be interesting to compare this approach with a more traditional stress based approach to predict the initiation of damage [2,3]. This may prove to be an effective way to predict failure initiation in FML’s and may be more robust than numerical method implement in the present work.
Acknowledgements The funding of this work through the scholarship SFRH/BD/16238/2004 from the Portuguese Foundation for Science and Technology is gratefully acknowledged. Special acknowledgements are addressed at Dr. Mário Vesco for carrying out fracture energy tests [11] and making the results available to this study. Also the valuable ideas of Dr. Doobo Chung in the introduction of probability in the analysis of the effects of porosity in FML’s are kindly acknowledged.
References [1] A.M. Rubin and K.L. Jerina (1994), Evaluation of Porosity in Composite Aircraft Structures , Mechanics of Composite Materials, Vol. 30, No. 6, pp. 587 600. [2] H. Jeong (1997), Effects of Voids on the Mechanical Strength and Ultrasonic Attenuation of Laminated Composites, Journal of Composite Materials, Vol. 31, pp. 276 292. [3] M.L. Costa, S.F.M. de Almeida and M.C. Resende (2001), The influence of Porosity on the Interlaminar Shear Strength of Carbon/Epoxy and Carbon/Bismaleimide Fabric Laminates, Composite Science and Technology, Vol. 61, pp. 2101 2108. [4] Z. Gürdal, A. P. Tomasino and S.B. Biggers (1991), Effects of Processing Induced Defects on the Laminate Response: Interlaminar Tensile Strength , SAMPE Journal, Vol. 27, No.4, pp. 39 49 [5] A. Mobuchon and Z. Gürdal (1991), Effects of Processing-Induced Defects on Failure of Graphite/Epoxy Angles , Mechanics and Mechanisms of Damage in Composites and Multi Materials, ESIS11, Mechanical Engineering Publications, London, pp. 95 115. [6] ABAQUS, Inc (2007), ABAQUS Version 6.7 User's Manual , Pawtucket, RI, USA. [7] J.C.J. Schellekens and R. de Borst (1994), Free Edge Delamination in Carbon-Epoxy Laminates: a novel numerical/experimental approach , Composites and Structures, Vol. 28, pp. 357 373. [8] P.P. Camanho, C.G. Dávila and M.F. Moura (2003), Numerical Simulation of Mixed-mode Progressive Delamination in Composite Materials , Journal of Composite Materials, Vol. 37, No. 16, pp. 1415 1438. [9] A. Turon, P.P. Camanho, J. Costa and C.G. Dávila (2004), An Interface Damage Model for the Simulation of Delamination Under Variable-Mode Ratio in Composite Materials. NASA/TM 2004 213277. Key Engineering Materials Vol. 383 51
[10] A. Turon, P.P. Camanho, J. Costa and C.G. Davila (2006), A Damage Model for the Simulation of Delamination in Advanced Composites under Variable-Mode Loading . Mechanics of Materials, Vol. 38, pp. 1072–1089. [11] M. Vesco and J. Sinke (2005), Response and damage evolution in GLARE laminates under indentation loads – Experimental results , Report B2V 05 01, Faculty of Aerospace Engineering TUDelft. [12] M.L. Benzeggagh and M. Kenane (1996), Measurement of Mixed-Mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus , Composite Science and Technology, Vol. 56, pp. 439 49. [13] Y. Mi and M.A. Crisfielfd (1996), Analytical Derivation of Load/Displacement relationship for the DCB and MMB and Proof of the FEA Formulation, Department of Aeronautics, Imperial College, London. [14] A. Korjakins (1997), Interlaminar Fracture Toughness of Glass Fibre Reinforced Polymeric Composites Influenced by Fibre Surface Treatment . Ph.D Thesis. Riga Technical University. [15] C. Schuecker and B.D. Davidson (2000), Evaluation of the accuracy of the four-point bend end-notched flexure test for mode II delamination toughness determination , Composites Science and Technology , Vol. 60, pp. 2137 2146. [16] Ad. Vlot (2001), Fibre Metal Laminates (An Introduction), Kluywer Academic Publishers. [17] A. Turon, C.G. Davila, P.P. Camanho and J. Costa (2005), An Engineering Solution for using Coarse Meshes in the simulation of Delamination with Cohesive Zone Models , NASA Technical Memorandum, NASA/TM 2005 213547.