A study on the failure behavior and mechanical properties of unidirectional fiber reinforced thermosetting and thermoplastic composites

Composites Part B 99 (2016) 162e172

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Composites Part B journal homepage: www.elsevier.com/locate/compositesb

Review article

A study on the failure behavior and mechanical properties of unidirectional fiber reinforced thermosetting and thermoplastic composites Yan Ma a, Yuqiu Yang b, c, *, Toshi Sugahara d, Hiroyuki Hamada a a

Advanced Fibro-Science, Kyoto Institute of Technology, Kyoto 6068585, Japan College of Textiles, Donghua University, Shanghai 201620, PR China Engineering Research Center of Technical Textiles, Ministry of Education, Shanghai 201620, PR China d Maruhachi Corporation, Fukui 910-0276, Japan b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 September 2015 Received in revised form 28 May 2016 Accepted 2 June 2016 Available online 4 June 2016

Failure behavior and mechanical properties of unidirectional (UD) carbon fiber reinforced polyamide 6 (CF/PA6) and epoxy resin (CF/Epoxy) laminates were investigated through tensile tests in this study. The fracture modes of both CF/PA6 and CF/Epoxy were discussed based on the fiber orientation, interfacial properties, Mode II interlaminar fracture toughness and the brush width. Meanwhile, Global load sharing (GLS) model was employed to compare with the experimental mechanical properties and corresponding fracture mechanics model was employed to analyze the fracture behavior. The results showed that UD CF/PA6 laminates with weak interface but high Mode II interlaminalr fracture toughness mainly exhibited step-like fracture modes (77%) in interfacial fracture mode (Adhesive failure), while CF/Epoxy laminates with stronger interface but lower Mode II interlaminalr fracture toughness mostly showed splitting fracture mode (69%) in matrix fracture mode (Cohesive failure). © 2016 Published by Elsevier Ltd.

Keywords: Polymer-matrix composites (PMCs) Failure behavior Damage mechanics Prepreg

Contents 1. 2.

3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Experimental methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 2.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 2.2. Experimental procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 2.2.1. Tensile tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 2.2.2. End notched flexure test (ENF test) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 2.2.3. Microscope observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 2.2.4. Scanning electron microscope (SEM) observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 3.1. model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 3.2. Fracture mechanics model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 4.1. Fundamental properties of composite laminates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 4.1.1. Fiber orientation and interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 4.1.2. Fiber volume fraction, Vf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 4.2. Mechanical properties of 0
laminates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 4.3. Interfacial shear strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 4.4. Mode II interlaminar fracture toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

* Corresponding author. College of Textiles, Donghua University, Shanghai 201620, PR China. E-mail address: [email protected] (Y. Yang). http://dx.doi.org/10.1016/j.compositesb.2016.06.005 1359-8368/© 2016 Published by Elsevier Ltd.

Y. Ma et al. / Composites Part B 99 (2016) 162e172

5. 6.

163

4.5. Fracture behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 4.6. The brushy width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 4.7. SEM observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

1. Introduction Near-term developments in processing and manufacturing technology of fiber reinforced plastics (FRPs) have given rise to an extensive range of engineering applications of types of materials to various application areas including aerospace and aircraft structure, yachts as well as wind generator blades and other products on the account of their outstanding mechanical properties, lightweight and longer service life [1e5]. Therefore, lots of traditional materials, metal for instance, were gradually substituted by brand new replacements such as carbon fiber reinforced plastics (CFRPs) [6e9]. Mechanical properties of CFRPs are affected by a lot of factors including properties of raw materials, fiber orientation, manufacturing processes and compatibility between fiber and resin. Therefore, one of the most efficient methods to ameliorate the capability of composites is to select a reasonable combination of reinforcement and matrix. Because reinforcements and matrices are chemically different, firm adhesion at their interfaces is necessary for an efficient transfer of stress and bond distribution throughout an interface [10]. Diverse raw materials including fibers and resins and various interfaces contribute to all sorts of fracture modes, which bring about different mechanical properties of CFRPs [11e15]. The tensile fracture mechanism of unidirectional (UD) CFRP has not been completely understood because the fracture speed of UD CFRP is quite fast (Over 500 m/sec [16]). Failure of FRPs often occurs abruptly without any symptom or visible signs of damage serving as an alarm. This characteristic is caused by the progressively development of microscopic damages. Such damage prediction is interesting and challenging, particularly in multidirectional CFRP composites. In many cases, however, the failure of multidirectional composites was simultaneous with the failure of reinforced fibers oriented in the loading direction. Hence, understanding the 0
tensile failure behavior of UD composite is vital. There are some proposed theories to figure out the tensile fracture of UD CFRPs by using numerical calculation methods [17,18] and numerical simulation methods [19] based on computational micromechanics, which were not experimentally verified. On the other hand, H.Kusano et al. introduced high-speed video cameras to observe the destruction in detail of CFRPs from images [16]. O.Siron et al. investigated the mechanical behavior of UD CFRPs by using acoustic emission to detect physical damage occurring within the specimens [20]. In a UD composites loaded along its fibers, unless the matrix is brittle, internal damage is in the form of individual broken fibers [21]. The tendency of one broken carbon fiber to cause neighboring carbon fibers break determines the fracture behavior and mechanical properties like tensile strength. This tendency, in turn, is dominated by basic parameters of composites such as the fiber and matrix properties, interfacial properties, fiber volume fraction (Vf) and fiber distributions/arrangements in the matrix. Many authors have researched various combinations of matrix, fiber and interfacial properties to investigate the load transfer from one broken

fiber to other fibers and to the matrix in its vicinity. On the other hand, in order to predict the strength and other properties of composites, a number of mathematical models of deformation, damage and failure of fiber reinforced composites have been developed. The shear lag model, developed by Cox [22] is one of most often used approaches in the analysis of strength and damage of fiber reinforced composites. This model is often employed to analyze the load redistribution in composites, resulting from failure of one or several fibers. This redistribution is described in the framework of various load sharing models. Two limiting cases including global load sharing (GLS) [22e36] and local load sharing (LLS) [21,37e39] are often considered. For GLS, load from a broken reinforcement is shed equally to all remaining intact reinforcements across the cross section of the composites. For LLS, one broken fiber sheds all the loads it carried before fracture to its immediate neighbors only. Hedgepeth [23] applied the shear lag model to model the multifiber system for studying the stress distribution around broken fibers in 2D unidirectional composites with infinite array of fibers. Hedgepeth and Van Dyke [24] generalized the elastic model to 3D case and included the elastic-plastic matrix into the model. Wagner and Eitan [25] employed the shear lag model to investigate the stress redistribution from a failed fiber to its neighbors. The effects of fiber/matrix debonding and fiber/matrix interfacial friction were incorporated in the model of stress redistribution after the fiber failure proposed by Zhou and Wagner [26]. Problem of independent and successive fiber fractures under GLS condition is reduced to the problem of failure of single fiber in the matrix by Curtin [27]. He estimated the ultimate strength of the composite as a function of the sliding resistance, and parameters of the Weibull distribution of the fiber strengths based on the assumption that the cumulative number of defects in fibers from the Weibull distribution of fiber strengths. Using Monte-Carlo method and shear lag-based models, Beyerlein et al. [28] and Beyerlein and Phoenix [29] investigated the effects of the statistics of fiber strengths (Weibull distribution) on the fracture process. It was found that variability in fiber strength can lead to a nonlinear deformation mechanism of the composites. Landis et al. [30,31] developed a three-dimensional shear lag model combining with the Weibull fiber statistics and the influence superposition technique, and applied it to analyze the effect of statistical strength distribution and size effects on the strength of composites. Curtin and colleagues [32e35] proposed an approach to the analysis of the interaction between multiple breaks in fibers, based on the Green’s functional model. Then Curtin and colleagues [32,33] employed the 3D lattice Green’s functional model to determine the stress distribution and to simulate damage accumulation. Xia and Curtin [34], and Xia et al. [35] employed 3D FE micro-mechanical analysis to investigate the deformation and stress transfer in fiber reinforced composites. However, most of above existing related studies [22e39] mainly focused on the mechanical behaviors, their influence factors and mechanisms, while ignored the interesting fracture modes, which closely related to fracture mechanisms.

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Table 1 Mechanical properties of raw materials. Material

Manufacturer

Type

E (GPa)

s (MPa)

d (%)

r (g cm3)

CF PA6 Epoxy

Toray Mitsubishi Gas Chemical Company Maruhachi Corp.

T700SC 12k MXD-PA MCP1110

230 2.4 3.2

4900 82 80.6

2.1 4.0 5.4

1.8 1.1 1.2

E: Tensile modulus;s: Tensile strength;d: Elongation;r: Density.

properties based on the fiber orientation, interfacial properties, Mode II interlaminar fracture toughness and the brush width using a range of experimental techniques including tensile tests, end notched flexure (ENF) tests, optical microscopy and scanning electron microscopy (SEM). Meanwhile, GLS model was employed to compare with the experimental mechanical properties and corresponding fracture mechanics model was employed to analyze the fracture behavior. 2. Experimental methods 2.1. Materials Fig. 1. CFRP plates (a) with thickness of 1 mm were fabricated by laminating 10 plies of prepreg sheets (b) with stacking sequences of [0]10 for tensile tests and curing at 280
C for 3.5 min under compression pressure 4 kg/cm2 and curing at 130
C for 50 min under compression pressure 25 kg/cm2 for CF/PA6 and CF/Epoxy laminates, respectively.

In this study, typical thermoplastic resin polyamide 6 (PA6) and thermosetting epoxy resin were used as matrices to manufacture UD carbon fiber reinforced PA6 resin laminates (CF/PA6) and epoxy resin laminates (CF/Epoxy) laminates through hot compression molding to investigate their failure behavior and mechanical

These CFRPs were manufactured from a unidirectional reinforced prepreg make of reinforcing carbon fiber grade T700SC 12K supplied from Toray and PA6 (Type:MXD-PA) and epoxy (Type:MCP939) supplied from Mitsubishi Gas Chemical Company and Maruhachi Corporation, respectively. Mechanical properties of raw materials were shown in Table 1. Mechanical properties including tensile modulus, tensile strength and density of PA6 and epoxy resin were similar. The thickness of a single ply lamina was 0.1 mm. CFRP laminates with thickness of 1 mm were fabricated by laminating 10 plies of prepreg sheets with stacking sequences of [0]10 for tensile tests and cured at 280
C for 3.5 min under compression pressure 4 kg/cm2 and 130
C for 50 min under

Fig. 2. Appearances of specimens before and after polishing.

Fig. 3. Specimen for tensile tests based on JIS K7165.

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165

Fig. 4. Specimen for end notched flexure test based on JIS K 7086.

compression pressure 25 kg/cm2 for CF/PA6 and CF/Epoxy laminates, respectively. CFRP laminate and prepreg sheet are shown in Fig. 1(a) and (b), respectively. The specimens of both CF/PA6 and CF/Epoxy composite laminates were cut with a size of 25  250  1 (Width  Length  Thickness:mm) for tensile tests. The fiber direction of both CF/PA6 and CF/Epoxy composite laminates were 0
. For specimens of compact tension tests, the fiber direction was 90
.

2.2.2. End notched flexure test (ENF test) Five specimens of both CF/PA6 and CF/Epoxy 0
laminates were manufactured to standard specimens according to JIS K 7086 standard [41]. Three-point flexure test with the span length 2L of 100 mm is used as schematized in Fig. 4. The ENF tests were conducted under a displacement controlled condition with the displacement rate of 1 mm/min. According to JIS K 7086, the interlaminar fracture toughness in mode II GIIc was evaluated using the Eqs. (1) and (2) based on beam theory in reference to JIS K 7086 standard [41]:

2.2. Experimental procedures The tensile tests and compact tension tests were performed in room temperature and relative humidity controlled laboratory (23 ± 0.5
C, 48 ± 2% RH). Before testing, two edges of the specimens were polished by polishing machine in order to eliminate the defects which formed during cutting process. The appearances of specimens before and after polishing were showed in Fig. 2.

2.2.1. Tensile tests 78 pieces of CF/PA6 and 52 pieces of CF/Epoxy 0
laminates were cut into standard sizes for tensile tests as shown in Fig. 3. The tensile tests were based on the JIS K 7165 standard [40]. Aluminum sheets were attached at the two grip sections of the specimens to increase the friction between specimen and collet. The tensile tests were carried out on a computer-controlled Instron 55R4206 screwdriven universal testing machine equipped with a 100 kN load cell at a speed of 1 mm/min.

GIIC ¼

a1 ¼

9a2 P 2 C1
1 C  2B 2L3 þ 3a31

   1 3 C1 3 2 C1 a0 þ  1 L3 3 C0 C0

(1)

(2)

Where PC is the critical load at the onset of crack growth, a0 and C0 are the initial crack length and load point compliance of the specimen. a1 and C1 are the crack length and load point compliance at P ¼ PC. 2.2.3. Microscope observation The fiber orientation was analyzed on a polished surface part of cross section of the laminates (roughly over 1000 fibers). Each micrograph contained typically 100 fully visible fibers. The fiber orientation for a given fiber was determined as follows: (i) Images taken in optical microscopy (VHX-500F CCD camera, which has a

Fig. 5. Cross section observation of CF/PA6 plates (a) and CF/Epoxy plates (b) after binarization and schematic diagram of cross section of the ith carbon fiber (c).

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Y. Ma et al. / Composites Part B 99 (2016) 162e172

resolution of 1600  1200 pixels in size) were preprocessed by the aid of the ImageJ software. (ii) Functions in ImageJ software “Make Binary” and “Watershed” used to get binary photos, then function of “Noise / Remove outlier” [21] employed to get clear boundary carbon fiber images of CF/PA6 and CF/Epoxy laminates as shown in Fig. 5(a) and (b), respectively. (iii) Four directions (0
, þ45
, 90
and 45
) diameters of the ith carbon fiber were measured by ImageJ software (Functions in ImageJ software “Measure”) and recorded as Li1, Li2, Li3 and Li4 respectively, which were shown in Fig. 5(c). The fiber volume fraction, Vf, was measured in a similar way as above fiber orientation described on a polished surface of the whole cross section of both CF/PA6 and CF/Epoxy laminates. The Vf for a given laminates could be measured as above steps (i) and (ii) then function in ImageJ software “Analyze/Analyze Particles” could be P  Fiber cross section used to calculate the area ratio cross section of CFRP , which is clearly

approximation [42].

d¼

sf r f 2ty

Where, sf is the stress in intact fiber, rf is the radium of radius of fiber, ty is the interfacial shear strength. The predicted composite strength can be predicted as shown in Eq. (4) [43].

sm 0 L0 ty

2.2.4. Scanning electron microscope (SEM) observation All fracture specimens were observed under the optical microscope, and then selected samples were coated with an AuePd layer and examined in more detail in a SEM Jelo JSM 5200.

sf ¼ s1

Rosen [36] introduced the weakest-link theory into the prediction of the unidirectional composite strength s*L , namely the “chain of bundles” model. He presented the UD composite as a chain of bundles in series; once one of the unit bundles is broken, the UD composite would be immediately fractured. Based on Cox’s shear-lag model [22] and Kelly and Tyson’s model [42], Curtin [27] proposed a global load sharing (GLS) model in which the stress released from a broken fiber is equally sustained by the remaining unbroken fibers. Following Rosen’s chain of bundle concept, important characteristic of the Curtin’s model is that it takes loading contributions of broken fibers and matrix shear loading recovers away from the fiber breakage into consideration. Rosen [36] considers the sustained load inside a bundle with length 2d, double ineffective length as the working section. The ineffective length d is defined as Eq. (3) according to the Kelly-Tyson

(4)

Where,

s1 ¼

3.1. model

!   5 sf mþ1 1 12 s1

sL ¼ sf Vf

related to the Vf owing to the unidirectional characteristics.

3. Theory

(3)

!

1 mþ1

(5)

rf 

 1 mþ1 12 5m þ 10

(6)

Where m and s0 are the Weibull modulus and the scaling parameter, respectively. L0 is the span length at determining Weibull parameters. Then, maximizing with respect to the strain yields the ultimate tensile strength

s*L ¼ Vf s1



 1   mþ1 12 mþ1 5m þ 10 mþ2

(7)

To construct a stress-strain curve, a linear relation between fiber stress and composite strain shown in Eq. (8) can be substitute into above equations, where Ef is fiber modulus.

sf ¼ Ef εf

(8)

3.2. Fracture mechanics model Criteria of splitting are deduced using a fracture mechanics approach [43]. A model with length L includes a fiber breakage cluster with length l, which defined as the representative length as schematized in Fig. 6. In this model, a unidirectional composite was divided into two parts: I) with cluster with a length l and II) without cluster with length L-l. A is the composite cross section, a is the cluster cross section area, s is the circumference of cluster, F is the tensile load and EL is the composite modulus in the intact part. The energy release rate (G) related to splitting at the edge of the cluster could be deduced according to the strain energy in region I (UI) and II (UII) as in Eq. (9). Table 2 kI value calculation. Type

CF/PA6 CF/Epoxy Fig. 6. Schematic of fracture mechanics model for splitting initiation [31].

Modulus (GPa)

kI

CF

Vf

Matrix

VR

Calculated

Tested

230 230

51.3% 59.3%

3.0 3.2

48.7% 40.7%

119.46 137.78

102.31 133.83

0.856 0.971

* Calculation was based on the consideration that carbon fiber orientation of both CF/PA6 and CF/Epoxy plates both were UD).

Y. Ma et al. / Composites Part B 99 (2016) 162e172

167

  1 dUI dUII ð1  lÞaF 2 þ ¼ s dl dl 2EL AfA  ð1  lÞags

G¼

ð1  lÞAas2L 2EL fA  ð1  lÞags

¼

(9)

Where l is effective rate of composite modulus inside the cluster. If A is large enough compare to a, G could be approximated as in Eq. (10).

G ¼ lim

A/∞

ð1  lÞAas2L ð1  lÞs2L a ¼ s 2EL fA  ð1  lÞags 2EL

(10)

a/s represents the geometry of the cluster. By submitting shear fracture toughness against splitting Gc into G in Eq. (11).

c≡

a * s

¼

2Gc Ef

(11)

ð1  lÞVf s2f

Finally the critical cluster geometry c is linked to the shear fracture toughness Gc, fiber volume fraction (Vf) and intact fiber stress (sf).

Fig. 7. Typical tensile stress-strain curves between experiments and predictions from GLS model.

Table 4 Material constants used in the present calculation.

4. Results and discussion 4.1. Fundamental properties of composite laminates 4.1.1. Fiber orientation and interface The modulus of UD composite laminates could be calculated by the Rule of Mixtures equation as shown in Eq. (12).

  EC ¼ kFO  kI  Ef  Vf þ Em  1  Vf

(12)

Material constants

CF/PA6

CF/Epoxy

Young’s modulus of fiber (Ef) Diameter of fiber (rf) Fiber gage length (L0) Weibull scale factor (s0) Weibull shape factor (m) Interfacial shear strength (t0) Fiber volume fraction (Vf)

230 GPaa 7 mma 25 mm 2426 MPab 5.48 53.8 MPab 0.513

230 GPaa 7 mma 25 mm 2426 MPab 4.22b 49.9 MPab 0.593

a b

Where EC is calculated modulus, kFO is fiber orientation factor, kI is interface factor, Ef is fiber modulus, Vf is fiber volume fraction, Em is matrix modulus. For investigating the fiber orientation of the i th carbon fiber, parameter Di was chosen as the evaluation index.

Di ¼

Limin Limax

(13)

Limin ¼ minfLi1 ; Li2 ; Li3 ; Li4 g

(14)

Limax ¼ maxfLi1 ; Li2 ; Li3 ; Li4 g

(15)

For both CF/PA6 and CF/Epoxy laminates, more than 1000 carbon fibers (n > 1000) were measured and tested for investigating the direction of all carbon fibers based on Eq. (16):

Pi¼n d¼

i¼1 Di

From Tory Corp. Cited from Ref. [31].

Table 5 The calculated modulus and strength from GLS model. Material constants

CF/PA6

CF/Epoxy

Modulus (GPa) Strength (MPa)

117.43 136.02

1776.26 2291.27

fiber orientation of both CF/PA6 and CF/Epoxy laminates both were almost unidirectional oriented. In this case, fiber orientation factor, kFO, of both CF/PA6 and CF/Epoxy is considered 100% at current study to simply the calculation, interface factor, kI, was calculated and listed in Table 2. Even a rough calculation, the values of kI-CF/PA6 and kI-CF/Epoxy were 0.856 and 0.971 respectively, which show that the interface of CF/Epoxy laminates seems better than CF/PA6 laminates.

(16)

n

Where d and n are direction parameter and tested number of all carbon fiber in CFRPs respectively. The calculating results showed that dCF/PA6 and dCF/Epoxy were 0.921 and 0.946 respectively, it could be considered that carbon

4.1.2. Fiber volume fraction, Vf Owing to their UD character, fiber volume fraction (Vf) of CF/PA6 and CF/Epoxy composites were calculated according to their cross section ratio (as shown in Fig. 5(a) and (b)) between fibers and laminates, which could be measured by image analysis software

Table 3 Mechanical properties of 0
composite boards. Composites

CF/PA6 CF/Epoxy

Vf (%)

51.3 59.3

Test

Tensile Tensile

Number

78 52

Modulus

Strength

Mean (GPa)

C.V. (%)

Mean (MPa)

C.V. (%)

102.3 133.8

10.5 10.5

1660 2428

16.2 18.3

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Fig. 8. Relationship between modulus and strength of tensile tests.

(ImageJ software) as explained in Section 2.2.3. The results of five specimens showed the Vf of CF/PA6 and CF/Epoxy laminates were 51.3% (±2.4%) and 59.3% (±4.1%), respectively.

4.2. Mechanical properties of 0
laminates Mechanical properties of 0
CF/PA6 and CF/Epoxy laminates were summarized in Table 3. Coefficient of variation (C.V.) value was calculated by the following Eq. (17) to indicate the stability of tensile properties of the CFRP and CFRTP composites.

C:V: ¼

s  100 m

(17)

Table 4. Results indicate the GLS and experimental results exhibited a good agreement especially for CF/PA6 laminates. Although the load carried by broken fibers is locally distributed in the actual composites (LLS), the difference in the stress-strain relation and fiber breakage between GLS and LLS are very small until just before failure [44]. At the same time, Kamoshida et al. [45] used a 3D shear lag model for more realistic calculations of the fiber damage and point out that the local strain concentration around a cluster of fiber breaks can be neglected before failure. According to the experimental and calculated stress-strain curve from Eq. (4), it is shown that the GLS model is valid and useful to evaluate the mechanical damage except for the final failure strength and strain (see Table 5). The relationship between modulus and strength of tensile tests together with results from GLS model (Different Vf) were shown in Fig. 8. The calculated modulus and strength by using GLS model of CF/PA6 and CF/Epoxy laminates is shown in Fig. 8 as closed triangle and circle, respectively. Experimental results (Open triangle and circle in Fig. 8) indicate that mechanical properties of CF/PA6 composites exhibited more concentrated behavior than CF/Epoxy composites. However, CF/PA6 laminates exhibited lower modulus than GLS model calculated modulus. According to the strain-stress curves of CF/PA6 laminates as shown in Fig. 7, it is clear that the modulus calculated from initial part of stress-strain curves is smaller than the part of strain over 0.5%, which could be explained by the difference of fiber orientation. The results shown in Table 3 clearly indicate that there is an appreciable scattering of tensile strength. The statistical distribution of composite strengths is usually described by means of the Weibull equation [46]. The Weibull distribution is given by

  a  sf PF ¼ 1  exp 

s0

(18)

Where s is standard deviation and m is mean value of all data. Calculated stress-strain curves from the modified Curtin’s model and typical experimental stress-strain curves (CF/PA6: Vf z 0.5, CF/ Epoxy: Vf z 0.6) are compared in Fig. 7. The basic parameters including young’s modulus, diameter and fiber gage length of fiber, Weibull scale and shape factors, interfacial shear strength and fiber volume fraction used in the present calculation are shown in

where PF is the cumulative probability of failure of composite at applied tensile strength sf, a is the Weibull modulus (Weibull shape parameter) of the composite, s0 a Weibull scale parameter (characteristic stress). Taking the logarithm of both sides of Eq. (18), rearrangement of the two-parameter Weibull statistical distribution expression gives the following:

Fig. 9. Weibull distribution of tensile strength (s) for unidirectional CF/PA6 and CF/ Epoxy laminates.

Fig. 10. Effect of interfacial shear strength on tensile strength of both CF/PA6 and CF/ Epoxy based on GLS model. (Material constants except interfacial shear strength used in this calculation as shown in Table 4).

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169

Fig. 11. Representative load-deflection curves (a) and fracture toughness results (b) of both 0
unidirectional CF/PA6 and CF/Epoxy composites based on End Notched Flexure tests.

  ln ln

1 1  Fi



 ¼ a ln sf  alnðs0 Þ

(19)

Hence the Weibull modulus, a, can be obtained by linear regression from a Weibull plot of Eq. (19). The probability of failure, Fi, at the ith ranked specimen from a total of N specimens is obtained from the symmetric rank method as

Fi ¼

i  0:5 N

(20)

where i is rank of the specimen from lowest strength to highest strength. The Weibull plots of tensile strength for 0
unidirectional CF/ PA6 and CF/Epoxy laminates are shown in Fig. 9. The Weibull modulus, a, for CF/PA6 and CF/Epoxy laminates were calculated to be 7.04 and 6.48, respectively.

The difference in Weibull modulus, a can be attributed to the nature and distribution of the flaws which are existed in the composites. It is well know that many defects in the composites were formed during precursor manufacturing and subsequent various treatments. In present study, these include defects in carbon fiber (misalignment, ultramicropores, etc.), carbon fiber misalignment, bubble, dry carbon fiber bundle (not good impregnation), etc. The existence of these defects in unidirectional composites results in scattering of tensile strength. As a result, the Weibull modulus a can be regarded as a defect frequency distribution factor [46]. High values of a indicates the defects are evenly distributed throughout the material. Low values of a indicated that defects are fewer and less evenly distributed, causing greater scatter in strength [47]. 4.3. Interfacial shear strength In GLS model used in this study, the value of interfacial shear strength is cited from Ref. [43]. The effect of interfacial shear strength on tensile strength of unidirectional CF/PA6 and CF/Epoxy laminates is shown in Fig. 10. It is clear that the tensile strength increased in similar Cube Root Function way with the improvement of interfacial shear strength. To investigate the relatively interfacial shear strength of CF/PA6 and CF/Epoxy laminates, experimental tensile strength of both CFRPs were employed to look for the corresponding interfacial shear strength as shown in Fig. 10. In detail, the corresponding interfacial shear strengths of CF/PA6 and CF/ Epoxy laminates are z44 MPa and z68 MPa, respectively, which means CF/Epoxy laminates possessed stronger interfacial shear strength than CF/PA6 laminates. 4.4. Mode II interlaminar fracture toughness The representative load-displacement curves of the ENF tests for both CF/PA6 and CF/Epoxy laminates were shown in Fig. 11(a). The calculated mode II fracture toughness of both CFRPs is depicted in Fig. 11(b). It is clear that the mode II interlaminar fracture toughness of CF/PA6 laminates (GIIc-CF/PA6 ¼ 2.60 J/m2) was better than CF/ Epoxy CFRP laminates (GIIc-CF/Epoxy ¼ 1.89 J/m2), which means the ability of CF/PA6 CFRP composites containing a crack to resist fracture was more excellent than CF/Epoxy ones under the shearing loading.

Fig. 12. Two typical fracture modes of both CF/PA6 and CF/Epoxy specimens; (a) Splitting fracture mode of CF/PA6 CFRP composite, (b) Step-like fracture mode of CF/ PA6 CFRP composite, (c) Splitting fracture mode of CF/Epoxy CFRP composite, (d) Steplike fracture mode of CF/Epoxy CFRP composite.

4.5. Fracture behavior After tensile tests, two typical fracture modes including splitting

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Fig. 13. Example of brush width measurement (a) and brush width distribution (b) of whole data.

Fig. 14. SEM observation of fractured area of CF/PA6 and CF/Epoxy composites.

and step-like mode of both CF/PA6 and CF/Epoxy laminates were observed as shown in Fig. 12. Specimens fractured in splitting mode exhibited broom-like head (Fig. 12(a) and (c)) while specimens fractured in step-like mode showed more smooth fracture surface (Fig. 12(b) and (d)). The big difference was that 0
CF/Epoxy composite laminates mostly (69%) showed splitting fracture mode after tensile tests, while CF/PA6 composite laminates mainly (77%) exhibited step-like fracture modes. 4.6. The brushy width The brushy width distribution of brush-shape fractured laminates in splitting fracture modes of CF/PA6 and CF/Epoxy laminates was investigated in this study. Example of brushy width measurement was shown in Fig. 13(a). In detail, the broken specimens after tensile test were taken photos by microscopy and measured the

width of each brush through ImageJ software. All data of every specimen was summarized as shown in Fig. 13(b). The results showed that CF/PA6 laminates had more brush with width below 0.5 mm than CF/Epoxy laminates.

4.7. SEM observation According to the observing results of CF/PA6 and CF/Epoxy laminates after tensile tests as shown in Fig. 14, it was found that lots of PA6 resins surround carbon fibers were torn from fibers which could be directly observed in CF/PA6 laminates. While for CF/ Epoxy laminates, lots of crack propagated in epoxy matrices and carbon fibers were hard to be imaged directly. These representative characteristics indicate the fracture modes of CF/PA6 and CF/Epoxy laminates belong to adhesive and cohesive failure, respectively.

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171

Fig. 15. Schematic diagram of tensile fracture modes of CF/PA6 and CF/Epoxy composite boards.

5. Discussion According to above investigation, it was found that CF/PA6 laminates with interface fracture form (Adhesive failure) have unidirectional fiber orientation, a relative weaker interface but high Mode II interlaminar fracture toughness, while CF/Epoxy laminates with matrix fracture form (Cohesive failure) have unidirectional fiber orientation, stronger interface but low Mode II interlaminar fracture toughness. Schematic diagram of typical tensile fracture modes is shown in Fig. 15. For CFRP laminates, fiber breakage occurred at stresses exceeding the strength of the weakest fiber. An isolated fiber break caused stress concentration on the interface around the tip of the broken fiber. If the interface between fiber and resin was not strong enough, the crack in specimens propagated along the interface. Otherwise, cracks in laminates with very strong interfaces propagated in vertical direction firstly. After the first fiber breakage, CF/ PA6 laminates with weak interfaces mainly exhibited interfacial fracture mode as shown in Fig. 15(b), while CF/Epoxy laminates with stronger interfaces mostly showed matrix fracture mode as shown in Fig. 15(c). In macroscopic view, both CF/PA6 laminates and CF/Epoxy laminates showed two fracture modes including splitting fracture mode (see Fig. 15(d) and (f)) and step-like fracture mode (see Fig. 15(e) and (g)) after tensile tests. In splitting fracture mode, cracks, parallel to the fiber orientation, propagated in the inner of matrices of CF/Epoxy laminates owing to their strong interface and low fracture toughness, while it was harder for CF/PA6 laminates to fracture in matrices easily owing to their high fracture toughness. On the other hand, the weak interface properties of CF/PA6 laminates led to the inner cracks propagate along the interfaces. Different fracture mode led to

different fracture behavior, various propagation forms of cracks related to the fractured brush width after tensile tests. Crack propagating in the inside of matrices contributed to attach more matrices around fibers after fracture. Tensile fracture modes of CF/PA6 laminates with lower tensile strength variation (16.2%) and lower Vf (51.3%) mainly exhibited step-like mode (77%). CF/Epoxy CFRP laminates with higher tensile strength variation (18.3%) higher Vf (59.3%) mostly showed splitting mode (69%). The lower variation, the more concentrated fracture mode was. Based on the research of Cook and Gordon [48], Gerberich [49] calculated the stress distribution ahead of a crack in an all-brittle system and found that the tensile stress in transverse direction reaches a maximum valure which is about one-fifth of the tensile stress in the longtitudinal direction. According to this mechanism, splitting occurs if

sc;T < 0:2; sc;L where sc,T and sc,T are the transverse and the longtitudinal strength of composites, respectively. According to Gerberich [49], sc,T decreased but sc,L increased with increasing volume fraction of fiber Vf, leading to the occurrence of splitting at high Vf. This is also approved by Eq. (11), which indicates the fracture bundle sizes related to the interlaminar shear fracture toughness GII and Vf because same carbon fibers (same Ef, l and sf) are used in present study. Therefore, CF/PA6 laminates with higher Vf possessed higher fracture toughness than CF/Epoxy laminates with lower Vf, which indicates that fiber bundles are easier to fracture in small size than CF/Epoxy laminates.

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6. Conclusion In this study, CFRPs were manufactured from a unidirectionalreinforced prepreg made of reinforcing carbon fiber and thermoplastic resin PA6 and thermosetting resin epoxy through hot compression molding process. Mechanical properties and failure behavior of carbon fiber reinforced PA6 and Epoxy resin laminates were investigated by tensile tests. The physicochemical parameters such as fiber volume fraction, fiber orientation, interfacial properties, Mode II interlaminar fracture toughness and brush width were measured and calculated through a range of experimental techniques including tensile tests, ENF tests, optical microscopy and SEM. Meanwhile, GLS model was employed to compare with the experimental mechanical properties and corresponding fracture mechanics model was employed to analyze the fracture behavior. It was found that 0
CF/PA6 laminates with weak interfaces but high Mode II interlaminar fracture toughness mainly exhibited step-like fracture modes (77%) in interfacial fracture mode (Adhesive failure), while CF/Epoxy laminates with stronger interfaces but low Mode II interlaminar fracture toughness mostly showed splitting fracture mode (69%) in matrix fracture mode (Cohesive failure). Acknowledgements The authors thank Maruhachi Corporation Ltd., Japan for manufacturing the specimens. The authors also thank a reviewer of this article for a very detailed and careful review of the original manuscript. References [1] Koronis G, Silva A, Fontul M. Green composites: a review of adequate materials for automotive applications. Compos Part B 2013;44(1):120e7. [2] Ku H, Wang H, Pattarachaiyakoop N, Trada M. A review on the tensile properties of natural fiber reinforced polymer composites. Compos Part B 2011;42(4):856e73. [3] Azeez AA, Rhee KY, Park SJ, Hui D. Epoxy clay nanocomposites-processing, properties and applications: a review. Compos Part B 2013;45(1):308e20. [4] Dhand V, Mittal G, Rhee KY, Park SJ, Hui D. A short review on basalt fiber reinforced polymer composites. Compos Part B 2015;73:166e80. [5] Xu J, Ma Y, Zhang Q, Sugahara T, Yang Y, Hamada H. Crashworthiness of carbon fiber hybrid composite tubes molded by filament winding. Compos Struct 2016;139:130e40. [6] Lignola GP, Jalayer F, Nardone F, Prota A, Manfredi G. Probabilistic design equations for the shear capacity of RC members with FRP internal shear reinforcement. Compos Part B 2014;67:199e208. [7] Ma Y, Sugahara T, Yang Y, Hamada H. A study on the energy absorption properties of carbon/aramid fiber filament winding composite tube. Compos Struct 2015;123:301e11. [8] Chung DDL. Cement reinforced with short carbon fibers: a multifunctional material. Compos Part B 2000;31:511e26. [9] Ma H, Jia Z, Lau K, Leng J, Hui D. Impact properties of glass fiber/epoxy composites at cryogenic environment. Compos Part B 2016;92:210e7. [10] Wang J, Zhou Z, Xiao H, Zhang L, Hu B, Qiu Y, et al. Effect of alcohol pretreatment in conjunction with atmospheric pressure plasmas on hydrophobizing ramie fiber surfaces. J Adhes Sci Technol 2013;27(11):1278e88. [11] Maria C. An overview of interface cracks. Eng Fract Mech 1990;37(1): 197e208. [12] Lu T, Liu S, Jiang M, Xu X, Wang Y, Wang Z, et al. Effects of modifications of bamboo cellulose fibers on the improved mechanical properties of cellulose reinforced poly (lactic acid) composites. Compos Part B 2014;62:191e7. [13] Jang KK, Man LS. Impact and delamination failure of woven-fabric composites. Compos Sci Technol 2000;60:745e61. [14] Pinho ST, Robinson P, Iannucci L. Fracture toughness of the tensile and compressive fibre failure modes in laminated composites. Compos Sci Technol 2006;66:2069e79. [15] Lu T, Jiang M, Jiang Z, Hui D, Wang Z, Zhou Z. Effect of surface modification of bamboo cellulose fibers on mechanical properties of cellulose/epoxy composites. Compos Part B 2013;51:28e34. [16] Kusano H, Aoki Y, Hirano Y, Hasegawa T, Nagao Y. Visualization on static

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