3D Fibre Reinforced Polymer Composites Part 11 pptx

Models have been developed for the cases where the stitches a rupture along the delamination crack path continuous stitching model and b failure at the surface and then pull-out from the

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to the toughness of the equivalent unstitched laminate (G,,) The figure shows a general increase to the interlaminar fracture toughness with increasing stitch density A few

outlying data points show that the delamination resistance can be improved by over 30 times by stitching with exceptionally thick, strong threads For most composites, however, stitching increases the delamination resistance by a factor of up to 10-15 This compares favourably with other types of 3D composites that have interlaminar fracture toughness properties that are up to 20 times higher than the equivalent 2D laminate

A number of micromechanical models have been proposed to determine the improvement to the mode I interlaminar fracture toughness properties of composites due

to stitching Of the models, there are two models proposed by Jain and Mai that have proven the most accurate (Jain and Mai, 1994a, 1994b, 1994~) Both models are based

on Euler-Bernoulli linear-elastic beam theory applied to a stitched composite with the double cantilever beam (DCB) geometry, as illustrated in Figure 8.22 The models can

be used to caIculate the effect of various stitching parameters (eg stitch density, thread strength, thread diameter) on the R-curve behaviour and GIR value of any laminated

composite

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I I I I I

Stitch Rupture

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I I I I I

I I I I I

Stitch Pull-Out

Figure 8.22 The DCB specimen geometry used as the basis for the Jain and Mai model

for mode I interlaminar fracture toughness of stitched composites Models have been developed for the cases where the stitches (a) rupture along the delamination crack path (continuous stitching model) and (b) failure at the surface and then pull-out from the composite (discontinuous stitching model) (From Jain and Mai, 1997)

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The first model proposed by Jain and Mai is known as the ‘continuous stitching model’ With this model it is assumed the stitches are interconnected and fail along the delamination crack plane (Figure 8.22a) This type of failure is also shown in Figure 8.18a The analytical expression for crack closure traction in the model contains terms for frictional slip and elastic stretching of the stitches in the bridging zone as well as an analytical term to predict when the stitches will rupture at the crack plane The second model by Jain and Mai is known as the ‘discontinuous stitching model’ For this model

it is assumed the stitches behave independently under mode I loading, and interlaminar

toughening occurs by the frictional resistance of the stitches as they are pulled from the

composite under increasing crack opening displacement (Figure 8.22b) To model this

failure process the expression for calculating the crack closure traction contains terms for frictional slip and pull-out of the stitches In some composites, stitch failure occurs during elastic stretching at the outer surface of the DCB specimen at the stitch loop, and the stitch thread subsequently pulls-out In this case, the continuous and discontinuous stitching models are combined into the so-called ‘modified model’ to account for the two stitch failure events

The mode I delamination resistance in terms of

composite with bridging stitches can be calculated

1994a, 199b, 1994~):

stress intensity factor, KIR(Aa), of a from the expression (Jain and Mai,

where KI, is the critical interlaminar fracture toughness of the unstitched composite, da

is the crack growth length, h, is the half-thickness of the composite, t is the distance

from the crack tip to the specimen end, P ( f ) is the closure traction due to stitches, and Y

and f(t/h,) are orthotropic and geometric correction factors, respectively Y is defined by:

(8.3)

where Eo is the orthotropic modulus and E, is the flexural modulus of the stitched

composite The termf(t/hc) in equation 8.2 is determined using:

The closure traction, P ( f ) , which is required to determine K I R ( h ) , is obtained by

iteratively solving the Euler-Bernoulli beam equation Once KIR(da) has been determined, the Mode I interlaminar fracture toughness, G ~ d d a ) may be obtained by:

2500

The Jain and Mai models have proven reasonably reliabIe for predicting the delamination properties of stitched composites For example, Figure 8.23 shows the measured R-curve for a stitched glasdvinyl ester composite (that was shown earlier in Figure 8.15) together with the theoretical R-curve predicted using the Jain and Mai

model, and there is good agreement between the two curves As another example,

Figure 8.24 compares the G,R values measured for stitched carbodepoxy composites

against theoretical G,R values calculated using the continuous and modified stitching models Excellent agreement exists for the modified stitch model while the GIR values are underestimated by about 50% with the continuous model The accuracy of the models is critically dependent on the failure mode of the stitch, that is whether failure occurs by thread breakage, thread pull-out or a combination of these two

Theoretical

Delamination Length (mm)

Figure 8.23 Comparison of a theoretical and experimental mode I R-curve for a stitched

glasshinyl ester composite The theoretical curve was determined using the Jain and Mai model

8.4.2 Mode I1 Interlaminar Fracture Toughness Properties

Stitching is also an effective technique for improving the delamination resistance under mode I1 loading (i.e shear crack opening) This is particularly significant because delamination cracks that form in composites under impact loading grow mostly under the action of impact-induced shear strains The effectiveness of stitching in raising the mode I1 delamination resistance is shown in Figure 8.25, which shows a large increase

to the mode I1 interlaminar fracture toughness (GIIR) of a carbodepoxy laminate with increasing stitch density (Dransfield et ai., 1995) It is worth noting, however, that the improvement to the delamination resistance is usually not as high as for the mode I

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toughness for equivalent stitch densities Most stitched composites exhibit a GIIR value that is typically 2 to 6 times higher than the unstitched laminate, depending on the type and amount of stitching It was shown earlier that the mode I delamination resistance can be increased by much more this

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Continuous Stitching Model

0 Modified Stitching Model

Measured (& (kJ/d)

Figure 8.24 Plot of measured against theoretical GIR values for stitched composites The theoretical GIR values were determined using the modified and continuous stitching

models by Jain and Mai The closer the data points are to the straight line the better the agreement between the measured and theoretical GIR value (Adapted from Mouritz and

Jain, 1999)

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Stitch Density Figure 8.25 The effect of stitch density on the mode I1 interlaminar fracture toughness

of a carbodepoxy composite (Data from Dransfield et al., 1995)

The toughening mechanisms responsible for the high mode I1 interlaminar fracture toughness of stitched composites are complex, with a number of different mechanisms operating along the length of a delamination crack The shear tractions generated in stitches with increasing sliding displacement between the opposing crack faces are shown in Figure 8.26 This figure by Cox (1999) shows typical sliding displacement and stress levels associated with the various mechanisms during shear loading of a stitched composite up to the point of failure The sliding displacement ( 2 ~ 1 ) is the distance the two crack faces have separated under mode I1 loading The vertical scales

show the average bridging traction across the stitches, q, (left-hand side) and the

bridging traction for a single stitch, T (right-hand side) The values shown for q, are representative, and will vary depending on the volume fraction of stitching and the mechanical properties of the threads

ploughing, debonding, and slip

/

sliding displacement, 2u (mm)

Figure 8.26 Schematic of the shear tractions for mode I1 loading of a stitch under increasing crack sliding distance (from Cox, 1999)

It is generally acknowledged that when an interlaminar shear stress is applied to a stitched composite containing a delamination then the stitches ahead of the crack front are not damaged or deformed When the crack tip reaches the stitches, however, the delamination causes the stitches to debond from the surrounding composite material The stitches are usually completely debonded from the composite when the total sliding

displacement ( 2 ~ ~ ) exceeds about 0.2 mm As the opposing crack faces continue to slide pass each other the stitches become permanently deformed Plastic deformation of the stitches can occur immediately behind the crack tip due to the low shear yield stress of the thread material It is estimated that permanent deformation in stitches begins when the sliding displacement distance exceeds about 0.1 mm The stitches experience

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increasing plastic shear deformation and axial rotation the further they are behind the crack tip As the stitches are deformed they are ploughed laterally into the crack faces

of the composite At a high amount of axial rotation the stitches experience splitting cracks and spalling, and this generally occurs when the sliding displacement rises above 0.6 mm This deformation and damage to a sheared stitch is shown in Figure 8.27, and

it is obvious a large degree of axial rotation has occurred on the fracture plane In this thread the fibres have been rotated by an angle (S, of up to about 45' The plastic deformation and ploughing of the stitches absorbs a large amount of the applied shear stress Furthermore, the large amount of axial rotation to the stitches causes them to bend near the fracture plane so a significant load of the applied shear stress is carried by the stitches in tension The combination of these effects lowers the shear strain acting

on the crack tip and thereby improves the delamination resistance Eventually the stitches at the rear of the stitch bridging zone break when the sliding displacement exceeds about 1 mm (Figure 8.27b) The stitch bridging zone can grow for long distances (up to -50 mm) before the stitches fail, and this is the principle toughening mechanism against mode I1 delamination cracks

Figure 8.27 Scanning electron micrograph showing (a) plastic shear deformation and

(b) shear failure to a stitch subject to mode I1 interlaminar loading

Micromechanical models have been proposed by Jain and Mai (1994e, 1995) and Cox et

al (Cox, 1999; Cox et al., 1997; MassabB et al., 1998, 1999; Massabb and Cox, 1999)

for determining the mode I1 delamination resistance of stitched composites The models by Jain and Mai use first order shear deformation laminated plate theory and Griffith's theory for strain energy release rate in fracture to calculate the effect of stitching on the mode I1 interlaminar fracture toughness (GIIR) Models have been proposed for stitched composites subject to shear loading using the end notched flexure (ENF) and end notched cantilever (ENC) test methods, which are methods for measuring the mode I1 interlaminar fracture toughness of laminated materials In both models it is assumed that as a delamination crack propagates under shear the stitch failure process consists of elastic stretching of the threads due to relative slip of the top and bottom sections of the delaminated region, followed by rupture of the stitch in the crack plane These assumptions do not accurately reflect the actual stitch failure process that has been observed in many stitched composites, which as described above consists of axial plastic shear rotation, splittinglspalling, and ploughing of the stitches

Jain and Mai (1994e, 1995) state that the mode I1 strain energy release rate for crack propagation is given by:

where z is the applied shear stress and is related to the applied load, a is a correction factor accounting for shear deformation, a] and @ are stitching parameters, and R is related to materials properties through A" and a/ Using the steady-state crack propagation condition, G,, = G//c, where GI/, is the mode I1 critical strain energy release rate for the unstitched composite, the shear stress zneeded for crack propagation can be determined The critical strain energy release rate for a stitched composite can then be calculated from:

G, = A * ~ ~ ( a - t - & , : ) ~

The accuracy of the Jain and Mai models for determining the mode I1 interlaminar fracture toughness of stitched composites is shown in Figure 8.28 This figure presents

a comparison of the measured and theoretical GIN values for stitched composites, and there is good agreement However, some studies (eg Cox, 1999) show significant

disagreement between the model and experimental data

Cox and colleagues have formulated one-dimensional analytical models for predicting the traction shear stress generated in through-thickness fibres (including stitches) when subject to mode I1 loading (Cox et al., 1997; Cox, 1999; Massab6 et al.,

1998; Massab6 and Cox, 1999) The models are based on the relationship between the

bridging tractions applied to the fracture surfaces by the unbroken stitches and the opening (mode I) and sliding (mode 11) displacements of the bridged crack The models consider the micromechanical responses of stitches bridging a delamination crack, including the elastic stretching, fibre rotation and some other affects that occur under mode 11 Criteria for failure of the bridging tow by rupture or pull-out is also

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considered in the models, leading to predictions of the ultimate strength of the bridging ligaments in mixed mode conditions

Measured GI,, (kJ/m2) Figure 8.28 Plot of measured against theoretical GIIR values for stitched composites

The theoretical GIIR values were determined using the Jain and Mai models The closer the data points are to the straight line the better the agreement between the measured

and theoretical GllR value (from Mouritz and Jain, 1999)

Cox (1999) has shown that the bridging shear traction ( T I ) generated in a single stitch can be related to the crack sliding displacement (u,) and crack opening displacement

(uj) by the expressions:

(8.8a)

(8.8b)

where a, is the axial stress in the stitch on the fracture plane, E, is the Young’s modulus

of the stitch, Tis the applied shear stress, z, is the shear flow stress of the stitch, P, is the

crush strength of the composite, and s is the circumferential length of the stitch The build-up in the traction stress within a stitch with increasing sliding displacement can be accurately predicted using the above equation For example, Figure 8.29 compares the predicted traction stress (thick line) with the experimentally measured traction stresses

(the two thinner curves) generated in a single Kevlar stitch subject to increasing sliding displacement The theoretical curve was calculated using the above equations by Cox (1999) and the experimental curves were measured by Turrettini (1996) There is excellent agreement between the theoretical traction curve and the two experimental curves up to the peak stress (TI - loo0 MPa), at which point failure of the stitch occurs

By determining the traction stress generated in a single stitch, it is then possible to determine the average traction stress (t) in a number of stitches bridging a mode I1 delamination crack in a composite using the simple expression (Cox, 1999):

where c, is the area fraction of stitching

sliding displacement, ui (mm)

Figure 8.29 Comparison of the Cox model for the shear traction in a single stitch (thick curve) with two experimental curves showing measured traction in a Kevlar stitch in a carbodepoxy laminate determined by Turrenttini (1996) (from Cox, 1999)

8.5 IMPACT DAMAGE TOLERANCE OF STITCHED COMPOSITES

8.5.1 Low Energy Impact Damage Tolerance

As discussed in Chapter 1, a problem with using 2D laminated composites in highly- loaded structures, particularly aircraft components, is their susceptibility to low energy impact damage The damage caused by a low energy impact is characterised by delamination cracking, matrix cracking and, in some instances, breakage of fibres Low energy damage to thin aircraft grade composites usually occurs at incident impact