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Compressive damage mode manipulation of fiber-reinforced polymer composites
Journal Pre-proofs Compressive Damage Mode Manipulation of Fiber-Reinforced Polymer Composites Yanan Yuan, Kangmin Niu, Zuoqi Zhang PII: DOI: Reference:
S0013-7944(19)30872-0 https://doi.org/10.1016/j.engfracmech.2019.106799 EFM 106799
To appear in:
Engineering Fracture Mechanics
Received Date: Revised Date: Accepted Date:
11 July 2019 22 November 2019 24 November 2019
Please cite this article as: Yuan, Y., Niu, K., Zhang, Z., Compressive Damage Mode Manipulation of FiberReinforced Polymer Composites, Engineering Fracture Mechanics (2019), doi: https://doi.org/10.1016/ j.engfracmech.2019.106799
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© 2019 Published by Elsevier Ltd.
Compressive Damage Mode Manipulation of FiberReinforced Polymer Composites Yanan Yuan*1, Kangmin Niu2, Zuoqi Zhang1 1School
of Civil Engineering, Wuhan University, Wuhan, 430072, China 2University
of Science & Technology Beijing, China *Email: [email protected]
Abstract The low compressive strength of fiber-reinforced polymer (FRP) composites has been one of the critical problems limiting their applications. The compressive damage behaviors of FRP composites are much more complicated than their tensile failure behaviors, usually including different modes, such as delamination and kink-band instability, thereby throwing a great challenge to increase the compressive strength of FRP composites by maneuvering the compressive damage mode. However, limited numerical and experimental studies exist on the compression damage mode control and design. In this study, we examined the competition mechanism between the two major compression damage modes, delamination and kink band, by simulations through finite element method and identified the interlaminar strength and yield strength of the polymer matrix as the crucial factors regulating the damage modes. Accordingly, we established a strategy of designing two material parameters to effectively regulate the compressive damage mode and increase the compressive strength of FRP composites. Furthermore, a series of experiments were conducted to validate the design strategy. The experimental results revealed that tuning the interlaminar strength and yield strength of the polymer matrix could effectively maneuver the compression damage modes and their conversion, and the optimal compressive strength of FPR composites could be achieved when the two damage modes coincide. This study would not only further our understanding of the compressive behaviors of FRP composites but also provide valuable guidelines for their compressive strength enhancement and design. Keywords： Laminates; Delamination; Buckling; Finite element analysis (FEA)
1. Introduction Currently, the difference between the tensile strength and the compressive strength of fiber-reinforced polymer (FRP) composites is noticeable. A comparison study on the tensile and compressive mechanical properties of FRP demonstrated that the tensile strength of carbon FRP (CFRP) composites almost doubled from T300 to T1000 carbon fibers; however, their compressive strength did not alter much. The findings suggested that the continuous enhancement of the tensile properties of carbon fibers cannot effectively overcome the limitation of low compressive strength of CFP composites because the compressive damage modes of FRP composites are more complicated than their tensile damage modes, and the tensile strength of fibers might not play a dominant role in the compression damage behaviors. To elucidate the occurring mechanism of different compressive damage modes [1, 2], the impact of the fiber arrangement [3, 4], fiber misalignment angle [5-7], tow geometric defects [8], interfacial debonding [9] on the interlaminar shear failure, and resin yield [10-12] were investigated. Moreover, some studies focused on the effects of the interfacial bonding strength [13], interfacial pore [14], defect [15], delamination [16], temperature [17], humid–thermal environment [18], fiber elastic modulus [19], fiber diameter [20], and matrix elastic modulus [21-23] on the compressive strength of FRP composites. Hsiao and Daniel [3] investigated the impact of different fiber ripple shapes on the compressive strength and compressive damage modes. The authors [3] believed that interlaminar shear failure is the primary failure mode of the unidirectional FRP composites. Sun and Chen [21] examined the impact of the nonlinear property of the resin and fiber misalignment angle on the compressive microbuckling of FRP composites. In addition, Daniel and Hsiao [6] reported that when the fiber misalignment angle exceeds 1.5–2, the impact of the fiber misalignment and the shear stress on the compressive buckling cannot be ignored. Suemasu et al. [24] experimentally and numerically investigated the compressive failure mechanism of the quasi-isotropic composite laminates with an open hole. The authors [24] observed that the final unstable fracture in the laminate occurs suddenly with high interlaminar toughness. Recently, Xu et al. [25] developed a computationally efficient multiscale model to precisely simulate and analyze the instability phenomena of long fiber-reinforced composites. The authors [25] reported that the first global macroscopic failure arises from the unstable composite structure, whereas the second local macroscopic failure
originates from the microscopic fiber buckling. Owing to the heterogeneity of FRP composites, usually the compressive damage modes do not occur individually but coexist and interact with each other. Fig.1a illustrates a typical process of failure evolution of the unidirectional FRP composites under axial compression. At the initial stage, the composites normally experience a uniform deformation. As the compression loading increases, the elastic instability stage comes into effect upon the impact of structural defects or external disturbances like fiber misalignment, interfacial defects, and lateral disturbances or impacts [17, 26]. After the elastic instability stage, the development of compression damage modes will be divergent—one way is dominated by interface debonding and delamination, while the other is featured with the kink-band formation and shear failure. Typically, the failure path is affected by the interfacial strength of laminates and the matrix material properties (Fig. 1b and c). The delamination primarily occurs when the interlaminar shear stress exceeds the interfacial strength of the laminates. For the kink-band formation, the plastic deformation of the resin matrix accounts for the instability of FRP composites when the compressive strain exceeds the yield strain of the resin. Hence, perhaps, the compressive damage modes could be regulated and designed by tuning the interfacial strength and the matrix yield property, so is the compressive strength of the composites. However, systematic studies on this issue remain scarce. The key novelty of this study is to present a design strategy to maneuver the compressive damage modes of FRP composites by tuning the interface and matrix properties and, finally, improving the compressive strength of FRP composites. This study aims to systematically investigate the competition mechanism between the two major compressive damage modes in the unidirectional FRP composites, namely delamination and kink band, with numerical and experimental methods. Through these studies, this study numerically scrutinizes the impact of the yield strength of the resin and the interlaminar strength of the laminates on the compressive damage modes, as well as the compressive strength of the unidirectional FRP composites, which are identified as the two dominant factors pertinent to the two common compressive damage modes. Finally, this study proposes an optimal design strategy to control the compression damage mode and improve the compressive strength of FRP composites, as well as verify the same by experimental results.
(a)
(b)
(c)
Figure 1. (a) Compressive failure development within the unidirectional FRP composites; (b) delamination induced by the interfacial property; (c) kink band induced by the yield property of the matrix.
2. Numerical Model Using the finite element method (FEM), we conducted a quantitative analysis of the kink band and delamination modes of the unidirectional FRP composites. In addition, we investigated the impact of different materials’ properties on the compressive damage modes and the compressive strength. Finally, an optimized strategy for the material design was proposed.
2.1
Traction–Separation Model In the finite element (FE) model, a traction–separation model, namely the cohesive
element-based model, was adopted to simulate the delamination damage mode. Based on the traction–separation model, the complex damage process was replaced by the relative separation force–displacement correlation between the two surfaces. Some of the many forms of the force–displacement correlation are bilinear, nonlinear, exponential, trapezoidal, and so on. In this study, we adopted a bilinear model [27], as shown in Fig. 2.
Figure 2. A bilinear traction–separation model.
The separated stress vector contains three components— tn , ts , and tt . The corresponding separated displacements are
n , s , and
t , respectively.
Subsequently, three nominal strains could be obtained by dividing the displacement to the element’s thickness T0 :
n
n , s s , t t T0 T0 T0
(1)
The elastic constitutive relations of the traction–separation are expressed by the following:
tn Enn t ts Ens t E t nt
Ens Ess Est
Ent n Est s Ett t
(2)
In addition, the maximum nominal stress is considered as the damage criterion. When the condition in Eq. (3) is satisfied, the damage begins to propagate as follows: t t t max n0 , s0 , 0t 1 ts tt tn
(3)
where tn0 , ts0 , and tt0 are the interfacial strength components. Furthermore, the strength reduction criteria for damage propagation are provided elsewhere [28]:
1 D t n , t n 0 tn t n , t n 0
(4)
ts 1 D t s
(5)
tt 1 D t t
(6)
In Eq. (4), if tn is the compressive stress, the strength reduction criterion is not adopted. In Eqs. (4)–(6), D denotes the damage factor. When the damage occurs, D varies from 0 to 1. When D reaches 1, it denotes the complete failure of the material. Using an appropriate cohesive element, we developed a perfect 3D ABAQUS FEM model to simulate the kink-band formation with 50% fiber volume fraction by eight fiber layers with linear elasticity property and nine matrix layers with the perfectly elastoplastic property. Notably, isotropic materials are considered for both fiber and matrix. In addition, the cohesive layers (element type: COH3D8) with thickness 1 m are considered between the fiber and matrix layers. The length, width, and thickness of the composite plate are 10, 1, and 1.6 mm, respectively. In addition, the thicknesses of each fiber and matrix element are 0.1 and 0.05 mm, respectively. Young’s modulus of the fiber layer is 200 GPa, whereas Young’s modulus of the matrix layer is 3 GPa. The compressive load FY, as well as the lateral load FZ, is applied on the composite material in different steps separately. In this study, we adopted the Riks method to analyze the snap-back behaviorof the load Fz for the force–displacement plots. Table 1 presents the part of input parameters for simulation. The impact of the cohesive element size on the final numerical results should be revealed to verify the numerical accuracy of the cohesive element. Fig.3b plots the compressive loads obtained by three types of the cohesive element with sizes 0.1, 0.05, and 0.025; the horizontal axis represents the arc length in the Riks step, whereas the vertical axis represents the normalized compressive load. The results revealed that the size of the cohesive element exerts a little impact on the maximum compressive load (i.e., the relative error is less than 5% error). The high modulus fiber layer (as opposed to the resin layer) is considered the dominant element in the bending problem, and the continuous shell element (SC8R) with higher accuracy was adopted. The full integral
analysis tends to cause shear locking when evaluating the bending problem; thus, the reduced integral element must be used. For boundary conditions, U 2 ( x, 0, z ) 0 ,
U1 (W , 0, 0) 0 , and U 3 (W , 0, 0) 0
were applied as the constraint conditions.
l Moreover, U3 ( x, L0 , t ) z was applied as the disturbance displacement. Here, we
set
zl = 0.1 mm , which is sufficiently large to cause the sample to buckle.
l Furthermore, F3 ( x, L0 , t ) Fz was applied as the disturbance load using the control
point technique. In the z-axis, Fc1st denotes the first-order eigenvalues of the laminated plate structure. Further details about the convergence of the element types (SC8R and C3D8), element size, and boundary conditions are provided elsewhere [29].
(a)
(b) Figure 3. (a) FEM model. (b) The impact of the cohesive element size on the numerical results.
E f (GPa) 200
2.2
Table 1. Input parameters for simulation vf Em (GPa) K nn (GPa/mm) vm 3
0.25
0.38
5000
Kss (GPa/mm) 80
Numerical Analysis
We investigated the damage modes of the unidirectional FRP composites subjected to compressive and lateral disturbances using FEM models. The compressive damage modes can be summarized as the following three cases: (1) the only kink-band formation occurs when the interlaminar strength of the laminates is sufficiently large to ensure that the delamination will not occur; (2) the only delamination occurs when the yield strength of the matrix is sufficiently large; and (3) both kink band and delamination occur concurrently. The material properties directly affect the compressive damage mode of the unidirectional FRP composites. Based on the numerical results (Fig. 4), the simultaneous occurrence of both kink band and delamination within the unidirectional FRP composites would be discussed emphatically. The simultaneous occurrence of two damage modes can be obtained by adjusting the yield strength of the matrix layer and the interlaminar strength of the laminates (Fig. 4a and b). Fig.4a presents the contour of the matrix’s equivalent plastic strain (PEEQ), and the local kink band is formed gradually at the center of the laminate. The entire process
includes uniform deformation, elastic instability, plastic deformation, and local kink band. During the entire process, the scalar stiffness degradation variable (SDEG) of the cohesive element is also evaluated. When SDEG = 1, the cohesive element is deleted; factually, it suggests the delamination formation. Fig.4b shows the delamination contour of the unidirectional FRP composites. The delamination region primarily focuses on the place in which the local kink band occurs. Notably, the large deformation in the kink-band region brings tremendous interlaminar shear stress that finally causes the delamination. Regarding the demonstrated results, Fig. 4c shows the load–displacement curves with the marked points, suggesting the occurrence of two damage modes (kink band and delamination); the kink-band formation inhabits the complete process from the load increment to decline. However, the delamination occurrence and propagation primarily correspond to the decrease stage of the load. Based on the numerical results, the local kink-band formation is a sufficient but not a necessary condition for generating considerable interlaminar shear stress. When the yield strength of the matrix is sufficiently large, the plastic local kink band does not occur. Nevertheless, the elastic instability could also result in sizeable interlaminar shear stresses that generate the delamination.
(a)
(b)
(c) Figure 4. (a) The PEEQ contour of the local kink band. (b) The contour of the delamination (c) The load–displacement curve.
2.3
Yield Strength of the Resin
Based on the numerical results, adjusting the yield strength of the matrix and the interlaminar strength could effectively control the compressive damage mode, which improves the compressive strength of the unidirectional FRP composites. Thus, we could propose a design strategy to increase the compressive strength: (1) first, determine the current properties of the material, including the yield strength of the matrix, as well as the interlaminar strength of the laminate; (2) then, validate the compressive damage modes (kink band or delamination); and (3) based on the current damage mode, adjust the corresponding material property. In this section, we numerically examine one situation of increasing the yield strength
of the resin (Fig. 5a). The abscissa represents the ratio of the yield strength of the resin to the interlaminar strength of the laminate. Here, the yield strength of the rain is altered, whereas the interlaminar strength of the laminates remains unaltered. In addition, the longitudinal coordinate denotes the maximum compressive load normalized by the 1st eigenvalue of the compressive load, denoted by Fc . First, the initial values of the
yield strength of the resin, as well as the interlaminar strength of the laminate, are set in advance so that the initial state of the compressive damage mode is the kink band. Next, with an increase of the yield strength of the resin, the compressive damage mode of the FRP composite changes from the kink band to the kink band/delamination coupling damage mode; finally, the delamination mode is reached. Alternatively, the compressive strength of the FRP composite increases linearly during the damage mode transformation from the kink band to the kink band/delamination coupling mode, which tends to converge gradually. Subsequently, increasing the yield strength of the resin would be no longer effective for both the compressive damage form and the compressive strength of the FRP composite.
2.4
Interlaminar Strength
This section focuses on the impact of the interlaminar strength of the laminate on the compressive strength of the FRP composite, as well as the compressive damage mode. In Fig. 5b, in the abscissa, the interlaminar strength of the laminate is changed, whereas the yield strength of the resin remains unchanged. In the initial state, the main compressive damage mode of the FRP composite is delamination. Then, by an increase of the interlaminar strength of the laminate, the compressive damage mode is transformed from the delamination to the delamination/kink band coupling damage mode. Finally, we arrive at the kink band, suggesting that increasing the interlaminar strength of the laminate could preserve the delamination effectively and promote the kink band. Meanwhile, the corresponding compressive strength of the FRP composite increases linearly, and then, tends to converge gradually.
(a)
(b) Figure 5. The impact of material properties on the compressive strength of the FRP composite, as well as the compressive damage mode, by (a) increasing the yield strength of the resin and keeping the interlaminar strength constant; (b) increasing the interlaminar strength of the laminate and keeping the yield strength of the resin constant.
The strategy to increase the compressive strength of the FRP composite can be summarized as follows. First, determine the existing compressive damage mode. If the current compressive damage mode is kink band, an increase of the yield strength of the resin would be an effective method to increase the compressive strength, as well as control the compressive damage mode transformed from the kink band to the delamination. Likewise, if the current compressive damage mode is delamination, then
growing the interlaminar strength of the laminate is an impressive approach to enhance the compressive strength, as well as regulate the compressive damage mode transformed from the delamination to the kink band. The optimum modification strategy is to determine the compressive damage mode of FRP composites in the kink band/delamination coupled state using experimental modification. Section 3 investigates the related experimental modification to adjust the yield strength of the resin and the interlaminar strength of the laminates.
3. Experiment 3.1
Material Preparation
In this experiment, we used phenol propane bisphenol and bisphenol epoxy resin as the monomer, and diamino-diphenyl sulfone (DDS) as the amine curing agent in the epoxy resin system. We prepared the modified molten resin system using the poly aryl ether ketone (PEK-C), as shown in Fig. 6a. In addition, phenol propane bisphenol A and bisphenol A epoxy resin were mixed at 60:40 weight ratio at 140C. Then, PEK-C was added to the molten resin with four different contents (0, 10, 20, and 30 wt%). Next, we added DDS with the weight of 40 to the modified molten epoxy. Finally, the prepared modified molten epoxy was introduced to a standard compression sample mold at 140C. After 3 h in the curing process at 180C, the modified epoxy with the standard compression sample 25 mm 10 mm 10 mm was prepared. Fig.6b shows the curing process. Furthermore, the FRP laminate composite was prepared with the modified epoxy system using PEK-C. Then, phenol propane bisphenol A and bisphenol A epoxy resin were mixed at 60:40 weight ratio. Then, dichloromethane solvent was added to the mixed epoxy resin monomer and stirred continuously with a glass rod until the resin dissolved completely. Next, PEK-C was added to the resin solution with four different contents (0, 10, 20, and 30 wt%). After that, we added DDS with a weight of 40 to the modified molten epoxy (Fig. 6c). Finally, the prepreg and laminates with T800 grade, as well as the modified epoxy system, were prepared after the layup and curing process (3 h at 180C). The laminates were tailored with two standard shapes, namely 18 mm 6 mm 2 mm for short-beam shear test and 140 mm 13 mm 2 mm for the compressive test (Fig. 6d).
(a)
(b)
(c)
(d) Figure 6. Materials and samples preparation: (a) the preparation process of the modified molten epoxy; (b) casting and curing process of the standard compressive epoxy samples; (c) the preparation process of the modified epoxy solution; (d) layup and curing process of the standard compressive laminate samples.
3.2
Experimental Tests
We experimentally studied the compressive properties of the epoxy and laminate composites, including the yield strength of the modified epoxy, interlaminar strength of the laminates, and the unidirectional compressive properties of the laminates. Fig.7 presents the standard tests. According to GB_T 2567-2008 [30], the compressive
behavior, as well as the yield strength of the resin modified by PEK-C, is characterized. Based on the ASTM D2344M [31], the short-beam shear test for FRP-laminated composites was used to measure the interlaminar shear strength of the laminates. Finally, per the ASTM D6641M [32], the compressive test for the FRP composite was used to characterize the compressive strength, as well as the compressive damage mode, of the laminate. Fig.7 demonstrates three experimental tests, including evaluation of the material properties, experimental setup, and damage morphologies.
Figure 7. Experiment methods to characterize the mechanical properties of the epoxy and the laminates modified by PEK-C.
4. Results and Discussion 4.1
Short-Beam Shear Test
We examined the impact of PEK-C on the interlaminar shear strength of the laminates using the short-beam shear test. The span of the experimental setup was 12 mm, the length of the specimen was 18 mm, and the compressive load was applied on the middle point of the top surface of the specimen (Fig. 8a). Fig.8b presents the effective damage mode of the interlaminar shear damage. Besides, a camera was used to record the damage propagation process of the composite’s cross-section in real time (Fig. 8c).
With an increase of the compressive load, the interlaminar shear damage occurs at the free edge because the stress singularity at the free edge is the highest [33, 34]. Then, the interlaminar shear damage gradually extends inside the domain until the specimen loses its capacity.
(a)
(b)
(c) Figure 8. (a) The experimental setup; (b) the typical interlaminar shear damage mode; (c) damage propagation.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 9. Load and displacement curves with different PEK-C contents: (a) 0 wt%; (b)10 wt%; (c) 20 wt%; (d) 30 wt%; (e) comparison of curves; and (f) comparison of the interlaminar shear strength of various laminates.
Fig.9a–d present the load–displacement curves of laminates with different contents (0, 10, 20, and 30 wt%) of PEK-C. The load increases linearly by an increase of the displacement until the load reaches its maximum value. During load dropping, no brittle
fracture occurs, such as the load drop, because the damage between the interlayers is gradually expanding and evolving, suggesting that the laminates still have a partial load capacity in the subsequent loading process. Fig.9e compares the load–displacement curves with four contents of PEK-C. The experimental results revealed that with the increased content of PEK-C, the interlaminar shear strength of the laminates grew gradually. Zhang et al. [35] suggested that the PEK-C–rich microphases (particulate phases) dispersed in the continuous epoxy-rich matrix. Although the mechanism of multiple phase changes in PEK-C nanofibers/epoxy system warrants further research, the separated phases in the interlayer region supported our experimental results on toughening of carbon/epoxy composites.
4.2
Compressive Behavior of the Resin
We conducted experiments of modified resin by PEK-C with six contents (i.e., 0, 5, 10, 15, 20, and 30 wt%). The experiment on the specimen with 30 wt% content failed because of adding too much PEK-C to the molten epoxy (in fact, it yields the excessive viscosity and fails to inject into the mold). The compressive test of the resin primarily affects the compressive yield strength, yield strain, and elastic modulus of the resin modified by PEK-C. Notably, the resin material is not like the low-carbon steel or the aluminum alloy to have a typical yield point. The compressive behavior of the resin is close to the ideal elastic–plastic curves. We compared the yield points of different epoxy specimens; the inflection point of each curve was assumed to be its yield point. Fig.10 plots the experimental results. The plotted results revealed that by increasing the content of PEK-C, the yield strain, as well as the yield strength of the resin, decreases gradually. When the PEK-C content is nearly 20 wt%, the yield strain of the modified epoxy would decrease by nearly 20% compared with that of the unmodified epoxy. Furthermore, the compressive elastic modulus grows with an increase of the PEK-C content because PEK-C belongs to relatively rigid particles.
(a)
(b)
(c) Figure 10. The impact of PEK-C on the compressive behaviors of the modified epoxy: (a) yield strain; (b) yield strength; and (c) elastic modulus.
Based on the presented results for the first two experiments, we investigated the impact of PEK-C on the double key mechanical parameters. With an increase of PEK-C, (1) the yield strain, as well as the yield strength of the resin, decreased gradually; and (2) the interlaminar shear strength of the laminates increased imperceptibly. Indeed, improvement of the interlaminar shear strength of the laminate could successfully retain the delamination, whereas the decrease of the yield strain or the yield strength results in the kink-band formation in advance. Hence, the modification of the epoxy by PEKC would inevitably lead to the restraint of the delamination and the promotion of the kink band. The compressive strength of FRP composites does not increase monotonously by increasing the PEK-C. Furthermore, the inflection point of the compressive strength would appear at certain content. Besides, it could also be speculated that the compressive damage mode would be changed with the PEK-C variation. Hence, series unidirectional compressive experiments of FRP composites with four contents of PEK-C were conducted to verify the deductions presented above.
4.3
Compressive Behavior of FRP Composites
Fig.11 summarizes the compressive load–displacement curves with different contents
of PEK-C (0, 10, 20, and 30 wt%). Six specimens were made for each content of PEK-C. Excluding the invalid damage modes, 4–5 valid experimental data for each content are shown in Fig. 11a–d. A comparative analysis of Fig. 11e revealed that by an increase of the PEK-C content, the compressive strength of FRP composites increased at first but, then, it decreased. The compressive strength of the specimen with 20 wt% content was the highest. Comparison with the unmodified specimens revealed that the compressive strength of the specimen with 20 wt% increased by about 28% (Fig. 11f). These experimentally observed data further validate the non-monotonic growth of the compressive strength of FRP composites by an increase of the PEK-C content, which we speculated in Section 4.2.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 11. Compressive load–displacement curves with different contents of PEK-C: (a) 0 wt%; (b)10 wt%; (c) 20 wt%; (d) 30 wt%; (e) comparison of curves; and (f) comparison of the compressive strength of FRP composites.
Conversely, the compressive damage modes of FRP composites also change by increasing the PEK-C content. Using scanning electron microscopy (SEM), we observed the microfracture morphology of FRP composites (Fig. 12). The compressive damage morphology of the unidirectional composites was primarily delamination without the PEK-C modification epoxy. With an increase of the PEK-C content, the compressive failure modes of FRP composites was a combination of delamination and shear failure. For the shear failure morphology, a large number of typical kink-band instability damage modes were found, as explained in the shear failure section. In conclusion, the kink-band damage mode induces the final shear failure. Furthermore, by an increase of the PEK-C content, the occurrence of delamination decreases and that of the kink band increases.
Figure 12. The compressive damage morphology using SEM images: (a) 0 wt%; (b) 10 wt%; (c) 20 wt%; and (d) 30 wt%.
Typically, the mechanism of different PEK-C contents on the compressive strength, as well as the compressive damage modes (Fig. 13), can be summarized as follows. For the unmodified resin composites, small defects would inevitably be produced between layers during the preparation process, and when they are subjected to compressive loads, cracks would gradually propagate along the layers. Before the whole system becomes unstable, it would be destroyed because of the large area of the interlaminar delamination. When an appropriate amount of the PEK-C toughening agent is added to the resin, the interlaminar shear strength of the resin increases, which could effectively inhibit the propagation of interlaminar delamination. Then, the entire composite system gradually destabilizes (kink-band formation), and its failure reaches. Compared with the unmodified composites, owing to the effective suppression of the interlaminar delamination, the ultimate failure mode would be the shear failure caused by the kink-
band instability, and the corresponding compressive strength is enhanced. When the PEK-C content continues to increase (30 wt%), as the buckling strength and the yield strain of the resin layer decreases, the kink-band instability is induced ahead of time; however, the ultimate compressive strength of the composite would lessen. This vital feature guides us to an optimum scheme for increasing the compressive strength, as well as realizing the compressive damage mode of FRP composites, in the kink band/delamination coupled state. In the near future, more research can be conducted such as the study of material modification to realize the simultaneous improvement of the resin yield strength (yield strain) and the interlaminar strength of the laminates. Besides, a structural design could be developed to control or change the compressive damage modes for more improvement of the compressive strength of FRP composites.
Figure 13. The mechanism of PEK-C on the compressive strength.
5. Conclusions This study innovatively proposes an optimum design strategy to enhance the compressive strength of FRP composites. The impact of the matrix yield strength, as well as the interlaminar strength on the compressive damage modes and strength, is examined quantitatively by the finite element simulations and experimental
characterizations. The major findings of this study can be summarized as follows: 1) By adjusting the yield strength of the matrix resin, as well as the interlaminar strength of the laminate, delamination and kink band could occur simultaneously, which lead to the optimal compressive strength of FRP composites. 2) Four contents of PEK-C (i.e., 0, 10, 20, and 30 wt%) were exploited to modify the thermosetting epoxy. By increasing PEK-C, the interlaminar shear strength of the laminates increases monotonously, whereas the yield strength, as well as the yield strain, of the resin decreases, which eventually causes the compressive strength of FRP composites to increase first but, then, decreases. 3) The modification of the resin by PEK-C could effectively convert the compressive damage modes from the delamination to the kink band. When the PEK-C content ranges 10–20 wt%, kink band and delamination coincide. In the case of 30 wt%, the kink band mode is dominant. 4) When the PEK-C content is approximately 20 wt%, the compressive strength of FRP composites increases approximately by 28% regarding the unmodified composites. Conversely, the compressive strength reverses to decrease when the content is about 30 wt%. In fact, the excessive use of PEK-C decreases the yield strength, as well as the yield strain of the resin, and this issue accelerates the occurrence of the kink-band formation.
Acknowledgements The author is grateful for the funding support for independent scientific research (2042019kf0039) in Wuhan University and funding support of start-up research by School of Civil Engineering, Wuhan University.
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Technology. 1996;56:581-93. [4] Jumahat A, Soutis C, Jones FR, Hodzic A. Fracture mechanisms and failure analysis of carbon fibre/toughened epoxy composites subjected to compressive loading. Composite Structures. 2010;92:295-305. [5] Sun CT, Jun AW. Compressive strength of unidirectional fiber composites with matrix non-linearity. Composites Science and Technology. 1994;52:577-87. [6] Daniel IM, Hsiao HM. Is there a thickness effect on compressive strength of unnotched composite laminates? Inter J Fract. 1999;95:143-58. [7] Drapier S, Wisnom MR. Finite-element investigation of the compressive strength of non-crimp-fabric-based composites. Composites Science and Technology. 1999;59:1287-97. [8] Song SJ, Waas AM, Shahwan KW, Xiao XR, Faruque O. Braided textile composites under compressive loads: Modeling the response, strength and degradation. Composites Science and Technology. 2007;67:3059-70. [9] Short GJ, Guild FJ, Pavier MJ. The effect of delamination geometry on the compressive failure of composite laminates. Composites Science and Technology. 2001;61:2075-86. [10] Pimenta S, Gutkin R, Pinho ST, Robinson P. A micromechanical model for kinkband formation: Part I — Experimental study and numerical modelling. Composites Science and Technology. 2009;69:948-55. [11] Gutkin R, Pinho ST, Robinson P, Curtis PT. On the transition from shear-driven fibre compressive failure to fibre kinking in notched CFRP laminates under longitudinal compression. Composites Science and Technology. 2010;70:1223-31. [12] Gutkin R, Pinho ST, Robinson P, Curtis PT. Micro-mechanical modelling of sheardriven fibre compressive failure and of fibre kinking for failure envelope generation in CFRP laminates. Composites Science and Technology. 2010;70:1214-22. [13] Martinez GM, Piggott MR, Bainbridge DMR, Harris B. The compression strength of composites with kinked, misaligned and poorly adhering fibres. J Mater Sci. 1981;16:2831-6. [14] Liu L, Zhang BM, Wang DF, Wu ZJ. Effects of cure cycles on void content and mechanical properties of composite laminates. Composite Structures. 2006;73:303-9. [15] Gillespie JW, Pipes RB. Compressive strength of composite laminates with interlaminar defects. Composite Structures. 1984;2:49-69. [16] Vlasveld DPN, Daud W, Bersee HEN, Picken SJ. Continuous fibre composites with a nanocomposite matrix: Improvement of flexural and compressive strength at elevated temperatures. Compos Part A: Appl Sci Manuf. 2007;38:730-8. [17] Soutis C. Modelling open hole compressive strength of composite laminates tested in hot wet conditions. Plas Rubber Compos. 2009;38:55-60. [18] Li Y, Xian XJ, Choy CL, Guo ML, Zhang ZG. Compressive and flexural behavior of ultra-high-modulus polyethylene fiber and carbon fiber hybrid composites. Composites Science and Technology. 1999;59:13-8. [19] Yerramalli CS, Waas AM. The effect of fiber diameter on the compressive strength of composites - A 3D finite element based study. Cmes-Comp Model Eng & Sci. 2004;6:1-16. [20] Subramaniyan AK, Sun CT. Enhancing compressive strength of unidirectional polymeric composites using nanoclay. Compos Part A: Appl Sci Manuf. 2006;37:225768. [21] Sun CT, Chen JL. A Simple Flow Rule for Characterizing Nonlinear Behavior of Fiber Composites. Journal of Composite Materials. 1989;23(10):1009-20. [22] Yokozeki T, Ogasawara T, Ishikawa T. Effects of fiber nonlinear properties on the compressive strength prediction of unidirectional carbon-fiber composites. Composites Science and Technology. 2005;65:2140-7. [23] Yokozeki T, Ogasawara T, Ishikawa T. Nonlinear behavior and compressive strength of unidirectional and multidirectional carbon fiber composite laminates. Compos Part A: Appl Sci Manuf. 2006;37:2069-79. [24] Suemasu H, Takahashi H, Ishikawa T. On failure mechanisms of composite laminates with an open hole subjected to compressive load. Composites Science and Technology. 2006;66:634-41.
[25] Xu R, Hui Y, Hu H, Huang Q, Zahrouni H, Ben Zineb T, et al. A Fourier-related FE2 multiscale model for instability phenomena of long fiber reinforced materials. Composite Structures. 2019;211:530-9. [26] Soutis C. Compressive strength of composite laminates with an open hole: Effect of ply blocking. Journal of Composite Materials. 2013;47:2503-12. [27] Benzeggagh ML, Kenane MJCS. Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Compos Sci Technolo. 1996;56:439-49. [28] Hibbett, Karlsson, Sorensen. ABAQUS/standard: User's Manual: Hibbitt, Karlsson & Sorensen, 1998. [29] Yuan YN, Yao XF, Niu KM, Liu B, Wuyun QQG. Compressive failure of fiber reinforced polymer composites by imperfection. Compos Part A: Appl Sci Manuf. 2019;118:106-16. [30] GB/T2567. Test methods for properties of resin casting body [S] 2008. [31] American Society for Testing and Materials. Standard test method for short-beam strength of polymer matrix composite materials and their laminates. ASTM International. 2006. [32] ASTM D 6641/D 6641 M-09. Standard test method for compressive properties of polymer matrix composite materials using a combined loading compression (CLC) test fixture. 2006. [33] Yuan YN, Wang S, Yang H, Yao XF, Liu B. Analysis of pseudo-ductility in thinply carbon fiber angle-ply laminates. Composite Structures. 2017;180:876-82. [34] Yuan YN, Yao XF, Liu B, Yang H, Imtiaz H. Failure modes and strength prediction of thin ply CFRP angle-ply laminates. Composite Structures. 2017;176:72935. [35] Zhang J, Lin T, Wang X. Electrospun nanofibre toughened carbon/epoxy composites: Effects of polyetherketone cardo (PEK-C) nanofibre diameter and interlayer thickness. Composites Science and Technology. 2010;70:1660-6.
` 1.
By maneuvering the compressive damage mode the compressive strength of FRP composites is increased;
2.
The competition mechanism between the two major compression damage modes, delamination and kink band is examined through finite element method;
3.
The interlaminar strength and yield strength of the polymer matrix as the crucial factors regulating the damage modes is identified;
4.
A series of experiments were conducted and results revealed that tuning the interlaminar strength and yield strength of the polymer matrix could effectively maneuver the compression damage modes and their conversion.
Conflict of interest statement We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
S0013-7944(19)30872-0 https://doi.org/10.1016/j.engfracmech.2019.106799 EFM 106799
To appear in:
Engineering Fracture Mechanics
Received Date: Revised Date: Accepted Date:
11 July 2019 22 November 2019 24 November 2019
Please cite this article as: Yuan, Y., Niu, K., Zhang, Z., Compressive Damage Mode Manipulation of FiberReinforced Polymer Composites, Engineering Fracture Mechanics (2019), doi: https://doi.org/10.1016/ j.engfracmech.2019.106799
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© 2019 Published by Elsevier Ltd.
Compressive Damage Mode Manipulation of FiberReinforced Polymer Composites Yanan Yuan*1, Kangmin Niu2, Zuoqi Zhang1 1School
of Civil Engineering, Wuhan University, Wuhan, 430072, China 2University
of Science & Technology Beijing, China *Email: [email protected]
Abstract The low compressive strength of fiber-reinforced polymer (FRP) composites has been one of the critical problems limiting their applications. The compressive damage behaviors of FRP composites are much more complicated than their tensile failure behaviors, usually including different modes, such as delamination and kink-band instability, thereby throwing a great challenge to increase the compressive strength of FRP composites by maneuvering the compressive damage mode. However, limited numerical and experimental studies exist on the compression damage mode control and design. In this study, we examined the competition mechanism between the two major compression damage modes, delamination and kink band, by simulations through finite element method and identified the interlaminar strength and yield strength of the polymer matrix as the crucial factors regulating the damage modes. Accordingly, we established a strategy of designing two material parameters to effectively regulate the compressive damage mode and increase the compressive strength of FRP composites. Furthermore, a series of experiments were conducted to validate the design strategy. The experimental results revealed that tuning the interlaminar strength and yield strength of the polymer matrix could effectively maneuver the compression damage modes and their conversion, and the optimal compressive strength of FPR composites could be achieved when the two damage modes coincide. This study would not only further our understanding of the compressive behaviors of FRP composites but also provide valuable guidelines for their compressive strength enhancement and design. Keywords： Laminates; Delamination; Buckling; Finite element analysis (FEA)
1. Introduction Currently, the difference between the tensile strength and the compressive strength of fiber-reinforced polymer (FRP) composites is noticeable. A comparison study on the tensile and compressive mechanical properties of FRP demonstrated that the tensile strength of carbon FRP (CFRP) composites almost doubled from T300 to T1000 carbon fibers; however, their compressive strength did not alter much. The findings suggested that the continuous enhancement of the tensile properties of carbon fibers cannot effectively overcome the limitation of low compressive strength of CFP composites because the compressive damage modes of FRP composites are more complicated than their tensile damage modes, and the tensile strength of fibers might not play a dominant role in the compression damage behaviors. To elucidate the occurring mechanism of different compressive damage modes [1, 2], the impact of the fiber arrangement [3, 4], fiber misalignment angle [5-7], tow geometric defects [8], interfacial debonding [9] on the interlaminar shear failure, and resin yield [10-12] were investigated. Moreover, some studies focused on the effects of the interfacial bonding strength [13], interfacial pore [14], defect [15], delamination [16], temperature [17], humid–thermal environment [18], fiber elastic modulus [19], fiber diameter [20], and matrix elastic modulus [21-23] on the compressive strength of FRP composites. Hsiao and Daniel [3] investigated the impact of different fiber ripple shapes on the compressive strength and compressive damage modes. The authors [3] believed that interlaminar shear failure is the primary failure mode of the unidirectional FRP composites. Sun and Chen [21] examined the impact of the nonlinear property of the resin and fiber misalignment angle on the compressive microbuckling of FRP composites. In addition, Daniel and Hsiao [6] reported that when the fiber misalignment angle exceeds 1.5–2, the impact of the fiber misalignment and the shear stress on the compressive buckling cannot be ignored. Suemasu et al. [24] experimentally and numerically investigated the compressive failure mechanism of the quasi-isotropic composite laminates with an open hole. The authors [24] observed that the final unstable fracture in the laminate occurs suddenly with high interlaminar toughness. Recently, Xu et al. [25] developed a computationally efficient multiscale model to precisely simulate and analyze the instability phenomena of long fiber-reinforced composites. The authors [25] reported that the first global macroscopic failure arises from the unstable composite structure, whereas the second local macroscopic failure
originates from the microscopic fiber buckling. Owing to the heterogeneity of FRP composites, usually the compressive damage modes do not occur individually but coexist and interact with each other. Fig.1a illustrates a typical process of failure evolution of the unidirectional FRP composites under axial compression. At the initial stage, the composites normally experience a uniform deformation. As the compression loading increases, the elastic instability stage comes into effect upon the impact of structural defects or external disturbances like fiber misalignment, interfacial defects, and lateral disturbances or impacts [17, 26]. After the elastic instability stage, the development of compression damage modes will be divergent—one way is dominated by interface debonding and delamination, while the other is featured with the kink-band formation and shear failure. Typically, the failure path is affected by the interfacial strength of laminates and the matrix material properties (Fig. 1b and c). The delamination primarily occurs when the interlaminar shear stress exceeds the interfacial strength of the laminates. For the kink-band formation, the plastic deformation of the resin matrix accounts for the instability of FRP composites when the compressive strain exceeds the yield strain of the resin. Hence, perhaps, the compressive damage modes could be regulated and designed by tuning the interfacial strength and the matrix yield property, so is the compressive strength of the composites. However, systematic studies on this issue remain scarce. The key novelty of this study is to present a design strategy to maneuver the compressive damage modes of FRP composites by tuning the interface and matrix properties and, finally, improving the compressive strength of FRP composites. This study aims to systematically investigate the competition mechanism between the two major compressive damage modes in the unidirectional FRP composites, namely delamination and kink band, with numerical and experimental methods. Through these studies, this study numerically scrutinizes the impact of the yield strength of the resin and the interlaminar strength of the laminates on the compressive damage modes, as well as the compressive strength of the unidirectional FRP composites, which are identified as the two dominant factors pertinent to the two common compressive damage modes. Finally, this study proposes an optimal design strategy to control the compression damage mode and improve the compressive strength of FRP composites, as well as verify the same by experimental results.
(a)
(b)
(c)
Figure 1. (a) Compressive failure development within the unidirectional FRP composites; (b) delamination induced by the interfacial property; (c) kink band induced by the yield property of the matrix.
2. Numerical Model Using the finite element method (FEM), we conducted a quantitative analysis of the kink band and delamination modes of the unidirectional FRP composites. In addition, we investigated the impact of different materials’ properties on the compressive damage modes and the compressive strength. Finally, an optimized strategy for the material design was proposed.
2.1
Traction–Separation Model In the finite element (FE) model, a traction–separation model, namely the cohesive
element-based model, was adopted to simulate the delamination damage mode. Based on the traction–separation model, the complex damage process was replaced by the relative separation force–displacement correlation between the two surfaces. Some of the many forms of the force–displacement correlation are bilinear, nonlinear, exponential, trapezoidal, and so on. In this study, we adopted a bilinear model [27], as shown in Fig. 2.
Figure 2. A bilinear traction–separation model.
The separated stress vector contains three components— tn , ts , and tt . The corresponding separated displacements are
n , s , and
t , respectively.
Subsequently, three nominal strains could be obtained by dividing the displacement to the element’s thickness T0 :
n
n , s s , t t T0 T0 T0
(1)
The elastic constitutive relations of the traction–separation are expressed by the following:
tn Enn t ts Ens t E t nt
Ens Ess Est
Ent n Est s Ett t
(2)
In addition, the maximum nominal stress is considered as the damage criterion. When the condition in Eq. (3) is satisfied, the damage begins to propagate as follows: t t t max n0 , s0 , 0t 1 ts tt tn
(3)
where tn0 , ts0 , and tt0 are the interfacial strength components. Furthermore, the strength reduction criteria for damage propagation are provided elsewhere [28]:
1 D t n , t n 0 tn t n , t n 0
(4)
ts 1 D t s
(5)
tt 1 D t t
(6)
In Eq. (4), if tn is the compressive stress, the strength reduction criterion is not adopted. In Eqs. (4)–(6), D denotes the damage factor. When the damage occurs, D varies from 0 to 1. When D reaches 1, it denotes the complete failure of the material. Using an appropriate cohesive element, we developed a perfect 3D ABAQUS FEM model to simulate the kink-band formation with 50% fiber volume fraction by eight fiber layers with linear elasticity property and nine matrix layers with the perfectly elastoplastic property. Notably, isotropic materials are considered for both fiber and matrix. In addition, the cohesive layers (element type: COH3D8) with thickness 1 m are considered between the fiber and matrix layers. The length, width, and thickness of the composite plate are 10, 1, and 1.6 mm, respectively. In addition, the thicknesses of each fiber and matrix element are 0.1 and 0.05 mm, respectively. Young’s modulus of the fiber layer is 200 GPa, whereas Young’s modulus of the matrix layer is 3 GPa. The compressive load FY, as well as the lateral load FZ, is applied on the composite material in different steps separately. In this study, we adopted the Riks method to analyze the snap-back behaviorof the load Fz for the force–displacement plots. Table 1 presents the part of input parameters for simulation. The impact of the cohesive element size on the final numerical results should be revealed to verify the numerical accuracy of the cohesive element. Fig.3b plots the compressive loads obtained by three types of the cohesive element with sizes 0.1, 0.05, and 0.025; the horizontal axis represents the arc length in the Riks step, whereas the vertical axis represents the normalized compressive load. The results revealed that the size of the cohesive element exerts a little impact on the maximum compressive load (i.e., the relative error is less than 5% error). The high modulus fiber layer (as opposed to the resin layer) is considered the dominant element in the bending problem, and the continuous shell element (SC8R) with higher accuracy was adopted. The full integral
analysis tends to cause shear locking when evaluating the bending problem; thus, the reduced integral element must be used. For boundary conditions, U 2 ( x, 0, z ) 0 ,
U1 (W , 0, 0) 0 , and U 3 (W , 0, 0) 0
were applied as the constraint conditions.
l Moreover, U3 ( x, L0 , t ) z was applied as the disturbance displacement. Here, we
set
zl = 0.1 mm , which is sufficiently large to cause the sample to buckle.
l Furthermore, F3 ( x, L0 , t ) Fz was applied as the disturbance load using the control
point technique. In the z-axis, Fc1st denotes the first-order eigenvalues of the laminated plate structure. Further details about the convergence of the element types (SC8R and C3D8), element size, and boundary conditions are provided elsewhere [29].
(a)
(b) Figure 3. (a) FEM model. (b) The impact of the cohesive element size on the numerical results.
E f (GPa) 200
2.2
Table 1. Input parameters for simulation vf Em (GPa) K nn (GPa/mm) vm 3
0.25
0.38
5000
Kss (GPa/mm) 80
Numerical Analysis
We investigated the damage modes of the unidirectional FRP composites subjected to compressive and lateral disturbances using FEM models. The compressive damage modes can be summarized as the following three cases: (1) the only kink-band formation occurs when the interlaminar strength of the laminates is sufficiently large to ensure that the delamination will not occur; (2) the only delamination occurs when the yield strength of the matrix is sufficiently large; and (3) both kink band and delamination occur concurrently. The material properties directly affect the compressive damage mode of the unidirectional FRP composites. Based on the numerical results (Fig. 4), the simultaneous occurrence of both kink band and delamination within the unidirectional FRP composites would be discussed emphatically. The simultaneous occurrence of two damage modes can be obtained by adjusting the yield strength of the matrix layer and the interlaminar strength of the laminates (Fig. 4a and b). Fig.4a presents the contour of the matrix’s equivalent plastic strain (PEEQ), and the local kink band is formed gradually at the center of the laminate. The entire process
includes uniform deformation, elastic instability, plastic deformation, and local kink band. During the entire process, the scalar stiffness degradation variable (SDEG) of the cohesive element is also evaluated. When SDEG = 1, the cohesive element is deleted; factually, it suggests the delamination formation. Fig.4b shows the delamination contour of the unidirectional FRP composites. The delamination region primarily focuses on the place in which the local kink band occurs. Notably, the large deformation in the kink-band region brings tremendous interlaminar shear stress that finally causes the delamination. Regarding the demonstrated results, Fig. 4c shows the load–displacement curves with the marked points, suggesting the occurrence of two damage modes (kink band and delamination); the kink-band formation inhabits the complete process from the load increment to decline. However, the delamination occurrence and propagation primarily correspond to the decrease stage of the load. Based on the numerical results, the local kink-band formation is a sufficient but not a necessary condition for generating considerable interlaminar shear stress. When the yield strength of the matrix is sufficiently large, the plastic local kink band does not occur. Nevertheless, the elastic instability could also result in sizeable interlaminar shear stresses that generate the delamination.
(a)
(b)
(c) Figure 4. (a) The PEEQ contour of the local kink band. (b) The contour of the delamination (c) The load–displacement curve.
2.3
Yield Strength of the Resin
Based on the numerical results, adjusting the yield strength of the matrix and the interlaminar strength could effectively control the compressive damage mode, which improves the compressive strength of the unidirectional FRP composites. Thus, we could propose a design strategy to increase the compressive strength: (1) first, determine the current properties of the material, including the yield strength of the matrix, as well as the interlaminar strength of the laminate; (2) then, validate the compressive damage modes (kink band or delamination); and (3) based on the current damage mode, adjust the corresponding material property. In this section, we numerically examine one situation of increasing the yield strength
of the resin (Fig. 5a). The abscissa represents the ratio of the yield strength of the resin to the interlaminar strength of the laminate. Here, the yield strength of the rain is altered, whereas the interlaminar strength of the laminates remains unaltered. In addition, the longitudinal coordinate denotes the maximum compressive load normalized by the 1st eigenvalue of the compressive load, denoted by Fc . First, the initial values of the
yield strength of the resin, as well as the interlaminar strength of the laminate, are set in advance so that the initial state of the compressive damage mode is the kink band. Next, with an increase of the yield strength of the resin, the compressive damage mode of the FRP composite changes from the kink band to the kink band/delamination coupling damage mode; finally, the delamination mode is reached. Alternatively, the compressive strength of the FRP composite increases linearly during the damage mode transformation from the kink band to the kink band/delamination coupling mode, which tends to converge gradually. Subsequently, increasing the yield strength of the resin would be no longer effective for both the compressive damage form and the compressive strength of the FRP composite.
2.4
Interlaminar Strength
This section focuses on the impact of the interlaminar strength of the laminate on the compressive strength of the FRP composite, as well as the compressive damage mode. In Fig. 5b, in the abscissa, the interlaminar strength of the laminate is changed, whereas the yield strength of the resin remains unchanged. In the initial state, the main compressive damage mode of the FRP composite is delamination. Then, by an increase of the interlaminar strength of the laminate, the compressive damage mode is transformed from the delamination to the delamination/kink band coupling damage mode. Finally, we arrive at the kink band, suggesting that increasing the interlaminar strength of the laminate could preserve the delamination effectively and promote the kink band. Meanwhile, the corresponding compressive strength of the FRP composite increases linearly, and then, tends to converge gradually.
(a)
(b) Figure 5. The impact of material properties on the compressive strength of the FRP composite, as well as the compressive damage mode, by (a) increasing the yield strength of the resin and keeping the interlaminar strength constant; (b) increasing the interlaminar strength of the laminate and keeping the yield strength of the resin constant.
The strategy to increase the compressive strength of the FRP composite can be summarized as follows. First, determine the existing compressive damage mode. If the current compressive damage mode is kink band, an increase of the yield strength of the resin would be an effective method to increase the compressive strength, as well as control the compressive damage mode transformed from the kink band to the delamination. Likewise, if the current compressive damage mode is delamination, then
growing the interlaminar strength of the laminate is an impressive approach to enhance the compressive strength, as well as regulate the compressive damage mode transformed from the delamination to the kink band. The optimum modification strategy is to determine the compressive damage mode of FRP composites in the kink band/delamination coupled state using experimental modification. Section 3 investigates the related experimental modification to adjust the yield strength of the resin and the interlaminar strength of the laminates.
3. Experiment 3.1
Material Preparation
In this experiment, we used phenol propane bisphenol and bisphenol epoxy resin as the monomer, and diamino-diphenyl sulfone (DDS) as the amine curing agent in the epoxy resin system. We prepared the modified molten resin system using the poly aryl ether ketone (PEK-C), as shown in Fig. 6a. In addition, phenol propane bisphenol A and bisphenol A epoxy resin were mixed at 60:40 weight ratio at 140C. Then, PEK-C was added to the molten resin with four different contents (0, 10, 20, and 30 wt%). Next, we added DDS with the weight of 40 to the modified molten epoxy. Finally, the prepared modified molten epoxy was introduced to a standard compression sample mold at 140C. After 3 h in the curing process at 180C, the modified epoxy with the standard compression sample 25 mm 10 mm 10 mm was prepared. Fig.6b shows the curing process. Furthermore, the FRP laminate composite was prepared with the modified epoxy system using PEK-C. Then, phenol propane bisphenol A and bisphenol A epoxy resin were mixed at 60:40 weight ratio. Then, dichloromethane solvent was added to the mixed epoxy resin monomer and stirred continuously with a glass rod until the resin dissolved completely. Next, PEK-C was added to the resin solution with four different contents (0, 10, 20, and 30 wt%). After that, we added DDS with a weight of 40 to the modified molten epoxy (Fig. 6c). Finally, the prepreg and laminates with T800 grade, as well as the modified epoxy system, were prepared after the layup and curing process (3 h at 180C). The laminates were tailored with two standard shapes, namely 18 mm 6 mm 2 mm for short-beam shear test and 140 mm 13 mm 2 mm for the compressive test (Fig. 6d).
(a)
(b)
(c)
(d) Figure 6. Materials and samples preparation: (a) the preparation process of the modified molten epoxy; (b) casting and curing process of the standard compressive epoxy samples; (c) the preparation process of the modified epoxy solution; (d) layup and curing process of the standard compressive laminate samples.
3.2
Experimental Tests
We experimentally studied the compressive properties of the epoxy and laminate composites, including the yield strength of the modified epoxy, interlaminar strength of the laminates, and the unidirectional compressive properties of the laminates. Fig.7 presents the standard tests. According to GB_T 2567-2008 [30], the compressive
behavior, as well as the yield strength of the resin modified by PEK-C, is characterized. Based on the ASTM D2344M [31], the short-beam shear test for FRP-laminated composites was used to measure the interlaminar shear strength of the laminates. Finally, per the ASTM D6641M [32], the compressive test for the FRP composite was used to characterize the compressive strength, as well as the compressive damage mode, of the laminate. Fig.7 demonstrates three experimental tests, including evaluation of the material properties, experimental setup, and damage morphologies.
Figure 7. Experiment methods to characterize the mechanical properties of the epoxy and the laminates modified by PEK-C.
4. Results and Discussion 4.1
Short-Beam Shear Test
We examined the impact of PEK-C on the interlaminar shear strength of the laminates using the short-beam shear test. The span of the experimental setup was 12 mm, the length of the specimen was 18 mm, and the compressive load was applied on the middle point of the top surface of the specimen (Fig. 8a). Fig.8b presents the effective damage mode of the interlaminar shear damage. Besides, a camera was used to record the damage propagation process of the composite’s cross-section in real time (Fig. 8c).
With an increase of the compressive load, the interlaminar shear damage occurs at the free edge because the stress singularity at the free edge is the highest [33, 34]. Then, the interlaminar shear damage gradually extends inside the domain until the specimen loses its capacity.
(a)
(b)
(c) Figure 8. (a) The experimental setup; (b) the typical interlaminar shear damage mode; (c) damage propagation.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 9. Load and displacement curves with different PEK-C contents: (a) 0 wt%; (b)10 wt%; (c) 20 wt%; (d) 30 wt%; (e) comparison of curves; and (f) comparison of the interlaminar shear strength of various laminates.
Fig.9a–d present the load–displacement curves of laminates with different contents (0, 10, 20, and 30 wt%) of PEK-C. The load increases linearly by an increase of the displacement until the load reaches its maximum value. During load dropping, no brittle
fracture occurs, such as the load drop, because the damage between the interlayers is gradually expanding and evolving, suggesting that the laminates still have a partial load capacity in the subsequent loading process. Fig.9e compares the load–displacement curves with four contents of PEK-C. The experimental results revealed that with the increased content of PEK-C, the interlaminar shear strength of the laminates grew gradually. Zhang et al. [35] suggested that the PEK-C–rich microphases (particulate phases) dispersed in the continuous epoxy-rich matrix. Although the mechanism of multiple phase changes in PEK-C nanofibers/epoxy system warrants further research, the separated phases in the interlayer region supported our experimental results on toughening of carbon/epoxy composites.
4.2
Compressive Behavior of the Resin
We conducted experiments of modified resin by PEK-C with six contents (i.e., 0, 5, 10, 15, 20, and 30 wt%). The experiment on the specimen with 30 wt% content failed because of adding too much PEK-C to the molten epoxy (in fact, it yields the excessive viscosity and fails to inject into the mold). The compressive test of the resin primarily affects the compressive yield strength, yield strain, and elastic modulus of the resin modified by PEK-C. Notably, the resin material is not like the low-carbon steel or the aluminum alloy to have a typical yield point. The compressive behavior of the resin is close to the ideal elastic–plastic curves. We compared the yield points of different epoxy specimens; the inflection point of each curve was assumed to be its yield point. Fig.10 plots the experimental results. The plotted results revealed that by increasing the content of PEK-C, the yield strain, as well as the yield strength of the resin, decreases gradually. When the PEK-C content is nearly 20 wt%, the yield strain of the modified epoxy would decrease by nearly 20% compared with that of the unmodified epoxy. Furthermore, the compressive elastic modulus grows with an increase of the PEK-C content because PEK-C belongs to relatively rigid particles.
(a)
(b)
(c) Figure 10. The impact of PEK-C on the compressive behaviors of the modified epoxy: (a) yield strain; (b) yield strength; and (c) elastic modulus.
Based on the presented results for the first two experiments, we investigated the impact of PEK-C on the double key mechanical parameters. With an increase of PEK-C, (1) the yield strain, as well as the yield strength of the resin, decreased gradually; and (2) the interlaminar shear strength of the laminates increased imperceptibly. Indeed, improvement of the interlaminar shear strength of the laminate could successfully retain the delamination, whereas the decrease of the yield strain or the yield strength results in the kink-band formation in advance. Hence, the modification of the epoxy by PEKC would inevitably lead to the restraint of the delamination and the promotion of the kink band. The compressive strength of FRP composites does not increase monotonously by increasing the PEK-C. Furthermore, the inflection point of the compressive strength would appear at certain content. Besides, it could also be speculated that the compressive damage mode would be changed with the PEK-C variation. Hence, series unidirectional compressive experiments of FRP composites with four contents of PEK-C were conducted to verify the deductions presented above.
4.3
Compressive Behavior of FRP Composites
Fig.11 summarizes the compressive load–displacement curves with different contents
of PEK-C (0, 10, 20, and 30 wt%). Six specimens were made for each content of PEK-C. Excluding the invalid damage modes, 4–5 valid experimental data for each content are shown in Fig. 11a–d. A comparative analysis of Fig. 11e revealed that by an increase of the PEK-C content, the compressive strength of FRP composites increased at first but, then, it decreased. The compressive strength of the specimen with 20 wt% content was the highest. Comparison with the unmodified specimens revealed that the compressive strength of the specimen with 20 wt% increased by about 28% (Fig. 11f). These experimentally observed data further validate the non-monotonic growth of the compressive strength of FRP composites by an increase of the PEK-C content, which we speculated in Section 4.2.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 11. Compressive load–displacement curves with different contents of PEK-C: (a) 0 wt%; (b)10 wt%; (c) 20 wt%; (d) 30 wt%; (e) comparison of curves; and (f) comparison of the compressive strength of FRP composites.
Conversely, the compressive damage modes of FRP composites also change by increasing the PEK-C content. Using scanning electron microscopy (SEM), we observed the microfracture morphology of FRP composites (Fig. 12). The compressive damage morphology of the unidirectional composites was primarily delamination without the PEK-C modification epoxy. With an increase of the PEK-C content, the compressive failure modes of FRP composites was a combination of delamination and shear failure. For the shear failure morphology, a large number of typical kink-band instability damage modes were found, as explained in the shear failure section. In conclusion, the kink-band damage mode induces the final shear failure. Furthermore, by an increase of the PEK-C content, the occurrence of delamination decreases and that of the kink band increases.
Figure 12. The compressive damage morphology using SEM images: (a) 0 wt%; (b) 10 wt%; (c) 20 wt%; and (d) 30 wt%.
Typically, the mechanism of different PEK-C contents on the compressive strength, as well as the compressive damage modes (Fig. 13), can be summarized as follows. For the unmodified resin composites, small defects would inevitably be produced between layers during the preparation process, and when they are subjected to compressive loads, cracks would gradually propagate along the layers. Before the whole system becomes unstable, it would be destroyed because of the large area of the interlaminar delamination. When an appropriate amount of the PEK-C toughening agent is added to the resin, the interlaminar shear strength of the resin increases, which could effectively inhibit the propagation of interlaminar delamination. Then, the entire composite system gradually destabilizes (kink-band formation), and its failure reaches. Compared with the unmodified composites, owing to the effective suppression of the interlaminar delamination, the ultimate failure mode would be the shear failure caused by the kink-
band instability, and the corresponding compressive strength is enhanced. When the PEK-C content continues to increase (30 wt%), as the buckling strength and the yield strain of the resin layer decreases, the kink-band instability is induced ahead of time; however, the ultimate compressive strength of the composite would lessen. This vital feature guides us to an optimum scheme for increasing the compressive strength, as well as realizing the compressive damage mode of FRP composites, in the kink band/delamination coupled state. In the near future, more research can be conducted such as the study of material modification to realize the simultaneous improvement of the resin yield strength (yield strain) and the interlaminar strength of the laminates. Besides, a structural design could be developed to control or change the compressive damage modes for more improvement of the compressive strength of FRP composites.
Figure 13. The mechanism of PEK-C on the compressive strength.
5. Conclusions This study innovatively proposes an optimum design strategy to enhance the compressive strength of FRP composites. The impact of the matrix yield strength, as well as the interlaminar strength on the compressive damage modes and strength, is examined quantitatively by the finite element simulations and experimental
characterizations. The major findings of this study can be summarized as follows: 1) By adjusting the yield strength of the matrix resin, as well as the interlaminar strength of the laminate, delamination and kink band could occur simultaneously, which lead to the optimal compressive strength of FRP composites. 2) Four contents of PEK-C (i.e., 0, 10, 20, and 30 wt%) were exploited to modify the thermosetting epoxy. By increasing PEK-C, the interlaminar shear strength of the laminates increases monotonously, whereas the yield strength, as well as the yield strain, of the resin decreases, which eventually causes the compressive strength of FRP composites to increase first but, then, decreases. 3) The modification of the resin by PEK-C could effectively convert the compressive damage modes from the delamination to the kink band. When the PEK-C content ranges 10–20 wt%, kink band and delamination coincide. In the case of 30 wt%, the kink band mode is dominant. 4) When the PEK-C content is approximately 20 wt%, the compressive strength of FRP composites increases approximately by 28% regarding the unmodified composites. Conversely, the compressive strength reverses to decrease when the content is about 30 wt%. In fact, the excessive use of PEK-C decreases the yield strength, as well as the yield strain of the resin, and this issue accelerates the occurrence of the kink-band formation.
Acknowledgements The author is grateful for the funding support for independent scientific research (2042019kf0039) in Wuhan University and funding support of start-up research by School of Civil Engineering, Wuhan University.
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` 1.
By maneuvering the compressive damage mode the compressive strength of FRP composites is increased;
2.
The competition mechanism between the two major compression damage modes, delamination and kink band is examined through finite element method;
3.
The interlaminar strength and yield strength of the polymer matrix as the crucial factors regulating the damage modes is identified;
4.
A series of experiments were conducted and results revealed that tuning the interlaminar strength and yield strength of the polymer matrix could effectively maneuver the compression damage modes and their conversion.
Conflict of interest statement We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.