Utilising fracture mechanics principles for predicting the mixed-mode delamination onset and growth in tapered composite laminates

Composite Structures 102 (2013) 294–305

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Utilising fracture mechanics principles for predicting the mixed-mode delamination onset and growth in tapered composite laminates Stefanos Giannis ⇑ Materials Engineering Research Laboratory (MERL) Ltd., Wilbury Way, Hitchin SG4 0TW, UK

a r t i c l e

i n f o

Article history: Available online 21 March 2013 Keywords: Fatigue Delamination Mixed mode Ply drop-offs LEFM

a b s t r a c t The quasi-static and fatigue performance of carbon and E-glass fibre reinforced tapered laminates was experimentally investigated. Utilising local strain measurements and digital photographs the load levels for delamination initiation were identified. In addition, the fatigue cycles for onset of delamination and growth to a predefined length, which defined the final failure criterion, were accurately evaluated. The data generated served as validation of a predictive methodology for onset of delamination and subsequent growth. The predictive methodology, which was based on a fracture mechanics approach, utilised the mixed mode fatigue delamination behaviour of the materials and finite element analysis of the laminates for evaluation of the strain energy release rate. Satisfactory prediction of the fatigue performance was obtained and the effect of fibre bridging, occurred during the test, on the fatigue life was demonstrated. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Tapered composite structures formed by terminating or ‘‘dropping-off’’ some of the plies have received much attention from researchers since the mid-1980s, because of their potential for creating significant weight savings compared to conventional laminated composite components. However, tapered composite structures create geometry and material discontinuities that act as potential sources for delamination initiation and propagation. There has been noteworthy research work to understand the failure mechanisms induced by ply drop-offs in tapered constructions through the determination of the state of interlaminar stresses in the vicinity of ply drop-offs, the calculation of strain-energy release rate associated with delamination within the tapered region, and the direct modelling of delamination progress by using finite elements [1–9]. The delamination analysis of tapered composite laminates involves the determination of interlaminar stresses using finite element methods or analytical tools, the prediction of delamination onset location, and simulation of delamination propagation. In order to predict delamination onset and growth and, hence, the performance of the composite laminates, some form of failure predictive methodology needs to be applied. Two general approaches exist for this purpose. They are the strength-of-materials approach (stress and strength approach) and the strain-energy-release-rate approach (fracture mechanics approach). In the strength-of-materials ⇑ Tel.: +44 (0)1462 427864; fax: +44 (0)1462 427851. E-mail address: [email protected] 0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.03.008

approach, the local stress or strain state is compared to the material strength allowables [10]. In the strain-energy-release-rate approach, which is based on fracture mechanics, failure in a composite laminate is associated with delamination growth to a critical level. Delamination growth occurs when the available strain energy of a delamination crack in a ply interface exceeds the critical strain-energy-release rate for the material [3–9]. Although much of the past research work was driven by commercial and military aircraft and rotorcraft applications, the benefits that tapered composite laminates offer to a design engineer, can also been seen in the design of load bearing spars for wind and tidal turbine blades. The basic difference is that in the renewable energy sector usually much heavier prepregs are used in outof-autoclave manufacture processes, which result in thicker plies and hence structures. In this study, the quasi-static and fatigue performance of tapered laminates comprising external ply drop-offs and carbon and glass reinforced materials was investigated experimentally. Utilising data collected from strain gauges and digital cameras during fatigue testing, the point of failure in the form of delamination at critical locations was identified. The experimental set-up also allowed tracking delamination growth and generating information for validating a predictive methodology for onset as well as growth of damage under fatigue loading conditions. The predictive methodology was based on a fracture mechanics approach. For its implementation, a mixed mode quasi-static and fatigue delamination criterion was developed for both carbon and glass reinforced materials, and is presented here, by interpolation between pure mode I and pure mode II experimental data.

S. Giannis / Composite Structures 102 (2013) 294–305

2.2. Quasi-static tests on tapered laminates

Table 1 Details of laminates and specimens tested.

a

Prepreg

Laminate Lay-up

HS-carbon/ epoxy E-glass/epoxy

ACF

–– 0° plies,

AGF

Sketcha

[0/0/0/0/ 04]S [0/0/0/0/ 04]S

+45° plies,

295

Static/ fatigue specimens 6/10 6/10

45° plies.

2. Experimental procedures 2.1. Materials and specimens Tests were carried out on tapered laminates made of two materials, namely E-glass/epoxy (AEL material MRC042) and HS-carbon/ epoxy (AEL material MRC044). Both prepregs had an areal weight of 600 g/m2, which resulted in cured ply thicknesses of 0.50 mm and 0.65 mm, respectively. The E-glass/epoxy prepreg had a 90° stitch with the same type of fibre. These prepregs are commonly used for laying up thick composite structures for renewable energy applications. Because of their high areal weight they facilitate fast lay-up of thick laminates, commonly found in load carrying members of wind and tidal turbine blades. Tapered laminates were hand laid-up and oven cured at 80 °C for 5 h. Pressure was applied through a vacuum bag. Two laminates were manufactured; one made of HS-carbon/epoxy and one of Eglass/epoxy. Both comprised only external ply terminations at a nominal distance of 30 mm and were manufactured following a unidirectional lay-up of [0/0/0/0/04]S. They were initially laid-up as half laminates, which were partially cured before laying up the other half back-to-back and the cure process completed. Parallel sided specimens were cut from the laminates with a nominal length of 350 mm and a nominal width of 15 mm. The nominal thickness of the thin section was 5.2 mm for the HS-carbon/epoxy laminates and 4 mm for the E-glass/epoxy laminates. Glass fibre reinforced end tabs were bonded at each end of each specimen to allow for better grip and load application. Details on the different laminates and number of specimens tested are given in Table 1. The geometry of the specimen is given in Fig. 1. Double Cantilever Beam (DCB) and End Loaded Split (ELS) specimens were used for characterising the delamination behaviour of the composite materials under quasi-static and fatigue loading. Flat panels were also cured at 80 °C for 5 h. The panels were sectioned into test specimens nominally 200 mm long and 20 mm wide. A 15 lm thick non-adhesive film insert was placed on the mid-plane through the thickness of the laminates, before curing, to provide an initial delamination approximately 75 mm in length. Aluminium hinges were bonded at the delaminated end to enable load application. After bonding the aluminium hinges the initial delamination length was approximately 50 mm long.

The quasi-static tests on tapered laminates were performed on a Zwick Z250 universal testing machine equipped with a 250 kN load cell and 150 kN capacity mechanical wedge grips. A Zwick Multisens™ contacting extensometer was used to measure the deformation of the specimens over a length of 150 mm and provide information of their global stiffness. All tests were conducted at ambient temperature with a loading rate of 1 mm/min. Two general purpose strain gauges (C2A-13-250LW-350, Vishay Micro-measurements) were bonded on opposite faces, near the anticipated location of failure initiation, on three out of six quasi-static specimens. Two PixeLINK™ digital cameras were employed to record photographs at specified time intervals during the tests to assist identifying the damage initiation and ultimate failure more accurately. In order to help identify the failure initiation locations, both edges of the specimens were painted with white correction fluid and a grid was marked to enable tracking of the delamination onset and growth. All data (i.e. load, displacement, and strain gauge measurements) were recorded using a purpose built LabViewÒ program. Delamination length was measured from the digital photos with 1 mm accuracy. The point of delamination initiation was cross-evaluated with the strain gauge recorded data. 2.3. Fatigue tests on tapered laminates The fatigue tests were conducted on a MTS 810 test machine equipped with a 250 kN servo-hydraulic actuator and a 250 kN load cell connected in series with 100 kN capacity hydraulic grips. Tests were conducted under load control with an R-ratio of 0.1. Displacements were taken from the actuator movement. The global compliance as well as the maximum and minimum load and displacement were monitored and recorded. Furthermore, for the specimens with attached strain gauges, the maximum and minimum strains were also monitored and recorded throughout the tests. All tests were carried out at ambient temperature with a frequency of 5 Hz. Two digital cameras were employed to record photographs at specified time intervals during the tests to help identify the damage initiation and ultimate failure. For the application of the load, there was an initial ramp up to the mean load followed by cycling to the test maximum and minimum loading conditions. Once the specimens were loaded with the mean load, fatigue loading conditions were achieved within the first few cycles. Tests were stopped when delamination from any point of initiation reached a total length of 20 mm or when no initiation or only limited growth was seen after one million cycles (run-out tests). 3. Fracture analysis 3.1. Mixed mode delamination criteria In order to conduct fracture analysis of the tapered laminates, a mixed mode delamination criterion had to be generated for the

Fig. 1. Geometry and nomenclature of tapered laminate specimen.

S. Giannis / Composite Structures 102 (2013) 294–305

Fig. 2. Mode I (DCB), mode II (ELS) and mixed mode I/II (FPS) loading conditions for evaluation of fracture toughness.

Table 2 Mean value of fracture toughness under mode I, mode II and mixed mode I/II loading. GIIc (J/m2)

GI/IIc (J/m2)

B–K exponent n

HS-carbon/epoxy NL 213 5% 232 Plateau 855

1155 1826 –

574 734 –

1.12 1.34 –

E-glass/epoxy NL 308 5% 365 Plateau 892

2912 4424 –

1048 1048 –

1.49 2.11 –

GIc (J/m2)

Gc (J/m2)

2000

GNorm Imax ¼ ðGImax =GIR ÞGc

ð1Þ

In Eq. (1) GImax is the applied maximum strain energy release rate, GIR is the respective level of critical strain energy release rate taken from the R-curve and GIc the quasi-static fracture toughness. In order to generate a mixed mode fatigue delamination criterion Eq. (2) was fitted to the experimental results in Fig. 3 while Eq. (3) to those in Fig. 4. Eq. (2) is an empirical power law that was found to describe adequately the behaviour of both materials and modes of loading for the onset of delamination growth. Parameters F and s were evaluated through curve fitting procedures and given in Table 3. Eq. (3) is an extension to Paris law that additionally describes the behaviour of the materials at high levels of Gmax,

6000 HS-carbon / epoxy f= 5 Hz, δmin/ δmax= 0.1

5000

mode I mode II

Gc (J/m2)

2500

Gmax (J/m2)

Material

two materials. Thus, mode I, mode II and mix mode quasi-static and fatigue tests were performed (Fig. 2). The Double Cantilever Beam (DCB) specimen was used to generate mode I data, following the ASTM D 5528 international standard [11], while the EndLoaded Split (ELS) specimen was used for mode II following the procedure highlighted in the ESIS T4 Protocol [12]. Quasi-static mixed mode tests at a mixed mode ratio comprising 43% mode II and 57% mode I were also performed using the Flexural Peel Specimen (FPS) configuration. The testing procedures for the mixed mode test were similar to the mode II described in [12]. The quasi-static test results are given in Table 2 for both materials used in this work, together with the fit parameter of the mixed mode delamination criterion proposed by Benzeggagh and Kenane (B–K) [13]. Once established, the B–K mixed mode delamination criterion allows the evaluation of the mixed mode I/II fracture toughness for any mix mode ratio ranging from pure mode I (GII/GTotal = 0) to pure mode II (GII/GTotal = 1). In addition to the quasi-static tests, displacement controlled fatigue delamination tests were performed under mode I and mode II loading conditions. Tests were performed at ambient laboratory conditions using the same specimens and test configurations as in the quasi-static tests. The loading ratio used was equal to 0.1 and the frequency of the tests was set to 5 Hz. The number of fatigue cycles for onset of delamination growth (G–N curve) was evaluated and presented in Fig. 3, following ASTM 6115 [14], wherever applicable. Moreover, delamination growth rate curves (da/dN–G curves) were also generated for mode I and mode II loading conditions (Fig. 4). Because fibre bridging was observed during quasi-static mode I testing, resulting in increasing R-curve for both materials, the mode I delamination growth curves were normalised to account and exclude such effects, following the procedure presented in [15–17].

1500 1000

4000

Gmax (J/m2)

296

E-glass / epoxy f= 5 Hz, δmin/ δmax = 0.1 mode I mode II

3000 2000

500 0

1000

0

10

1

10

2

10

3

10

4

10

5

10

6

10

7

10

0

0

10

1

10

2

10

3

10

4

10

5

10

6

10

Cycles to Delamination Onset of Growth, N

Cycles to Delamination Onset of Growth, N

(a)

(b)

Fig. 3. Fatigue experimental G–N curves and best fit lines for the (a) HS-carbon/epoxy and (b) E-glass/epoxy materials.

7

10

297

S. Giannis / Composite Structures 102 (2013) 294–305

100

100

HS-carbon / epoxy

f = 5 Hz, δmin / δmax= 0.1

-1

10

E-glass / epoxy

f = 5 Hz, δ min / δmax= 0.1

-1

10

mode I

10-2

mode II

da / dN (mm/cycle)

da / dN (mm/cycle)

mode I

10-3 10-4 10-5 10-6 10-7 10-8

10-2

mode II

10-3 10-4 10-5 10-6 10-7

1

10

100

1000

10-8

1

10

100

1000

Maximum Cyclic Strain Energy Release Rate, Gmax (J/m2)

Maximum Cyclic Strain Energy Release Rate, Gmax (J/m2)

(a)

(b)

Fig. 4. Fatigue experimental da/dN–Gmax curves and best fit lines for the (a) HS-carbon/epoxy and (b) E-glass/epoxy materials.

Table 3 Eq. (2) curve fitting parameters for mode I, mode II and interpolated values for mixed mode I/II.

Mode II

Mixed mode I/II, GII/GTotal = 0.43a

HS-carbon/epoxy A1 3.16  1012 B1 3.94 Gth 14

1.27  1012 3.57 24

2.43  1012 3.80 18

E-glass/epoxy A1 1.76  1013 B1 4.37 Gth 21

6.27  1014 3.55 56

1.44  1013 4.14 31

Mode II

Mixed mode I/II, GII/GTotal = 0.43a

Material

HS-carbon/epoxy F 0.021 s 0.217

0.289 0.210

0.107 0.215

E-glass/epoxy F s

0.210 0.283

0.043 0.254

Material

a

Table 4 Eq. (3) curve fitting parameters for mode I, mode II and interpolated values for mixed mode I/II.

Mode I

0.009 0.248

Interpolated values.

Mode I

Note: parameter D was set equal to 20 for all cases. a Interpolated values.

approaching the quasi-static fracture toughness Gc, as well as at very low levels of Gmax, approaching the fatigue threshold Gth [18,19]. Again, parameters A1, B1 and D were evaluated by curve fitting and given in Table 4. s Gmax ¼ G5% c ½1 þ FðN 0  1Þ

0  D 1 th 1  GGmax da C B1 B ¼ A1 ðGmax Þ @  D A dN Gmax 1  GNL

ð2Þ

ð3Þ

c

By interpolating between mode I and mode II, using the relationship established for the quasi-static fracture toughness (B–K criterion in Table 2), a mixed mode delamination criterion for both onset and growth was created [20]. This was used to describe the delamination behaviour under any mixed mode I/II loading condition. 3.2. Finite element models Three-dimensional finite element (FE) models of the two laminate configurations were created in Abaqus™/CAE. Threedimensional models were used, although a two-dimensional approximation could provide a fair degree of accuracy, in order to account for any anti-clastic bending effects on the specimen. The geometry and boundary conditions are shown in Fig. 5. It was assumed that delamination initiates and propagates equally on the two sides of the symmetric laminates, thus, only half of the specimen was modelled in FE and symmetry conditions were applied along the whole length of the mid-plane. A unit load

(P = 1 N) was applied at one end via a reference node rigidly attached to the end of the specimen. Displacement related degrees of freedom were constrained at the other end. One element per composite ply thickness was used, while the element width was 0.5 mm and the element length 0.2 mm. Linear elastic materials were used as well as linear geometry modelling procedures. The engineering constants were experimentally determined for the two materials and they are given in Table 5. Linear brick elements (C3D8) were used for both glass and carbon FE models. The Virtual Crack Closure Technique (VCCT) was used to evaluate the three components of the strain energy release rate GI, GII and GIII, across the width of the laminates. This was achieved by introducing a delamination (duplicate nodes) to the potential locations that delamination failure could occur. These locations were identified by using the analytical solution presented in the next section. The analytical equations of the VCCT procedure can be found in [21]. In this work, the VCCT procedure as this was implemented in ABAQUS™/CAE was used for the calculations. The three components of the strain energy release rate were evaluated for a number of delamination lengths and the total level of the strain energy release rate, GTotal, was computed using the following equation:

GTotal ¼ GI þ GII þ GIII

ð4Þ

In addition to VCCT, the strain energy release rate was also evaluated by the macroscopic change in the elastic stored strain energy between two consecutive delamination length increases. This is

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Fig. 5. Finite element model for the tapered laminates.

Table 5 Engineering constants for the two materials used in FE modelling.

E1 (GPa) E2, E3 (GPa)

v12 G12, G13 (GPa) G23a (GPa)

v23b a b

G¼

HS-carbon/epoxy

E-glass/epoxy

118 7.4 0.33 4.0 2.8 0.45

39 12 0.29 3.9 4.7 0.45

Calculated. Assumed.

P 2 @C 2b @a

ð8Þ

Eq. (6) is derived by differentiating Eq. (7) with respect to the delamination length and substituting the result into Eq. (8). Use of this simple analytical solution allows the determination of G at the various critical locations of laminates ACF and AGF. In this way the critical locations for delamination can be identified prior to employing the VCCT method to perform a detailed fracture analysis. 4. Experimental results from tapered laminates

expressed by Eq. (5), where b is the specimen width ai and ai+1 are two consecutive delamination lengths and U ai , U aiþ1 is the corresponding elastic stored energy in the specimen.

GGlobal

dU 1 U aiþ1  U ai ¼ ¼ dA b aiþ1  ai

ð5Þ

3.3. Closed form solution For a delamination located below any step n of a tapered laminate comprising only external ply drop-offs and being subjected to uni-axial loading, as this is presented in Fig. 6, the strain energy release rate can be expressed analytically through the following equation:

Ga ¼

P2 2

2b



1 1  E0 t0 En tn

 ð6Þ

where P is the applied load, b is the width of the laminate, t0 is the thickness of the laminate below the delamination, E0 is the effective modulus of the sub-laminate below the delamination, tn is the thickness of the laminate at the nth step and En is the effective modulus of the laminate including the nth step. This analytical solution is derived by considering the compliance for the delaminated tapered beam in Fig. 6, which is as follows:

C¼

  1 L0 þ a L1  a L2 Ln þ þ þ  þ þ  b E0 t 0 E1 t 1 E2 t 2 En t n

ð7Þ

For a specimen with constant width, G is given as a function of the applied load P and the variation of the compliance C with the delamination length, a, as:

4.1. Quasi-static results The load for failure initiation in the form of delamination was established using the visual evidence from the digital camera and, for the specimens with strain gauges attached, from the first sudden drop on the recorded strain of the strain gauges, which indicated significant damage. The ultimate failure load was taken as the point where a significant drop in the load was observed combined with the delamination rapidly growing along the full length of the specimens. For both ACF and AGF laminates, failure initiated in the form of a 0.5 to 1 mm delamination crack below the 1st step at the interface between the core and the first 0° ply (i.e. 0°/0° interface). Delamination propagated at the 0°/0° interface along the core towards the thick end of the specimens throughout the test for both materials, as illustrated in Fig. 7 for laminate ACF. For laminate ACF failure initiation in the form of a delamination crack at the 0°/0° interface occurred at 44 ± 3 kN (first visible crack on the recorded pictures) corresponding to a stress level at the core of 513 ± 40 MPa (Table 6). The delamination initiation load established by the strain gauges was 43.5 ± 7 kN, which is in excellent agreement with the values established using the visual evidence of the pictures. After initiation, delamination propagated slowly up to about 5 mm before becoming unstable and leading to rapid catastrophic failure of the specimens. The initial slow propagation could be an indication of possible fibre bridging, although this was not evident during the test. Similarly, for laminate AGF specimens (Table 6) initiation of delamination type failure occurred at 24 ± 2 kN corresponding to a stress level at the core of 388 ± 39 MPa. The average initiation load established by the strain gauges was 19 ± 3 kN, which is

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S. Giannis / Composite Structures 102 (2013) 294–305

Fig. 6. Schematic of a tapered laminate under uni-axial load comprising external ply drop-offs.

Fig. 7. Initiation of delamination and delamination path for laminate ACF; (a) Just before initiation, (b) initiation and (c) delamination growth path.

slightly lower than the values established using the visual evidence of the pictures. The strain gauges are more sensitive to the local changes in the laminate caused by the initiation of the delamination and hence could pick the events before these were visible at the digital images. Moreover, during the quasi-static tests only the edge of the specimens was observed. It became apparent during the experimental programme that for laminate AGF the delamination front was not straight and consequently while delamination already had initiated at the middle across the width (data provided from the strain gauges) that was not necessarily true for the edges. 4.2. Fatigue results For all fatigue testing, failure was defined as a crack growth of nominally 20 mm from any point of initiation. Hence, the number of cycles to failure reported here is the number of cycles it takes at the specific load level for a delamination crack from any point of initiation to grow by 20 mm. For the ACF specimens the crack growth was monitored on the side edges of the specimens whereas for the AGF specimens the front or back face was also used as specimens were translucent. The behaviour of the laminates in fatigue was the same as documented in quasi-static testing. For all specimens damage initiated in the form of a 0.5 to 1 mm delamination crack at the 1st step at the interface between the core and the first 0° ply, i.e. 0°/0° interface, at the terminating 0° ply. Delamination propagated at the 0°/0° interface along the core towards the thick end of the specimens throughout the test, until final failure, i.e. 20 mm growth of the delamination from the point of initiation. The number of cycles to initiation and failure at the different loading levels are given in Tables 7 and 8.

Table 6 Quasi-static experimental results for the two laminates (key: mean ± StDev).

Delamination initiation load Delamination initiation load Ultimate failure load (kN) Elastic stiffness (kN/mm)

a

(kN) b (kN)

ACF

AGF

44 ± 3 43.5 ± 7 58 ± 2.5 80 ± 6.5

24 ± 2 19 ± 3 45 ± 2 20 ± 1

a

Evaluated from the digital photos. Evaluated from the point where a significant drop on the strain gauge measurements occurred. b

A sudden drop on the strain gauge recording strain, indicating significant damage, was taken as the delamination initiation point for the strain gauged specimens (Fig. 8). The strain gauges (SG1 and SG2 in Fig. 8) pick up the point of delamination initiation before it can be established using the pictures from the camera. This might be because strain gauges are positioned mid-way across the width of the specimens and if the delamination front is not uniform the local strain at that location will be affected prior to seeing any delamination at the edge of the specimens (Fig. 9). 5. Analysis results and fatigue life prediction 5.1. Analytical calculation of strain energy release rate The closed form solution in Eq. (6) was used to identify the potential location of delamination initiation for the two tapered laminates. To apply the fracture mechanics principles it is assumed that an initial damage of finite size is present at each one of the ply termination locations (i.e. stress singular locations). The calculated results are given in Figs. 10 and 11 for the ACF and AGF

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S. Giannis / Composite Structures 102 (2013) 294–305

Table 7 Fatigue experimental results for laminate ACF.

a b c

Specimen

Load Fmax (kN)

Stress at thin end rmax (MPa)

Cycles Ninita

Cycles Ninitb

Cycles Nf

13 kN #1 15 kN #2 20 kN #1 20 kN #2 25 kN #1 25 kN #2 30 kN #1 30 kN #3 37.5 kN #1 37.5 kN #2

13.0 15.0 20.0 20.0 25.0 25.0 30.0 30.0 37.5 37.5

154 183 242 233 301 289 357 337 447 444

– – – 8050 – 555 – 65 – 1

– 332,009 11,846 13,312 1118 1486 210 282 121 52

1,170,000 c 1,062,278 77,755 78,649 23,745 22,940 5942 9728 1358 2610

Evaluated from the point where a significant drop on the strain gauge measurements occurred. Evaluated from the digital photos. Run-out. No evidence of failure initiation found on the monitored surface.

Table 8 Fatigue experimental results for laminate AGF.

c

Load Fmax (kN)

Stress at thin end rmax (MPa)

Cycles Ninita

Cycles Ninitb

Cycles Nf

12 kN #1 13.5 kN #1 15 kN #2 15 kN #3 17.5 kN #1 17.5 kN #2 20 kN #1 20 kN #2 25 kN #1 25 kN #2

12.0 13.5 15.0 15.0 17.5 17.5 20.0 20.0 25.0 25.0

196 219 244 244 293 285 336 338 409 417

– 340 – 75 – – – 70 – 43

1506 1505 1504 1503 306 305 106 84 35 36

955,425 c 326,634 154,161 159,352 38,429 33,596 12,708 8865 2137 2178

Evaluated from the point where a significant drop on the strain gauge measurements occurred. Evaluated from the digital photos. Run-out. Delamination did not reach 20 mm of growth criteria for total failure (2 mm growth at end of test).

laminates, respectively. The analysis suggests that delamination will initiate below the 1st step for both laminates, since this is the location with the highest Ga level. This is in good agreement with the experimental observations, presented earlier. An increase of the strain energy release rate while delamination is growing below the 1st step (i.e. between the 1st step and the core) and passing below the 2nd step suggests that delamination growth will become unstable at that stage. During quasi-static testing it was found that this transition from stable to unstable growth occurred between 5 to 10 mm. 5.2. Strain energy release rate analysis and quasi-static failure prediction

2500 Laminate ACF

1500

1000

500

0

Utilising the VCCT the distribution of the GI, GII and GIII components of the strain energy release rate were evaluated across the width of the tapered laminates at the locations of delamination initiation, as these were identified in the previous paragraph. In Figs. 12 and 13 the distribution of GI and GII is presented, for six different delamination lengths in laminate ACF at the interface between the 1st step and the core (i.e. 0°/0° interface). GIII was found to be two orders of magnitude lower than GI and GII. Both GI and GII were found to be fairly constant across the width of the specimen for delamination lengths up to 29.4 mm (i.e. when the delamination approaches the 2nd step). In particular, GI is fairly constant in the centre part of the specimen and progressively increases towards the edges. This is in contrast to evidence in the literatures [22,23] where it is reported that GI is usually fairly constant in the centre part and progressively decreases towards the edges, which will cause the initial straight front to grow into a curved front. However, as it is comprehensively explained in [24] this deviation at the edges of the specimen

Initiation of failure point

Specimen 25kN #2 SG1, maximum SG1, minimum SG2, maximum SG2, minimum

2000

Strain, ( με )

a b

Specimen

1

10

100

1000

10000

Cycles, N Fig. 8. Variation of cyclic strain (maximum and minimum) with respect to the number of fatigue cycles for laminate ACF specimen 25 kN #2.

is effectively caused by the use of C3D8 elements. In reference [24] it was shown that the GI component in a mixed-mode single leg bending specimen was not accurately captured at the edges by C3D8 elements but was well predicted across the remainder of the width. The mode II strain energy release rate as shown in Fig. 13 is fairly constant across almost the entire width of the specimen, peaking in the immediate vicinity of the edges. This is in agreement with findings in the literature [24]. For the fracture analysis, the average values of GI and GII across the width were evaluated excluding the values at the nodal positions close to the sides of the specimens (i.e. two nodes in each side). In this way, effect particular to the element type were

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Fig. 9. Photographs showing non-uniform delamination front for the AGF specimens tested under fatigue loading.

20

5 Laminate ACF

3

step 3

step 4

P

2

1

step 3 step 2

Analytical Solution Delamination growth under step 1 step 2 step 3

16

P

a

step 4

Laminate A GF

18

step 1

G / P2 (× 10-9 1/Nmm)

Analytical Solution Delamination growth under step 1 step 2 step 3

4

G / P2 (× 10-9 1/Nmm)

step 2

14 12

step 1

P

P

a

10 8 6 4 2

0 0

20

40

60

80

100

120

Delamination length, a (mm)

0

0

20

40

60

80

100

120

Delamination length, a (mm)

Fig. 10. Results from analytical solution for the distribution of normalised G along the delamination length for laminate ACF.

Fig. 11. Results from analytical solution for the distribution of normalised G along the delamination length for laminate AGF.

excluded from the analysis. These average values are presented in Fig. 14 together with the GIII, and the total strain energy release rate GTotal as normalised values with respect to the applied load. The strain energy release rate, Gglobal, from the global energy considerations is also plotted here and agrees very well with the VCCT results. The FE fracture analysis results in Fig. 14 suggested that the delamination propagation along the particular interface would be stable (i.e. zero gradient of the G–a curve) up to a delamination length of 15 mm, where the gradient becomes positive (+ve). This positive gradient suggests unstable delamination growth when

G P Gc. If compared to the experimental observations this somehow an over-prediction since during the quasi-static tests delamination became unstable after 5–10 mm of initial stable growth. From the VCCT results it is also suggested that the initiation of delamination at this interface would be mode I dominated (62% mode I compared to 38% mode II in Fig. 15) and as delamination is propagating the mode I component would increase further. The load for delamination initiation under quasi-static load can be predicted by considering the values of GTotal/P2 and GII/GTotal when a ? 0. The consideration of a finite but very small delamination length is made to satisfy the fracture mechanics principles

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3.0

2200 0.4 mm 10 mm 20 mm

1800

5 mm 15 mm 29.4 mm

2.5

G / P2 (× 10-9 1/Nmm)

2000

GI (× 10-12 N/mm)

Laminate A CF

Laminate A CF VCCT Results

1600 1400 1200 1000

2.0

GII GIII

1.5

GTotal Energy Balance GGlobal

1.0 0.5

800 600 0.0

VCCT GI

2.5

5.0

7.5

10.0

12.5

0.0

15.0

0

5

10

Width, b (mm)

15

20

25

30

Fig. 12. Variation of the mode I (GI) component of the strain energy release rate across the width of laminate ACF for six different delamination lengths.

45

1.0 Laminate A CF VCCT Results

Laminate A CF

5 mm 15 mm 29.4 mm

0.8

Mode Mixity Ratio

0.4 mm 10 mm 20 mm

1000

GII (× 10-12 N/mm)

40

Fig. 14. Normalised strain energy release rate as a function of delamination length for laminate ACF.

1200

800

600

400

200 0.0

35

Delamination length, a (mm)

GII / GTotal GI / GTotal

0.6

0.4

0.2

2.5

5.0

7.5

10.0

12.5

0.0

15.0

0

5

10

Width, b (mm)

15

20

25

30

35

40

45

Delamination length, a (mm)

Fig. 13. Variation of the mode II (GII) component of the strain energy release rate across the width of laminate ACF for six different delamination lengths.

Fig. 15. Mixed mode ratio as a function of delamination length for laminate ACF.

under the assumption that a characteristic finite size flaw will exist or form because of high stress concentration at this location.

delamination initiation was predicted at 26 kN applied load which is in very good agreement with the experimental results (26 ± 2 kN).

9 > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1:459  109 1=Nmm > = 0:668 N=mm ) P ¼ 2  ¼ 0:38 > 1:459  109 1=Nmm > ; Gc ¼ 0:668 N=mm

GTotal P2 GII GTotal

¼ 42:7 kN ð9Þ The predicted load for failure initiation was found equal to 42.7 kN (or 547 MPa applied stress at the thin end of the specimen), which is in excellent agreement with the experimental measured one of 44 ± 3 kN from the quasi-static tests. In Fig. 16 the variation of the computed normalised G values for the AGF laminate is presented. The fracture analysis revealed identical behaviour to the ACF laminates, but the level of GTotal was approximately three times higher, indicating that delamination will initiate and propagate under lower applied loads, considering that there was no excessive difference in the fracture toughness of the two materials. The mixed mode ratio GII/GTotal was also slightly higher at 0.4 for very small delamination lengths. The mixed mode ratio was found constant for delamination lengths up to 20 mm (Fig. 17). The positive gradient (+ve) of the normalised GTotal curve, for delamination lengths longer than 20 mm, indicated unstable growth. From the FE fracture analysis results the load for

5.3. Fatigue delamination onset prediction The FE fracture analysis results together with the fatigue delamination criterion were used to predict the fatigue cycles for onset of delamination growth and subsequent growth to 20 mm. For predicting the onset of delamination growth Eq. (2) is solved for N0:

 N0 ¼

Gmax =G5% c F

s

1

þ1

ð10Þ

For delamination length a0 ? 0 and a given applied load P, Gmax was evaluated from the FE fracture analysis and the respective mixed mode ratio GII/GTotal was considered. Parameters G5% c , F, and s are all functions of the mixed mode ratio and were evaluated for the particular mixed mode ratio from interpolation between pure mode I and mode II. This enabled the prediction of the onset of delamination fatigue cycles for any given load and the results for laminate ACF and AGF are presented as solid lines in Figs. 18 and 19, respectively. The agreement of the predicted values to the experimental data is very good both at low and high cycles. Note that for unit cycle the quasi-static results and predictions are presented in Figs. 18 and 19.

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10

1000 Laminate A GF

Laminate AGF

GII

6

GIII GTotal

4

2

0

600

400

200

0

5

10

15

20

25

30

35

40

0 0 10

45

Delamination length, a (mm)

1.0

1

10

2

10

3

10

4

10

5

10

6

10

7

Fig. 19. Experimental results and numerical prediction of delamination onset and growth by 20 mm for laminate AGF.

increment, i, from the GTotal–a curve in Fig. 14. These energy release rate values were then used to obtain the delamination growth rate Da/DN from the extended Paris Law for the specific mixed mode ratio GII/GTotal. The number of cycles for delamination growth, Ngrowth, was calculated by summing the increments DNi.

Laminate A GF 0.8

10

Cycles, N

Fig. 16. Normalised strain energy release rate as a function of delamination length for laminate AGF.

Mode Mixity Ratio

Experimental Onset 20 mm growth Prediction Onset 20 mm growth 20 mm growth fibre bridging

800

VCCT GI

Stress, (MPa)

G / P2 (× 10-9 1/Nmm)

8

GII / GTotal GI / GTotal

0.6

Ngrowth

0.4

2 0  D 131 Gth k k 1  X X Gi;max 6 C7 B B ¼ DN i ¼ 4A1 ðGi;max Þ 1 @   A 5 Da Gi;max D i¼1 i¼1 1  GNL

ð11Þ

c

where k is the number of increments. The corresponding delamination length, a, was calculated by adding the incremental lengths Da to the initial length a0.

0.2

0.0

0

5

10

15

20

25

30

35

40

45

a ¼ a0 þ

Delamination length, a (mm)

k X Da

ð12Þ

i¼1

Fig. 17. Mixed mode ratio as a function of delamination length for laminate ACF.

1000 Laminate A CF

Stress, (MPa)

N ¼ N0 þ Ngrowth

Experimental Onset 20 mm growth Prediction Onset 20 mm growth

800

600

400

200

0 0 10

1

10

2

10

3

10

4

10

5

10

Finally, the total fatigue life as a combination of onset of delamination and growth to the specified delamination length (i.e. 20 mm), was evaluated as:

6

10

7

10

Cycles, N Fig. 18. Experimental results and numerical prediction of delamination onset and growth by 20 mm for laminate ACF.

5.4. Fatigue delamination growth prediction The number of fatigue cycles for delamination growth under specific applied load (stress at the thin end) can be obtained by solving Eq. (3) for Ngrowth. Starting from an initial delamination length a0, the energy release rates Gi,max were obtained for each

ð13Þ

In Fig. 18 the correlation of the predicted number of cycles for a delamination length of 20 mm is shown to be in very good agreement to the experimental values. Moreover, for each applied load level, corresponding to a specific level of tensile stress at the thin end of the specimens, the delamination length growth was evaluated and is plotted against experimental results in Fig. 20. For three stress levels experimental evidence of two specimens in each case were available, while for the lower stress level only one specimen was monitored. The predicted delamination length growth was found to be in good agreement with the test results. The same procedure for predicting the delamination growth to 20 mm for a number of loading cases was followed for the AGF laminate. As shown in Fig. 19 the predicted fatigue life under-estimates the experimentally determined performance of the laminates. During the development of the mixed mode delamination criterion it was postulated that any fibre bridging occurring during mode I testing should be excluded so the material characteristics are independent of this particular inherent property of the unidirectional DCB specimen [15–17]. The extended Paris law constants in Table 4 were evaluated by excluding these effects. While testing laminate ACF, although delamination propagated between a 0°/0° interface, there was no evidence of fibre bridging and hence the

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S. Giannis / Composite Structures 102 (2013) 294–305 0

30

10

25 20

Stress Exp. Pred. 347 MPa 295 MPa 247 MPa 183 MPa

10

3

mode I

-2

5

2

δ min / δ max = 0.1

10

10

10

f = 5 Hz

-1

15

0 1 10

E-glass / Epoxy

10

da / dN (mm/cycle)

Delamination Length, a (mm)

Laminate A CF

10

4

10

5

10

6

10

7

-3

10

excl. fibre -4

10

bridging effects

-5

10

-6

10

incl. fibre

Cycles, N

bridging effects

-7

10

Fig. 20. Delamination length vs. number of fatigue cycles for different applied stress levels for laminate ACF specimens.

-8

10

6. Conclusions The quasi-static and fatigue behaviour of two tapered composite laminates were experimentally investigated and analysed using an analytical approach confirmed by finite element analysis. In the experimental programme, the delamination failure initiation and growth in the laminates under uni-axial loading was identified. The locus of delamination failure was the same between quasi-static and fatigue loading conditions. The location of delamination initiation was predicted through the analytical approach and three dimensional FE models were created and fracture analysis by the VCCT method was used to locally investigate the behaviour of the tapered laminates. The FE results of the fracture analysis were

1

10

100

1000

Gmax (J/m2) Fig. 21. Effect of fibre bridging on the mode I delamination growth rate of E-glass/ epoxy material.

25

Delamination Length, a (mm)

Laminate A GF 20

Prediction including fibre bridging

Stress Exp. 289 MPa

15 Prediction excluding fibre bridging 10

5

0 1 10

2

10

3

10

4

10

5

10

6

10

Cycles, N Fig. 22. Delamination length vs. number of fatigue cycles for an applied stress level of 289 MPa for laminate AGF specimens.

25 Laminate A GF

Delamination Length, a (mm)

material model resulted in very satisfactory predictions. However, this was not the case for the AGF laminate, mainly because bridging effects are more pronounced in this laminate because apart from the delamination propagating along a 0°/0° interface there is also the 90° stitching that also contributes to such effects. Therefore, the extended Paris law constants that include the effects of fibre bridging should also be considered for the E-glass/epoxy under mode I loading. These are A1 = 4.7  1019, B1 = 6.09 and were evaluated from the experimental mode I delamination fatigue data without the normalisation procedure discussed in Section 3.1 and presented in detail in Refs. [15–17]. The difference between the two sets of data is presented in Fig. 21. Delamination growth rate, including the fibre bridging effects, is much slower under the same applied Gmax. The mixed mode delamination criterion was re-established by interpolating between the new constants for mode I, listed above, and the mode II data in Table 4. The revised predicted fatigue life for 20 mm delamination growth is shown in Fig. 19, as dotted line, and agrees very well with the experimental results. The above was further investigated by plotting the predicted delamination length for an applied stress level of 289 MPa (20 kN) with respect to the fatigue cycles (Fig. 22), and comparing the prediction from the two approaches (i.e. fibre bringing and no fibre bridging effects) with the experimental data. When bridging effects are taken into account the predicted delamination growth agreed reasonably well to the experimental measurements of the delamination length, especially for high fatigue cycles. There was large deviation between the experimental results and the growth predictions when bridging effects were excluded. Taking into account the bridging effects, satisfactory predictions of the delamination length for applied stress levels of 337 MPa, 248 MPa and 219 MPa were derived and presented in Fig. 23.

20

15

Stress Exp. Pred. 337 MPa 289 MPa 248 MPa 219 MPa

10

5

0 1 10

2

10

3

10

4

10

5

10

6

10

Cycles, N Fig. 23. Delamination length vs. number of fatigue cycles for different applied stress levels for laminate AGF specimens.

S. Giannis / Composite Structures 102 (2013) 294–305

companied with a mixed mode delamination criterion, by non-linear interpolation between mode I and mode II experimental results, to generate predictions for the onset of delamination growth and the delamination growth rate. The correlation between the predicted quasi-static strength and fatigue life and the experimental results was very good in the case of HS-carbon/epoxy tapered laminates with external ply drop-offs. For the same tapered configuration but with the E-glass/epoxy prepreg, fibre bridging had to be taken into account in the mixed mode delamination criterion to derive satisfactory predictions. The reason for this system presenting fibre bringing, or additional delamination resistance, was attributed to the 90° stitch was in the construction of the prepreg. Overall, very satisfactory predictions for onset delamination and growth were derived using this method; however, the importance of generating suitable delamination fracture material data should be highlighted. Although in this particular case mode I and mode II fatigue data were sufficient and only an interpolation was performed for mixed-mode, there could be cases that specific mixed-mode I/II information should be generated, making this a laborious exercise. In addition, issues like fibre bridging should always be considered when building a material model to reflect the actual behaviour of the composite. The significant advantage of this method, when compared to cohesive zone modelling, is that avoids introducing further constants, sometimes with no physical meaning, for the prediction of the onset of delamination. On the other hand, it assumes the existence of a finite small crack to enable prediction of delamination onset, which is not true for a pristine laminate. Finally, assessment of the applicability of the method on more complex tapered laminates will provide further validation and increase confidence for its use. Acknowledgments The author would like to acknowledge the UK Technology Strategy Board for co-funding this research work under the NEW-MMEETT (New Materials and Methods for Energy Efficient Tidal Turbines) Project (Project No. 100514). Special thanks to Aviation Enterprises Ltd. (AEL) for preparing all specimens tested in this work and Mr. Kim Hansen at MERL for assisting with the testing. References [1] Hoa SV, Du BL, Vu-Khanh T. Interlaminar stresses in tapered laminates. Polym Compos 1988;9:337–44. [2] Daoust J, Hoa SV. Parameters affecting interlaminar stresses in tapered laminates under static loading conditions. Polym Compos 1989;10:374–83. [3] Salpekar SI, Raju IS, O’Brien TK. Strain-energy-release rate analysis of delamination in a tapered laminate subjected to tension load. J Compos Mater 1991;25:118–41.

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[4] Murri GB, O’Brien TK, Salpekar SA. Tension fatigue of glass/epoxy and graphite/ epoxy tapered laminates. J Am Helicopter Soc 1993;38:29–37. 5 Murri GB, Salpekar SA, O’Brien TK. Fatigue delamination onset prediction in unidirectional tapered laminates. In: O’Brien TK, editor. Composite materials: fatigue and fracture ASTM STP 1110. Philadelphia: American Society for Testing and Materials; 1991. p. 312–39. [6] Wisnom MR, Jones MI, Cui W. Failure of tapered composites under static and fatigue tension loading. AIAA J 1995;33:911–8. [7] Wisnom MR, Dixon R, Hill G. Delamination in asymmetrically tapered composites loaded in tension. Compos Struct 1996;35:309–22. 8 Wisnom MR, Jones MI, Cui W. Delamination in composite with terminating internal plies under tension fatigue loading. In: Martin RH, editor. Composite materials: fatigue and fracture ASTM STP 1230. Philadelphia: American Society for Testing and Materials; 1995. p. 486–508. [9] Murri GB, O’Brien TK, Rousseau CQ. Fatigue life methodology for tapered composite flex-beam laminates. J Am Helicopter Soc 1998;43:146–55. [10] Curry JM, Johnson ER, Starnes Jr JH. Effect of dropped plies on the strength of graphite–epoxy laminates. AIAA J 1992;30:449–56. [11] ASTM D 5528. Standard test method for mode I interlaminar fracture toughness of unidirectional fibre-reinforced polymer matrix composites; 2007. [12] ESIS T4 Protocol. Fibre composites – the determination of the mode II fracture resistance GIIc of unidirectional fibre-composites using the calibrated end loaded split (C-ELS) test and an effective crack length approach; 2008. [13] Benzeggagh ML, Kenane M. Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixedmode bending apparatus. Compos Sci Technol 1996;56:439–49. [14] ASTM D 6115. Standard test method for mode I fatigue delamination growth onset of unidirectional fiber-reinforced polymer matrix composite; 2004. [15] Giannis S, Hansen K, Martin RH. Accounting for the R-curve effects on the mode I fatigue delamination growth characterisation of unidirectional composites. In: Presented at the 25th annual technical conference of the American Society for composites/14th US–Japan conference on composites materials, September 20–22, 2010. [16] Murri GB. Effect of data reduction and fibre-bridging on mode I delamination characterisation of unidirectional composites. In: Presented at the 26th annual technical conference of the American Society for composites/2nd US–Canada conference on composites materials, September 26–28, 2011. [17] Giannis, S. On the evaluation the fatigue delamination growth rate and thresholds for CFRP and GFRP composites under mode I loading; in press. [18] Martin RH, Murri GB. Characterisation of mode I and mode II delamination growth and thresholds in AS4/PEEK composites. In: Garbo SP, editor. Composite materials: testing and design ASTM STP 1059. West Conshohocken: American Society for Testing and Materials; 1990. p. 251–70. [19] Shivakumar K, Chen H, Abali F. A total fatigue life model for mode I loaded composite laminates. Int J Fatigue 2006;28:33–42. [20] Giannis S. Development of delamination onset and growth criteria for damage tolerant design of small aircraft composite structures. In: Presented at the 14th European conference on composite materials, June 7–10, 2010. [21] Krueger R. Virtual crack closure technique: history, approach, and applications. Appl Mech Rev 2004;57:109–43. [22] Krüger R, König M, Schneider T. Computation of local energy release rates along straight and curved delamination fronts of unidirectional laminated DCB and ENF specimens. In: Presented in 34th AIAA/ASME/ASCE/AHS/ASC SSDM conference, La Jolla, CA; 1993. [23] Davidson BD. An analytical investigation of delamination front curvature in double cantilever beam specimens. J Compos Mater 1990;24:1124–37. [24] Krueger R, Goetze D. Influence of finite element software on energy release rates computed using the virtual crack closure technique. Report NASA/CR2006-21452; 2006.