Modelling the effect of tufted yarns in composite T-joints

Y Wang BEng, MSc, PhD

Research Associate, School of Materials, University of ManchesterSackville Street, Manchester M1 3NJ, UK

C Soutis* PhD(Cantab), FREng, CEng, FRAeS, FIMechE, FIM, AFAIAA

Professor, School of Materials, University of ManchesterDirector of Aerospace Research Institute, University of Manchester

Sackville Street, Manchester M1 3NJ, UK

*Corresponding author email: constantinos.soutis@manchester.ac.uk Tel: +44(0)161 306 8592

Abstract

This paper presents a finite element simulation of the mechanical response of a composite T-

joint subjected to a tensile (pull-out) loading. The finite element (FE) model includes the

analysis of effect of the tufted yarns and interlaminar properties on the ultimate load to

failure, and comparison between the full and strip FE model. The FE results show that the

ultimate load to failure increases when the tufted yarns are introduced. The tufted

configuration increases the deflection capacity of the T-joint, and therefore more energy is

required to cause ultimate failure. The FE prediction was validated using experimental data

for E-glass fibre/epoxy T-joints.

1. Introduction

The composite T-joints are found in structural components such as skin-spar in wind turbine

blades (Figure 1(a)) (Sloan, 2009) and aircraft wings and road vehicles. It supports mainly

bending loads that the blade experiences when in operation and transfers shear stresses to the

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skin; the whole blade of course in addition to bending, experiences torsional loading that

introduces additional direct and shear stresses in the blade’s components, which form a 3D

stress field (Shenoi and Hawkins, 1992, Rispler et al., 1997, Pilipchuk and Ibrahim, 2010,

Nanayakkara et al., 2013). The aim of material development for wind turbine blades is to find

materials capable of extending the blade’s working life and minimizing geometry related

fatigue issues. To achieve this goal a T-joint test coupon was often designed as a

representative element of the blade's shear web to skin connection in order to determine their

mechanical response. The interfacial zones become natural sites for the initiation of damage,

which weaken the T-joint, affecting the overall structural efficiency and integrity (Guo and

Morishima, 2011). Therefore, it is important to understand the way delamination occurs and

develop methods of improving performance.

Composite T-joints if badly designed and fabricated are prone to premature failure due to

damage that mainly occurs in the form of delamination within the joint and skin-flange

debonding. The development of interlaminar stresses is the primary cause of delamination in

laminated fibrous composites. The interlaminar stress level is associated with the test coupon

geometry and loading conditions while the interlaminar strength is related to the material

properties. The interlaminar strength is the weak link as it relies on the brittle matrix

properties and the bonding strength of the fibre/matrix interface (Liu, 1990, Dransfield et al.,

1994). To overcome this weakness, through-thickness reinforcement is widely considered to

be an efficient way to increase the resistance of laminated composites and bonded joints

against out-of-plane failures. Various techniques, such as stitching, interlaminar veils, 3D

weaving and z-pining have been proposed to improve the properties in the through-thickness

direction (Mouritz et al., 1997, Mouritz et al., 1999, Burns et al., 2012, Leong et al., 2000,

Mouritz, 2007, Kuwata and Hogg, 2011).

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The stitching of composites has been reviewed in some detail by some researchers

(Dransfield et al., 1994, Mouritz et al., 1999, Mouritz and Cox, 2000). Stitching can

improve the delamination resistance while producing a more integrated composite structure.

This technique significantly improves out-of-plane properties but in-plane fibre damage and

the creation of resin pockets can degrade other properties (Dransfield et al., 1994). The extent

to which the mechanical properties are affected by stitching is dependent on the stitching and

testing parameters, and on the fabrication techniques. An optimal combination of the stitching

and fabrication parameters will need to be identified in order to maximize delamination

resistance with minimal loss of in-plane mechanical properties.

Numerous studies have developed finite element models to simulate and predict the

delamination of a composite T-joint (Allegri and Zhang, 2007, Bianchi et al., 2012, Chen et

al., 2009, Stickler et al., 2000, Hélénon et al., 2012, Wang et al., 2015). The properties of

these composite T-joints and possible toughening methods very much depend on the

manufacturing method of the part, i.e. z-pinning is more suitable for prepreg-based

manufacturing method while stitching is mostly to sew dry fabric preforms before they are

consolidated with a resin into a composite.

Delamination of composite structures has been widely investigated, both experimentally and

numerically, because it can often be a cause of local failure and, sometimes, of a sudden

structural collapse especially under compressive loading (Alfano and Criseld, 2001). Despite

this, stitching has the potential to be used for improving delamination resistance of joining

laminates and has been studied over the past 20 years, a number of scientific and technical

issues still need to be resolved, e.g. predictive models for determining strength of stitched

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composites have not been satisfactorily developed. A detailed analysis of tufted composite T-

joint has not so far been attempted, and it is the subject of this paper.

In this study, a finite element failure analysis was performed using ABAQUS to model the

effect of tufted yarns on delamination of a composite T-joint. T-sections were made of glass

fabric infused with epoxy resin using a vacuum assisted resin transfer moulding technique.

The veil layer and tufting techniques are adopted to increase their interlaminar strength and

fracture toughness. Pull-out mechanical tests on different T-joint configurations were

conducted in earlier work (Hajdaei, 2014, Hajdaei et al., 2013) and used to validate the FE

model. Experimental measurements and FE simulations are presented and discussed in the

following sections.

2. Finite element modelling of composite T-joint

2.1 Model geometry

2.1.1 Full model

The geometry of T-joints used in this study is shown in Figure 2. The width of the T-joint is

50 mm. The flange and skin parts consist of five layers of equal thickness arranged in a

stacking sequence of [45o/-45o]5 while the web consists of a 10-layer [45o/-45o]10 plate. The

bottom stiffener (that controls the out-of-plane deflection) consists of 5-layer UD [0o]5 and is

used to prevent large deflections that may not be representative of the larger structure. The T-

joint is subjected to tensile pull-out loading along the web. The skin and stiffener parts are

considered to be supported near the two ends of the T-joint, as indicated in Figure 2.

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Discrete system was used to describe the layup direction in the composite T-joint hence, axis

3 is always representative of the through thickness direction in all parts of the model (Figure

3). Directions 1 and 2 are defined as direction of the fibres and perpendicular to the fibre

directions respectively. Under this coordinate system the engineering constants for the

composite material are: the elastic moduli E1=38 GPa, E2=E3=9 GPa; Poisson’s ratios

12=13=0.3, 23=0.28 and the shear moduli G12=G13=3.6GPa, G23=3.46GPa. The elastic

modulus and Poisson’s ratio for the epoxy resin are equal to 4 GPa and 0.34, respectively.

A commercial ABAQUS software was utilised to perform the finite element analysis. The FE

simulations were run under displacement-control by applying an increasing tensile

displacement along the web. To simulate the roller bar supports, the skin surface is restricted

in the vertical direction at both sides of the web. Three elements were used in the thickness

direction and an 8-node linear brick element (C3D8R) was used. The detailed mesh of the

model with the kinematic and loading boundary conditions is shown in Figure 3.

2.1.2 Strip model

The strip model was developed to investigate how the tufted yarns affect the mechanical

response of the T-joint. The purpose is to reduce the model size, provided that the stress

results are not affected by this simplification. The tufted T-joint was laid up with the same

stack of fabric as for the full model, reinforced with Kevlar thread in the through-thickness

direction. Stitch density was 10 mm along the length direction (axis 1) and 10 mm in the

width direction (axis 2), Fig.4. The strip model contains three rows of stitch yarns on both

sides of the web. Five solid elements are used in the thickness direction. The detailed mesh of

the model is shown in Figure 4.

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2.2 Modelling delamination of T-joint

The initiation and growth of delamination crack are modelled using cohesive zone elements.

Linear elastic traction-separation behaviour is used to model the interface where the

delamination is expected to occur. The traction-separation model in ABAQUS (ABAQUS,

2012) assumes initially linear elastic behaviour followed by the initiation and evolution of

damage.

The initiation of delamination damage can be estimated using the quadratic nominal stress

criterion defined by the following expression:

{ ⟨t n ⟩t n

0 }2

+{t s

t s0 }

2

+{ tt

t t0 }

2

=1 , (1)

where t n0 is the interlaminar normal tensile strength, t s

0 and t t0 are shear strengths in the two

transverse directions (ABAQUS, 2012). The maximum stress criterion could be employed,

but equation (1) captures the stress interaction; of course equation (1) could be linear but it is

customary to use it in its quadratic form.

The evolution of delamination damage is described using a linear softening fracture-based

law, where a mixed mode fracture energy criterion is used (ABAQUS, 2012). Failure under

mixed-mode conditions is governed by a power law interaction of the energies required to

cause failure in the individual interlaminar modes (I, II, III). It is given by the following

expression:

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{Gn

Gnc }

❑

+{Gs

Gsc }

❑

+{G t

Gtc }

❑

=1 , (2)

where Gnc is the normal strain energy release rate, Gs

c and Gtc are shear strain energy release

rates in the two transverse directions; is assumed to be equal to 1, but could be 2. Various

critical fracture energy values are selected to investigate its effect on crack propagation.

Selecting ‘appropriate’ stress based or fracture based criteria remains a debating issue.

2.3 Modelling the damage of tufting material

For tufting materials, the yarn is considered to be isotropic although the yarns are made of

bundled fibres. In the case that the fibre material is aramid, the volumetric density of the yarn

is 1440 kg/m3 and the Poisson ratio is 0.35. The elongation and Young's modulus of the

aramid yarn are 3 % and 94 GPa, respectively, while its tensile strength is taken as 2500

MPa.

It is assumed that progressive damage and ultimate failure of the tuft yarn can be estimated

using the ductile failure criterion in ABAQUS (ABAQUS, 2012). This ductile criterion is a

model for predicting the onset of damage due to nucleation, growth, and coalescence of

voids. The model assumes that the equivalent plastic strain at the onset of damage, ε Dpl, is a

function of stress triaxiality and strain rate: ε Dpl( , ε̇ pl), where = -p/q is the stress triaxiality, p

is the pressure stress, q is the Mises equivalent stress, and ε̇ pl is the equivalent plastic strain

rate. The criterion for damage initiation is met when the following condition is satisfied:

wD=∫ d ε̇ pl

ε Dpl (, ε̇ pl)

=1 , (3)

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where wD is a state variable that increases monotonically with plastic deformation. At each

applied displacement during the analysis the incremental increase in wD is computed by

∆ wD=∆ ε̇ pl

εDpl( , ε̇ pl)

≥ 0 . (4)

The damage evolution defines the post damage-initiation material behaviour; it describes the

rate of degradation of the material stiffness once the corresponding initiation criterion is

satisfied. The formulation is based on a scalar damage approach as below:

σ=(1−D)σ , (5)

where D is the overall damage variable and σ is the stress tensor in the absence of damage

computed in the current increment. The damage variable D captures the combined effect of

all active damage mechanisms, fracture occurs when damage variable D = 1, as shown in

Figure 5.

3. Calculation results and discussion

3.1 Analysis of interlaminar stresses

The stresses within the different regions were computed using the full model. Figure 6 shows

the locations where the stresses were monitored, the coordinate system indicating the stress

directions and stress contours. The regions of interest are: the central line of the web (line

AB, as indicated in Figure 6); the interface between the corner and epoxy resin rich pocket

(arc BC in Figure 6); the bonded connection between skin and flange (line CD in Figure 6)

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and the interface between epoxy resin pocket and skin (line OC in Figure 6). The stress

values from these regions are then plotted to determine their distribution along those

identified critical paths.

Figure 7 shows the distribution of the stresses (normal stress 33 and two shear stresses 31

and 32, in terms of the coordinate system in Figure 3) along the path ABCD where

delamination can be triggered according to equation (1). It can be seen from the figure, in the

web region (path AB), the stresses are hardly seen until near the corner where a sudden

increase in the stresses is seen. There is a big stress jump in the region of the corner (path

BC) and after the corner only the shear stresses are seen except near the end of the flange

where there is a discontinuity. The higher stresses produced at the corner will initiate

delamination cracks when the damage criterion of equation (1) is met. This is in agreement

with delamination cracks observed in the experiments.

Figure 8(a) presents the great details of the stress distribution at the corner (arc BC in Figure

6). It can be seen from the figure, the 33 reaches its maximum value at = 22.5o while the

maximum values of the 31 and 32 occur at = 37.5o, the stress distribution of 31 is almost

as the same as 32. The normal stress is larger than shear stress and consequently the normal

stress dominates the initiation of delamination cracks. Figure 8(b) shows the stress

distribution on the interface between the skin and epoxy resin (line OC in Figure 6).

Comparison of Figure 8(a) and 8(b) reveals that the magnitude of the stresses in this region

(line OC) is smaller compared to the stresses at the corner region (arc BC). This can explain

why the delamination cracks almost always are initiated at the corners.

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The thickness of the plate (flange + skin + stiffener, Figure 2) is difficult to keep constant

when using the Resin Transfer Moulding (RTM) method. As a result the thickness of the T-

joint is varied with each manufacturing process. Therefore it is important to understand how

the plate thickness affects the magnitude and distribution of the stresses (33, 31 and 32),

which is presented in the following discussion. According to Figure 8 (a), the maximum

normal stress (33) occurs at =22.50, the maximum shear stresses (31 and 32), occur at

=37.50. Because the spatial location of the maximum stress remains fixed, these maximum

stresses are used for comparison and results are shown in Figure 9(a). It can be seen that the

stresses are decreased as the thickness increases. For example, 11.3% increase (from 7.66 to

8.66mm) in the plate thickness results in 19.1% decrease in stress 33 and 23.8% decrease in

stresses 31 and 32. The calculated results suggest that the load for the initiation of

delamination crack is increased as the total thickness of the plate increases (less deflection

and hence lower stresses), as would be expected. The effect of loads on these maximum

stresses is shown in Figure 9(b), where a linear relationship is observed.

3.2 Influence of interlaminar properties

Delamination occurs when the interlaminar stress level exceeds the interlaminar strength. The

subsequent propagation of delamination cracks depends upon the interlaminar fracture

toughness (GIC) as delamination is actually an energy dependant mechanism. The effect of

interlaminar properties is discussed below.

Figure 10 presents the mechanical response of T-joints under the pull-out loading. Figure

10(a) shows the effect of interlaminar tensile strength on load-deflection curves of the T-

joint. Four cases were selected to compare and they are: 3 MPa for case A, 4 MPa for case B,

5 MPa for case C and 6 MPa for case D. It can be seen that the stress to failure increases with

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increasing interlaminar strength that plays an important role on crack initiation. This has been

confirmed by the experimental results, e.g. tufting and veil layer techniques, which will be

discussed later.

In Figure 10(b), the effect of interlaminar fracture energy on load-deflection curves is plotted.

It is observed that the ultimate tensile load to failure is significantly increased when the

critical strain energy release rate GIC is increased from 300 J/m2 to 600 J/m2. The load-

carrying capacity is increased by approximately 35%. Comparison of Figures 10(a) and 10(b)

reveals that the effect of interlaminar fracture toughness (GIC) is larger than that of

interlaminar strength.

3.3 Influence of tufting materials

The width of the full model is 10 times larger than that in the strip model. Also, the symmetry

plane is introduced in the strip FE model to further reduce the size of model. All these

simplifications may result in the variation in the load-deflection characteristics of the joint. A

comparison study between the two models (no tuft yarns applied) was carried out and the

result is shown in Figure 11(a). As can be seen in figure 11 (a) there is no change in load-

deflection curves before approaching the maximum load for both; a very small variation is

observed after the maximum load. The comparison confirmed the validation of the strip

model, which can be used to identify the load deflection behaviour of the joint.

The effect of tuft yarns on load-deflection response was investigated using the strip model

and FE simulation result is shown in Figure 11(b). The FE simulation shows that the tufted

configuration increases not only the ultimate pull-out load but also the ‘ductility’ capacity,

and therefore greater energy is absorbed until final failure occurs.

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Figure 12 demonstrates the stress distribution contour of the delaminated T-joint containing

tuft yarns. The high stresses are seen in the tuft yarns (Figure 12(a)) and the stresses are

released after the tuft yarn is fractured (Figure 12(b)). The tuft yarn may be fractured or

pulled out during delamination, dissipating energy and delaying final failure, this have been

confirmed by experimental observations.

4. Experimental validation

In this section, a brief description of the fabrication method and mechanical tests performed

on the selected T-joints is given. The load-deflection curves are presented and damage

evolution is described, which are then compared to FE simulations. Further experimental

details can be found in references (Hajdaei, 2014, Hajdaei et al., 2013).

4.1 Geometry, layup and manufacture

The geometry of T-joints is shown in Figure 2. The layup comprises 5 layers of ±45 glass

fabric to represent the outer blade skin with 5 layers of ±45 glass fabric for each shear web

flange, resulting in 10 layers of fabric within the web. The stiffener consists of 5 layers of

unidirectional glass fabric to prevent large deflections. The various specimen configurations

and details such as fibre type, matrix material and lay-up architecture are listed in Table 1.

The test coupon with polyester veil was laid up in the same way but with a polyester veil

layer added between the L-shaped fabric section and the flat outer skin fabric section. The

tufted test coupon was laid up with the same stack of fabric as for the base specimen,

reinforced with Kevlar thread in the through-thickness direction. Stitch density was 10 mm in

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the length direction and 10 mm in the width direction. The tufting was performed using a 2-

axis robotic machine. All T-section samples were made of glass fabric infused with an epoxy

resin using a vacuum assisted resin transfer moulding technique.

4.2 Experimental methods

To identify the mechanical properties of the T-joints with different architectures, the T-joint

specimens were tested under static loading conditions to obtain the ultimate failure load. An

Instron 5982 electro mechanical testing machine was employed to perform the pull-out tests.

The test was run under displacement-control mode with a displacement rate of 2 mm per min.

Load and displacement values were measured during the test using the machine’s load cell

and grip movement sensor, respectively. A criterion to terminate the test was set as either a

40% drop in the measured load or a total crack length of 50 mm between flange and skin of

the T-joint.

4.3 Experimental results

The test results are presented in terms of maximum bending stress developed due to pull-out

force on the plate (flange-skin-stiffener) section in order to remove the effect of specimen

geometry. Taking into account of bending, the maximum tensile stress occurring in the plate,

11, in terms of the coordinate system shown in Figure 3, is calculated using the beam

bending theory (Ugural and Fenster, 1995) and the maximum nominal stress can be

calculated using the following expression:

σ 11=3 L2b ( P

h2 ) , (6)

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where P is the applied load, L is the span of the T-joint, h is the thickness of the plate and b is

the width of T-joint, Figure 2.

The normalised stresses () calculated by equation (6) are plotted against the deflections ()

and these - curves are shown in Figure 13. Damage initiation is determined by the point

where the curve’s slope starts to decrease. The reduction in the curve’s slope is associated

with initiation of delamination cracks developed in the T-joint and it continues until the

maximum pull-out load is reached. For the Base specimen (Figure 13(a)), the slope of the

curve starts to decrease at the applied stress of around 65 MPa. The mean value of the

maximum pull-out load for this configuration is 2.3 kN and the corresponding applied stress,

11 =117.8 MPa. For the polyester veil specimen the slope of the curve is reduced at an

applied stress, 11 = 110 MPa, approximately. When the applied stress reaches the maximum

value (11 =169.6 MPa), a sudden drop in stress is seen in the - curve (Figure 13(b)). In the

tufted T-joints (Figure 13(c)), the slope of the - curve begins to decrease at the applied

stress of around 95 MPa. The delamination crack starts to propagate when the applied stress

11 =149.6 MPa. The propagated crack will be arrested by the tuft yarns and therefore a

further increase in load is required to propagate delamination cracks.

In Figure 13(d) the typical - curves from these three cases are plotted together in order to

compare. As can be seen from the figure, when the defection () is less than a certain value, a

linear relationship exists between the deflection () and the applied stress () produced by the

load. The slope of the - curves (or ‘stiffness’) is almost the same when the applied stress

() is less than around 65 MPa (or < 0.8 mm) for all joints. In other words, the ‘stiffness’

appeared in the linear stage is not influenced by the veil layer or stitching techniques.

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The experimental results confirmed that the tufted specimen shows relatively higher strength

to failure comparing to the sample without tuft yarns (Base specimen) and the deflection at

the high level of stresses is significantly increased as well. The drop in loads is moderate after

the maximum load when the tufted technique is applied, and the T-joints can experience

larger deflections at a relatively higher stress level. In other words, the deflection at the high

level of stresses in the - curve is significantly increased for the tufted T-joints.

The veil layers significantly increase the ultimate strength of T-joint as well. However, it

must be emphasized that the veil technique increases the ultimate strength of the T-joint but

the deflection capacity at the high stress level in the - curve is reduced when compared

with the tufting technique. All these test results provide experimental evidence for the

validation of the FE simulation results.

Figure 14 presents the comparison between FE simulations and experimental observations. It

can be seen from the diagram, the - curves from FE simulations show a good agreement

with experimental observations, although it remains difficult to accurately capture all the

non-linearities and fluctuations seen in the measured - response. The further work will be

needed to fully understand the effect of manufacturing defects that can affect the fracture

behaviour of such T-joints.

5. Conclusions

A finite element modelling was developed to simulate the mechanical response of composite

T-joints with through-thickness reinforcement (tufting). The FE predictions were validated by

experimental measurements and observations that confirmed the validity of the assumptions

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and simplifications introduced in the FE simulation, although it remains difficult to

accurately capture all the non-linearities and fluctuations seen in the measured load-

deflection response.

The mechanical response of T-joints was investigated using the strip model. This is

advantageous when investigating the effect of the tufted yarns on the mechanical response of

the T-joint, due to the additional complexity of modelling the fracture of individual yarns.

The FE simulation confirmed that the load-carrying capacity of T-joints is significantly

improved when through-thickness reinforcement is introduced. FE simulation shows that the

tufting configuration increases not only the load to failure but also the deflection capacity of

the T-joint, and therefore more energy is required to cause ultimate fracture. This is

consistent with the experimental observations.

The veil layer significantly increases the ultimate strength of T-joint under the tensile pull-out

loading and its ultimate strength is increased with increasing level of interface fracture energy

(GIC). Interface fracture energy plays an important role in improving the T-joint performance,

but further work is needed to understand the effect of manufacturing defects that can affect

the fracture behaviour of such T-joints. The veil technique increases the ultimate strength of

the T-joint but the deflection to failure is reduced.

Acknowledgement

The authors acknowledge the research grant from EPSRC (EP/H018662/1) for this research.

References

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Table 1 Joint codes and lay-up specifications

Code Architectures Description

Base Web: [±45]10

Flange-Skin-Stiffener: [±45]5 [±45]5 [0]5

T-joint made from glass fibre and epoxy matrix

Polyester veil

Web: [±45]10

Flange-Skin-Stiffener: [±45]5[PE][±45]5[0]5

Type Base T-joint + polyester veil added between the flange and the skin

Tufted Web: [±45]10

Flange-Skin-Stiffener: [±45]5[±45]5[0]5

Type Base T-joint + reinforced with Kevlar thread in the through-thickness direction on

the flange-skin-stiffener

Notation

E1 Elastic modulusG12 Shear modulus12 Poisson’s ratiost n traction in normal directiont s traction in first shear directiont t traction in second shear directiont n

0 interlaminar normal tensile strengtht s

0 shear strength in first shear directiont t

0 shear strength in second shear directionGn normal strain energy release rateGs shear strain energy release rateGt shear strain energy release rateGn

c critical fracture energy in normal directionGs

c critical fracture energy in first shear directionGt

c critical fracture energy in second shear direction ε D

pl equivalent plastic strain at the onset of damage stress triaxialityp pressure stress q Mises equivalent stressε̇ pl equivalent plastic strain ratewD state variableD overall damage variableσ stress tensor ❑11 maximum tensile stress occurring in the plateL span of T-jointP applied loadh thickness of the plate

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b width of T-joint

(a) (b)

Figure 1 Photographs showing: (a) cross-section of a wind turbine blade; (b) the T-joint test coupon was manufactured in the University of Manchester Composites Centre.

Figure 2 Geometry and boundary conditions of the composite T-joint subjected to a tensile pull-out load; all dimensions in mm.

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Figure 3 Diagrams showing FE meshing, boundary conditions and local coordinate system of the T-joint FE model; fibre direction is axis 1, width and through-thickness correspond the directions 2 and 3, respectively.

Figure 4 Overall view of the strip FE model; three rows of tuft yarns on each side of the web

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Figure 5 Schematic showing stress-strain response with progressive damage.

Figure 6 Schematic showing the locations where the stresses are measured and the stress contours of through-thickness direction (33).

Figure 7 The distribution and magnitude of the stresses (33, 31 and 32) along the path ABCD of Figure 6 at load = 2000 N.

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(a) (b)

Figure 8 The distribution and magnitude of the stresses (33, 31 and 32) at load = 2000N: (a) along arc BC of Figure 6; (b) along line OC of Figure 6.

(a) (b)

Figure 9 Diagrams showing: (a) effect of plate thickness on the maximum stress (33, 31 and 32) for load = 2000 N; (b) effect of load on the maximum stress (33, 31 and 32) for plate thickness = 8.66 mm.

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(a) (b)

Figure 10 Load-deflection curves from FE simulations showing: (a) effect of interlaminar strength, t n

0; (b) effect of interlaminar fracture toughness, GIC.

(a) (b)

Figure 11 Load-deflection curves from FE simulations showing: (a) predictions from the full and strip models are nearly the same; (b) tufted configuration increases the load to failure and corresponding deflections.

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(a) (b)

Figure 12 Images from FE simulation showing stress distribution contours of tufted T-joint: (a) high stresses are seen in the tuft yarns; (b) the stress is released after the tuft yarn is fractured. Stress unit in the picture is Pa.

(a) (b)

(c) (d)Figure 13 Stress ()–deflection () curves of T-joints from pull-out tests showing: (a) base specimen; (b) polyester veil specimen; (c) tufted specimen; (d) comparison of these three cases.

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Figure 14 Diagrams showing the comparison between experimental observations and FE simulations.

Ying Wang, PhD

Constantinos Soutis, PhD, FREng

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