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Influence of Porosity on the Interlaminar Shear Strength of Fibre-Metal

Laminates

Cláudio S. Lopes1, a, Joris J.C. Remmers2,b and Zafer Gürdal1,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

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(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

36 Progress in Fracture and Damage Mechanics

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.

250mm

Glare 3-2/1-0.4

Al 7075-T6

Al 7075-T6

Pre-

crack

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

Key Engineering Materials Vol. 383 37

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.

Interface GIc

[J/m2]

GIIc

[J/m2]

GI/IIc

[J/m2]

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, GIc is

lower than GIIc 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 GIc.

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


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.


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 νννν12 0.195 G12 [MPa] 5500

E22 [MPa] 9500 νννν13 0.195 G13 [MPa] 5500

E33 [MPa] 9500 νννν23 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:

2= c

cz

u

Gl E

τ. (1)

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.


(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.


0

200

400

600

800

0 5 10 15 20 25 30 35

Displacement [mm]

Load [N]

Numerical, del. 1 interfaceFracture Mechanics CurveBeam Theory CurveExperimental ResultsNumerical, del. 2 interfaces

0

1000

2000

3000

4000

0 0.5 1 1.5 2 2.5 3 3.5

Displacement [mm]

Load [N]

Numerical Results

Fracture Mechanics Curve

Beam Theory Curve

Experimental Results

0

200

400

600

800

1000

1200

0 2 4 6 8

Load Point Displacement [mm]

Load [N]

Numerical Results

Fracture Mechanics Curve

Beam Theory Curve

Experimental Results

(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 analytical1 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/GT):

( ) , =IIIC IIC IC T I II

T

GG G G G G G

G

η

+ − +

(2)

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


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.


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

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50

X [mm]

Shear Stress [MPa]

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50

X [mm]

Shear Stress [MPa]

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50

X [mm]

Shear Stress [MPa]

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50

X [mm]

Shear Stress [MPa]

(a) Interface 1 (b) Interface 2 (c) Interface 3 (d) Interface 4

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50

X [mm]

Shear Stress [MPa]

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50

X [mm]

Shear Stress [MPa]

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50

X [mm]

Shear Stress [MPa]

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50

X [mm]

Shear Stress [MPa]

(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.


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.

0

500

1000

1500

2000

2500

0 0.05 0.1 0.15 0.2 0.25

Displacement [mm]

Load [N]

interface 1

interface 2

interface 3

interface 4

interface 5

interface 6

interface 7

interface 8

interface 9

Porosity in:

0

500

1000

1500

2000

2500

0 0.05 0.1 0.15 0.2 0.25

Displacement [mm]

Load [N]

No porosity

50% porosity

25% porosity

25% porosity in interface 5

(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


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.

1400

1800

2200

2600

0 10 20 30 40 50

Porosity Level [%]

Maximum Load [N]

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.


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.

0

400

800

1200

1600

2000

0 0.05 0.1 0.15 0.2

Displacement [mm]

Load [N]

0

400

800

1200

1600

2000

0 0.05 0.1 0.15 0.2

Displacement [mm]

Load [N]

(a) Porosity in interface 5 (level: 25%) (b) Porosity in interface 5 (level: 50%)

0

300

600

900

1200

1500

1800

2100

0 0.05 0.1 0.15 0.2

Displacement [mm]

Load [N]

0

300

600

900

1200

1500

0 0.05 0.1 0.15 0.2

Displacement [mm]

Load [N]

(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


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

0.002

0.004

0.006

1393.8 1473.2 1552.6 1632.0 1711.4 1790.8 1870.2

Failure Load [N]

P(failure)

0

0.001

0.002

0.003

1490.9 1631.6 1772.4 1913.1 2053.8 2194.6 2335.3

Failure Load [N]

P(failure)

(a) Porosity in interface 5 (level: 25%). Av. value =

1913.1N. St. deviation = 140.7N. 95% of the

specimens fail at a load in the range 1631.6-2194.6N

(b) Porosity in interface 5 (level: 50%). Av. value =

1632.0N. St. deviation = 79.4N. 95% of the specimens

fail at a load in the range 1473.2-1790.8N

0

0.001

0.002

0.003

0.004

0.005

970.8 1062.4 1154.1 1245.7 1337.4 1429.0 1520.6

Failure Load [N]

P(failure)

0

0.001

0.002

0.003

0.004

1416.9 1532.1 1647.3 1762.5 1877.6 1992.8 2108.0

Failure Load [N]

P(failure)

(c) Global porosity (level: 25%). Av. value =

1762.5N. St. deviation = 115.2N. 95% of the

specimens fail at a load in the range 1532.1-1992.8N

(d) Global porosity (level: 50%). Av. value = 1245.7N.

St. deviation = 91.6N. 95% of the specimens fail at a

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.


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


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.

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