Fatigue behavior of nanoparticle-filled fibrous polymeric composites

Fatigue behavior of nanoparticlefilled fibrous polymeric composites

5

M. Esmkhani, M.M. Shokrieh, F. Taheri-Behrooz Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

5.1

Introduction

Fatigue is a major cause for catastrophic failure in materials. The fatigue behavior of composite and nanocomposite materials was studied by many researchers. For composite materials, three principal approaches were used to predict fatigue life: residual strength [1], residual stiffness [2, 3], and empirical methodologies [4]. In each category, phenomenological, mechanistic, statistical, and mixed methods were utilized by different authors [5–8]. Recently, many researchers have focused on the experimental works and added nanofillers into epoxy polymers and reported improvement on fatigue behavior of nanocomposites [9–26]. There are numerous remarkable efforts in the literature that study the effect of nanoparticles on the mechanical properties of epoxy nanocomposites; like tensile strength and stiffness [27–33]. The electromechanical response (electrical resistance change method) as a damage index of quasi-isotropic carbon fiber-reinforced laminates under fatigue loading was investigated by Vavouliotis et al. [27]. Effect of adding carbon nanotube (CNT) into the glass/epoxy composite was investigated by them and the electrical resistance method was used as a damage control parameter in dynamic fatigue loading condition. A direct correlation between the mechanical loading and the electrical resistance change was established for the investigated specimens [28]. The fatigue behavior and lifetime of polyimide/silica hybrid films were investigated by Wang [29] to evaluate the fatigue property of this class of hybrid films, where the stress-life cyclic experiments under tension-tension fatigue loading were carried out. A semiempirical model [29] was proposed based on the fatigue modulus concept to predict the fatigue life of this class of hybrid films. An exponential model of fatigue stiffness degradation was suggested [30, 31] to predict the fatigue life of matrix-dominated polymer composite laminates based on the nonlinear stress/strain response of most polymers or matrix-dominated polymer composites under uniaxial tension. The fatigue strength assessment of a short-fiber composite using the specific heat dissipation based on an energy approach [32] was proposed and validated to analyze the fatigue strength of the plain and weakened rounded notched specimens made of short-fiber-reinforced plastics. Grimmer [33] showed that the addition of small volume fractions of multiwall carbon nanotube (MWCNT) to the matrix resulted in a Fatigue Life Prediction of Composites and Composite Structures. https://doi.org/10.1016/B978-0-08-102575-8.00005-X © 2020 Elsevier Ltd. All rights reserved.

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significant increase in high-cycle fatigue life. Rosso et al. [34] employed the welldispersed silica nanocomposites for tensile and fracture tests, indicating that the addition of 5 vol.% of silica nanoparticles could improve the stiffness and fracture energy to 20% and 140%, respectively. Guo and Li [35] performing compressive loading on SiO2/epoxy nanocomposites under different loading rates revealed that the compressive strength of composites with silica nanoparticles was higher than that of the pure epoxy at higher strain rates. They showed that there was no clear connection between the compressive strength and the nanoparticle contents at lower strain rates. Johnsen et al. [36] increased the fracture energy of epoxy polymers nanosilica (NS) particles. A set of sudden material property degradation rules, such as stiffness degradation, for various failure modes of a unidirectional ply under a multiaxial state of static and fatigue stress was developed by Shokrieh and Lessard [37]. A comprehensive survey in the available literature reveals the lack of an intensive model to predict the property degradation and fatigue life of the nanoparticle-filled fibrous polymeric composites with thermosets or thermoplastics matrix. In this chapter, after a deep review of the available models, a fatigue model to predict the stiffness reduction of nanoparticle/fibrous polymeric composites has been presented. The model was evaluated in different circumstances based on various industrial applications of composite and nanocomposite materials.

5.2

Fatigue life prediction based on the micromechanical and normalized stiffness degradation approaches

5.2.1 Material properties degradation It is assumed that the major effective reason for material properties’ reduction is due to matrix degradation while in cyclic load conditions nanofillers remain unchanged under different states of stress. Due to the crack propagation in the composite, material properties of composites are changed by a set of sudden material property degradation. The sudden material property degradation rules for some failure modes of a unidirectional ply under a bi-axial state of stress are available in the literature [38, 39] and shown in Fig. 5.1. The degraded ply is modeled by an intact ply of lower material properties. A complete set of sudden material property degradation rules for all various failure modes of a unidirectional ply under a multiaxial state of static and fatigue stress was developed by Shokrieh and Lessard [37]. The lack of models to predict the property degradation of nanoparticle-filled epoxy composites can be observed by a comprehensive survey in the available literature. In this chapter, it is tried to develop a fatigue model to predict the stiffness reduction of polymeric composites with nanoparticles as reinforcement.

5.2.2 Normalized stiffness degradation approach The residual stiffness of the material is also a function of the state of stress and the number of cycles. Since the residual stiffness can be used as a nondestructive measure

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

137

Fig. 5.1 Degraded ply is modeled by an intact ply of lower material properties [37].

of the damage evaluation, the stiffness degradation models have been developed by many investigators. By using the normalization technique, all different curves for different states of stress can be shown by a single master curve. Shokrieh and Lessard [37] developed a method of normalization and the present study follows the mentioned method to predict the stiffness degradation of nanocomposite materials using the micromechanics approaches. An epoxy matrix under a constant uniaxial fatigue loading, and under static loading, or equivalently at n¼ 0.25 cycles (a quarter of a cycle) in fatigue is considered for static stiffness of the neat matrix of composites. By increasing the number of cycles, under constant applied stress, σ, the fatigue stiffness, E(n), decreases. Finally, after a certain number of cycles, which is called the number of cycles to failure (Nf), the magnitude of the stiffness decreases to a critical magnitude (Ef). At this point, the composite fails catastrophically. The stiffness degradation of a unidirectional ply is shown in Fig. 5.2. The aforementioned critical value for stiffness Ef can be expressed by the following equation: Ef ¼

σ εf

(5.1)

The average strain to failure, εf, is assumed to be constant and independent on the state of stress and number of cycles. This assumption was used by many authors [40–43] and was experimentally verified in the present study. It should be mentioned that for different states of stress, the stiffness degradation of the composites is different. The same as for the residual strength case, under a highlevel state of stress, the residual stiffness as a function of a number of cycles is nearly constant and it decreases drastically at the number of cycles to failure (Fig. 5.2). However, at the low-level state of stress the residual stiffness of the composite, as a function of the number of cycles, degrades gradually. In practice, designers must deal with a wide range of states of stress varying from low to high. Therefore, similar to the strength degradation case, a model to present the residual stiffness behavior of composite materials under a general state of stress is essential.

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Fig. 5.2 Stiffness degradation under different states of stress [37].

To present the residual stiffness as a function of the number of cycles in a normalized form, the following equation was developed [37]: 2 Eðn, σ, K Þ ¼ 41 

!λ 31γ   log ðnÞ  log ð0:25Þ 5 σ σ
 Es  + εf εf log Nf  log ð0:25Þ

(5.2)

where E(n, σ, K)¼residual stiffness, Es ¼ static stiffness, σ ¼ magnitude of applied maximum stress, εf is an average strain to failure, n ¼ number of applied cycles, Nf ¼ fatigue life at σ, λ, γ ¼ experimental curve-fitting parameters. By using the normalization technique [37], all different curves for different states in Fig. 5.2 collapse to a single curve that has been shown in Fig. 5.3.

Fig. 5.3 Normalized stiffness degradation curve [37].

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139

5.2.3 Normalized fatigue life model The effect of mean stress (σ max + σ min)/2 on fatigue life was presented efficiently by using the constant life (Goodman-type) diagrams [44]. The establishing and interpolation of the constant life diagram data in a traditional form is a tedious task. However, there are analytical methods [45–49] for predicting the effect of mean stress on the fatigue life based on a limited number of experiments. In a paper by Adam et al. [45], an analytical method has been proposed to convert and present all data from a constant life diagram in a single two-parameter fatigue curve, which can reduce the number of required experiments drastically. In this study, this model is called the normalized fatigue life model. The normalized fatigue life model was modified by Harris and his coworkers for more general cases [48, 49]. In the following, this model is explained in detail. Introducing the nondimensional stresses by dividing of the mean stress σ m, the alternating stress σ a, and the compressive strength σ c by the tensile strength σ t, where q ¼ σ m/σ t, a ¼ σ a/σ t, and c ¼ σ c/σ t, an empirical interaction curve may be derived [48, 49]: a ¼ f ð1  qÞu + ðc + qÞv

(5.3)

where f, u, and v¼ curve-fitting constants, alternating stress, σ m ¼ (σ max + σ min)/ 2 ¼ mean stress, q ¼ σ m/σ t, a ¼ σ a/σ t, and c ¼ σ c/σ t. A typical curve for fatigue life of 106 cycles is shown in Fig. 5.4. The bell-shaped curve is the fatigue life curve. Experimental results by Gathercole et al. [49] showed that their previous quadratic model [46] is inappropriate for the constant life curve especially in both low and high mean stress regions (Fig. 5.4). Therefore, they introduced a power law model (Eq. 5.4) that produces a bell-shaped curve, which corresponds closely to the material behavior under the fatigue loading. In a paper by

Fig. 5.4 Typical constant life diagram [37].

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Fatigue Life Prediction of Composites and Composite Structures

Gathercole et al. [49], it was shown that the exponents u and v determine the shapes of the left and right wings of the bell-shaped curve. However, it was also shown that the degree of curve-shape asymmetry was not very great, therefore, they assumed u and v are equal and are linear functions of the fatigue life Nf. u ¼ v ¼ A + B log Nf

(5.4)

where A and B are the curve-fitting constants. By substituting Eq. (5.4) into Eq. (5.3), the following equation is obtained: a ¼ f ½ð1  qÞ + ðc + qÞA + B log Nf

(5.5)

The following example helps to explain the normalized fatigue life model. To predict the fatigue life, the following steps must be performed. First, the σ max  log Nf curve for different stress ratios should be established experimentally (Fig. 5.5). Different symbols in Fig. 5.5 represent different applied stress ratios. It is obvious that testing in more states of stress results in more accurate results. Then, by rearranging Eq. (5.5), the following equation is derived and shown graphically in Fig. 5.6: u¼

lnða=f Þ ¼ A + Blog Nf ln ½ð1  qÞðc + qÞ

(5.6)

In Figs. 5.5–5.7, this procedure has been applied to numerical data from the paper by Adam et al. [45]. In Fig. 5.5, the original fatigue data are presented. Then, based on the data from Fig. 5.6, setting f ¼ 1.06 (suggested by Gathercole et al. [49]) and Eq. (5.7), u ¼ ln(a/f )/ ln[(1  q)(c + q)] vs log Nf curve is extracted (Fig. 5.6), from which A and B are found.

CFRP

s max, GPa

1.5

1.0

0.5 1

2

3

4

5

Log Nf

Fig. 5.5 S-log Nf curve, σ t ¼1.91 (GPa), and σ c ¼ 1.08 (GPa) [45].

6

7

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

141

Fig. 5.6 u vs log Nf curve [37].

Fig. 5.7 Predicted constant life diagram [37].

In Fig. 5.7, based on all previous information, the constant life diagram for a different number of cycles to failure is predicted. Fig. 5.7 is generated by knowing A, B, and f, three constants which can be determined from a relatively small quantity of tests, as demonstrated in this example. Thus, the method is very useful for reducing the number of experiments for the characterization of materials.

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Fatigue Life Prediction of Composites and Composite Structures

5.2.4 Modeling strategy for the filled fibrous composites with nanoparticles A comprehensive survey in the available literature reveals the lack of models to predict the property degradation of nanoparticle-filled fibrous epoxy composites. In this chapter, a fatigue model is developed to predict the stiffness reduction of nanoparticle/ fibrous polymeric composites. For this purpose, a schematic framework of the modeling strategy is shown in Fig. 5.8. The model is an integration of two major components: the micromechanical (such as the Halpin-Tsai or Nielsen models) and the normalized stiffness degradation approaches. The model is able to predict the final fatigue life of nanoparticle/fibrous polymeric composites under general fatigue loading conditions. As shown in Fig. 5.8, in the first step, the model predicts the equivalent stiffness of nanoparticle/epoxy nanocomposites using a micromechanical approach with pure epoxy resin and nanoparticles parameters. Then, the normalized stiffness degradation model for fibrous polymeric composites under fatigue loading was used to predict the stiffness degradation of fibrous polymeric composites. While the archived equivalent stiffness is used for stiffness of fibrous polymeric composites. By coupling of the normalized stiffness degradation model of fibrous polymeric composites and the micromechanical approach, the normalized stiffness degradation model for nanoparticle/fibrous polymeric composites under fatigue loading was developed.

Pure epoxy resin

Nanoparticles

Micromechanical Models

Equivalent stiffness of nanoparticle/epoxy nanocomposites

Normalized stiffness degradation model for fibrous polymeric composites under fatigue loading

Normalized stiffness degradation model for nanoparticle/fibrous polymeric composites under fatigue loading

Fig. 5.8 A schematic flowchart of the present model.

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

143

5.2.5 Micromechanical models 5.2.5.1 The Halpin-Tsai micromechanics model There are several models for the prediction of elastic properties of nanocomposite materials, based on the geometry, the orientation of the filler, the elastic properties of the filler and matrix, such as the Halpin-Tsai model [50–52], the Nielsen model [53–56], the Mori-Tanaka model, the Eshelby model, etc. The Halpin-Tsai model is based on the self-consistent field method, although often considered being a semiempirical also a simple but accurate model that takes into account the shape and the aspect ratio of the reinforcing particles. In this model, the quality of the bonding and fillers arrangements was not considered. It can predict the modulus of a composite material (Ec), containing nanoparticles as a function of the modulus of the polymer (Em) containing no nanoparticles and of the modulus of the particles (Ep). The predicted modulus of the nanoparticle-modified epoxy polymer (Ec) is given by the following equation: w 1 + 2 ηVp t Ec ¼ Em 1  ηVp

(5.7)



   Ep Ep w where, η ¼ 1 = +2 t Em Em

(5.8)

where w/t is the shape factor and Vp is the volume fraction of particles. The equivalent modulus can be derived for nanoparticles in different types based on the particles shapes. For instance for the plane shape (such as graphene nanoparticles), the predicted modulus of filled composite (EC) is given by Eq. (5.9). 

   ðEG =Em Þ  1 ðEG =Em Þ  1 1 + ½ðw + lÞ=t 1+2 VG VG EC 3 5 ðEG =Em Þ + ½ðw + lÞ=t ðE =E Þ + 2    G m  ¼ + ðEG =Em Þ  1 ðEG =Em Þ  1 8 Em 8 1 1 VG VG ðEG =Em Þ + ððw + lÞ=tÞ ðEG =Em Þ + 2 (5.9) where EG is the elastic modulus of plane nanoparticles and Em is the composite modulus without nanoparticles. Moreover, L, W, and t are the length, width, and thickness of the plane nanoparticles, respectively. In terms of using carbon nanofibers (CNFs) as particles, the Halpin-Tsai equations are represented as the following equation:      L ðECNF =Em Þ  1 ðECNF =Em Þ  1 1+2 1+2 VCNF VCNF Enc 3 5 d ECNF =Em + 2  ðL=d Þ ðE =E Þ + 2    CNF m  ¼ + ðECNF =Em Þ  1 ðECNF =Em Þ  1 8 Em 8 1 1 VCNF VCNF ½ECNF =Em Þ + 2  ðL=dÞ ðECNF =Em Þ + 2 (5.10)

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Fatigue Life Prediction of Composites and Composite Structures

where L and d are the length and diameter of CNFs [50, 53, 57]. Furthermore, the Halpin-Tsai model can be implemented to predict the stiffness of chopped strand mat (CSM)/polymer composites (ECSM,nc) reinforced with nanoparticles, as a function of the stiffness of the pure matrix (Em), the stiffness of CSM (ECSM), and the stiffness of nanoparticles (Ep) in static loading conditions. The predicted stiffness of the nanocomposites (ECSM,nc) reinforced with CSM and nanoparticles is given by the following equation:   1 + ξ1 η1 VCSM + ξ2 η2 Vnanoparticles ECSM, nc ¼ Em (5.11) 11 η1 VCSM  η2 Vnanoparticles where VCSM and Vnanoparticles are the volume fractions of CSM and nanoparticles, respectively. Moreover, ξ is the shape factor of CSM and nanoparticles. Also, η1 and η2 are defined as below: ECSM =Esm  1 ECSM =Esm + ξ1 Enanoparticles =Esm  1 η2 ¼ Enanoparticles =Esm + ξ2 η1 ¼

(5.12)

where ECSM and Enanoparticles are the stiffness of CSM and nanoparticles under static loading conditions. Moreover, ξ1 and ξ2 are shape factors of CSM and nanoparticles, defined as ξ1 ¼ 2

l1 l2 , ξ2 ¼ 2 d1 d2

(5.13)

5.2.5.2 Nielsen micromechanics model The Nielsen model predicts Young’s modulus of nanocomposite materials, especially for spherical particles. In his model, the effect of slippage between the nanoparticle and matrix was evaluated using a coefficient factor. The Nielsen model used to predict the modulus of a material containing nanoparticles (Ec) as a function of the modulus of the polymer containing no nanoparticles (Em), and of the modulus of the particles (Ep). The predicted modulus of the nanoparticle-modified epoxy polymer (Ec) is given by the following equation [55, 58]: EC ¼

1 + ðKE  1Þβ Vf Em 1  μ β Vf

(5.14)

where KE is the generalized Einstein coefficient and β and μ are the constants. The constant β is given by     EP EP 1 + ð K E  1Þ (5.15) β¼ Em Em

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145

It should be noted that β is identical to h in the Halpin-Tsai model when a shape factor of ζ ¼ (KE  1) is used. The value of μ depends on the maximum volume fraction of particles (νmax) that can be incorporated and calculated by the following equation:

 1  νf  μ¼1+ νmax νf + ð1  νmax Þ 1  νf (5.16) νmax where values of νmax have been published by Nielsen and Landel [55] for a range of particle types. Nielsen and Landel [59] quoted a value of νmax ¼ 0.632 for such random close-packed, non-agglomerated spheres and this value is used in the present model. The value of KE varies with the degree of adhesion of the epoxy polymer to the particle. For the epoxy polymer with a Poisson’s ratio of 0.5 which contains dispersed spherical particles: (a) KE ¼ 2.5 if there is “no slippage” at the interface (i.e., very good adhesion), or (b) KE ¼ 1.0 if there is “slippage” (i.e., relatively low adhesion) [55]. However, the value of KE is reduced when the Poisson’s ratio of the polymer is less than 0.5 [56]. These earlier studies have also found that at relatively high values of vf, above about 0.1 of silica nanoparticles, the Nielsen “slip” model gave the best agreement with the measured values. However, the present study found that relatively low values of vf (i.e., at values of vf below about 0.1) the Halpin-Tsai and the Nielsen “no-slip” models show better agreement. Thus, an overall conclusion is that the measured modulus of the different silica nanoparticle-filled epoxy polymers approximately lay between an upper-bound value set by the Halpin-Tsai and the Nielsen “no-slip” models, and a lower-bound value set by the Nielsen “slip” model, with the last model being the more accurate at relatively higher values of vf [59].

5.2.6 The normalized stiffness degradation model for nanocomposites (Nano-NSDM) 5.2.6.1 The Nano-NSDM based on the Halpin-Tsai model By coupling of the normalized stiffness degradation approach (Eq. 5.2) for fibrous polymeric composites under fatigue loading and the Halpin-Tsai micromechanics model, the normalized stiffness degradation model for nanoparticle/fibrous polymeric composites under fatigue loading in form of Eq. (5.17) was developed.     EP EP 2 1 + 2w=t 1 + 2w=t Vf Em Em 41      EC ¼ EP EP 1 1 + 2w=t Vf Em Em    EP EP 1 + 2w=t 1 + 2w=t Vf σ Em Em +      εf EP EP 1 1 + 2w=t Vf Em Em

!λ 31γ   log ðnÞ  log ð0:25Þ 5 σ
 Es  εf log Nf  log ð0:25Þ



(5.17)

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Fatigue Life Prediction of Composites and Composite Structures

5.2.6.2 The Nano-NSDM based on the Nielsen model After a combination of the normalized stiffness degradation approach for fibrous polymeric composites under fatigue loading with the Nielsen micromechanics model, the normalized stiffness degradation model for nanoparticle/fibrous polymeric composites under fatigue loading in form of Eq. (5.18) is developed. 

   EP EP 1 + ðKE  1Þ Vf Em Em    
 EP EP νf + ð1  νmax Þ 1  νf 1 + ðKE  1Þ Vf Em Em

1 + ðKE  1Þ

EC ¼


 1  νf  1 1+ νmax νmax 

2 41 

log ðnÞ  log ð0:25Þ
 log Nf  log ð0:25Þ

!λ 31γ ! σ σ 5 Es  + εf εf

    EP EP 1 + ðKE  1 Þ 1 + ðKE  1Þ Vf Em Em
      
 1  νf  EP EP 1 1+ νmax νf + ð1  νmax Þ 1  νf 1 + ð K E  1Þ V f Em Em νmax (5.18)

5.2.7 The evaluation of Nano-NSDM In this section, the evaluation of the Nano-NSDM is performed under different following circumstances.

5.2.7.1 Fatigue life prediction for epoxy resin modified by silica nanoparticles In this research, the silica nanoparticles have been employed to modify the epoxy resin. In general, the dimensions of these particles are in micron ranges. However, with the advance of nanotechnology as well as the processing techniques, various types of particles in nanoscales have recently been developed and utilized as reinforcement in polymeric composites [26]. Experimental results obtained from tension-tension fatigue tests on a bulk epoxy confirm the reduction of the epoxy laminated composite stiffness, caused by the presence of cracks, which can effectively be compensated by silica nanoparticles. In a work by Manjunatha et al. [26], 185 g/mol of epoxy resin, LY556, bisphenol A (DGEBA), supplied by Huntsman, Duxford UK and the silica (SiO2) nanoparticles supplied by Nanoresins, Geesthacht, Germany were used. For the spherical silica nanoparticles used in the present work, the aspect ratio is unity and hence, w/t ¼ 1 was used. Also, in this case study, νmax ¼ 0.632, νf ¼ 0.048 so

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

147

the values of KE is 2.5 and the Nielsen “no-slip” model was implemented. So Eq. (5.15) will be changed in form of the following equation:     ESio2 ESio2 2 1+2 1 + 2 Vf Em Em     41  EC ¼ ESio2 ESio2 1 1 + 2 Vf Em Em     ESio2 ESio2 1+2 1 + 2 Vf σ E E  m   m  +  ESio2 ESio2 εf 1 1 + 2 Vf Em Em

log ðnÞ  log ð0:25Þ
 log Nf  log ð0:25Þ

!λ 31γ   5 Es  σ εf

(5.19)

Typical stiffness variation curves obtained at σ max ¼ 225 MPa are shown in Fig. 5.9A. In general, all materials exhibit a stiffness reduction with fatigue cycles, as has been previously observed in FRPs [60, 61]. The stiffness reduction was quite steep and very significant in GRP nanocomposites. By using the neat resin (NR), data of Fig. 5.9A and using the normalized technique, curve-fitting parameters, λ and γ are obtained (see Fig. 5.9B). The other properties of the GRP composites and NS are shown in Tables 5.1 and 5.2. For evaluating of the accuracy of derived equations for the NR, according to Fig. 5.10, the trend for stiffness of NR vs the number of cycles is depicted and good agreement with experimental data was obtained. This compatibility shows that obtained curve-fitting parameters are suitable for this composite. Fig. 5.11 shows that the reported stiffness vs the number of cycles for 10 wt% silica nanoparticle-filled epoxy polymers is in a good agreement with the modified normalized stiffness degradation models. Also, the behavior of the modified Nielsen “noslip” model is nearer to the result of the experiment compared with the modified Halpin-Tsai model. In Table 5.3, the results and value of the errors for each modified model are presented.

5.2.7.2 Fatigue life prediction for GFRP with nanoparticles As a next verification of the model, the results presented in Ref. [26] are considered. The fatigue limit, that is, the maximum applied stress for a life of 106cycles of the neat epoxy is about 95 MPa. The presence of silica particles in the matrix raises this fatigue limit by about 15% to 110 MPa. At this state of stress, the normalized stiffness degradation curve was generated and after 2,000,226 cycles, the stiffness of modified composites with nanoparticles (Ec) and the tensile strength were obtained equal 5.54 GPa and 111.92 MPa, respectively (see Table 5.4). On the other hand, the results presented in Ref. [20] as shown in Fig. 5.12 are considered. It was assumed that the curve-fitting parameters represented in Fig. 5.9A are again valid. This assumption has a negligible error. The final results, after applying the

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Fatigue Life Prediction of Composites and Composite Structures 1.00 NR NRR NRS

Normalised stiffness

0.95

0.90

0.85

0.80

0.75 0

500

1000

1500

2000

2500

Number of cycles, N

(A)

Normalized stiffness degradation curve for LY556 epoxy resin 1 0.9 0.8

Normalized stiffness

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

(B)

0.2

0.4 0.6 Normalized number of cycles

0.8

1

Fig. 5.9 (A) The stiffness variation during fatigue cycling in the GFRP composites at σ max ¼ 225 MPa, (i) neat resin (NR), (ii) resin with 9 wt% rubber microparticles (NRR), (iii) resin with 10 wt% silica nanoparticles (NRS), and (iv) resin with a “hybrid” matrix containing both 9 wt% rubber and 10 wt% silica particles (NRRS) [26]. (B) Normalized stiffness degradation curve for LY 556 epoxy resin, λ ¼ 3.348, γ ¼ 0.357, and εf ¼ 0.02 [62].

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Table 5.1 Properties of GFRP composites [26] Tensile properties Material

Condition

Strength, Xt (MPa)

Modulus, E (GPa)

GFRP

Without nanoparticles

365

17.5 0.6

Table 5.2 Properties of Silica nanoparticles [26] Tensile properties Mean diameter, D (nm)

Modulus, E (GPa)

20

85

18 Em(n)- Manjunatha et al. (2009) Em(n)- Model

Em (GPa)

17

16

15

14 0

200

400 n (cycles)

600

800

Fig. 5.10 Stiffness reduction for neat epoxy resin, σ max ¼ 225 MPa [62].

developed model at 22,143 cycles, are presented in Table 5.5. The tensile strength for 10 wt% SiO2 /LY556 epoxy nanocomposites calculated by the model is equal to 29.24 MPa (in comparison to the 28.8 MPa presented in the reference). Therefore, the accuracy of the developed model is acceptable. The results are expressed in Table 5.5 [62].

150

Fatigue Life Prediction of Composites and Composite Structures 20 Manjunatha et al. (2009) The Nano-NSDM based on Halpin-Tsai model The Nano-NSDM based on Nielsen model

19

Ec (GPa)

18

17

16

15

14 0

500

1000

1500

2000

n (cycles)

Fig. 5.11 The stiffness reduction of 10 wt% silica epoxy nanocomposites, σ max ¼ 225 MPa [62]. Table 5.3 Results and value of error for modified models [62]

n (cycles)

Em(n): Present model

Ec(n): Experimental results [26]

Ec(n): HalpinTsai model

Error (%)

Ec(n): Nielsen model

Error (%)

11 118 182 300 589 705

17.19 16.00 15.67 15.24 14.58 14.40

18.82 17.58 17.18 16.88 16.22 16.13

19.82 18.45 18.06 17.56 16.80 16.59

5.33 5.00 5.11 4.00 3.56 2.84

18.85 17.61 17.25 16.79 16.09 15.90

0.19 0.18 0.39 0.55 0.79 1.43

Table 5.4 Results of the neat epoxy and 10 wt% nano-silica modified GFRP composites, σ ¼ 95 MPa [62] Material

Condition

GFRP

0 wt% nanoparticles 10 wt% nano silica-modified epoxy [26] 10 wt% nano silica filled epoxy, based on the Halpin-Tsai model

Strength (MPa) 95 110 111.92

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151

Maximum Stress, smax (MPa)

45 Bulk Epoxies R = 0.1 n = 1 Hz 20°C, 55% RH

40 35

30 25

Neat epoxy (EP) Epoxy+Rubber (ER)

20

Epoxy+Silica (ES) Epoxy+Rubber+Silica (ERS)

15 1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

No. of cycles, Nf

Fig. 5.12 Stress vs lifetime (S-N) curves of neat epoxy and nanoparticle-filled epoxy [20]. Table 5.5 Properties of nanoparticle-filled GFRP composites [62] Material

Condition

Bulk Epoxy

0 wt% nanoparticles, Experimental Result [20] 0 wt% nanoparticles, Present work

GFRP without nanoparticles GFRP with nanoparticles GFRP with nanoparticles

10 wt% nano-silica-modified epoxy, Experimental result [20] 10 wt% nano-silica filled epoxy, presentwork based on the HalpinTsai model

Strength (MPa)

Error (%)

25.0

–

25.3

1.2

28.8

–

29.2

1.5

5.2.7.3 Fatigue modeling of CSM/epoxy composites There are many applications for CSM composites in various industries because of their intrinsic properties. In a published paper by the present authors [63], the normalized stiffness degradation method was utilized for CSM/epoxy composites to predict the fatigue life. Moreover, the fatigue damage accumulation model developed by Ye [64], for E-glass fabric in CSM form with isophthalic polyester resin, was not applied for CSM/epoxy composites. So, in this research, the capability of this model for epoxy matrix composites was also investigated. A series of tests in tension-tension fatigue condition at room temperature was carried out at different load levels to evaluate the capabilities of both models with experimental observations [63].

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Fatigue Life Prediction of Composites and Composite Structures

Fatigue damage accumulation model Damage accumulation and cyclic degradation are critical issues for design and life prediction of composites under fatigue loading conditions. The fatigue damage theory for the CSM composites based on the phenomenological aspects of damage accumulation in composite materials has been assessed by Ye et al. [64]. They assumed that the residual stiffness is a monotonically decreasing function of the fatigue cycle and depends on the damage variable as follows: D¼1

E Es

(5.20)

where E is the current stiffness and Es is the initial static stiffness of the material. The characteristics of fatigue crack growth and a damage accumulation law for composites can be defined as  2 n dD σ ¼ C max dN D

(5.21)

where C and n are material constants that can be determined by testing specimens at various applied stresses. Using the definition of the damage variable in Eq. (5.20), the damage development in the composites is shown in Fig. 5.13 [65, 66]. Due to the inherently heterogeneous microstructure of the chopped fiber-reinforced composites, various kinds of stress concentrators exist in the material, including fiber/matrix interfaces, fiber ends, process-induced defects, laminate stress-free edges or discontinuities, and residual stress concentrations developed during the curing process [64]. The presence of these stress concentrators results in significant energy storage.

Fig. 5.13 Fatigue damage development in composite materials [65, 66].

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

153

The energy storage tends to approach an energy balanced state, as indicated by the feature of entropy in nonlinear irreversible thermodynamics [64]. In the early stage (stage I) of fatigue damage development, rates of energy dissipation and material degradation are rapid. In this stage, fatigue damage appears predominantly in the form of matrix cracking along fibers in plies of composite laminates [67] and in addition, fiber-matrix interface debonding in the case of chopped fiber composites. The fibers aligned ahead of a matrix crack are obstacles to the crack growth. Therefore, it is more difficult to break a fiber than to break the matrix. Hence, during stage II of fatigue damage development, energy dissipation and material degradation rates decrease when the matrix cracks reach fibers aligned at some angle in front of them. In the final stage (stage III) of fatigue damage development, sudden coalescence of micro-cracks and severity of interaction, in addition to the rapid growth of the most favorable cracks, lead to the catastrophic fracture of composites [64]. Finally, the predicted modulus after N cycles can be expressed by the following expression: h i ðn + 1Þ E ¼ 1  fNCðn + 1Þg1=n + 1 σ 2n= Es max

(5.22)

It can be used to predict the number of cycles required to reach a given stiffness reduction for a known fatigue maximum applied stress. In this relation, C and n, as material constants have to be identified by testing specimens after measuring the stiffness reduction at various applied stresses [63].

Tests results—Model evaluation A series of tests in static loadings was carried out to determine tensile properties of fabricated composites using CSM short glass fibers as isotropic fiber-reinforced composites. The stress-strain relationship of a sample is presented in Fig. 5.14. In order to evaluate the fiber weight fraction, the burn-off test was performed to obtain the glass fiber content. In order to maintain statistical reliability, minimum of four samples were tested in each step. The mean tensile strength of the four samples was achieved equal to 158 MPa. The Young’s modulus of fabricated composites was around 8.9 GPa. In addition, the tension-tension fatigue tests were conducted at three different stress levels. The maximum stresses were chosen to be 50%, 60%, and 70% of the ultimate tensile strength of the specimen. The fatigue tests were carried out under a loadcontrol condition at a frequency of 2 Hz. During all fatigue tests, the stress ratio (minimum applied stress/maximum applied stress) was set at 0.1 under room temperature condition. The applied maximum stress and the number of cycles to failure from experiments for CSM/epoxy composites under the load control fatigue loading are demonstrated in Table 5.6. In the normalized stiffness degradation approach for CSM polymeric composites under fatigue loading to predict the fatigue life of CSM/epoxy composites, λ, γ experimental curve-fitting parameters from Eq. (5.2) have to be determined. By using the normalization technique and obtaining parameters as discussed in the previous

154

Fatigue Life Prediction of Composites and Composite Structures 160 140

Stress (MPa)

120 100 80 60 40 20 0 0.00

0.01

0.02

0.03

0.04

Strain

Fig. 5.14 The stress-strain curve of CSM/epoxy composites [63]. Table 5.6 Sample of experimental results of CSM/epoxy composites under tension-tension fatigue loading at room temperature condition, R ¼0.1, strain to failure ¼0.0187 [63] Stress level (%)

Applied stress (MPa)

Number of cycles to failure (cycles)

70 60 50

111 95 79

6121 19398 36481

sections, all different curves for different states of stress collapse to a single curve as shown in Fig. 5.15. The obtained value of λ and γ is 7.348 and 0.852, respectively. Moreover, the empirical parameters of C and n for the fatigue damage accumulation approach (Ye’s Model, [64]) are found from experiments equal to 2E  43 and 8.1256, respectively. Finally, during the stage II of the fatigue life (4000–24,000 cycles), the normalized stiffness reduction of CSM/epoxy composites at 79 MPa stress loading or 50% of the ultimate strength has been achieved and demonstrated. Then, the results of both models have been compared with achieved experimental results by Shokrieh et al. [63] and represented in Fig. 5.16. Evaluation of models indicates there was a better correlation between the normalized stiffness degradation technique and the experimental results in comparison with the Ye model [64]. In addition, the results show that the normalized stiffness degradation technique is properly applicable for CSM/

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

155

1 0.9

Normalized stiffness

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.5

0.55

0.6

0.7 0.75 0.8 0.85 0.65 Normalized number of cycles

0.9

0.95

1

Fig. 5.15 Normalized stiffness degradation curve for CSM/epoxy composites, λ ¼ 7.348, γ ¼ 0.852, and εf ¼ 0.0187 [63]. 1

E/Es

0.8

Experimental data 0.6 Normalized Stiffness Degradation Model Lin Ye Model, C = 2E-43, n = 8.1256 0.4 4000

9000

14000 n (cycles)

19000

24000

Fig. 5.16 Stiffness reduction of CSM/epoxy composites, stress level 50% of UTS (comparison between models and experimental data [63]).

epoxy composites and the application of this approach is not limited to unidirectional ply composites [63].

5.2.7.4 Fatigue life of thermoplastic nanocomposites In order to evaluate the present model for thermoplastic nanocomposites, experimental results (Fig. 5.17) of Ramkumar and Gnanamoorthy [68] are used. They investigated the effect of adding nanoclay on the temperature rise and the modulus drop during

156

Fatigue Life Prediction of Composites and Composite Structures

Fig. 5.17 Temperature rise during fatigue testing in PA6 and PA6NC specimens tested at 30 and 22 MPa [68].

35

Temperature rise (K)

30 25

PA6-30MPa PA6NC-30MPa PA6-22MPa PA6NC-22MPa

20 15 10 5 0 1.E+00

1.E+01 1.E+02 1.E+03 No. of cycles

1.E+04

1.E+05

the biaxial cyclic loading for thermoplastic modulus behavior of the neat matrix and clay/polyamide-6 (PA6) nanocomposites (PA6NC). The major reason for the modulus reduction of PA6NC and neat PA6 under fatigue loading conditions are assumed to be due to the temperature rise and thermal softening phenomena. The investigated temperature rise during the fatigue testing in PA6 and PA6NC specimens are presented in Fig. 5.17 at 30 and 22 MPa [68]. Ramkumar and Gnanamoorthy [68] employed commercial grades of PA6 pellets and hectorite clay (bentone) nanoparticles in micron dimensions to modify the PA6 thermoplastic matrix. The clay was organically modified with a hydrogenated tallow quaternary amine complex. PA6 pellets and 5 wt% clay nanofillers were mixed in their research to make PA6NC and measured tensile properties of PA6 and PA6NC shown in Table 5.7 [68]. In Fig. 5.18, the normalized modulus drop as a function of the number of cycles for the PA6 thermoplastic matrix without nanoparticles at 30 and 22 MPa stress magnitudes is demonstrated to verify the present model for PA6. Then, the normalization technique was applied and the normalized stiffness degradation curve for PA6 thermoplastic resin without nanoparticles was implemented [69]. Next, the curve-fitting parameters, λ and γ were obtained as shown in Fig. 5.19 equal to 3.984 and 1.169, respectively. For evaluating the accuracy of the derived equations for the neat PA6 thermoplastic resin without nanoparticles, the trend of the stiffness vs the number of cycles is depicted in Fig. 5.20 and a good agreement with experimental data Table 5.7 Tensile properties of PA6 and PA6NC [68] Material

Tensile modulus (MPa)

Tensile strength (MPa)

PA6 PA6NC

720 2310

34 52

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

157

1.2

Modulus (normalized )

1.0

0.8

0.6 PA6NC, 30 MPa PA6NC, 22 MPa PA6, 30 MPa PA6, 22 MPa

0.4

0.2 1e+0

1e+1

1e+2

1e+3

1e+4

1e+5

No. of cycles Fig. 5.18 Modulus drop (normalized) as a function of the number of cycles for PA6 and PA6NC specimens tested at 30 and 22 MPa stress magnitudes [68].

1 0.9

Normalized stiffness

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.2

0.3

0.6 0.7 0.4 0.5 Normalized number of cycles

0.8

0.9

Fig. 5.19 Normalized stiffness degradation curve for polyamide-6 (PA6) thermoplastic resin without nanoparticles,λ ¼ 3.984, γ ¼ 1.169, and εf ¼ 0.52 [69].

158

Fatigue Life Prediction of Composites and Composite Structures

Fig. 5.20 Stiffness reduction for PA6 thermoplastic resin without nanoparticles [69].

was obtained. This compatibility shows that obtained curve-fitting parameters are suitable for this thermoplastic resin. The major capability of the present model is the fatigue life prediction of thermoplastic-filled with two-dimensional (2D) nanoparticles composites under fatigue loading condition based on the experimental data of the neat thermoplastic resin without nanofillers. For this purpose, the properties of the nanoparticles and the neat thermoplastic matrix are replaced in the present model. The properties of the hectorite clay were used from the available data in the literature [70], both aspect ratio and width are 100 nm. The stiffness of hectorite clay was found equal to 120 GPa by means of an inverse technique and the Halpin-Tsai micromechanical model (Eq. 5.9) while subjected to static loading conditions. The present model was also verified at 22 and 30 MPa of stress magnitudes. First, the stiffness vs the number of cycles for 5 wt% PA6NC at 30 MPa stress magnitude was found and shown in Fig. 5.21. It shows that the normalized stiffness degradation vs the number of cycles for 5 wt% hectorite PA6NC, calculated by the present model, is in a good agreement with experiments. The behavior of the Nano-NSDM based on the Halpin-Tsai model completely covers the result of the experiment. For more elaboration, the results and error value of 2D nanoparticles are presented in Table 5.8. For instance, while the number of cycles was 474 cycles, according to the experimenf tal results, EPA6NC was 1.88 GPa. The predicted stiffness by the present model for 5 wt% PA6NC material is 1.87 and only 0.39% error is observed. The error percent at the number of cycles between 0.25 and 100 is more than 1% which confirms the primary assumptions of the normalized stiffness degradation technique and the capability of the established model in this region. Furthermore, the present model was applied for the reinforced nanocomposite at 22 MPa of stress magnitude to show

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

159

Fig. 5.21 The stiffness reduction for 5 wt% clay/PA6 nanocomposites (PA6NC), σ max ¼ 30 MPa [69].

Table 5.8 Results and value of error for modified model [69] (PA6NC), σ max ¼ 30 MPa

n (Cycles)

Experiments PA6NC [68] Efnc (GPa)

Nano-NSDM based on The Halpin-Tsai Model Efnc (GPa)

Error (%)

3 10 31 102 474 1010

2.12 2.13 2.08 2.03 1.88 1.79

2.07 2.07 2.05 2.00 1.87 1.78

2.40 2.69 1.39 1.31 0.39 0.86

the capability of the model in another stress level. According to Ramkumar and Gnanamoorthy [68], the stiffness of 5 wt% PA6NC in this state, while the number of cycles equal to 800 cycles, was 1.9 GPa. To apply Nano-NSDM, it was assumed that curve-fitting parameters in the normalized stiffness degradation techniques are valid. Then, the stiffness vs the number of cycles for this nanocomposite predicted by the present model is equal to 1.8 GPa. A comparison shows there is a good consistency between the obtained results and experimental observation. It means that the developed model is also applicable to this stress level [69].

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Fatigue Life Prediction of Composites and Composite Structures

5.2.7.5 Fatigue life of nanoparticles/CSM/polymer hybrid nanocomposites In this step, to evaluate the capability of the present model (Nano-NSDM) in the calculation of the fatigue life of nanoparticles/CSM/polymer hybrid nanocomposites, the CNF is selected as the nanoparticle and experiments are carried out in the present work.

Experimental procedure The ML-526 epoxy resin based on bisphenol-A was used in the present study. The ML-526 epoxy was selected because of its low viscosity and extensive applications in composites industries. The curing agent was HA-11 (polyamine). The ML-526 epoxy resin and polyamine hardener HA-11 were supplied by Mokarrar Engineering Materials Co., Iran. The E-glass fabric in form of CSM was supplied by Taishan Fiberglass Inc., China. The randomly distributed fibers have an average diameter of approximately 13 μm; around 5 cm lengths and a surface density of 450 g/m2. The CNF was supplied by Grupo Antolin SL, Spain. The CNF has an average diameter of approximately 20–80 nm, and the length is about 30 μm. Fig. 5.22 shows the scanning electron microscopy (SEM) and the transmission electron microscopy (TEM) images of the procured CNF. The specifications of CNF, E-glass CSM, and the resin are presented in Tables 5.9–5.11.

Fig. 5.22 (A) The scanning electron microscopy and (B) the transmission electron microscopy images of carbon nanofiber, prepared by Grupo Antolin SL, Spain [71]. Table 5.9 Specifications of carbon nanofiber [71] Parameter

Value

Fiber diameter (TEM) (nm) Fiber length (SEM) (μm) Tensile modulus (GPa) Aspect ratio

20–80 30 550 375

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

161

Table 5.10 Specifications of the E-glass CSM fiber [63] Parameter

Value

Fiber diameter (μm) Fiber length (mm) Tensile modulus (GPa) Aspect ratio

10–20 25–50 71 2500

Table 5.11 Properties of ML-526 epoxy resin [71] Physical properties

Mechanical properties

Viscosity at 25 °C (Centipoise)

Glass transition temperature (°C)

Tensile modulus (GPa)

Tensile strength (MPa)

1190

72

2.6

60

57

R76

R76

33

19

13

R76

3

R76

To fabricate CSM/epoxy composite specimens, the hardener was added to the epoxy resin at a ratio of 15:100 and stirred gently by using a mechanical stirrer (Heidolph RZR2102) for 5 min at 100 rpm. The stirring at low speed was very important to avoid any undesirable bubble formation. The CSM/epoxy composite specimens were manufactured using the hand layup process. Six layers of E-glass CSM were cut into a sheet of dimensions of 210 200 3 mm. Then, layers were stacked with ML-526 epoxy resin and impregnated at room temperature. A roller was used to release the trapped air and voids. Later, samples were kept under 12 kPa static pressure to get the trapped bubbles out. The fabricated sheet was also pre-cured under the static pressure for 48 h. For post-curing, the sheet was placed in an oven for 2 h at 80°C and further 1 h at 110°C. Finally, the test specimens were cut in accordance with type 1 in ISO 527-4 standard by the water jet cutting process. The drawing of the test specimen is shown in Fig. 5.23. In order to prepare composite specimens with CNF particles, all previous steps were kept as same as before, but the following processes were followed before adding the hardener. First, epoxy resin was mixed with 0.25 wt% of CNF and stirred for 10 min at 2000 rpm and then the mixture was sonicated via 14 mm diameter probe

165

Fig. 5.23 Drawing of the test specimen (dimensions in mm).

162

Fatigue Life Prediction of Composites and Composite Structures

160 140 Sonication time (min)

120 100 80 60 40 20 0 0.0

0.2

0.6 0.4 0.8 Filler Content (wt%)

1.0

1.2

Fig. 5.24 The sonication time vs filler content (wt%) [71].

sonicator (Hielscher UP400S) at an output power of 200 W and 12 kHz frequency. The approach was used to disperse the CNF in bisphenol A-based thermosetting epoxy resin. Time for sonication depends on the filler contents and has been defined on the basis of experiments until fillers remain intact. In Fig. 5.24, the suitable time for sonication vs the filler contents is reported. It is worth mentioning that during the sonication, the mixture container was kept both by the aid of an ice bath to prevent the overheating of the suspension. The universal testing machine, STM-150 made by Santam Co., Iran was utilized to perform the tensile tests in accordance with DIN EN ISO 527–4 standard. The crosshead speed for the tensile test was set at 2 mm/min. For fatigue loading, servo hydraulics Instron 8802 uniaxial fatigue testing machine was used. Furthermore, a series of tests under static loadings were carried out to determine the tensile properties of fabricated composites as isotropic fiber-reinforced composites. The stress-strain behavior of the CSM/epoxy composite specimen is presented in Fig. 5.25. In order to evaluate the fiber weight fraction, the burn-off test was performed to obtain the glass fiber content. In order to maintain the statistical reliability, four samples were tested in each step. The mean values of the tensile strength and Young’s modulus of CSM/epoxy composites and 0.25 wt% CNF/CSM/epoxy hybrid nanocomposites are demonstrated in Tables 5.12 and 5.13. The tension-tension fatigue tests were conducted at different stress levels. The applied maximum stresses were chosen as different percentages of the ultimate tensile strength of the specimen. The fatigue tests were carried out under the load-control condition at a frequency of 2 Hz. During all fatigue tests, the stress ratio (minimum applied stress/maximum applied stress) was set at 0.1 under room temperature condition. The applied maximum stress and the number of cycles to failure from experiments for CSM/epoxy composites with 0.25 wt% CNF/CSM/epoxy hybrid nanocomposites are demonstrated in Tables 5.14 and 5.15.

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

163

160 140

Stress (MPa)

120 100 80 60 40 20 0 0.00

0.01

0.02 Strain

0.03

0.04

Fig. 5.25 The stress-strain behavior of the CSM/epoxy composite specimen.

Table 5.12 Tensile strength and Young’s modulus of CSM/epoxy composites Mechanical properties Experimental Young’s modulus (GPa)

Model-estimated Young’s modulus (GPa)

Ultimate tensile strength (MPa)

E-glass CSM weight fraction (%)

8.9 0.2

8.82

1502.7

50.5

Table 5.13 Tensile strength and Young’s modulus of 0.25 wt% CNF/CSM/epoxy hybrid nanocomposites Mechanical properties Experimental Young’s modulus (GPa)

Model-estimated Young’s modulus (GPa)

Ultimate tensile strength (MPa)

E-glass CSM weight fraction (%)

11.8  0.2

11.91

183.5  2.7

50

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Fatigue Life Prediction of Composites and Composite Structures

Table 5.14 Number of cycles to failure for CSM/epoxy composites at R ¼ 0.1 Applied stress (MPa)

R0 (%) (Applied stress/UTS)×100

Mean number of cycles to failure (cycles)

150 105 94 90 75

100 70 63 60 50

1 1274 3577 25034 148467

Table 5.15 Number of cycles to failure for 0.25 wt% CNF/CSM/epoxy hybrid nanocomposites at R ¼ 0.1 Applied stress σ a (MPa)

R0 (%) (σ a/UTS)×100

Mean number of cycles to failure (cycles)

183.50 128.45 120.00 110.10 91.75

100 70 65 60 50

1 332 431 8270 47366

Moreover, the trends of normalized modulus degradation (dynamic modulus divided by static Young’s modulus) of CSM/epoxy composites during fatigue loading condition were monitored under R0 ¼ 50 % , 60 % , and 70% and shown in Figs. 5.26–5.28. By means of the normalization technique and obtained parameters as discussed in the previous sections, all different curves for different states of stress (R0 ¼ 50 % , 60 % , and 70%) collapse to a single curve as shown in Fig. 5.29. The obtained values of λ, γ are 2.473 and 9.07, respectively. For evaluating of the accuracy of derived equations for CSM/epoxy composites, according to Fig. 5.30, the trend of the stiffness reduction for CSM/epoxy composites vs the number of cycles was depicted and a good agreement with experimental data was obtained. This compatibility shows that obtained curve-fitting parameters are suitable for this composite. As similar to the previous steps, all experiments were followed again for 0.25 wt% CNF/CSM/epoxy composite under R0 ¼ 50% state of stress and the trend of the normalized modulus degradation (dynamic modulus divided by static Young’s modulus) of 0.25 wt% CNF/CSM/epoxy composites during fatigue loading condition was monitored (Fig. 5.31). By means of the obtained parameters value of λ, γare 2.473 and 9.07, the stiffness vs the number of cycles for 0.25 wt% CNF/CSM/epoxy composite are found as shown in Fig. 5.32. It is observed that a vital agreement with the experimental and predicted results by Nano-NSDM exists. The observed error (%) is represented in Table 5.16.

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

165

1.02

Normalized modulus (E/Es)

1 0.98 0.96 0.94 0.92 0.9 0.88 R' = 50%

0.86 0.84 0

20,000

40,000

60,000 n (cycles)

80,000

100,000

120,000

Fig. 5.26 The normalized modulus (E/Es) vs number of cycles of CSM/epoxy composites, R0 ¼ 50, σ a ¼ 75 MPa, and Fr ¼ 2 Hz. 1.06

Normalized modulus (E/Es)

1.04 1.02 1 0.98 0.96 0.94 0.92 R' = 60%

0.9 0.88 0.86 1

10

100 n (cycles)

1000

10,000

Fig. 5.27 The normalized modulus (E/Es) vs the number of cycles of CSM/epoxy composites, R0 ¼ 60, σ a ¼ 90 MPa, and Fr ¼ 2 Hz.

The bottleneck of Nano-NSDM is that in each state of stress, at least one experiment is needed. In order to solve this restriction, by choosing another stress state such as R0 ¼ 70, the S-N curve can be experimentally obtained. Then, without performing new tests, the model is able to predict the number of cycle to failure in each stress state and the model can be applied without any limitation (see Fig. 5.33). As

166

Fatigue Life Prediction of Composites and Composite Structures

1.02

Normalized modulus (E/Es)

1.01 1 0.99 0.98 0.97 R' = 70%

0.96 0.95 1

10

100

1000

n (cycles)

Fig. 5.28 The normalized modulus (E/Es) vs the number of cycles of CSM/epoxy composites, R0 ¼ 70, σ a ¼ 105 MPa, and Fr ¼ 2 Hz.

1 0.9

Normalized stiffness

0.8 0.7 0.6 0.5 0.4 0.3 0.2 R' = 50%, 60%, 70%

0.1 0 0

0.1

0.2

0.3 0.6 0.4 0.7 0.5 Normalized number of cycles

0.8

0.9

1

Fig. 5.29 The normalized stiffness degradation curve CSM/epoxy composites, R0 ¼ 50 % , 60 % , and 70%, Fr ¼ 2 Hz, λ ¼ 2.473 , γ ¼ 9.07, and εf ¼ 0.017.

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

167

Fig. 5.30 The verification of the stiffness reduction for CSM/epoxy composite, R0 ¼ 50, σ a ¼ 75 MPa, and Fr ¼ 2 Hz.

Normalized modulus (E/Es)

1.2

1

0.8

0.6

0.4 R' = 50% 0.2

0.25 wt% CNF/CSM/Epoxy composites

0 1

10

100

1000

10,000

100,000

n (cycles)

Fig. 5.31 The normalized modulus (E/Es) vs number of cycles of 0.25 wt% CNF/CSM/epoxy composite, R0 ¼ 50, σ a ¼ 92 MPa, and Fr ¼ 2 Hz.

previously mentioned, based on the experimental observations, it is necessary to state that the average strain to failure (εf) can be considered to be a constant and independent on the state of stress and number of cycles. For instance, as depicted in Fig. 5.33, the S-N curve for CSM/epoxy composite and 0.25 wt% CNF/CSM/epoxy composites are obtained and the number of cycles to failure can be anticipated in each applies stress, generally. The material constants, A and B are as shown in Table 5.17.

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Fatigue Life Prediction of Composites and Composite Structures

11 R' = 50%

10.5

Effib, nc (GPa)

10 9.5 9 8.5 8

Experimental results, 92 MPa The Nano-NSDM based on the Halpin-Tsai model, 92 MPa

7.5 7

10,000

0

20,000

30,000

40,000

50,000

n (cycles)

Fig. 5.32 The verification of stiffness reduction for 0.25 wt% CSM/epoxy composite, R0 ¼ 50, σ a ¼ 92 MPa, and Fr ¼ 2 Hz.

Table 5.16 Results and value of error for Nano-NSDM for 0.25 wt% CSM/epoxy composite, R0 ¼ 50, σ a ¼ 92 MPa, Fr ¼ 2 Hz

n (cycles)

Ec(n): Experimental results Effib, c (GPa)

Nano-NSDM based on The Halpin-Tsai model Effib, c (GPa)

Error (%)

1000 2500 5000 7500 10000 20000

10.46 10.21 10.01 9.87 9.83 9.48

10.23 10.09 9.95 9.84 9.76 9.45

2.25 1.14 0.62 0.32 0.69 0.34

5.3

Fatigue life prediction based on the micromechanicalenergy method

In this section, a novel method is developed in order to predict the fatigue life of nanoparticle/CSM/polymer hybrid nanocomposites. The established model will be a combination of the micromechanics and the energy method. The special feature of the present model is the capability of predicting the fatigue life of hybrid nanocomposites by means of the experimental fatigue data of the same composites without adding any nanoparticles. A survey of the literature shows the energy method has not been fully developed for CSM composites. Thus, in this section, a novel model based on the

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

169

Applied stress (MPa)

200 180

0.25 wt% CNF/CSM/Epoxy nanocomposites

160

CSM/Epoxy nanocomposites

140 120 100 80 60 40 20 0 1

10

100

1000

10,000

100,000

1,000,000

Number of cycles to failure, Nf

Fig. 5.33 The S-N curve for CSM/epoxy composite and 0.25 wt% CNF/CSM/epoxy composites R0 ¼ 50 % , 60 % , and 70%, Fr ¼ 2 Hz, and εf ¼ 0.017 Table 5.17 A and B material constants for Neat CSM/epoxy composite and 0.25 wt% CNF/CSM/epoxy composites σ Applied 5A ln(Nf) +B

A

B

Neat CSM/epoxy composites 0.25-wt%-CNF/CSM/epoxy composites

148.25 185.06

6.187 8.147

micromechanics and the energy method is developed in order to predict the fatigue life of CSM polymeric composites. The fatigue life of nanoparticle/CSM/polymer hybrid nanocomposites can also be predicted by the present model. Later, a series of tests in tension-tension fatigue conditions at room temperature for CSM/epoxy composites and for 0.1 wt%, and 0.25 wt% CNF/CSM/epoxy hybrid nanocomposites are carried out at different load levels to evaluate the capabilities of the present model [72].

5.3.1 The energy method The energy method is a simple approach and can be used for laminated composites with different fiber orientations and loading conditions. Kachanov, Lemaitre, and Ladeveze [73–75] presented the relationship between the strain energy density and the damage in composites. Ellyin and El-Kadi [76, 77] used the strain energy density as a damage function for composite materials. A major portion of the useful life of a composite structure component involves subcritical damage accumulation, which was

170

Fatigue Life Prediction of Composites and Composite Structures

finally manifested in various combinations of the matrix cracking, fiber-matrix debonding, delamination, and fiber breakage failure modes. A precise characterization of a composite material would require knowledge of the way the energy dissipates throughout the inhomogeneous structure as damage is being accumulated [76]. The strain energy density is a parameter which can be related to this damage process [77]. Shokrieh and Taheri [78] developed a unified fatigue life model based on the energy method for unidirectional polymer composite laminates. Their proposed model is capable of predicting the fatigue life of unidirectional composite laminates over a range of positive stress ratios in various fiber orientation angles. It was shown that the total input energy was directly related to fatigue life and can be expressed using a power law relation as follows:
 ΔW ¼ g Nf ! ΔW ¼ kN αf

(5.23)

where k and α are materials constants and ΔW is the total input energy and Nf is the fatigue life (the number of cycles to failure). For the elastic plane stress condition, the strain energy density can be expressed in terms of stresses and strains as follows: W¼

 1
σ x εx + σ y εy + τxy γ xy 2

(5.24)

For the uniaxial loading condition: h i ΔW ¼ Sxx Δσ 2x =2ð1  Rx Þ2

(5.25)

where Δσ indicates the stresses range: Δσ ¼ σ max  σ min

(5.26)

Rx (the stress ratio) and Sxx (the compliance component) are defined as below: max Rx ¼ σ min , Sxx ¼ x =σ x

1 Ex

(5.27)

5.3.2 Modeling strategy (Nano-EFAT model) A schematic framework of the modeling strategy is shown in Fig. 5.34. The model is an integration of two major components: the micromechanical (such as Halpin-Tsai model) and the energy method and called Nano-EFAT model. The novel model is able to predict the fatigue life of nanoparticle/CSM/polymer hybrid nanocomposites. By coupling of the energy method for composite specimens without nanoparticles and the micromechanical Halpin-Tsai approach, a comprehensive model for nanoparticle/CSM/polymer hybrid nanocomposites under fatigue loading was developed. As shown in Fig. 5.34, in the first step, according to the micromechanical model (Eq. 5.11), the stiffness of the nanocomposites (EsCSM, nc) is obtained by using the

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

Stiffness of pure epoxy resin

Stiffness of nanoparticles

Stiffness of CSM

171

Fig. 5.34 The schematic flowchart of the Nano-EFAT model [72].

Micromechanical Models

Equivalent stiffness of nanoparticle/CSM/polymer hybrid nanocomposites

Energy model for composites under fatigue loading condition without nanoparticles

Fatigue life of nanoparticle/CSM/polymer hybrid nanocomposites

moduli of the pure matrix (Esm), nanoparticles (Esp), and CSM (EsCSM) measured under static loading conditions. Later, the material constants (i.e., α and k) as experimental curve-fitting parameters of composite specimens without nanoparticles are needed under tension-tension fatigue loading condition in order to find the fatigue life of nanoparticle/CSM/polymer hybrid nanocomposites. According to the inherent property of CSM composites like an isotropic material, stiffness and ΔW can be simplified and able to estimate the fatigue life of nanoparticle/ CSM/polymer hybrid nanocomposites by having the applied stress Δσ and the stress ratio R [72]. ΔW ¼

Δσ 2 2  ð1  RÞ2  EsCSM,nc

¼ kN f α

(5.28)

5.3.3 Tests results A series of tests under static loadings are carried out to determine the tensile properties of fabricated composites as isotropic reinforced composites. In order to maintain the statistical reliability, four samples were tested in each step. The mean values of the tensile strength and Young’s modulus of CSM/epoxy composites and 0.1 wt%

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Fatigue Life Prediction of Composites and Composite Structures

Table 5.18 The tensile strength and Young’s modulus of 0.1 wt% CNF/CSM/epoxy hybrid nanocomposites [72] Mechanical properties Experimental Young’s modulus (GPa)

Model-estimated Young’s modulus(GPa)

Ultimate tensile strength (MPa)

E-glass CSM weight fraction (%)

10.8 0.2

10.6

160.5  2

50

CNF/CSM/epoxy hybrid nanocomposites are demonstrated in Tables 5.12, 5.13, and 5.18 [72]. The tension-tension fatigue tests were conducted at different stress levels. Applied maximum load levels were chosen to develop maximum stresses at different percentages of the ultimate tensile stress of the specimen. The fatigue tests were carried out under the load-control condition at a frequency of 2 Hz. During all fatigue tests, the stress ratio (minimum applied stress divided by maximum applied stress) was set at 0.1 under room temperature condition. The applied maximum stress and the number of cycles to failure from experiments for neat CSM/epoxy composites and reinforced with 0.25 wt% and 0.1 wt% CNF particles are demonstrated in Tables 5.14, 5.15, and 5.19, respectively. By comparing Tables 5.14 and 5.15, it can be found about 300% increase in fatigue life of 0.25 wt% CNF/CSM/epoxy hybrid in some cases by adding 0.25 wt% CNF to CSM/epoxy composites. Also, by comparing Tables 5.14 and 5.19, it can be found about 150% increase in fatigue life of 0.1 wt% CNF/CSM/epoxy hybrid in some cases by adding 0.1 wt% CNF to CSM/epoxy composites.

5.3.4 Evaluation of the Nano-EFAT model In this section, the capability of the present model has been evaluated by experimental results. In the first step, the present model was evaluated by the experimental data of the CSM/epoxy composites. In the next step, the model was evaluated by the experimental data of 0.1 wt% and 0.25 wt% CNF/CSM/epoxy hybrid nanocomposites. Table 5.19 Number of cycles to failure for 0.1 wt% CNF/CSM/epoxy hybrid nanocomposites at R ¼ 0.1 [72] Applied stress (MPa)

Mean number of cycles to failure (cycles)

160.50 120.40 100.20 89.70

1 224 4804 31182

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

173

In order to use the model, material constants α and k are needed to be calculated. By using the test data of the CSM/epoxy composite specimen without adding any nanoparticle (Table 5.14), applying them to Eq. (5.28) and by using a simple curve fitting (Fig. 5.35), α and k are obtained (Table 5.20). The modulus of nanocomposites (EsCSM, nc) was calculated using the Halpin-Tsai model equal to 10.6 GPa for 0.1 wt% and 11.91 GPa for 0.25 wt% CNF/CSM/epoxy hybrid nanocomposites. Then, material constants α, k (shown in Table 5.20) and s ECSM, nc were used in Eq. (5.28) and the results were plotted in Fig. 5.35. This figure presents a comparison of the results obtained by the present model with experimental results (Tables 5.15 and 5.19) for 0.1 wt% and 0.25 wt% CNF/CSM/epoxy hybrid nanocomposites. The capability of the present model in the simulation of the fatigue life of the 0.1 wt% and 0.25wt% CNF/CSM/epoxy composites is clearly shown in Fig. 5.35.

5.4

Displacement-controlled flexural fatigue behavior of composites with nanoparticles

The flexural fatigue behavior of composites and nanocomposites has been carried out by many researchers [79–82]. For composites under the displacement-controlled

Fig. 5.35 Obtaining α and k using a curve-fitting method for CSM/epoxy composites and evaluation of the present model with experimental data for 0.1 wt% and 0.25 wt% CNF/CSM/ epoxy hybrid nanocomposites [72]. Table 5.20 Material constants α and k for CSM/epoxy composites Parameter

Value

α k

0.1135 1.2980  106

174

Fatigue Life Prediction of Composites and Composite Structures

fatigue loading, Paepegem and Degrieck [79] developed an experimental setup for bending fatigue test. They adopted a residual stiffness model which describes the fatigue damage behavior of the composite material [80]. Also, Paepegem et al. [81] used a finite element approach for composites fatigue life prediction. El Mahi et al. [82] studied the flexural fatigue behavior of the sandwich composite materials using three-point bend test and the derived approach permitted them to predict the fatigue life of the sandwich composite materials while avoiding a large number of experiments, normally required in fatigue testing. A survey in the available literature reveals that the addition of nanoparticles can improve the fatigue behavior of composites under displacement control loading and has been carried out by many researchers [83–86]. Ramkumar and Gnanamoorthy [83] studied the stiffness and flexural fatigue life improvements of polymer-matrix reinforced nanocomposites with nanoclay. They described the effect of adding nanoclay fillers on the flexural fatigue response of PA6. Rajeesh et al. [84] considered the influence of humidity on the flexural fatigue behavior of commercial grade PA6 granules and hectorite clay nanocomposites. Timmaraju et al. [85] considered the influence of the environment on the flexural fatigue behavior of polyamide 66/hectorite nanocomposites. They also found the effect of initial absorbed moisture content on the flexural fatigue behavior of polyamide 66/hectorite nanocomposites conducted under deflection control method using a custom-built, table-top flexural fatigue test rig at a laboratory condition [86]. A survey in the literature also reveals that the presence of multi-nanoparticles in composites improves the properties of nanocomposites. Some researchers used hybrid fillers in order to have a perfect potential of both fillers. For instance, as a first group, a combination of microrubber and NS has been used to improve the fracture toughness and fatigue behavior of [87–91]. Liang and Pearson [87] used two different sizes of NS particles, 20 and 80 nm in diameter, and carboxyl-terminated butadiene acrylonitrile (CTBN) which was blended into a lightly cross-linked, DGEBA/piperidine epoxy system in order to investigate the toughening mechanisms. It was shown that the addition of a small amount of NS particles into CTBN caused an increase in the fracture toughness. Manjunatha et al. [19, 26, 88–91] investigated the fatigue behavior of reinforced composites by adding a combination of micro rubber and NS particles into the epoxy matrix in several states. For instance, they [19] studied the tensile fatigue behavior of modified micron-rubber and NS particle epoxy polymers. They [26] also addressed the tensile fatigue behavior of a glass-fiber-reinforced plastic (GFRP) with the participation of rubber microparticles and silica nanoparticles. They [88] also observed the enhanced capability to withstand longer crack lengths, due to the improved toughness together with the retarded crack growth rate, to enhance the total fatigue life of the hybridmodified epoxy polymer. Also, Manjunatha et al. [89] enhanced the fatigue behavior of fiber-reinforced plastic composites by means of 9 wt% of rubber microparticles and 10 wt% of silica nanoparticles and showed the fatigue life under WISPERX load sequence was about 4–5 times higher than that of the neat composites. Manjunatha et al. [90] also used another hybridization of carboxyl-terminated butadieneacrylonitrile rubber microparticles and silica nanoparticles to increase the tensile fatigue behavior of GFRP composites at a stress ratio equal to 0.1. Manjunatha et al. [91] conducted the fatigue crack growth test on a thermosetting epoxy polymer

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

175

which was hybrid modified by incorporating 9 wt% of CTBN rubber microparticles and 10 wt% of silica nanoparticles. The fatigue crack growth rate of the hybrid epoxy polymer was observed to be significantly lower than that of the unmodified epoxy polymer. In the next category, applying CNTs with different nanoparticles as hybrid fillers were taken into account in the literature [23, 92–94] to improve the fatigue behavior, mechanical and electrical properties of reinforced composites. Boeger et al. [23] used silica and MWCNT hybrid nanoparticles to increase the high-cycle fatigue life of epoxy laminates and finally reported that the life was increased by several orders of magnitude in a number of load cycles. Fritzsche et al. [92] investigated the CNT-based elastomer-hybrid-nanocomposites prepared by melt mixing and showed promising results in electrical, mechanical, and fracture-mechanical properties. Witt et al. [93] improved mechanical properties such as tensile strength and strain to failure of a conductive silicone rubber composite using both CNTs and carbon black (CB). Al-Saleh and Walaa Saadeh [94] fabricated nanostructured hybrid polymeric materials based on CNTs, CB, and CNFs and investigated electrical properties and electromagnetic interference shielding effectiveness in the X-band frequency range. The other various hybrid nanoparticles were discussed in the literature are considered here as the last category [95, 96]. Jen et al. [95] applied hybrid magnesium/carbon fiber to increase the fatigue life of nanocomposite laminates. On the other hand, applying CNT and graphite nanoplatelets (GNPs) to epoxy nanocomposites was conducted by Jing Li et al. [96]. It was represented that the flexural mechanical and the electrical properties of the NR were marginally changed by the hybridization. The present survey reveals that the effect of hybrid particles is mostly positive and can improve the static and dynamic properties of composites. However, it is figured out that in case of displacement control fatigue loading condition, there is a lack of research on the hybrid nanofillers/epoxy nanocomposites. Therefore, in the chapter, the flexural fatigue behavior of graphene/carbon-nanofiber/epoxy hybrid nanocomposites under displacement control flexural loading is investigated and compared with those of the pure epoxy resin [97].

5.4.1 Materials specification In this section, ML-526 epoxy resin as matrix and CNF as reinforcement nanoparticles were selected. Moreover, the graphene nanoplatelets (GPL) were synthesized by a stirring grinding driven by changing the magnetic field as shown in Fig. 5.36 [97]. Physical properties of synthesized graphene powders are shown in Table 5.21. The TEM image of the synthesized GPL powder is shown in Fig. 5.37. The D, G, and 2D bands of Raman spectra of the synthesized GPLs powder are demonstrated in Fig. 5.38.

5.4.2 Specimen preparation The polymer reinforced with 0.5 wt% of hybrid graphene/carbon-nanofiber was prepared as described below. First, epoxy resin was mixed with 0.25 wt% CNF and stirred for 10 min at 2000 rpm and then the mixture was sonicated via 14 mm diameter probe

176

Fatigue Life Prediction of Composites and Composite Structures

Fig. 5.36 GPL synthesis method. (A, B) Still condition and (C) moving condition [97].

Table 5.21 GPL nanoparticles specifications Nanoparticle

Diameter (nm)

Thickness (nm)

Specific surface area (m2/g)

GPL

40–120

3–5

500

Fig. 5.37 The transmission electron microscopy (TEM) of the synthesized graphene nanoplatelets [97].

sonicator (Hielscher UP400S) at an output power of 200 W and 12 kHz frequency. The mixture was sonicated for 60 min. It is worth mentioning that during the sonication, the mixture container was kept with the aid of ice bath to prevent the overheating of the suspension to keep the temperature around 40°C. Second, the suspension was mixed with 0.25 wt% GPL under the same condition within 30 min by the sonication. After sonication, the hardener at a ratio of 15:100 was added to the mixture and stirred gently for 5 min. Then, it was vacuumed at 1 mbar for 10 min to remove any trapped air. Six samples were prepared and cured at room temperature for 48 h and followed by 2 h at 80°C and 1 h at 110°C for post-curing. The approach was used to disperse GPL/CNF hybrid nanoparticles into epoxy resin, is adapted from a combination of supplementary research [98]. Time for the sonication depends on the filler contents

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

177

350

300

1339.4 cm–1

1580.7 cm–1

Intensity (a.u.)

250 2677.0 cm–1

200

150

100

50

0

1200

1600

2000

2400

2800

3200

–1

Wave number (cm )

Fig. 5.38 Raman spectra of synthesized graphene nanoplatelets, D, G, and 2D bands [97].

and has been defined based on the experiments until fillers remain intact. For CNF fillers, Shokrieh et al. [98] investigated the suitable time for sonication vs contents of the filler and pointed out for 0.25 wt% CNF materials, the optimum value of sonication with regard to Fig. 5.39 was found around 90 min with the same compartment and conditions. Also, the optimum sonication time for 0.25 wt% GPL was equal to 30 min. In addition, to inspect the dispersion state of nanofillers, a new technique based on SEM, which utilizes the burn-off test, was introduced to visualize the dispersion state of nanofillers [99].

5.4.3 Calculation of the bending stress In this section, high-cycle fatigue properties of nanocomposites are measured by a modified cantilever beam bending test. A typical fatigue life test specimen for the cantilever beam bending test is shown in Fig. 5.40. The specimen was designed based on ASTM: B593-96 standard and the method presented by Ramkumar and Gnanamoorthy [83]. The wide end of the specimen was clamped to a bed plate, while the narrow end is cyclically deflected (see Fig. 5.40A). To catch reliable results of the flexural fatigue strength, the gage area of the specimen is designed based on the stress concentration concept (Fig. 5.40B). The stress concentration of the critical location of the specimen has the maximum magnitude; therefore, the failure will start in this area. For the wedge-shaped beam as

178

Fatigue Life Prediction of Composites and Composite Structures

Fig. 5.39 The viscosity (mPa.s) vs sonication time (min) of 0.25 wt% CNF/epoxy nanocomposites [98].

an applied specimen, the cross section is not uniform and defined by means of a parameter called “local B” according to Eq. (5.29) (Fig. 5.41): BðxÞ ¼

B0 ðL0  xÞ L0

(5.29)

where L0 is the length of the specimen and B0 is the width at the base of the wedgeshaped beam. Therefore, the magnitude of the second moment of area of the cross section depends on the position along the x-axis as Eq. (5.30): I ðxÞ ¼

B0 ðL0  xÞH3 12L0

(5.30)

where H is the thickness of the beam. Finally, the maximum tension or compression stress at a given cross section for small displacements within elastic deformation behavior is calculated according to the following equation [100]: σ max ¼ 

z0  E  H L0 2

(5.31)

where σ max is the maximum stress, H is the thickness of the beam, z0 is the displacement at point x¼ L0, and E is Young’s modulus. The relation between the displacement z0 at the tip and the maximum stress σ max for a small deformation is linear.

Upper clamp

Bolt

Specimen

Lower clamp

Cyclic displacement

(A) 41

44.1

Span=30

9.44

10.4

(B)

23.9

Fig. 5.40 (A) A schematic of specimen clamping procedure. (B) A schematic picture of the bending fatigue specimen [97].

B0

Fig. 5.41 A schematic view of a beam, with coordinates [97].

F H

L0

M+

x z

180

Fatigue Life Prediction of Composites and Composite Structures

5.4.4 Test equipment 5.4.4.1 Static testing instruments The Santam universal testing machine STM-150 was utilized to perform bending tests in accordance with the ASTM D790 standard. The cross-head speed for bending tests was 16 mm/min. To analyze hybrid nanoparticles, gold sputtered samples were used. The field-emission scanning electron microscopy (FESEM) photographs were taken by using Zeiss-Germany Sigma microscope.

5.4.4.2 Experimental setup for flexural bending fatigue The pure epoxy and reinforced polymer specimens are mounted into a fixed cantilever, constant deflection type fatigue testing machine. The machine called BFM-110 was designed and manufactured based on a developed version of a testing machine designed by Paepegem and Degrieck [79] and shown in Fig. 5.42. The specimen was held at one end, acting as a cantilever beam and cycled until a complete failure was achieved. The number of cycles to failure was recorded as a measure of the fatigue life during the test. Generally, the shaft of the motor has a rotational speed of 0–1450 rpm. The power is transmitted via a V-belt to the second shaft, provides a fatigue testing frequency between 2 and 20 Hz and gives the possibility to investigate the influence of the frequency in this range of values. The power transmission through a V-belt ensures the motor and the measuring system are electrically isolated. The second shaft bears a crank-linkage mechanism, as shown in Fig. 5.42. Hence, the sample is loaded as a cantilever beam. The amplitude of the imposed displacement is a controllable parameter and the adjustable crank allows choosing between single-sided and fully reversed bending, that is, the deflection can vary from zero to a maximum deflection in one direction, or in two opposite directions, respectively. The maximum deflection was measured by a displacement dial gauge at the back of the lower clamp. The number of cycles to failure should be counted directly for each test specimen. A counting signal was generated once per cycle by a PES-R18PO3MD reflector speed sensor which was supplied by IBEST Electric, LTD., China. The counting signal was transferred to the counter fabricated by RASAM Madar electronic Co., Iran. In this setup, there are two parallel stands with counting system implemented separately. To stop the counter of speed sensors, at the bottom of each specimen a thin wire as an electrical contact was used and after failure, the damaged specimen drops down and disconnects the wire and stops the counting system. Therefore, after the failure of both specimens, control system acts and turns off the main current of the machine completely.

5.4.5 Results and discussion 5.4.5.1 Static bending strength The calculation of the maximum bending stress was performed using Eq. (5.31). This expression was valid when the specimen is subjected to a small and linear deformation. The static bending strength of GPL/epoxy nanocomposites for 0.25 wt% of GPL content was found 118 MPa and it was 121 MPa for 0.25 wt% CNF/epoxy

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

181

Main frame

V-belt

Counter Linkage

Speed sensor

Frequency inverter

Dial gauge Nanocomposites specimen

Strain gauge

Connection wire

Fig. 5.42 The experimental setup for the displacement controlled flexural bending fatigue loading [97].

nanocomposites [98]. Also, the static flexural modulus of 0.25 wt% graphene/epoxy nanocomposites was demonstrated at 3.4 GPa and for 0.25 wt% of CNF content was 3.18 GPa [98]. While, the static bending strength and modulus of the neat epoxy resin were 110 MPa and 3 GPa, respectively. For 0.25 wt% of GPL plus 0.25 wt% of CNF (i.e., 0.5 wt% of GPL/CNF) hybrid nanoparticles/epoxy nanocomposites based on the ASTM D790 standard, static tests to measure the flexural strength and stiffness have been conducted and eventually, 123 MPa for the strength and 3.43 GPa for the stiffness were found. The flexural strength and stiffness were presented in Figs. 5.43 and 5.44.

182

Fatigue Life Prediction of Composites and Composite Structures 130 123 121

Flexural strength (MPa)

120

110

118

110

100

90

80 Pure epoxy resin

0.25 wt.% CNF

0.25 wt.% GPL 0.5 wt.% Hybrid

Fig. 5.43 The flexural strength (MPa) for pure epoxy resin, 0.25 wt% GPL, 0.25 wt% CNF, and 0.25 wt% of GPL plus 0.25 wt% of CNF hybrid nanoparticles epoxy nanocomposites [97].

3.6 3.40

Flexural stiffness (GPa)

3.4 3.18

3.2

3.0

3.43

3.00

2.8

2.6

2.4

2.2

2.0 Pure epoxy resin

0.25 wt.% CNF

0.25 wt.% GPL 0.5 wt.% Hybrid

Fig. 5.44 The flexural stiffness (GPa) for pure epoxy resin, 0.25 wt% GPL, 0.25 wt% CNF and 0.25 wt% of GPL plus 0.25 wt% of CNF hybrid nanoparticles epoxy nanocomposites [97].

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

183

5.4.5.2 Cyclic flexural bending fatigue life There is not a special standard test method for epoxy matrix and epoxy-based nanocomposites under flexural bending stress in fatigue. The ASTM: B593-96 standard and a publication of Ramkumar and Gnanamoorthy [83] are used for copper alloy spring material, filled thermoplastic nanocomposites, respectively. In the experiments presented in this chapter, the loading frequency was 5 Hz. The effective length of the specimen subjected to the bending is 32.84 mm. The drawing and picture of the specimen used in the current research are shown in Fig. 5.45. Although the BFM-110 testing machine is capable of applying the reversal bending fatigue loading, however, in the present study, the specimens were subjected to zero-bending fatigue loading conditions. The flexural bending stress vs the number of cycles for the neat epoxy resin, 0.25 wt% GPL nanoparticles, 0.25 wt% CNF nanoparticles, and 0.5 wt% of GPL/CNF hybrid nanoparticles epoxy nanocomposites, at a frequency equal to 5 Hz is illustrated in Fig. 5.46. The strength ratios (the bending stress normalized by the bending strength) vs the number of cycles to failure is presented in Fig. 5.47. For instance, the experimental observations show that at the strength ratio equal to 43% by using 0.5 wt% of hybrid nanoparticles; 37.3-fold improvement in flexural bending fatigue life of the neat epoxy was observed. While, enhancement of adding only graphene or CNF was 27.4-and 24-folds, respectively. The enhancement of the fatigue life for composites in the presence of nanofillers has been stated in the literature. For instance, Ramkumar and Gnanamoorthy [83] expressed that the nanoclay addition can be attributed to enhanced modulus coupled with reduced dissipation factor and improved surface hardness. The fibrillated 50.8

R2

10.4

R8 .2

2.84

23.9

0 R1

.85

17

9.44

50°

Fig. 5.45 Drawing of the specimen (dimensions in mm) [97].

30

81.8

41.4

t = 3.5

184

Fatigue Life Prediction of Composites and Composite Structures

60.0 Neat epoxy resin

58.0

0.25 %wt GPL / Epoxy nanocomposites 0.25 %wt CNF / Epoxy nanocomposites

Flexural stress (MPa)

56.0

0.25 wt% GPL + 0.25 wt% CNF / Epoxy hybrid nanocomposites

54.0 52.0 50.0 48.0 46.0 44.0 42.0 1000

10,000

100,000

1,00,0000

Number of cycles to failure

Fig. 5.46 Bending stress vs the number of cycles to failure for neat epoxy resin, 0.25 wt% GPL, 0.25 wt% CNF, and 0.25 wt% of GPL plus 0.25 wt% of CNF hybrid nanoparticles epoxy nanocomposites, at a frequency equal to 5 Hz [97].

appearance of the filled nanocomposite fracture surface suggests that the addition of the nanofiller promotes the toughening and influences the crack propagation characteristics of the pure polymer. Ramanathan et al. [101] argued that the micrometer-size dimensions, high aspect ratio and 2D sheet geometry of graphene make them effective in deflecting cracks in bending. In addition, hydrogen-bonding interaction or an enhanced nanofiller-polymer mechanical interlocking due to the wrinkled morphology of graphene is additional factors that can contribute to composite reinforcement. Whilst, Rafiee et al. [102] pointed out that this enhancement may be related to their high specific surface area, enhanced nanofiller-matrix adhesion/interlocking arising from their wrinkled (rough) surface.

5.4.5.3 Dispersion and morphology analysis The observation of the fracture surfaces of the damaged specimens can explain the improvement of the fatigue life of the hybrid nanocomposites. The fracture surfaces of specimens 0.25 wt% GPL/epoxy, 0.25 wt% CNF/epoxy, and 0.5 wt% of GPL/CNF hybrid nanoparticles epoxy nanocomposites are presented in Fig. 5.48. As depicted in Fig. 5.48A, dispersion of GPL was observed and shown that the dispersion was not

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

185

50 Neat epoxy resin 0.25 %wt GPL / Epoxy nanocomposites

48

0.25 %wt CNF / Epoxy nanocomposites

Flexural strength ratio (%)

0.25 wt% GPL + 0.25 wt% CNF / Epoxy hybrid nanocomposites

46

44

42

40

38 1000

10,000

100,000

1,000,000

Number of cycles to failure

Fig. 5.47 The flexural stress ratio (%) vs the number of cycles to failure for neat epoxy resin, 0.25 wt% GPL, 0.25 wt% CNF, and 0.25 wt% of GPL plus 0.25 wt% of CNF hybrid nanoparticles epoxy nanocomposites, at a frequency equal to 5 Hz [97].

sufficient and the stiffness of reinforced composites with GPL improved and the strength was not influenced like the stiffness. Also, as shown in Fig. 5.48B, the fracture surface of 0.25 wt% CNF/epoxy nanocomposites was monitored and found that the dispersion of CNF into epoxy resin was appropriate as observed and was efficient for improving mechanical properties. Fig. 5.48C and D shows that a combination of both nanofillers in the fractured surface and dominant failure mechanism is pullout which leads to a higher strength for nanocomposites. The GPL increased the stiffness of the nanocomposites and the pullout of the CNT increases the strength. Therefore, hybridization of these nanoparticles promotes the toughening and influences the crack propagation characteristics of the pure polymer, which in turn causes a significant improvement in fatigue life of the nanocomposites. In concluding this section, the effect of adding hybrid nanoparticles into epoxy resin was investigated and it was found that hybrid particles can improve the static and dynamic properties of composites. For 0.25 wt% of GPL plus 0.25 wt% of CNF (i.e., 0.5 wt% of GPL/CNF) hybrid nanoparticles/epoxy nanocomposites was achieved 123 MPa. While the static bending strength of GPL/epoxy nanocomposites for 0.25 wt% of GPL content was found 118 and 121 MPa for 0.25 wt% CNF/epoxy nanocomposites. The flexural fatigue behavior of graphene/carbon-nanofiber hybrid nanocomposites under displacement control flexural loading was investigated and

186

Fatigue Life Prediction of Composites and Composite Structures

Fig. 5.48 FESEM of the fractured surface, (A) 0.25 wt% GPL/epoxy nanocomposites, (B) 0.25 wt% CNF/epoxy nanocomposites, and (C) and (D) 0.5 wt% of GPL/CNF hybrid nanoparticles epoxy nanocomposites [97].

results were compared with pure epoxy resin, pure epoxy resin with the presence of GPL or CNF nanofillers. Due to the addition of hybrid nanoparticles, a remarkable improvement in fatigue life of epoxy resin was observed in comparison with results obtained by adding 0.25 wt% graphene or 0.25 wt% CNF into the resin. Also, the strength ratio (the bending stress normalized by the bending strength) vs the number of cycles to failure for the neat epoxy resin, 0.25 wt% GPL nanoparticles, 0.25 wt% CNF nanoparticles, and 0.5 wt% of GPL/CNF hybrid nanoparticles epoxy nanocomposites, have been investigated. The experimental observations show that at the strength ratio equal to 43% by using 0.5 wt% of hybrid nanoparticles; 37.3-fold improvement in flexural bending fatigue life of the neat epoxy was observed. While, enhancement of adding only graphene or CNF was 27.4- and 24-folds, respectively. The improvement of the fatigue life of hybrid nanocomposites can be explained by a closed look at the fracture surface. The GPL increased the stiffness of nanocomposites and the pullout of the CNT increases the strength. Therefore, hybridization of these nanoparticles promotes the toughening and influences the crack propagation characteristics of the pure polymer which in turn causes a significant improvement in fatigue

Fatigue behavior of nanoparticle-filled fibrous polymeric composites

187

life of nanocomposites. In addition, based on the literature, the addition of the nanofiller promotes toughening and influences the crack propagation characteristics of the polymer without nanoparticles. Also, they attribute to enhance the modulus coupled with a reduced dissipation factor and improved the surface hardness [97].

5.5

Conclusions and outlook

To conclude this section, it needs to be stressed that using nanoparticles in most of the industries have positive attraction and opened a contemporary world as like as an industrial revolution for designers to prevent sudden failure due to fatigue. Nanofillers are playing as reinforcement materials in polymeric matrices and changing the border of industrial applications dramatically. For instance, nanofillers inside polymer matrix composites are comprising a majority of aerospace applications in structures, coating, tribology, structural health monitoring, electromagnetic shielding, and shape memory applications [103]. Another sample can be addressed on engine mounts which suffer from fluctuating forces result in sudden failure due to fatigue and nanoparticles can compromise the border [104]. Therefore, modeling this phenomenon is always attractive for researchers and has a vast prospect. In this chapter, after a deep review of the available models for predicting composites fatigue life, a fatigue model was developed to predict the stiffness reduction of nanoparticle/fibrous polymeric composites. The model called Nano-NSDM and evaluated in different circumstances as the following cases based on various industrial applications of composite and nanocomposite materials: – – – – –

Fatigue life Fatigue life Fatigue life Fatigue life Fatigue life

prediction prediction prediction prediction prediction

of an epoxy resin modified by silica nanoparticles. of GFRP with nanoparticles. of CSM/epoxy composites. of thermoplastic nanocomposites. of nanoparticles/CSM/polymer hybrid nanocomposites

Consequently, the results obtained by the model are in very good agreement with experiments. Furthermore, by means of a combination of the micromechanics and energy methods, a new model named Nano-EFAT was derived. The model has the capability of predicting the fatigue life of hybrid nanocomposites by means of the experimental fatigue data of the same composites without adding any nanoparticles. In order to evaluate the model, a series of tests have been performed. The results obtained by the model are in very good agreement with the experimental data. Finally, due to easy access for industries and low tests cost, the displacementcontrolled flexural bending fatigue method was taken into consideration. Then, the behavior of nanocomposites was considered using BFM-110 experimental test setup. By means of the testing device, effects of adding synthesized graphene nanosheets and CNFs (independently and simultaneously) on the flexural fatigue behavior of epoxy polymer were investigated and a remarkable improvement in fatigue life of epoxy resin was observed at the presence of graphene and CNF nanoparticles.

188

Fatigue Life Prediction of Composites and Composite Structures

Finally, the following outlines are represented to have an outlook on future works: – – – – –

Fatigue life prediction of nanoparticle-filled fibrous polymeric composites based on the residual strength approach. Progressive fatigue damage modeling for nanoparticle-filled fibrous polymeric composites. Multiscale numerical simulation of fatigue behavior of nanoparticle-filled fibrous polymeric composites. The effect of stress ratio on fatigue behavior of nanoparticle-filled fibrous polymeric composites. Promotion of Nano-EFAT model for fatigue behavior of nanoparticle-filled fibrous laminated composites.

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