Effect of span/thickness ratio on fatigue properties of thick quasi-isotropic CFRP laminates subjected to three-point bending loading

In this study, three-point bending fatigue tests were conducted to investigate damage growth behavior of thick quasi-isotropic carbon fiber reinforced plastic (CFRP) laminates. The span/thickness ratio L/h was varied for both static tests and fatigue tests to determine failure mechanisms. In the static tests, the failure mode changed from delamination to compressive buckling as span/thickness ratio increases. The apparent interlaminar shear strength was higher for the specimens with lower span/thickness ratios, and the shear failure was likely to be caused by oblique crack in 90° plies. In the fatigue tests, the specimens with span/thickness ratio L/h=7 caused delamination regardless of stress level. For the specimens with span/thickness ratio L/h =15, three types of failure modes were obtained depending on stress level; delamination near the neutral plane, buckling at compressive area and matrix crack at tensile area. During the fatigue tests, stiffness of specimens with different span/thickness ratios which fail in shear was compared using digital image correlation (DIC) method. The specimens with span/thickness ratio 4 suddenly decreased in stiffness without increasing normal strain over cycles. Both specimens with span/thickness ratio 4 and 11 finally failed by delamination but they showed different failure process in how normal or shear strain developed.


Introduction
In recent years, carbon neutral society is widely aimed and carbon fiber reinforced plastics (CFRPs), with high corrosion resistance, have been adopted for several marine structures including blades for tidal turbines and ship propellers as well.Applying to ship propellers is said to contribute to reduction of fossil fuels use [1].The application to ship propellers is subjected to very high cyclic loadings, resulting in 10 9 cycles.In addition, bending load will increase at the root of blades where thicker materials are used.Thus, it is necessary to accurately evaluate the bending fatigue properties for thick CFRP laminates to ensure long-term reliability.
The damage growth behaviors of composites by three-point bending test have been widely investigated in previous works.Makeev [2] studied shear properties under three-point bending cyclic loading for unidirectional carbon/epoxy composites with 3.8 mm thick.A sharp increase in shear strain was found just before the failure and a likely reason for this result was concluded that accumulation of non-visible damage increased in matrix.It was found that undetectable micro matrix cracking caused a sharp increase in shear strain just before the failure.He and Makeev [3] performed three-point bending tests of unidirectional polymer matrix composites with different span/thickness ratios.They showed good agreement between numerical and experimental shear strength properties when the nonlinear shear properties of the coupon materials were considered in the finite element simulation.May and Hallett [4] also investigated initiation of damage for unidirectional carbon/epoxy laminates with 2.55 mm thick.They showed progressive internal damage growth prior to shear failure of the specimens indirectly as a result of fatigue testing by X-ray computed tomography.
Currently, both static and fatigue bending properties have been widely studied for thinner samples [5] whereas research of thick laminates bending behavior is limited.Moreover, some specimens have shown brittle failure under fatigue bending loading with no prior indication [6], but the failure mechanisms have not been revealed for thick quasi-isotropic CFRP laminates.Previous researches [7][8] pointed the effect of span/thickness ratio on failure modes as well.However, little research has been completed to examine how it happens, resulting in the overestimate of ship propeller blades safety.In this paper, both static and fatigue three-point bending tests were conducted for 16 mm thick quasiisotropic CFRP laminates to evaluate the effect of span/thickness ratio on failure modes and damage mechanisms.

Material and specimen
In this research, the material was made from T700 carbon-fiber (Toray Co., Ltd) and amine-cured epoxy resin (DIC Co., Ltd.), and manufactured by vacuum-assisted resin transfer molding (VaRTM).An 80ply quasi isotropic layup ([(+45/-45)/(0/90)]10s) was adopted as specimens for all tests and they are about 16 mm thick, and 20 mm wide.The length of the specimens is determined depending on span/thickness ratio L/h.The fiber-volume fraction is about 59.4%.Three-point bending test was done as shown in figure 1 where specimens were put symmetrically between two supports and loading nose.

Static three-point bending test
Static tests were conducted to obtain shear and bending strength with a universal testing machine Autograph AG-Xplus.9 types of specimens with different span/thickness ratios L/h = 4, 5, 7, 9, 11, 13, 15, 20 and 30 were prepared to investigate the effect of L/h and were subjected to three-point bending.Test configuration is shown as figure 1 and a loading nose with 15 mm diameter was adopted to avoid excessive stress concentration in the vicinity of loading nose.Each specimen was loaded at 1.0 mm/min until failure.Shear and bending strength were calculated based on classical beam theory.Failure modes were obtained after tests for each specimen.Several specimens were used to observe the crack using replica, stopping the test at the severities of 20%, 40%, 60%, 80%, 90% relative to failure load.To capture the images of failure behavior, a digital microscope (KEYENCE VHX5000) was used with the resolution of 1600×1200 pixels, at the magnification of 200 ×.

Fatigue three-point bending test
Fatigue three-point bending tests have been carried out under load control to assess failure cycles and failure mechanisms of specimens.Test configuration is the same as figure 1.A servo hydraulic test machine was employed, setting the stress ratio R = 0.1.The frequency of the applied stress was flexibly changed in the range 0.8-2.0Hz depending on maximum deflection of specimens and the performance of machines.The maximum stress of the fatigue tests was set at the severities of 50%, 60%, and 70% relative to static shear strength τb and the tests were stopped when specimens failed by shear or compressive buckling and exceeded its displacement limit in this study.The span/thickness ratio L/h of specimens was varied in the range 4-15 to determine failure mechanisms.After each test, the failure cycle was recorded and used to produce S-N curve.DIC software VIC-2D (Correlated Solutions Inc, version 7) was also employed in this work for assessment of shear strain distribution on the surface of tested specimens.

Static three-point bending test
Figure 2 shows the result of static three-point bending test for thick quasi-isotropic laminates, and the relationship between span/thickness ratio and shear or bending strength.9 types of tested specimens with different span/thickness ratios were divided into two groups according to failure modes.The shear or bending strength was calculated based on the classical beam theory.By the static tests, it was revealed that the failure modes changed from delamination to bending buckling at ratio 15.There was an obvious correlation between span/thickness ratio and strength.Whereas the bending strength indicates almost the same, the apparent shear strength decreased with the increase in span/thickness ratio.The previous research [9] mentioned that thinner specimens with smaller span/thickness ratios are influenced by nonlinearity of shear modulus, which is likely to be the same as thicker samples used in this study.Double notch shear (DNS) test was also done [10] and obtained 42.5MPa (standard deviation: 6.41) as interlaminar shear strength (ILSS), which is shown in figure 2   The onset of shear failure was also studied through static tests with replica using the specimen with span/thickness ratio 11.The test ended with a typical delamination failure in the vicinity of neutral plane.Figure 3 compares the crack of specimen depending on the percentage of the applied load relative to the failure load.From the observation of failed sample, oblique crack was confirmed in 90° ply directly above the delamination.It is likely to originate the initial defects on the surface of a sample and stress concentration there could cause sudden delamination of specimen failure.As explained above, the crack in 90° ply could initiate delamination between 0°/90° plies.Previous research, aimed at 0° unidirectional    2).When loaded at higher stress, stress level τmax/τb = 70%, specimens failed by delamination in the vicinity of neutral plane as figure 5.In the case of stress level τmax/τb = 60%, buckling occurred at compressive area in a stable manner.Contrary to those two types of failure modes, only matrix crack in 90° ply and delamination were observed at the stress level τmax/τb = 50%.This is attributed to the fact that the compressive strength of 90° ply basically exceeds the tensile strength of 90° ply.Tests at lower stress level induced only damage at tensile area, therefore, stress concentration here could cause the final tensile bending failure to happen.Stiffness, normalized by the first cycle value, is plotted against number of cycles in figure 8 (a) and (b) for the specimens with span/thickness ratio 4 and 11, respectively.Both specimens failed in a sudden manner by delamination and showed a gradual decrease in stiffness during tests.However, there was a significant difference in how they decreased their stiffness and while the former specimen caused its delamination at about 90% stiffness, the latter specimen's stiffness gradually decreased, resulting in its delamination at about 60%.The slope of the curve in figure 8  where the shear strain along through-thickness was almost maximum.The specimen with span/thickness ratio 4 failed by shear in the vicinity of neutral plane with shear strain concentration whereas the specimen with span/thickness ratio 11 had the same behavior below the neutral plane.From the DIC measurement in figure 10, shear strain concentration occurred approximately at the center for longitudinal direction, at which delamination was surely initiated.This shear strain concentration seemed to be affected by fiber buckling at the compressive area almost directly below the loading nose.
Since the several layers at the top failed and were no longer able to transfer the load, the shear strain concentration was likely to occur at through-thickness lower area.While the both specimens showed a steady increase in shear strain with cycles, normal strain's (εxx) behavior was a little different according to span/thickness ratio.For the specimen with span/thickness ratio 4, normal strain at the compressive area was almost the same εxx = -0.6 % over cycles but the specimen with span/thickness ratio 11 showed its increase from εxx = -0.83% to -6.2 %, which seems attributed to the difference of stress distribution by the effect of span/thickness ratio.It has to be cared that the value -6.2 % is the apparent strain due to fiber buckling before delamination.Furthermore, comparing (b) and (c) in figure 10, a significant increase in normal strain was obtained between 24500 and 26410 cycles.Seen from figure 8(b), there was a sharp decrease in stiffness during these cycles, therefore, the correlation was confirmed between the value of normal strain and specimen's stiffness.From these results, it can be seen that the specimen with larger span/thickness ratios shows buckling failure prior to shear failure as both normal and shear strain increase during fatigue tests, followed by final delamination.However, the specimen with smaller span/thickness ratios does not clearly develop its normal strain and shear failure happens before even the increase in the effect of the bending strain.As the above results demonstrated, although the specimens show the same failure behavior by delamination, the failure process depends on span/thickness ratio and normal or shear strain developed in a different manner.

Conclusion
The effect of span/thickness ratio of the specimens on bending fatigue properties was investigated using thick CFRP laminates in this research.The results of three-point bending test show that the apparent interlaminar shear strength and failure modes depend on the span/thickness ratio.The DIC method was also used to study shear fatigue behavior of the specimens with different span/thickness ratios over cycles.It confirmed that even though the specimens showed the same failure by delamination, shear and normal strain developed differently and the specimens with smaller span/thickness ratios exhibit no increase in bending strain.New experiments will be performed to investigate the detailed relationship between span/thickness ratio and the effect of shear/bending stress, focusing on the stress state of each span/thickness ratio.

Figure 1 .
Figure 1.Specimen and support rollers geometry of three-point bending test． Figure2shows the result of static three-point bending test for thick quasi-isotropic laminates, and the relationship between span/thickness ratio and shear or bending strength.9 types of tested specimens with different span/thickness ratios were divided into two groups according to failure modes.The shear or bending strength was calculated based on the classical beam theory.By the static tests, it was revealed that the failure modes changed from delamination to bending buckling at ratio 15.There was an obvious correlation between span/thickness ratio and strength.Whereas the bending strength indicates almost the same, the apparent shear strength decreased with the increase in span/thickness ratio.The previous research[9] mentioned that thinner specimens with smaller span/thickness ratios are influenced by nonlinearity of shear modulus, which is likely to be the same as thicker samples used in this study.Double notch shear (DNS) test was also done[10] and obtained 42.5MPa (standard deviation: 6.41) as interlaminar shear strength (ILSS), which is shown in figure2by a red dashed line.ILSS exceeds the shear strength of samples with span/thickness ratio = 7 or more in three-point bending tests.

Figure 2 .
Figure 2. Relationship between shear or bending strength and span/thickness ratio． .1088/1757-899X/1293/1/012019 4 composites, accounted for the impossibility of predicting the onset of damage but it can be said that thick quasi-isotropic laminates show different damage mechanism from that.

Figure 3 .
Figure 3. Image of transverse crack in 90° ply at each loading point3.2.Fatigue three-point bending testFigure4shows S-N diagram of specimens with different span/thickness ratios generated from the result of fatigue tests.This diagram confirmed that the specimens with larger span/thickness ratios are likely to fail by buckling at compressive area.Furthermore, about 14 MPa was referred as a boundary of the failure modes between shear and bending in accordance with maximum loaded shear stress.

Figure 4 .
Figure 4. S-N diagram of specimens with different span/thickness ratio