Fatigue and reliability analysis of nano-modified scarf adhesive joints in carbon fiber composites

Accepted Manuscript Fatigue and reliability analysis of nano-modified scarf adhesive joints in carbon fiber composites U.A. Khashaba, A.A. Aljinaidi, M.A. Hamed PII:

S1359-8368(16)30135-4

DOI:

10.1016/j.compositesb.2017.04.001

Reference:

JCOMB 5002

To appear in:

Composites Part B

Received Date: 28 March 2016 Revised Date:

29 March 2017

Accepted Date: 2 April 2017

Please cite this article as: Khashaba UA, Aljinaidi AA, Hamed MA, Fatigue and reliability analysis of nano-modified scarf adhesive joints in carbon fiber composites, Composites Part B (2017), doi: 10.1016/ j.compositesb.2017.04.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Fatigue and reliability analysis of nano-modified scarf adhesive joints in carbon fiber composites U.A. Khashaba1,2, A. A. Aljinaidi1, M.A. Hamed1 1

RI PT

Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia 2

Mechanical Design and Production Engineering Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt

SC

ABSTRACT

Enhancing the fatigue performance of scarf adhesive joints (SAJs) in carbon fiber-reinforced epoxy (CFRE) composite structures via incorporation of nanofillers into the epoxy adhesive has not yet been fully investigated and

M AN U

is the subject of this study. The optimum weight percentages of multi-walled carbon nanotubes (MWCNTs), SiC and Al2O3 nanofillers were ultrasonically dispersed in Epocast 50-A1/946 epoxy. The nanophased matrices were used to fabricate the SAJs with 5° scarf angle. Fatigue tests were conducted at constant-load amplitude, frequency of 10 Hz and stress ratio of 0.1. Result from fatigue tests showed that the gain/loss in the fatigue lives of the modified SAJs with MWCNTs, SiC and Al2O3 are respectively 19%, 52% and -22% at fatigue limit of 36 MPa. The load-

TE D

displacement hysteresis loops of the nano-modified SAJs showed higher fatigue stiffness compared to neat epoxySAJ. The stiffness of the SAJs was increased with increasing number of cycles up to about N/Nf=0.01. As the number of cycles increases the damage level is increased and thus the slope of the hysteresis loop (stiffness) is

EP

decreased and the hysteresis loop area becomes wider. The highest penalty paid to gain safe lives was observed for Al2O3-SAJs, which has highest scatter in the fatigue lives.

AC C

KEYWORDS: A. Polymer-matrix composites (PMCs), B. Fatigue, C. Statistical properties/methods, E. Joints/joining

1. INTRODUCTION

Fiber-reinforced polymer (FRP) composite materials are characterized by their superior specific strength, light weight, chemical and corrosion resistance, and unique flexibility in design and tailoring their mechanical properties by choosing their constituent materials. These properties make FRP composites attractive not only to the military, *

Corresponding author. Tel.: +966553507515; Fax: +96626952181 E–mail addresses: [email protected], [email protected] (U.A. Khashaba).

ACCEPTED MANUSCRIPT

but also to the civilian aircraft, space, and automobile industries. In these applications, adhesively bonded joints are increasingly being used as alternatives to conventional mechanical fasteners in which the drilled holes reduces the net cross sectional area of the structure and introduce localized stress concentration. Among the advantages of the

RI PT

adhesive bonded joints are the following: adhesives distribute stress load evenly over a broad area, reducing stress concentration in adherends, adhesives are applied inside the joint and are nearly invisible within the assembly, adhesives form a seal as well as a bond that can protect the joint from corrosion, relatively lightweight, lower fabrication cost and time, and improved damage tolerance [1]. Therefore, the demand for improving the mechanical

SC

properties of the adhesive bonded joints is required forever and is the main objective of this study.

Recently, many researchers [1-7] have focused on the improving the mechanical properties of the epoxy adhesive

M AN U

through nanofillers infusion. They have been investigating the nanofiller effects on the mechanical properties of nanophased epoxy and the overall strength of single-lap joints [1-5] and double strap joints [6,7]. The interfacial bond strength plays a very important role in transferring the load from lower strength matrix to higher strength nanofillers and thus, improving the mechanical properties of the nanophased matrix. For example, carbon nanotubes are known to have superior mechanical properties, such as the typical Young's modulus of 1 TPa and failure stress

TE D

ranging from 63 GPa [6] to 200 GPa [8]. Jakubinek et al. [1] reported that the peel and lap-shear strengths of the modified epoxy with 0.5 wt% single-walled carbon nanotubes (SWCNT) were unchanged while the addition of 1 wt% resulted in 30% increase of peel strength but the lap-shear strength was reduced by 10–15%. Korayem et al. [6,7] found that the incorporation of CNTs into the pure epoxy leads to an increase of about 20% in Young's

EP

modulus and 30% in tensile strength, while elongation-to-failure is reduced by about 41%. Agglomeration of the nanofillers in polymer matrix leads to decrease in interfacial bonding and can work as stress riser or discontinuity,

AC C

which results in deterioration of the mechanical properties of the developed epoxy adhesives [9]. Therefore, in the present work, special attention has been paid to define all the sonication parameters and select the most suitable. The present study is a continuation of earlier work [10,11] on the static tensile behavior of developed scarf adhesive joints (SAJs) with optimum weight percentages of MWCNTs [10], SiC and Al2O3 nanoparticles [11]. The optimum weight percentages of MWCNTs, SiC and Al2O3 were determined earlier by Khashaba et al. [12] as 0.5wt%, 1.5wt% and 1.5wt% respectively. The ultimate tensile strength of the modified scarf adhesive joints (SAJs) showed enhancement up to 41% compared to neat epoxy (NE)-SAJs. The bondline and adherend-tip strains were monitored

2

ACCEPTED MANUSCRIPT

using instrumented SAJs with 8-strain gauges. The highest strain was observed at the adherend-tip-ends-edges, which have the maximum interfacial shear stress [10,11]. In automotive and aircraft industries the bonded joints are extensively used as a primary method for assembly and repairs of the structure components. The service life of the

RI PT

bonded structures in these applications is dominated by fatigue failure. For this reason, successful designs of the adhesively bonded structures should include fatigue analysis as a design criterion, which is the subject of the present study.

The strength of scarf joints has recently attracted much interest [10,13,14,16] because of the applied loads in practice

SC

are not absolutely perpendicular or parallel to the bonding surfaces of the adherends. Therefore, the scarf angle can play a very important role in controlling the combined peeling and shear stresses at the adhesive/adherend interface

M AN U

and thus the failure mode [13]. The interfacial shear stress in the scarf adhesive joint (SAJ) was affected by many factors such as the scarf angle, stress transformation, local stress multiaxiality and the locations experiencing the extreme shear stress along the interface. The scarf joints can be considered the weakest part of the fiber composite structures due to the discontinuity of reinforcing fibers at the joint interfaces [17]. The enhancing of fatigue performance of nano-adhesive joints in fiber composite structures is a quite new topic and one may find some traces

of this study.

TE D

on the development of lap joints in aluminum substrates [3], composite to aluminum adherends [4] and is the subject

Mactabi et al. [3] and Kang et al. [4] developed amazing technique for monitoring crack initiation, propagation and delamination in fatigue tests of adhesively bonded single-lap joints (SLJs) modified with MWCNTs through in situ

EP

measurement of the electrical resistance perturbation of the joints. Kang et al. [4] showed that incorporation of 2wt% of carbon nanotubes into the adhesive of composite to aluminum SLJ leads to improving the fatigue strength and

AC C

decreasing the static strength of the joint. Mactabi et al. [3] showed that the average electrical resistances of modified adhesive aluminum joints with 0.5 wt.%, 1 wt.% and 2 wt.% of MWCNTs were decreased by 7, 8 and 10 orders of magnitude than that of the neat epoxy joint. The safe fatigue life zone, waning zone and failure zone were effectively detected using the developed technique. Their results also showed a high scatter in the static as well as fatigue life data of SLJ. Therefore, they cannot conclude any improvement to the static shear strengths as well as fatigue lives of the nano-modified SLJs. Therefore, one of the important goals of the present work is to develop theoretical model to analysis the scatter in the fatigue life data and predict fatigue lives at different reliability levels.

3

ACCEPTED MANUSCRIPT

The experimental results of fatigue life of composite materials always have a remarkable scatter due to their nonuniformity, inhomogeneity, anisotropic and quasi-brittle nature compared with conventional metallic materials [1820]. Selecting the suitable distribution function to perform the statistical analysis of fatigue life data can play a key

RI PT

role in successful design with composite materials. Weibull distribution has a wide variety of shapes, for example, when the shape parameter (α) = 1 it became two-parameter exponential distribution, Rayleigh distribution is a Weibull distribution with α = 2 and approximating a normal distribution when α = 3.2. Therefore, it has been extensively used by many investigators [18-22] and in the present work to describe the scatter in the fatigue life data

SC

of scarf adhesive joints (SAJs) with different adhesive materials.

Recently Olajide and Arhatari [23] have investigated the fatigue performance of scarf adhesive joints with 3°-taper

M AN U

angle in carbon-fiber reinforced composite adherends under constant amplitude as well as variable amplitude fatigue loads (VAF). They pointed that constant amplitude fatigue was used to produce supporting evidence of the main damage development mechanism in the joint, which is enough to study the effect of fatigue and materials parameters on fatigue life or damage development mechanism. Whereas, variable amplitude fatigue was used to study damage development mechanism and hysteretic heating effect in the joint, which can be experienced during its life time. Until now, there is no research or evidence available to support the science of failure mechanisms in adhesively

TE D

bonded joint under variable fatigue loading [24]. Therefore, special attention should be given to develop new lifeprediction methods that take into account any VAF induced damage acceleration effects. To the best of the authors’ knowledge, enhancing the fatigue performance of bonded scarf joint in CFRE composite

EP

structures via incorporation of MWCNTs, SiC and Al2O3 nanofillers into epoxy has not yet been fully investigated and is the main objective of this work. The optimum weight percentages of MWCNTs, SiC and Al2O3 nanofillers

AC C

were ultrasonically dispersed in Epocast 50-A1/946 epoxy adhesive. The nano-modified adhesives are used to assembly tapered CFRE composite adherends with 5o-scarf angle. The scarf adhesive joints (SAJs) were subjected to uniaxial static tensile and constant amplitude fatigue loading. Statistical and reliability models were applied to investigate the scatter in the fatigue life data and predicting the fatigue lives at different reliability levels. The most important aspects are discussed and future research topics are identified.

4

ACCEPTED MANUSCRIPT

2. EXPERIMENTAL WORK 2.1. Materials 2.2.1. Adherends

RI PT

Carbon fiber reinforced epoxy (CFRE) composite adherends were fabricated using prepreg technique with 25 layer of T300-3k plain woven carbon fiber fabrics (200g/m2) and YPH-120-23A/B epoxy matrix. The laminate dimensions are 500x500x5 mm. The tensile and in-plane shear properties of CFRE composite were determined earlier by

SC

Khashaba et al. [10,11] and presented in Table 1. 2.1.2. Adhesives

M AN U

The used epoxy is bisphenol A diglycidyl ether resin consists of two parts, which are epoxy part-A (Epocast 50-A1 resin) and epoxy part-B (Hardener 946) manufactured by Huntsman Advanced Materials Americas Inc. The epoxy system is an unfilled, solvent-free, easy-to-handle material for the manufacture and repair of composite structures. The mixing ratio is 100g from epoxy part-A: 15g part from epoxy part-B. The viscosity of the epoxy system is 2,400 cP at 25oC. Details of the Epocast 50-A1/946 epoxy, MWCNTs, SiC and Al2O3 nanofillers are indicated in Table 2.

TE D

The epoxy resin was modified with the optimum weight percentages of MWCNTs, SiC and Al2O3. The optimum weight percentages of MWCNTs, SiC and Al2O3 nanofillers are 0.5wt%, 1.5wt% and 1.5wt% as described earlier [12]. The nanofillers were ultrasonically dispersed in the Epocast epoxy using a high intensity Ultrasonic Processor (750 W), Cole–Parmer, Inc., with the following parameters:

EP

• The predetermined wt% of nanofillers is mixed manually in 150 cm3 epoxy part-A by adding them little by little to the epoxy for 5 min. Small diameter (50 mm) of high thermal conductivities aluminum beaker was used to

AC C

maximize the nanofillers/epoxy mixture–probe surface area that exposed to the acoustic waves and accordingly, de-agglomerate the nanofillers owing to the van der Waals attractive interactions. • Full sonication power (750W) was applied to disperse SiC and Al2O3 nanoparticles in epoxy resin for 60 min. To reduce the damage of MWCNTs the sonication amplitude and time were reduced to 50% (375W) and 30 min respectively. • The maximum temperature of the mixture was kept lower than 50oC using temperature probe that fixed at the maid distance between the beaker wall and the sonicator probe (25 mm diameter).

5

ACCEPTED MANUSCRIPT

• Sonication without cooling bath was applied to keep the mixture temperature at 50oC and at which the mixture viscosity is reduced and thus improving the dispersion of nanofillers in epoxy resin. • The sonicated mixture is put in a wide glass beaker to reduce its height and accordingly, increasing the mixture

RI PT

surface area. The beaker is then placed in drying vacuum oven model DZF-6050 at 133 vacuum pressure and 40oC for 1h. Under such conditions (low viscosity and large surface area), the included bubbles were easily removed from the mixture.

Table 3 shows the tensile and in-plane shear properties of the modified epoxy with the optimum weight percentages

SC

of MWCNTs, SiC and Al2O3 nanofillers. 2.2. Preparation of the SAJs

M AN U

Two CFRE composite laminates of 500x500 mm2 were cut to eight panels each of 500x125 mm2. A 5o tapered-scarf angle was machined on the eight panels as shown in Fig. 1a. Two panels were used to fabricate the SAJ for each adhesive type. To avoid contamination from loosely held debris after the machining process, the scarf surfaces of the adherends were cleaned by wiping them with acetone-dampened cloth. To ensure drying of the mating sides of the

ASTM D 2093.

TE D

scarf surfaces, the specimens are left 2h in a clean, dust-free area with bonding surfaces upwards as described by

Two gauge foils were bonded at the tapered panel edges to kept constant adhesive (bondline) thickness of 0.25 mm. Enough adhesive layers were spread onto the mating taper surfaces of two CFRE panels. The panels placed carefully

EP

on each other and pressed between two waxed glass plates. The fabricated bonded panels were held at room temperature (23o± 1C) for 10 days to ensure complete curing of the epoxy. The cured panels (500x250 mm) were cut

AC C

into about 20 specimens with 24 mm width and 250 mm length as shown in Fig. 1b. The tensile properties of the SAJs were determined previously by Khashaba et al. [10,11] and the results are presented in Table 4. 2.3. Fatigue characterization of the SAJs The 5o-SAJs were tested in tension–tension fatigue using an Instron servohydraulic universal testing machine model 8872 (10 kN) at ambient laboratory environment. All the fatigue tests were performed under sinusoidal waveforms, constant load amplitude, frequency of 10 Hz and stress ratio of 0.1 [25-28]. The maximum load during fatigue tests was varied from 5 kN to 7 kN, which approximately equal 35% to 50% of the average ultimate tensile loads of the

6

ACCEPTED MANUSCRIPT

SAJs, Table 4 [10,11]. Therefore, the capacity of the testing machine (10 kN) is sufficient to performing accurate fatigue tests on the fabricated SAJs. Before implementing the fatigue tests, the machine was auto tuned for the specimen stiffness as recommended by the Instron manual. The bond line strains and the degradation of material

RI PT

stiffness were monitored during the fatigue tests using Instron dynamic extensometer Model 2620-604 with 12.5±2.5 mm travel and 50 mm gauge lengths as shown in Fig. 2. The SAJ was loaded via WaveMatrix dynamic fatigue block-loading testing software. To construct the S-N curve, each type of the SAJs was tested at three different stress levels. The fatigue thresholds were determined as the highest load at which no damage is observed for 106 cycles

SC

[29,30]. The fatigue lives of the composites materials often showing considerable scatter even that the specimens are prepared and tested in well controlled environments, Khashaba et al. [18,19]. Therefore, at least seven specimens

2.4. Scanning electron microscopy (SEM)

M AN U

were tested for each stress level. Note, the MWCNT was abbreviated to CNT in the figures legends of section 3.

The fracture surfaces of the notched specimen with 50-mm hole diameter were examined using scanning electron microscope (SEM) model Nova NanoSEM–230. The SEM specimens were cut from the hole edges at x and y-axis and bonded to metallic support using carbon tab. To improve conductivity of the fracture surfaces, the specimens

TE D

were deposited with a thin gold layer of 3 µm using a vacuum evaporator. 3. RESULTS AND DISCUSSIONS 3.1. S-N curves of SAJs

EP

Table 5 shows the experimental results of fatigue life data of the NE, MWCNTs, SiC and Al2O3 SAJs. The experimental results of fatigue lives of SAJs were fitted to two-parameter power equation, which extensively used

AC C

for FRP composite materials [8,9,19,31]. The experimental results of fatigue tests and the power law equations of NE, MWCNT, SiC and Al2O3 SAJs were illustrated in Fig. 3. Based on the fact that the S-N curves of FRP composites are continues to slope downwards even after 108 cycles, the fatigue limits of the different SAJs were calculated by the power law equations at 107 cycles, JIS K 7118. The fatigue lives of the SAJs were calculated at fatigue limit (36 MPa), lower stress level (42 MPa) and higher stress level (57 MPa), Fig. 4. This figure also shows the improvement percentages in the fatigue lives of the developed SAJs with nano-modified adhesives compared to NE-SAJ.

7

ACCEPTED MANUSCRIPT

Although, Da Silva and Campilho [32] reported that the fatigue strength is generally higher for ductile adhesives, which have higher damping energy and more uniform stress distribution the fatigue lives of the developed SAJs with higher stiffness nano-modified epoxies were improved compared to the NE-SAJ as shown in Fig. 4. This result was

RI PT

attributed to the higher improvement in the interfacial bonding and accordingly the interfacial shear resistance of the modified SAJs. The results in Fig. 4 also showed that the maximum improvement in the fatigue lives of MWCNTs, SiC and Al2O3 SAJs were respectively 42%, 133% and 160% at the higher stress level (57 MPa). The improvement percentages in fatigue life data were gradually decreased with decreasing the applied stress level i.e. longer fatigue

SC

lives.

The S-N curve of Al2O3-SAJ has the higher slope (= -0.0648) compared to the -0.0554, -0.0566 and -0.0584 for NE,

M AN U

MWCNTs and SiC SAJs respectively as shown in Fig. 3. Therefore, among the investigated SAJs, the Al2O3-SAJ has the higher improvements in the fatigue life (160%) at the higher stress level (57 MPa), while the calculated fatigue life at fatigue limit of 36 MPa was decreased by 22% compared to NE-SAJ, Fig. 4. The SiC-SAJ has the highest improvement in UTS (41.2%, Table 4) and the fatigue endurance life (52%, Fig. 4) at 36 MPa. When the SAJs with 5°-scarf angle is subjected to a uniaxial load of σ0 the resultant shear stress (τsn) is about 11.5

TE D

times higher than that normal stress (σn) [10,11] as shown in Fig. 1b. For example, the maximum applied load of 7 kN (σmax = 58.33 MPa) result in shear stress of τsn = 5.06 MPa and normal stress of σn = 0.44 MPa. Therefore, the failure of the fatigue test specimens was due to the interlaminar shear stress between the bond-layer and adherends

EP

tapered surfaces.

Based on the visual and SEM examinations of the fractured SAJs, the failure sequence is as follows: interfacial shear

AC C

failure that was initiated at one stiffer adherend root and transversely propagated toward the specimen center as shown in Fig. 5a. The bond layer peel-up the transverse (weft) fibers at the thread ends of each layer of the tapered surface while the longitudinal (warp) fibers at the thread ends had sheared under fatigue loads, Fig. 5b. The cleavage fracture surface of Fig. 5b was due to the peeled weft fibers and the fractured warp fibers. The final fracture of the SAJ was attributed to the fracture of the adhesive layer, which visually observed closed to the adherend tip-ends as shown in Fig. 5a. This behavior was attributed to the lower stiffness of the adherends tip ends [10,11,33] and thus the higher fatigue stress. Because of the MWCNTs are randomly distributed in the epoxy matrix, some of them are normal to the bond layer surface, which can play a key role in increasing the normal and shear resistance of the SAJ

8

ACCEPTED MANUSCRIPT

and accordingly, increasing the fatigue properties compared with neat epoxy-SAJ. Pulled out MWCNTs are clearly observed on the fractured surface of the bond layer as shown in Fig. 5c,d. The main reason for enhancing the fatigue limit of SiC-SAJ (52%) is the strong interfacial bonding as clearly

RI PT

observed form the SEM images of the adhesive layer, Fig. 5e,f. The images evidently showed the strongly adhered nanophased epoxy to the carbon fibers. 3.2. Fatigue stiffness of the SAJs

The cyclic displacements in fatigue tests were measured using Instron dynamic extensometer with 50 mm gauge

SC

length as shown in Fig. 2. The gauge length of the extensometer is centered with the bondline (5 mm/tan (5o) ≈ 57 mm). Fig. 6 shows fatigue displacement vs number of cycles of NE-SAJ under fatigue stress of 60% ultimate tensile

M AN U

strength. The figure showed sharp increases in the displacement for the first few cycles and then gradually increased. The sharp increase of the displacement in the first few cycles was attributed to the period required to achieve the full mean stress and stress amplitude.

To illustrate the nanofillers effect on the stiffness of the SAJs, a natural log fit y = a ln x + b to displacement-N/Nf was presented at different fatigue loads as shown in Fig. 7. The results in this figure showed that for the same N/Nf,

TE D

the displacement was increased with increasing fatigue load. The maximum displacement (lower stiffness) was observed for NE-SAJs while, the maximum stiffness (lower displacement) was observed for SiC-SAJs. These results were attributed to the higher stiffness of SiC/epoxy nanophased matrix compared to NE [12].

EP

Fig. 8 shows the variation of normalized stiffness vs normalized fatigue life of MWCNT/E, SiC/E and Al2O3/E SAJs at maximum stress of 42 MPa (5 kN) as example. This figure shows that the stiffness of the investigated materials

AC C

were sharply decreased after few cycles from the beginning of the fatigue tests, N/Nf = 10-5. At this number of cycles, the mean stress was gradually increased up to 23.1 MPa (2.75 kN), which can interpret the initial sharply increased displacements in Fig. 7. As the normalized number of cycles exceeds 10-5, the stiffness of the SAJs was increased with increasing number of cycles up to about N/Nf = 0.01. This result was attributed to the formation of microcracks in the adhesive phase after a few cycles that result in relieving the local stress concentration owing to higher increases of exothermic reaction temperature during curing process. Some researchers [34-36] reported similar behavior for different FRP composites. Tanimoto and Amijima [34] found that the static strength of GFRP

9

ACCEPTED MANUSCRIPT

after cyclic loading to N/Nf = 0.02 retains original value in spite of many cracks occurring in the specimen. Sturgeon [35] has pointed out that the residual static strength of carbon fiber reinforced plastics subjected to cyclic load to moderate number of cycles is greater than that of virgin material. The results in Fig. 8 also showed that the

RI PT

incorporation of MWCNTs, SiC and Al2O3 nanofillers into epoxy matrix improve the stiffness of the SAJs. As described by Broughton et al. [37] the load-displacement hysteresis loops, Fig. 9, has a lot of information, which include: joint stiffness (dynamic and secant moduli), storage modulus E', loss modulus E'' and loss factor tan δ (= E'/E''), where δ is the phase angle between dynamic load and the dynamic displacement. The storage modulus is

SC

proportional to the maximum energy stored during a loading cycle and represents the stiffness of the joint. The loss modulus is proportional to the energy dissipated (lost) during one loading cycle. The enclosed area by hysteresis loop

M AN U

represents the dissipated energy for each cycle [38]. In the present work, the WaveMatrix software of fatigue tests was programed to record the first 10 cycles, two cycles for multiples of 10 (10-11, 20-21, ….,100-101 cycles), two cycles for multiples of 100, two cycles for multiples of 1000, ……etc. and the last ten cycles. Each complete cycle (hysteresis loops) was represented by 100 points. For example, Fig. 10 shows load-displacement hysteresis loops of NE-SAJ under fatigue stress of 42.3% ultimate tensile strength and number of cycles of 5, 10, 100, 1000, 10000,

TE D

100000 and 654258 (Nf).

The hysteresis loop at few number of cycles (5-cycles) has a larger area, which was supported by the finding of some researchers [36,39]. They attributed this behavior to the damage activity during the initial phase of fatigue loading.

EP

As described before, the formation of microcracks in the adhesive phase after a few cycles result in relieving the local high stress concentration owing to the high exothermic reaction temperature during curing process and

AC C

accordingly, the stiffness of the joint was increased. This is clearly observed in the load-displacement hysteresis loops of Fig. 10 in which the slope (stiffness) was increased from 26.718 kN/mm to 27.474 kN/mm as the number of cycles increased from 5 to 1000 cycles. Decreasing the hysteresis loop area with increasing number of cycles up to 1000 cycles was attributed to stiffening of composites [36]. The results in Fig. 10 also showed that the stiffness of the SAJ was decreased from 27.474 kN/mm to 23.166 kN/mm as the number of cycles increased from 1000 to Nf (= 654,258 cycles). This result was attributed to the damages of the adhesive joint near the overlap edges. These damages consist of interfacial debonding and micro-cracking of the

10

ACCEPTED MANUSCRIPT

adhesive [37]. As damage accumulates the slope of the hysteresis loop (stiffness) is decreased and the hysteresis loop area is increased as shown in Fig. 10 at 654,258 cycles. Figs. 11-13 show respectively, load-displacement hysteresis loops of MECNT/E-SAJ, SiC/E-SAJ and Al2O3/E-SAJ

RI PT

under fatigue load of 6 kN compared to NE-SAJ. The results in these figures showed that the modified SAJs with different types of nanofillers have higher stiffness compared to NE-SAJ. The stiffness of the SAJs decreased with increasing number of cycles due to increasing the damage level. In addition, for the modified SAJs with different nanofillers, the large difference in the strains between nanofiller and matrix leads to interfacial slipping and

SC

developing “stick–slip” motion, which is responsible for energy dissipation in interfacial friction and accordingly,

3.3. Statistical Analysis of Fatigue Life Data

M AN U

decreasing the joint stiffness [40-42].

The fatigue life data of the SAJs in Table 5 showed a remarkable scatter although they have been prepared and tested under identical conditions. This result was attributed to the fact that the SAJs involve several materials (matrix, fiber, adhesive and nano-reinforcements), some of which brittle, anisotropic and inhomogeneous. Mactabi et al. [3] could not conclude any improvement in the static shear strengths as well as fatigue lives of the nano-modified SLJs due to

TE D

the high scatter in the experimental results. Two-parameter Weibull distribution function has been successfully used earlier by Khashaba et al. [18,19] and in the present work to describe the scatter in the fatigue life data of the SAJs. The probability density function f(Nf), probabilities of failure Pf(Nf) and probabilities of survival Ps(Nf) of two-

  

α −1

  N exp −  f   β

AC C

αN f(N f ) =  f β β

EP

parameter Weibull distribution are given as:

  N Pf (N f ) = 1 − exp −  f   β

  

α

  

α

  

(1)

  

  Nf Ps(N f ) = 1 − Pf (N f ) = exp −    β

(2)

    

α

(3)

where β is the scale parameter that locates the life distribution and α is the Weibull shape parameter that has inverse relationship with the scatter in the fatigue lives. The values of α and β can be determined by rewriting Eq. (2) as:

11

ACCEPTED MANUSCRIPT

Ln(N f ) =

 1 1 LnLn  1 − P (N α f f 

  + Ln( β ) ) 

(4)

Eq. (4) represents a straight line in the following form: y = bx + c

(5)

RI PT

where y = Ln(Nf), b = 1/α, c = Ln(β) and x = LnLn[1/(1-Pf(Nf))].

The variables in Eq. (4) are the experimental data of fatigue lives (Nf), which were rearranged in ascending order and the mean rank, Pf(Nf) that was estimated from the following equation:

i n +1

SC

Pf (N f ) =

(6)

M AN U

where “i” is the failure order number and “n” is the total number of samples in each test. The values of α and β were estimated for each stress level of the fatigue life data of NE, MWCNT/E, SiC/E and Al2O3/E SAJs by the least squares curve fitting and the results are illustrated in Table 5.

1  M = β.Γ 1 +   α

2 1   Γ  1 +  − Γ 2 1 +   α  α 1  Γ 1 +   α

(7)

(8)

EP

CV =

TE D

Mean value and coefficient of variation of fatigue life data were calculated respectively using Eqs. (7 and 8) [43].

AC C

where M is the mean and CV is the coefficient of variation (direct measure of the scatter in the fatigue life data) and

Γ is the gamma function. Table 5 shows the calculated values of Mean (M) and coefficient of variation (CV) of the scatter in the fatigue life data of NE, MWCNT/E, SiC/E and Al2O3/E SAJs. The two-parameter Weibull fatigue life distributions were plotted in Figs. 14a and 14b for SiC/E and Al2O3/E SAJs, which have respectively the minimum and maximum scatter in their fatigue life data as shown in Table 5. The Weibull function in these figures were drawn in Weibull probability paper in which the abscissa is Ln(Nf) and the ordinate is LnLn[1/(1-Pf(Nf))] and accordingly, it has a linear relationship (with slope equal to 1/α) in accordance

12

ACCEPTED MANUSCRIPT

with Eq. (5). So, for higher slope (lower value of α) the line will be approximated by a vertical line with minimum variation (scatter) in fatigue life data (on the abscissa) and vice versa for lower value of α. Therefore, the slopes (1/α) of the lines in Figs. 14a and 14b can effectively represent the scatter in the fatigue life data of the SAJs.

RI PT

The results in Table 5 showed that the scatter (CV%) in fatigue lives of NE, MWCNT/E, SiC/E and Al2O3/E SAJs respectively was not uniform at all stress levels. The fatigue life scatter tends to increase for longer fatigue lives (i.e. at lower stress) of NE and MWCNT/E SAJs. On the other hand, the lowest scatter in the fatigue life data of SiC/ESAJ was observed at longer fatigue lives as shown in Fig. 14a. The results in Fig. 14b showed that the highest scatter

SC

in was observed in Al2O3/E-SAJs (CV = 73%) compared to NE, MWCNT/E and SiC/E SAJs, which have CVs% of 44%, 50% and 41% respectively as shown in Table 5. Higher scatter in the fatigue life data will result in increasing

M AN U

the penalty paid to gain certain reliability and confidence levels of safe fatigue life of the SAJs as will be discussed in the next section.

Weibull fatigue life distribution curves are of considerable value to the designer with composite joints because of the probability of failure of the SAJs after a given number of cycles can be predicted directly from Fig. 14. In addition, the fatigue failure life (Nf) of NE, MWCNT/E, SiC/E and Al2O3/E SAJs can be predicted at any probability of failure,

TE D

Pf(Nf), either from the figure or by substituting the values of α and β in Table 5 into Eq. (2). 3.4. Safe fatigue life based on time to first failure (TTFF) concept In the past, the scatter in the experimental results of the automotive structure components was compensated by large

EP

safety factors, which result in high materials (structure) weights, large size components and accordingly, high cost, fuel consumption and low performance. The scatter in the fatigue life data is significant for high performance

AC C

composite aircraft and aerospace applications, where any failure is catastrophic. Therefore, the design criteria should consider the lowest lives in the fatigue life data, not the average, mean or other central values [18]. In addition, the design criteria of the SAJs should not, based on selection stress level to ensure that the joint will never fail but to guarantee that the structure survives its function for a prescribed period of time [19]. The latter design criterion can lead to saving material and increasing the reliability of composite structures. In the present work, safe fatigue life models based on time to first failure (TTFF) concept were developed with the aid of Weibull distribution of the normalized fatigue life data in Table 5. For each stress level, the fatigue lives (Nf)

13

ACCEPTED MANUSCRIPT

were normalized by their scale parameter (β). For each adhesive type the normalized fatigue lives (of the three stress levels) of the SAJs were rearranged in ascending order and the mean rank was calculated using Eq. (6). The normalized fatigue lives are plotted in Weibull probability paper with abscissa equal Ln(Nf/β) and the ordinate equal

RI PT

LnLn[1/(1-Pf(Nf/β))] as shown in Figs. 15a and 15b for SiC/E and Al2O3/E SAJs, which have respectively the lowest and highest scatter in their fatigue lives.

The normalized Weibull shape parameters (αn) and scale parameters (βn) that were estimated from the normalized fatigue life data (Nf/β) of the SAJs with different adhesive materials are illustrated in Table 5. The results in Table 5

SC

showed that the highest overall scatters (i.e. lowest αn) was observed for Al2O3/E-SAJ (αn = 2.19) compared to NE, MWCNT/E and SiC/E SAJs, which have normalized Weibull shape parameters of 3.881, 3.02 and 4.442

M AN U

respectively. These results were agree with the higher slope of SiC/E-SAJs curve (lowest scatter), Fig. 15a, compared to the lower slope of Al2O3/E-SAJ curve (highest scatter), Fig. 15b.

Safe fatigue life ( NR) based on TTFF concept can be estimated as follows [18,19,43]:

βγ βˆ βˆ = = S S M .S N .S R S N .S R

(9)

TE D

NR =

where S is the scatter factor that equal the product of SN, SM and SR. SM is the sample size factor that represents the penalty paid to gain confidence γ from a finite sample size (m). In the

EP

present work m = 2 (the first two lowest fatigue lives) and γ = 0.99. The value of SM was estimated as follows: 1

 1 2  αn SM =  X γ (2m )  2m 

AC C

(10)

where X2γ(2m) is the chi-square distribution of 2m degree of freedom (the value of X2γ(2m) = 13.277 at confidence level γ = 99 % and m = 2, [19,43]). SN is the fleet size factor that depend on the number of samples for each stress level (n). SN can be calculated as follows: −1

 1  αn SN =   n

(11)

14

ACCEPTED MANUSCRIPT

SR is the reliability factor that illustrate the penalty paid to gain certain reliability level (R) in the fleet (of SAJ with specific adhesive). SR can be calculated as follows: −1

  1   αn S R =  Ln     R 

RI PT

(12)

β^ and βγ are the characteristic and the lower bound lives respectively. The values of β^ and βγ can be estimated as:

βˆ SM

M AN U

βγ =

1

 αn     

SC

 m αn  ∑ N fi ˆβ =  i =1  m  

(13)

(14)

In this work, safe fatigue lives (NR) of SAJs were estimated at two reliability levels (R). The first R value is 0.368, which is the probability that the joint will survival the characteristic life or large (Nf = β). This reliability levels (0.368) can be estimated from Eq. (3) by substituting Nf = β. Hence, the value of Ps(Nf) = R = exp(-1) = 0.368; in

reliability level.

TE D

such case SR = 1. The second value of R is 0.99, which was used to predict the fatigue lives of the SAJs at very high

The developed reliability analysis models were used to predict the safe fatigue lives of NE, MWCNT/E, SiC/E and Al2O3/E SAJs at 0.99 confidence level and 0.368 and 0.99 reliability levels as shown in Figs. 16-19 respectively. In

EP

addition, the mean, characteristic and lower bond fatigue lives were presented in these figures. The penalties paid to gain safe fatigue life of SAJs are essential for aerospace applications, where any failure is catastrophic. Fig. 20 shows

AC C

a comparison between the penalties that were paid to gain safe fatigue lives of NE, MWCNT/E, SiC/E and Al2O3/E SAJs at 42 MPa stress level. The penalty percentages in this figure were calculated at 0.368 and 0.99 reliability levels as follows:

Penalty percentage =

 NR − N f   x100   N  f  

(15)

where NR is the safe fatigue life and Nf is the mean fatigue life. The values of NR and Nf of NE, MWCNT/E, SiC/E and Al2O3/E SAJs were determined from Figs. 16-19 respectively at 42 MPa stress level.

15

ACCEPTED MANUSCRIPT

The results in Fig. 20 showed that the penalties paid to gain safe fatigue lives of NE, MWCNT/E, SiC/E and Al2O3/E SAJs were 68%, 84%, 56% and 96% respectively at reliability level of 0.368. The highest penalty paid is for Al2O3/E-SAJs which has highest normalized coefficient of variation of 48% (scatter) compared to 29%, 36% and

RI PT

25% respectively for NE, MWCNT/E and SiC/E SAJs as shown in Table 5. On the other hand, the lowest penalty paid to gain safe fatigue life was observed for SiC/E-SAJ at 0.368 and 0.99 reliability levels, which has the lowest normalized coefficient of variation (25%, approximately half CV% of Al2O3/E-SAJs) compared to the other SAJs as shown in Table 5. The developed models for predicting safe fatigue

SC

life of SAJs are of considerable value to the designer with SAJs in aerospace composite structures, where the stress level can be selected based on that the structure will survival performing their functions for prescribed period of time

M AN U

as shown in the S-N curves of Figs. 16-19.

4. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH

The performance of scarf adhesive joints (SAJs) modified with optimum weight percentages of MWCNTs, SiC and Al2O3 nanofillers was studied under static and fatigue loading. From the experimental results and reliability analysis of fatigue life data of the SAJs the following concluding remarks were drawn:

TE D

• The maximum improvement in the fatigue lives of MWCNT/E, SiC/E and Al2O3/E SAJs were respectively 42%, 133% and 160% at the maximum stress level (57 MPa). The improvement percentages in fatigue life data were gradually decreased with decreasing the applied stress level (i.e., longer fatigue life). The SiC/E-SAJ has

EP

the highest improvement in fatigue endurance life (52%) at 36 MPa. The load-displacement hysteresis loops of the modified SAJs with different types of nanofillers showed higher stiffness compared to NE-SAJ. The

AC C

stiffness of the SAJs was increased with increasing number of cycles up to about N/Nf = 0.01. This result was attributed to the formation of microcracks in the adhesive phase after a few cycles that are relieving the local high stress concentration owing to the exothermic reaction temperature during curing process. Further increase in the number of cycles increases the damage level and thus the slope of the hysteresis loop (stiffness) decreased and the hysteresis loop area was increased. • The two parameter of Weibull distribution function was used to analysis the scatter in fatigue life data of the SAJs. The statistical results showed that the scatter in fatigue lives of NE, MWCNT/E, SiC/E and Al2O3/E SAJs

16

ACCEPTED MANUSCRIPT

is not uniform at all stress levels. The highest scatter was observed in Al2O3/E-SAJs compared to NE, MWCNT/E and SiC/E SAJs. The developed reliability analysis models were used to predict mean, characteristic and lower bond fatigue lives as well as safe fatigue lives of NE, MWCNT/E, SiC/E and Al2O3/E

RI PT

SAJs at 0.368 and 0.99 reliability levels. The penalties paid to gain safe fatigue life of SAJs are essential for aerospace applications, where any failure is catastrophic. The highest penalty paid is for Al2O3-SAJs which has highest normalized coefficient of variation of 48% compared to 29%, 36% and 25% respectively for NE, MWCNT/E and SiC/E SAJs. The developed models for predicting safe fatigue life of SAJs are of considerable

SC

value to the designer with SAJs in aerospace composite structures, where the stress level can be selected based on that the structure will survival performing their functions for prescribed period of time. This design criterion can lead to saving material and increasing the reliability of composite structures.

M AN U

• Most of the bonded joints in structural applications are subjected to different thermal stresses that can be ranged from +50C to -70C. The first temperature level (+50°C) represents the summer midday temperature of some countries such as Mexico, Kuwait and Qatar, while -70°C can simulate the skin temperature of an aircraft in flight. Fatigue performance of SAJs with and without CNTs under different cyclic thermal fatigue loads is a quite new topic that has not yet been reported and is the subject of the following paper. In addition, most of the

TE D

bonded joints in structural applications are subjected to variable amplitude fatigue (VAF) and thus, special attention should be given to develop new life-prediction methods that take into account any VAF induced damage acceleration effects.

EP

Acknowledgements: This work was funded by King Abdulaziz City for Science and Technology (KACST), Riyadh, Saudi Arabia under grant DRP-5-3. The authors, therefore, gratefully appreciated to KACST for providing technical

AC C

and financial support. REFERENCES 1.

Jakubinek MB, Ashrafi B, Zhang Y, Martinez-Rubi Y, Kingston CT, Johnston A, Simard B. Single-walled carbon nanotube–epoxy composites for structural and conductive aerospace adhesives. Compos Part B-Eng 2015;69: 87–93

2.

Meguid SA, Sun Y. On the tensile and shear strength of nano-reinforced composite interfaces. Mater and Design 2004;25:289–296

17

ACCEPTED MANUSCRIPT

3.

Mactabi R, Rosca ID, Hoa SV. Monitoring the integrity of adhesive joints during fatigue loading using carbon nanotubes. Compos Sci Technol 2013;78:1–9

4.

Kang M-H, Choi J-H, Kweon J-H. Fatigue life evaluation and crack detection of the adhesive joint with carbon

5.

RI PT

nanotubes. Compos Struct 2014;108:417–422 Gkikas G, Sioulas D, Lekatou A, Barkoula NM, Paipetis AS. Enhanced bonded aircraft repair using nanomodified adhesives. Mater and Design 2012;41:394–402 6.

Korayem AH, Li CY, Zhang QH, Zhao XL, Duan WH. Effect of carbon nanotube modified epoxy adhesive on

7.

SC

CFRP-to-steel interface. Compos Part B-Eng 2015;79: 95–104

Korayem AH, Chen SJ, Zhang QH, Li CY, Zhao XL, Duan WH. Failure of CFRP-to-steel double strap joint

M AN U

bonded using carbon nanotubes modified epoxy adhesive at moderately elevated temperatures. Compos Part BEng 2016;94: 95–101 8.

Loos MR, Yang J, Feke DL, Manas-Zloczower I, Unal S, Younes U. Enhancement of fatigue life of polyurethane composites containing carbon nanotubes. Compos Part B-Eng 2013;44:740–744

9.

Jen Y-M, Wang Y-C. Stress concentration effect on the fatigue properties of carbon nanotube/epoxy composites. Compos Part B-Eng 2012;43:1687–1694

TE D

10. Khashaba UA, Aljinaidi AA, Hamed MA. Analysis of Adhesively Bonded CFRE Composite Scarf Joints Modified with MWCNTs. Compos Part A–Appl S 2015;71:59–71. 11. Khashaba UA, Aljinaidi AA, Hamed MA. Development of CFRE composite scarf adhesive joints with SiC and

EP

Al2O3 nanoparticle. Compos Struct 2015;128: 415–427. 12. Khashaba UA, Aljinaidi AA, Hamed MA. Nanofillers modification of Epocast 50-A1/946 epoxy for bonded

AC C

joints. Chin J Aeronaut 2014;27(5):1288–1300. 13. Jen Y-M. Fatigue life evaluation of adhesively bonded scarf joints. Int J Fatigue 2012;36:30–39. 14. Baldan A. Adhesion phenomena in bonded joints. Int J Adhes Adhes 2012;38:95–116 15. Hayes-Griss JM, Gunnion AJ, Khatibi AA. Damage tolerance investigation of high-performance scarf joints with bondline flaws under various environmental, geometrical and support conditions. Compos Part A–Appl S 2016;84:246–255 16. Niedernhuber M, Holtmannspötter J, Ehrlich I. Fiber-oriented repair geometries for composite materials. Compos Part B-Eng 2016;94:327–337

18

ACCEPTED MANUSCRIPT

17. Kwon YW. Strength of composite scarf joints. In: Brahim Attaf , Editor. Advances in Composite Materials Ecodesign and Analysis, ISBN 978-953-307-150-3, DOI: 10.5772/14320, InTech Open Access Publisher, Inc.; 2011: 467–491.

Rods. Int J Qual Reliab Manage 1996;13(12):88–98.

RI PT

18. Abd-Allah MH, Abdin EM, Selmy AI, Khashaba UA. Reliability Analysis of GFRP Pultruded Composite

19. Khashaba UA, Sebaey TA, Alnefaie KA. Failure and reliability analysis of pinned-joints composite laminates: Effects of stacking sequences. Compos Part B-Eng 2013;45:1694–1703

point flexural fatigue. Compos Part B-Eng 2016;91: 539-547

SC

20. Rajaneesh A, Satrio W, Chai GB, Sridhar I. Long-term life prediction of woven CFRP laminates under three

M AN U

21. El-Assal AM, Khashaba UA. Fatigue Analysis of Unidirectional GFRP Composites under Combined Bending and Torsional Loads. J Compos Struct 2007;79:599–605.

22. Nixon-Pearson OJ, Hallett SR. An experimental investigation into quasi-static and fatigue damage development in bolted-hole specimens. Compos Part B-Eng 2015;77: 462-473

23. Olajide SO, Arhatari BD. Progress on interacting fatigue, creep & hysteretic heating in polymer adhesively bonded composite joints. Int J Fatigue 2017;98:68–80

Fatigue 2017;96:224–236

TE D

24. Olajide SO. Progress on investigation on damage analysis in bonded polymer composites under fatigue. Int J

25. Fu M, Mallick PK. Fatigue of hybrid (adhesive/bolted) joints in SRIM composites. J Adhes Adhes

EP

2001;21:145–159.

26. Zhang Y, Vassilopoulos AP, Keller T. Stiffness degradation and life prediction of adhesively-bonded joints for

AC C

fiber reinforced polymer composites. Int J Fatigue 2008;30:1813–1820. 27. Xiong JJ, Shenoi RA. Integrated experimental screening of bonded composites patch repair schemes to notched aluminum-alloy panels based on static and fatigue strength concepts. Compos Struct 2008;83:266–272. 28. Azari S, Jhin G, Papini M, Spelt J.K. Fatigue threshold and crack growth rate of adhesively bonded joints as a function of load/displacement ratio. Compos Part A–Appl S 2014;57:59–66. 29. Ashcroft IA, Abdel Wahab MM, Crocombe AD, Hughes DJ, Shaw SJ. The effect of environment on the fatigue of bonded composite joints. Part 1: testing and fractography. Compos Part A–Appl S 2001;32:45–58

19

ACCEPTED MANUSCRIPT

30. Abdel Wahab MM, Ashcroft IA, Crocombe AD, Hughes DJ, Shaw SJ. The effect of environment on the fatigue of bonded composite joints. Part 2: fatigue threshold prediction. Compos Part A–Appl S 2001;32:59–69 31. Khashaba UA, Selmy AI, El-Sonbaty IA, Megahed M. Behavior of notched and unnotched [0/±30/±60/90]s

RI PT

GFR/Epoxy Composites under static and fatigue loads. J. Compos Struct 2007;81:606–613. 32. Da Silva LFM, Campilho RDSG. Design of adhesively-bonded composite joints. in: Vassilopoulos AP. Fatigue and Fracture of Adhesively-bonded Composite Joints. Ch2, ISBN: 9780857098061, 2015; 1st Ed:43-71. 33. Gunnion AJ, Herszberg I. Parametric study of scarf joints in composite structures. J Compos Struct

SC

2006;75:364–76.

34. Tanimoto T, Amijima S. Progressive nature of fatigue damage of glass fiber reinforced plastics. J. Compos.

M AN U

Mater. 1975; 9:380–390

35. Sturgeon J B. Fatigue and creep testing of unidirectional carbon fiber reinforced plastics. In Proceedings of the 28th Annual Technical Conference. The Society of the Plastic Industry. Inc., 1973. pp. 12–13. 36. Towo AN, Ansell MP. Fatigue of sisal fibre reinforced composites: Constant-life diagrams and hysteresis loop capture. Compos Sci Technol 2008;68: 915–924

37. Broughton WR, Mera RD, Hinopoulos G. Cyclic fatigue testing of adhesive joints test method assessment. NPL

TE D

Report CMMT(A) 191, Project PAJ3 - Combined Cyclic Loading and Hostile Environments 1996–1999. 38. Idriss M, El Mahi A, Assarar M, El Guerjouma R. Damping analysis in cyclic fatigue loading of sandwich beams with debonding. Compos Part B-Eng 2013;44:597–603

522:18–23

EP

39. Fantozzi G, Reynaud P. Mechanical hysteresis in ceramic matrix composites. Mat Sci Eng A-Struct 2009;521–

AC C

40. Yang A, Mall S. Cohesive-Shear-Lag Model for Cycling Stress–Strain Behavior of Unidirectional Ceramic Matrix Composites. Int J Damage Mech 2003;12:45–64. 41. Khashaba UA. Development and characterization of high performance nano-hybrid GFRE composites for structural applications. Compos Struct 2014;116:523–534. 42. Alnefaie KA, Aldousari SA, Khashaba UA. New development of self–damping MWCNT composites. Compos Part A–Appl S 2013;52:1–11. 43. Khashaba UA. Fatigue and reliability analysis of unidirectional GFRP composites under rotating bending loads. J. Compos Mater 2003;37:317-331.

20

ACCEPTED MANUSCRIPT

Table 1. Tensile, shear and compressive properties of CFRE composites [10,11] In-plane shear properties

σt (MPa)

Strength

Modulus Et (GPa)

Poisson’s ratio

895.28

81.66

0.052

Strength τ (MPa) 145.41

6.94

SC

Table 2. Details of the used materials

Modulus G (GPa)

RI PT

Tensile Properties

Materials

Details

M AN U

Viscosity: 2400 cP at 25°C. Gel time: 20 min at 25°C. Mix ratio: parts by weight (Part A:Part B) is 100:15 Curing: 50-A1 resin/Hardener 946 system post cured at 77-93°C for two hours or five days at 25°C after room temperature gel. • Handling and machining may be done after 8-16 hours at room temperature. Epocast 50-A1 Resin was manufactured by Huntsman Advanced Materials Americas Inc. • Outer diameter < 8 nm • Inner diameter 2-5 nm • Length ≈ 30 µm Purity > 95 wt% Density = 2.1 g/cm3 Manufactured by Timesnano, Chengdu Organic Chemicals Co. Ltd, Chinese Academy of Sciences. • Spherical with outer diameter = 20 nm. • Purity > 99.9 wt%. Manufactured by Timesnano, Chengdu Organic Chemicals Co. Ltd, Chinese Academy of Sciences. • Spherical with outer diameter = 15 nm • Purity > 99.9 wt% Manufactured by Timesnano, Chengdu Organic Chemicals Co. Ltd, Chinese Academy of Sciences.

TE D

Epocast 50-A1 Resin (epoxy part-A) and Hardener 946 (epoxy Part-B)

• • • •

EP

Non-functionalized Multi-Walled Carbon Nanotubes (MWCNTs)

AC C

SiC nanoparticles

Al2O3 nanoparticles

28

ACCEPTED MANUSCRIPT

Table 3. Mechanical properties of the used adhesives [12] Neat and modified epoxy adhesives Neat epoxy

1.5 wt% Gain/ SiC Loss %

1.5 wt% Gain/ AL2O3 Loss %

Tensile strength (MPa)

75.53

81.21

7.5

78.55

4.0

75.88

0.5

Tensile modulus (GPa)

3.43

4.06

18.4

4.11

19.8

3.68

7.3

Poisson’s ratio

0.32

0.313

-2.2

0.318

-0.6

0.314

-1.9

Shear strength (MPa)

50.71

53.51

5.5

53.21

4.9

53.91

6.3

Shear modulus (GPa)

1.45

1.60

10.3

1.68

15.9

1.57

8.3

SC

0.5 wt% Gain/ MWCNTs Loss %

RI PT

Properties

Table 4. Mechanical properties of the SAJs with different adhesives UTS (MPa)

NE-SAJ [10,11] MWCNT/E-SAJ [10] SiC/E-SAJ [11] Al2O3/E-SAJ [11]

Gain/Loss %

Strain at UTS (x10-3)

23.5 41.2 22.5

1.44 1.755 1.913 1.828

Overall modulus (GPa) 54.352 58.869 56.912 55.942

Gain/Loss %

M AN U

SAJs with different adhesives

99.67 123.05 140.75 122.11

21.9 39.8 26.9

Gain/ Loss % 8.3 4.7 2.9

Table 5. Number of cycles to failure and statistical analysis of SAJs at different stress levels MWCNT/E-SAJ

42.246 50.238 59.434 227234 18907

592

289522 20665

866

320153 22424

916

497000 23757

953

TE D

Nf

NE-SAJ

Al2O3/E-SAJ

44.951

49.831

53.280

42.751

48.177

56.658

42.751

50.609

57.017

17814

6241

419348

83519

3027

248334

11413

4451

112879

25032

9105

466665

112795

3511

252556

19793

5017

150972

28277

11562

518615

116532

4996

312854

41578

5640

179952

30504

12964

531329

114675

5195

334346

45468

5753

33029

14154

601582

120700

6195

420311

50352

6535

15270 23758

650437

135228

7019

521734

60233

7122

702185

139832

8248

837674

89443

8442

2.299

5.219

6.013

2.648

2.367

1.382

4.470

543261 25246

1045

566369 29452

1141

188105 248614

654258 31543

1324

395431

35007 35429

2.416 5.267 α 505220 26512 β 447925 24416 M 44 22 CV% 3.881 αn 0.9956 βn 29 CVn %

3.826

2.125

4.037

AC C

SiC/E-SAJ

101295

EP

SAJs σmax

1078

223307

32221

15196

600343

125880

6193

468387

53778

6692

975

197770

29220

13462

552580

116796

5504

415116

49119

6105

29

50

28

46

22

19

41

45

73

25

3.020

4.442

2.190

0.9904

1.0049

1.0012

36

25

48

29

ACCEPTED MANUSCRIPT

(a) 500 Scarf angle

A Two 0.25 mm thickness gage foils

RI PT

125 0.25 mm gage foils

Stiffness reduction toward the tip-end

Section A-A

A 250

SC

24

(b) 5

σn = σ0 sin2 θ

θ = 5o

σ0

σ0

M AN U

τsn = σ0 sinθ cosθ

Fig. 1. Dimensions of machined adherend and SiC-SAJ: (a) 500x125 mm CFRE adherend panel and (b) top and side views of assembled 250x24 mm SiC-SAJ with 5o scarf angle.

Extensometer gauge length.

TE D

Test specimen

Loading head

AC C

EP

Extensometer Model 2620-604.

Wave matrix fatigue software

Instron universal testing machine model 8872 (10 kN) Fig. 2. Experimental setup of Instron servohydraulic universal testing machine model 8872 (10 kN) for fatigue testing of the structural bonded joint specimens.

19

ACCEPTED MANUSCRIPT

70

NE-SAJ: σmax = 87.1(Nf)-0.0554 CNT-SAJ: σmax= 89.652(Nf)-0.0566 Al2O3-SAJ: σmax = 99.584(Nf)-0.0648

RI PT

σe at 107 cycles, JIS K 7118

50

40

30 104 105 Cycles to failure, Nf

106

107

M AN U

103

SC

Maximum stress, σmax (MPa)

SiC-SAJ: σmax = 93.626(Nf)-0.0584

60

TE D

Fig. 3. S-N curves of SAJs modified with different nanofillers. (σe is the fatigue limit at 107 cycles).

17%

75%

26%

52%

19%

106

4

160%

10

133%

105

42%

AC C

NE-SAJ CNT-SAT SiC-SAJ Al2O3-SAJ

-22%

10

7

EP

Nf of two-parameter power equations

108

103 102 36 42 57 Maximum stress, σmax (MPa)

Fig. 4. Gain/loss in fatigue lives at fatigue limit (36 MPa), lower stress level (42 MPa) and higher stress level (57 MPa).

20

ACCEPTED MANUSCRIPT

Weft fibers

RI PT

Fracture of warp fibers

Peeling of the Weft fibers

Warp fibers (b) Al2O3-SAJ

SC

(a) MWCNT-SAJ

M AN U

Pull-out MWCNTs

(d) MWCNT-SAJ

AC C

EP

(c) MWCNT-SAJ

TE D

MWCNTs

(e) SiC-SAJ

(f) SiC-SAJ

Fig. 5. (a) Photograph of the fractured surface of SAJ. (b) to (f) are SEM images for different SAJs and magnifications.

21

RI PT

ACCEPTED MANUSCRIPT

Fig. 6. Displacement vs number of cycles of NE-SAJ under fatigue stress of 60% ultimate tensile strength

SC

(a) 5 kN NE-SAJ CNT-SAJ SiC-SAJ Al2O3-SAJ

0.13

Displacement (mm)

M AN U

0.13 Displacement (mm)

(b)

0.15

0.15

0.11

0.09

0.11

0.09

6 kN NE-SAJ CNT-SAJ SiC-SAJ Al2O3-SAJ

0.07

0.05 0

TE D

0.07

0.2 0.4 0.6 0.8 Normalized number of cycles (N/Nf)

0

1

0.2 0.4 0.6 0.8 Normalized number of cycles (N/Nf)

(c)

EP

0.15

0.05

AC C

Displacement (mm)

0.13

0.11

0.09 7kN NE-SAJ CNT-SAJ SiC-SAJ Al2O3-SAJ

0.07

0.05 0

0.2 0.4 0.6 0.8 Normalized number of cycles (N/Nf)

1

Fig. 7. Displacement vs N/Nf of SAJs with different adhesives under fatigue loads of: (a) 5 kN, (b) 6 kN and (c) 7 kN.

22

1

ACCEPTED MANUSCRIPT

Load, P

1

RI PT

Normalized stiffness

1.05

0.95 E/Eo at 40% UTS NE-SAJ CNT-SAJ SiC-SAJ Al2O3s-SAJ

Displacement, d

10

-6

-5

10

10

-4

-3

-2

10

10

10

-1

SC

0.9 0

10

Normalized fatigue life (N/Nf)

Fig. 9. Schematic of load-displacement hysteresis loop, “A” denotes the amplitude of the load and displacement.

M AN U

Fig. 8. Normalized stiffness vs normalized fatigue life of MWCNT, SiC and Al2O3 SAJs at 42 MPa.

6

Y = 26.718 X + 1.743

TE D

5

3

EP

Load (kN)

4

2

AC C

1

0

0.05

0.1

NE-SAJ at 5kN (42.3% UTS), Nf = 916 cycles Cycle# 5, Stiffness = 26.718 kN/mm Cycle# 10, Stiffness =26.971 kN/mm Cycle# 100, Stiffness = 27.252 kN/mm Cycle# 1000, Stiffness = 27.474 kN/mm Cycle# 10000, Stiffness = 27.259 kN/mm Cycle# 100000, Stiffness = 27.014 kN/mm Cycle# 566369, Stiffness = 23.166 kN/mm

0.15 Displacement (mm)

0.2

0.25

Fig. 10. Load-displacement hysteresis loops of NE-SAJ under fatigue load of 42.6% ultimate tensile strength.

23

0.3

ACCEPTED MANUSCRIPT

6

5

RI PT

3

SAJs at 6kN Cycle# 10, NE-SAJ Cycle# 10,000 NE-SAJ Nf, NE-SAJ Cycle# 10 CNT-SAJ Cycle# 10,000 CNT-SAJ Nf, CNT-SAJ

2

1

0.05

0.1

0.15 Displacement (mm)

0.2

0.25

M AN U

0

SC

Load (kN)

4

0.3

TE D

Fig. 11. Comparison between load-displacement hysteresis loops of NE and MWCNT-SAJs under fatigue load of 6 kN.

6

5

EP

3

2

AC C

Load (kN)

4

SAJs at 6kN Cycle# 10, NE-SAJ Cycle# 10,000 NE-SAJ Nf, NE-SAJ Cycle# 10 SiC-SAJ Cycle# 10,000 SiC-SAJ Nf, SiC-SAJ

1

0

0.05

0.1

0.15 Displacement (mm)

0.2

0.25

0.3

Fig. 12. Comparison between load-displacement hysteresis loops of NE and SiC-SAJs under fatigue load of 6 kN.

24

ACCEPTED MANUSCRIPT

6

RI PT

5

Load (kN)

4

3

SAJs at 6kN Cycle# 10, NE-SAJ Cycle# 10,000 NE-SAJ Nf, NE-SAJ Cycle# 10 Al2O3-SAJ Cycle# 10,000 Al2O3-SAJ Nf, Al2O3-SAJ

SC

2

0

0.05

M AN U

1

0.1

0.15 Displacement (mm)

0.2

0.25

0.3

0.9 0.8 0.7 0.6 0.5 0.4 0.3

0.2 0.1 0.05

1.0

0.2 0.1

0.1 Al2O3-SAJ

σmax = 48.177 MPa

0.0

σmax = 50.609 MPa

σmax = 42.751 MPa

2

10

3

4

0.05

σmax = 57.017 MPa

5

10 10 10 Cycles to failure, Nf

10

σmax = 42.751 MPa

0.0

0.01

2

6

10

3

4

10 10 10 Cycles to failure, Nf

Fig. 14. Weibull fatigue life distributions of: (a) SiC-SAJ and (b) Al2O3-SAJ.

25

0.01 5

10

6

Probability of failure %

SiC-SAJ σmax = 56.658 MPa

0.99

0.9 0.8 0.7 0.6 0.5 0.4 0.3

LnLn[1/(1-Pf(Nf)]

EP

0.1

AC C

LnLn[1/(1-Pf(Nf)]

1.0

(b)

0.99

Probability of failure %

(a)

TE D

Fig. 13. Comparison between load-displacement hysteresis loops of NE and Al2O3-SAJs under fatigue load of 6 kN.

ACCEPTED MANUSCRIPT

(a)

(b) 0.99

0.1

0.1

0.05

0.1

0.0

0.01 0.2

0.4

0.6

0.2 0.1 0.05

Pf(Nf/β)=1-exp[-[(Νf/β)/1.001]2.1897]

0.0

SC

Pf(Nf/β)=1-exp[-[(Νf/β)/1.005]4.442]

0.9 0.8 0.7 0.6 0.5 0.4 0.3

Probability of failure %

0.2

1.0

RI PT

1.0

LnLn[1/(1-Pf(Nf/β)]

0.9 0.8 0.7 0.6 0.5 0.4 0.3

Probability of failure %

LnLn[1/(1-Pf(Nf/β)]

0.99 Νf/β of Al2O3-SAJ

Νf/β of SiC-SAJ

0.8

2.0

0.2

1.0 Normalized cycles to failure, Ln(Ν/β)

0.4

0.6

0.01 0.8

2.0

1.0

Normalized cycles to failure, Ln(Ν/β)

60

EP

50

40

30

20

NE-SAJ Mean fatigue life Characteristic life Lower bound life Safe life, R = 0.368 Safe life, R = 0.99

AC C

Maximum stress, σmax (MPa)

70

2

10

3

10

4

70

Maximum stress, σmax (MPa)

TE D

M AN U

Fig. 15. Weibull normalized fatigue life distribution of: (a) SiC-SAJ and (b) Al2O3-SAJ.

60

50

40

CNT-SAJ Mean fatigue life Characteristic life Lower bound life Safe life, R = 0.368 Safe life, R = 0.99

30

20 5

10 10 Cycles to failure, Nf

6

2

10

10

10

3

4

5

10 10 Cycles to failure, Nf

6

10

Fig. 17. Prediction of fatigue life of MWCNT-SAJ at different reliability levels.

Fig. 16. Prediction of fatigue life of NE-SAJ at different reliability levels.

26

70

60

60

50

40 SiC-SAJ Mean fatigue life Characteristic life Lower bound life Safe life, R = 0.368 Safe life, R = 0.99

30

50

RI PT

Maximum stress, σmax (MPa)

70

40

Al2O3-SAJ Mean fatigue life Characteristic life Lower bound life Safe life, R = 0.368 Safe life, R = 0.99

30

20 102

6

10 10 Cycles to failure, Nf

10

Fig. 18. Prediction of fatigue life of SiC-SAJ at different reliability levels.

96%

M AN U 84%

σmax= 42 MPa

56%

60

68%

80

EP

40

20

0 0.368

0.99 Reliability level

NE-SAJ

105

106

Fig. 19. Prediction of fatigue life of Al2O3-SAJ at different reliability levels.

TE D

Penalty paid to gain safe fatigue life (%)

100

103 104 Cycles to failure, Nf

100%

5

86%

10

4

97%

10

3

91%

2

SC

20

AC C

Maximum stress, σmax (MPa)

ACCEPTED MANUSCRIPT

CNT-SAJ

SiC-SAJ

AL2O3-SAJ

Fig. 20. Penalty paid to gain safe fatigue life of SAJs at 42 MPa stress and different reliability levels.

27