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aluminum alloy lap joints using Weibull distribution
Accepted Manuscript Fatigue life assessment of electromagnetic riveted carbon fiber reinforce plastic/ aluminum alloy lap joints using Weibull distribution Hao Jiang, Tong Luo, Guangyao Li, Xu Zhang, Junjia Cui PII: DOI: Reference:
S0142-1123(17)30363-8 http://dx.doi.org/10.1016/j.ijfatigue.2017.08.026 JIJF 4451
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
25 April 2017 16 August 2017 27 August 2017
Please cite this article as: Jiang, H., Luo, T., Li, G., Zhang, X., Cui, J., Fatigue life assessment of electromagnetic riveted carbon fiber reinforce plastic/aluminum alloy lap joints using Weibull distribution, International Journal of Fatigue (2017), doi: http://dx.doi.org/10.1016/j.ijfatigue.2017.08.026
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Fatigue life assessment of electromagnetic riveted Carbon Fiber Reinforce Plastic/Aluminum alloy lap joints using Weibull distribution Hao Jiang1, Tong Luo1, Guangyao Li1, 2, Xu Zhang3, Junjia Cui1, 2* 1 State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China 2 Joint Center for Intelligent New Energy Vehicle, Shanghai, 200092, China 3 College of Mechanical and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, 411100, China ABSTRACT Electromagnetic riveting (EMR) has received increasing attention as a new kind of riveting technique in engineering industry. In this paper, EMR process was used to connect carbon fiber reinforced plastics (CFRP) and aluminum alloy (Al) hybrid joints. The mechanical behaviors (including static and fatigue properties) of the electromagnetic riveted lap joints were comprehensively investigated. The microstructure observation and the mechanical property tests were conducted to evaluate the joints performance. The mechanical test results showed that the failure modes of shear specimens were bending of the Al sheet and damage of the CFRP sheet, which was caused by rivet squeezing effect under static loading. However, the failure mode of fatigue specimens under each stress level was all ruptured at the Al sheet and the fracture analysis showed that cracks firstly initiated around the hole of Al sheet. This was caused by the fretting wear between Al sheet and rivet under cyclic loading. Two-parameter Weibull distribution was employed to analyze statistically fatigue cycles results. The S-N curves were drawn for different reliability levels (10%, 36.8%, 50% and 90%) for engineering applications. In addition, Hysteresis loop analysis implied that the specimens had no obvious flaw after EMR. Keywords: Electromagnetic riveting; Carbon fiber Reinforced Plastics; Weibull distribution; Fatigue behaviors; *
Corresponding author: Tel.:+86 731 88664001 ; Fax:+86 731 88822051 ; Email: [email protected] 1
1. Introduction Lightweight materials such as composites and aluminum alloys have been increasingly applied in engineering applications (e.g. automotive, railway and aerospace fields) due to their light weight and superior mechanical properties. Therefore, the demands of advance joining techniques for dissimilar materials are becoming more apparent, especially metal and nonmetal materials. Due to the great differences of material properties, only mechanical joining methods (e.g. riveting [1] and bolting [2, 3]) and adhesive bonding [4] can be competent for this challenging task. Among them, adhesive bonding process takes longer time (requiring surface preparation and curing) and consumes more energy [5]. Bolting joints are prone to loose and bolting process counts against automated assembly. Conversely, riveting joints are more stable and reliable, as well as riveting process is simple and efficient [6]. Consequently, riveting techniques have been widely used in aircraft fuselage [7], automotive frame [8] and bridge structures [9]. However, composite sheets are liable to damage due to inhomogeneous hole expansion under the conventional riveting process (pneumatic riveting and hydraulic riveting), which would further reduce the joining quality [10]. Compared to conventional riveting process [11], electromagnetic riveting (EMR) is a relatively new riveting technology based on mutually exclusive magnetic pulse force, which has advantages of high-speed loading, larger impact force, deformation stability and uniform hole expansion. Many studies [12-14] have also been conducted experimentally and numerically on the joining strength of the electromagnetic riveted joints. For example, Repetto et al. [12] firstly proposed a finite element mode for electromagnetic riveting which simultaneously took thermal and dynamic effects into account. Reinhal et al. [13] presented a new rivet die, which could produce high quality and crack free riveted joints. Li et al. [14] found that the fatigue properties of EMR joints were about 1-3 times higher than that of regular pressure riveted joints. In addition, adiabatic shear band (ASB) is one of the most significant microstructure deformation behaviors during EMR, which has a direct influence on the microstructure properties of the rivet. For microscopic characteristics, Deng et al. [15] 2
discovered that the twinning deformation was primary grain evolution mechanism inside the ASB of Ti Grade 1 rivet in low voltage electromagnetic riveting. Zhang et al. [16] explored the microstructural evolution of Al-Cu alloy bars using electromagnetic upsetting, and the results showed that dynamic nucleation particles and equiaxed recrystallization grains were generated in ASBs. Note that aforementioned works mainly focused on the metal connection performances. The fatigue strength of joining structures with metal and nonmetal materials recently gained increasing attention in manufacturing industry for guaranteeing safe and reliable applications. However, few studies have been reported on fatigue reliability of EMR joints so far. This paper aimed to investigate fatigue behaviors of electromagnetic riveted lap joints comprehensively. Firstly, microstructures on the joint interface were characterized by metallographic observations. The shear properties under quasi-static loading were tested and the maximum shear loads were obtained to determine fatigue dynamic loads. After that, the fatigue tests were conducted to evaluate fatigue life. The fatigue data were statistically analyzed by using two parameters Weibull distribution, and hysteresis loops of whole fatigue test process were also presented. Finally, the fracture appearances of fatigue specimens were observed. 2. Experimental materials and methods 2.1. Sample preparation In this study, the riveted specimens were constructed by CFRP sheets and 5182 T6 aluminum alloy sheets with 2A10 aluminum alloy rivets. It can be seen from Fig. 1 that 5182 T6 aluminum alloy sheet with size of 140 × 40 mm and thickness of 1.8 mm was placed in the upper, while CFRP sheet with size of 140 × 40 mm and thickness of 2.5 mm was put in the bottom (close to manufactured head). The overlap area was designed as 40 × 40 mm. The riveted holes placed in the center of this area, and its diameter was set to 5.1 mm. Finally, the rivet with diameter of 5.0 mm and length of 11.0 mm was accordingly selected.
3
Fig. 1 Geometry dimensions of the riveted specimens The CFRP sheets were manufactured by Toray T300 unidirectional carbon fiber and epoxy resin (resin content about 40%) using an autoclave. Those laminates were obtained overlaying 17 layers with thickness of 0.15 mm per layer, the laying orientation of which was 0°/90° in this research. The curing cycle were composed of three stages. The first stage heated up to 60° and kept for half an hour. The second stage kept the temperature at 90° for half an hour. The third stage heated up to 130° and kept for about 2 hours. Mechanical properties of Al and CFRP are presented in Table 1 and Table 2, respectively. Table 1 Mechanical properties of 2A10 aluminum alloy rivet and 5182 aluminum alloy sheet Aluminum alloy
Density (g/cm3)
Tensile strength (MPa) 400
Tensile modulus (GPa) 73.8
Poisson ratio
2.7
Yield strength (MPa) 250
2A10 5182
2.8
150
225
70
0.33
0.33
Table 2 Properties of carbon fiber composite laminate Fiber
Fiber
Fiber
Fiber
Tensile
Tensile
Ply
Resin
density
modulus
strength
density
strength
modulus
thickness
content
(g/cm3)
(GPa)
(MPa)
(g/cm3)
(MPa)
(GPa)
(mm)
(%)
1.76
230
3530
1.76
911
76
0.2
40
Considering of both material properties and machining accuracy, Al and CFRP sheets were perforated using different methods. Specifically, Wire Cut Electrical Discharge Machining was used to cut Al sheets. Drilling machine with the spindle 4
speed of 1500 RPM and feed rate of 1.5 mm/min were used to drilling CFRP sheets. In addition, the burrs around holes were removed. 2.2. Electromagnetic riveting The schematic of the electromagnetic riveting process is presented in Fig. 2. It mainly consists of two parts: electromagnetic equipment and riveting die. The electromagnetic equipment is used to provide riveting energy, while the riveting die is used to join the sheets. In detail, Capacitors firstly get charged to a predetermine discharge energy. When closing the switch, the stored energy is discharged through the plate copper coil. This causes the driver plate (copper with high conductivity) further producing reverse eddy current. Consequently, a repulsive magnetic force quickly forms between the coil and driver plate, and accelerates the punch to impact the rivets. Fig. 2 (b) shows the rivet forming process. It can be seen that the rivet driven head is upset like drum shape and locks the two sheets with manufactured head.
Fig. 2 The schematic of electromagnetic riveting: (a) electromagnetic setup; (b) riveting process 5
The EMR experiments were carried out by a PS 48-16 electromagnetic forming (EMF) machine (produced by PST company), as shown in Fig. 3. This machine has maximum discharge energy of 48 kJ and maximum capacitance of 408 μF. Higher discharge energies always lead to larger impact force, so the diameter of the driven head increased and the height of that decreased with the increasing of discharge energies. According to previous studies [17], the dimensions of driven head had significant influence on the mechanical properties. The previous results showed that normalized dimension D/D0 (D is the diameter of rivet driven head and D0 is the diameter of rivet shaft as shown in Fig. 4) of 1.5 was the optimal one. Therefore, after a series of process parameters experiments, discharge energy of 5 kJ was selected for electromagnetic riveting in this paper.
Fig. 3 The diagram of the electromagnetic riveting equipment
Fig. 4 Schematic of rivet driven head dimensions 6
2.3. Mechanical property test and microstructure observations Quasi-static shear and fatigue tests were conducted using Instron 5985 universal testing machine and Instron 8801 Electro-hydraulic servo fatigue machine, respectively. Six quasi-static shear specimens were tested under a loading velocity of 2 mm/min. The fatigue tests were applied under a load of sinusoidal wave shape, a frequency of 20 Hz and a stress ratio (R=minimum stress/maximum stress) of 0.1. The maximum cyclic stresses were determined by certain percentages of the maximum quasi-static shear stress. In this paper, four different maximum cyclic stress levels (55%, 60%, 65% and 70%) were adopted and six fatigue specimens were tested at each maximum stress. Taking the bend of specimens into consideration, the aluminum balance plates which had the same thickness of riveted sheets were assembled during fatigue tests as shown in Fig. 5. To avoid slippage during the tests, the clamping area on the CFRP side was roughen by sandpaper. Besides, the quasi-static shear specimens were gripped through the same way.
Fig. 5 Fatigue test process for CFRP/Al electromagnetic riveted joint The specimens after EMR were firstly split along the axis. After that, the section of specimens was mechanically polished and etched by Keller solution (2.5 ml HNO3, 1.5 ml HCL, 1 ml HF, and 95 ml H2O). Then the solution of 10 ml HNO3 and 40 ml H2O was used to remove corrosion products on the surface of etched specimens. Metallographic characterizations were carried out with a Leica optical microscope. 7
Static and fatigue rupture appearances were characterized with FEI QUANTA 200 Scanning Electron Microscope after cleaning up by ultrasonic cleaning machine. 3. Results and discussion 3.1. Microstructure The microstructural characteristics had greatly influence on fatigue properties of joining joints. In order to gain insight into the performances of CFRP/Al electromagnetic riveted specimens, microstructure observation of the joints was conducted. Fig. 6 shows the section metallographical structure of CFRP/Al electromagnetic joint. It could be seen that the rivet driven head and manufactured head locked the sheets, and the rivet shaft fitted tightly with CFRP and Al sheets. In the Al sheet part, the expansion degree of rivet shaft was relatively larger and Al sheet produced severe plastic deformation in zone 5. Furthermore, according to Manes’s study [18], it easily produced contact stress concentration in this area. This suggested that this part was relatively vulnerable. In the CFRP sheet part, the expansion of the rivet shaft in CFRP sheet was homogeneous. The matrix cracks and delamination in CFRP sheet were not observed. This demonstrated that this part was correspondingly secure and EMR technique was suitable for composite joining. In addition, the symmetric distribution of ASBs was clearly observed and divided the driven head into four zones: small deformation zone (zone 1), mixed deformation zone (zone 2), adiabatic shear band (zone 3) and large deformation zone (zone 4). In the zone 3, it could be found that the width of ASBs was about 100 μm. Moreover, the dynamic plastic deformation behaviors resulted in the grains elongating to threadiness. In the zone 1, the gains had little deformation and nearly kept original size. This was due to the material plastic flow in this zone was restricted by the friction effect between the punch and the driven head [19]. In the zone 2, the microstructure deformation was the most severe, and the grains were obviously distorted and elongated. The phenomenon was caused by the multiple effect of three-dimensional comprehensive stress and shear deformation [19]. In the zone 4, the material could flow toward the horizontal direction. Consequently, the grains in this area only had a certain degree of deformation. In general, although severe microstructure deformation 8
existed in the rivet driven head, no obvious defects were found.
Fig. 6 Microstructure observation in the section of CFRP/Al riveted joint and typical areas 3.2. Shear behaviors Three repeated shear tests for CFRP/Al electromagnetic riveted specimens were conducted under quasi-static loading. Fig. 7 presents the shear load-displacement curves. It could be clearly seen that the repeatability of results was excellent. The maximum shear load of the six specimens was about 5.50 kN and the complete failure location was around 11 mm. In particular, it could be seen that all the curves could be 9
obviously divided into two stages: elastic and plastic stages. At the elastic stage (0-1mm), the curves were linear increase. During this linear process, the shear load was caused by the extrusion pressure between hole wall and rivet as well as friction resistance between CFRP and Al sheets. At the plastic stage (characterized by reduction of curves slope at around 1 mm), it was observed that the shear load first increased to the maximum value at around 5 mm and then decreased. This illustrated the joints became damaged progressively. The phenomenon resulted from bending effect (the asymmetric construction of the riveted lap joint caused the torque) of the sheets in the lapping zone [20]. In this stage, the shear load was only offered by the damage resistance of CFRP and Al sheets.
Shear load (kN)
6 Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6
4
2
0 0
3
6
9
12
Displacement (mm)
Fig. 7 The shear load-displacement curves of CFRP/Al electromagnetic riveted lap specimens Fig. 8 shows the shear failure appearance of CFRP/Al electromagnetic riveted lap joints. This was a typical failure behavior of riveted joints which was referred to as unbuttoning phenomenon [21]: the rivet manufactured head locked CFRP sheet and broke away from Al sheet. In addition, bending of the Al sheet and damage of the CFRP sheet were obviously observed. Specifically, It could be clearly seen that there were two typical failure mechanisms of CFRP sheets: fiber broken and layer separation. The fibers around the hole suffered squeezing of the rivet in the shear test process. Therefore, a number of 0° and 90° fiber layers were separated as well as many carbon fibers were broken. 10
Fig. 8 The shear failure appearance of CFRP/Al electromagnetic riveted lap joints: (a) driven head side; (b) manufactured head side 3.3. Fatigue behaviors 3.3.1. Statistics analysis Two-parameter Weibull distribution function was adopted to analyze statistically fatigue cycles due to the simple function and calculation, accurate failure analysis and suitable for data analysis of small samples [22-24]. The probability density function f(t) and corresponding cumulative distribution function F(t) are expressed as following Eq. (1) and Eq. (2), respectively.
t f (t )
1
t exp
t F (t ) 1 exp
(1)
(2)
where β and η are the shape and scale parameter, respectively; t is the random variable value and represents the fatigue life in this paper. The reliability function R(t) is defined as Eq. (3). 11
t R(t ) exp
(3)
By taking the natural logarithm twice on both sides of Eq. (3), the following Eq. (4) is obtained.
InIn
1 In(t ) In R(t )
(4)
It can be observed that the relationship between InIn[1/R(t)] and In(t) is linear. The substituted reliability Ṙ(t) is calculated by a proliferation function of Eq. (5).
i 0.3 R (t i ) 1 n 0.4
（i=1, 2, …, n）
(5)
where i and n are the failure sequence number and the total number of specimens, respectively. Weibull probability plot can be obtained from fatigue results. The shape parameter β and scale parameter η can be calculated by the linear slope and intercept. Consequently, Weibull mean life (mean time to failure, MTTF), standard deviation (SD) and coefficient of variation (CV) can be calculated from following Eq. (6), Eq. (7) and Eq. (8), respectively. 1 E (T ) t f (t )dt 1 0
2 1 SD(T ) 2 1 2 1
CV
SD(T ) ) E (T )
2 1 2 1 1 1 1
(6)
(7)
(8)
where is Г the gamma function [25]. Table 3 shows the fatigue results of the CFRP/Al electromagnetic riveted specimens under four different maximum cyclic stress levels and corresponding InIn[1/R(t)] and In(t) are also presented. Fig. 9 shows the Weibull probability plot for the specimens under different maximum cyclic stress levels. The value of the shape parameter β and scale parameter η was obtained by linear regression. Furthermore, MTTF values and CV values were obtained from Eq. (6)-(8). The specific Weibull 12
parameters results are shown in Table 4. The relationship between MTTF and CV under four different maximum cyclic stress levels is presented in Fig. 10. CV is a non-dimensional parameter which represents the volatility of the fatigue data under a certain stress level. It could be observed that the CV value under maximum cyclic stress of 185.5 MPa was the highest. This demonstrated that the performance of CFPR/Al electromagnetic riveted specimens under high dynamic loading fluctuated greater than that under low dynamic loading. Table 3 Fatigue test results for CFRP/Al electromagnetic riveted specimens Maximum cyclic stress (MPa)
185.5
172.2
159.0
145.7
Fatigue life (cycles)
InIn[1/R(t)]
In(t)
77519
-2.150
11.26
131610
-1.566
11.79
154120
-0.607
11.95
210111
-0.142
12.26
221531
0.269
12.31
223826
0.792
12.32
287520
-2.150
12.57
361046
-1.566
12.80
364164
-0.607
12.81
371601
-0.142
12.83
420501
0.269
12.95
563409
0.792
13.24
571770
-2.150
13.26
640425
-1.566
13.37
695238
-0.607
13.45
736251
-0.142
13.51
793356
0.269
13.58
804120
0.792
13.60
948968
-2.150
13.76
956202
-1.566
13.77
968595
-0.607
13.78
1256031
-0.142
13.95
1138042
0.269
14.04
1278542
0.792
14.06
13
1.0
185.5 MPa 172.2 MPa 159.0 MPa 145.7 MPa
0.5
In In [R(t)]
0.0 -0.5 -1.0 -1.5 -2.0
y=4.41x-57.22
-2.5 y=2.46x-29.94
y=6.73x-93.95 y=8.04x-108.78
-3.0 11.0
11.5
12.0
12.5
13.0
13.5
14.0
In (t)
Fig. 9 Weibull probability plot for CFRP/Al electromagnetic riveted joints under different maximum cyclic stress levels Table 4 Weibull parameters for four maximum cyclic stress levels Maximum cyclic stress (MPa)
Shape parameter
Scale parameter
η
Mean fatigue life （cycles）
Coefficient of variation
β
185.5 172.2 159.0 145.7
2.46 4.41 8.04 6.73
193055 431515 751518 1155312
171226 393328 707907 1078484
0.8616 0.6346 0.5382 0.5824
SM=185.5 MPa
Coefficient of Variation
0.8
SM=172.2 MPa SM=159.0 MPa
SM=145.7 MPa
0.4
0.0
171226
393328
707907
1078484
Mean fatigue life (cycles)
Fig. 10 The relationship between MTTF and CV under four maximum cyclic stresses Based on the above results of Weibull distribution analysis, the fatigue life of different reliability at a certain stress level can be calculated by Eq. (9). N Rx [ In( Rx )]1 / 14
(9)
where NRx is the fatigue life with x% reliability. In this study, Reliability of 10%, 36.8% (corresponding characteristic life), 50% and 90% were taken into account, respectively. In addition, the fatigue life was fitted by the following power function [26]:
S M a( N f ) b
(10)
where SM and Nf are the maximum cyclic stress and fatigue life, respectively; a and b are constants, which can be obtained using the least square method. Fig. 11 depicts the S-N curves of CFRP/Al electromagnetic riveted specimens under four different reliability levels. These curves could predict the possibility of fatigue life according to the reliability levels, which were desired by the engineering applications. Especially, the S-N curves with higher reliability level (R=90%) were recommended to design the automobile and airplane for higher security. In general, the prospective fatigue cycles are lower for higher security levels [26].
Maximum cyclic stress (MPa)
200
Reliability R=10% R=36.8% R=50% R=90%
190
180
Related formula -0.1503 SM=1227.0Nf -0.1293 SM=904.0Nf -0.1216 SM=809.3Nf -0.0928 SM=533.7Nf
170
160
150
140 0.0
2.0x10
5
4.0x10
5
5
6.0x10 8.0x10
5
1.0x10
6
1.2x10
6
1.4x10
6
Fatigue life
Fig. 11 S-N curves for different reliability levels 3.3.2. Hysteresis loop analysis Fig. 12 shows typical hysteresis loops of CFRP/Al electromagnetic riveted specimen under four different stress levels. It could be observed that the variation law of hysteresis loops was similar under four stress levels. In particular, at the early fatigue test stage, the slope of hysteresis loops had small increases. This implied that the stiffness of the specimens increased at this stage, and the phenomenon was caused by fastener tightening effect and hole wall hardening effect under dynamic loading 15
[27]. At the medium fatigue test stage, it could be observed that the displacement increased with the fatigue cycles, illustrating that the riveted hole gradually expanded by the cyclic loading. At the final fatigue test stage, the slope of hysteresis loops dramatically decreased. This illustrated that the specimens lost the fastener tightening and occurred failure causing by the further hole expansion. In general, the hysteresis loops recorded the state of specimens during the fatigue test process. The specimens exhibited stable performance in the ahead about 90% of the fatigue cycles, while lost stability in the remaining fatigue cycles. This further implied that the specimens had no obvious flaw after EMR and the crack initiation process consumed most of the fatigue cycles. 200
Stress level 102.0 MPa 160
120
100 cycles 1000 cycles 10000 cycles 100000 cycles 150000 cycles 190000 cycles 200000 cycles 210000 cycles
80
40
Cyclic stress (MPa)
Cyclic stress (MPa)
160
0.2
0.3
0.4
120
100 cycles 10000 cycles 100000 cycles 200000 cycles 300000 cycles 350000 cycles 360000 cycles 371000 cycles
80
40
0 0.1
Stress level 94.7 MPa
0
0.5
0.1
0.2
Displacement (mm)
0.3
0.4
0.5
Displacement (mm) 160
160
Stress level 80.2 MPa
Stress level 87.4 MPa
Cyclic stress (MPa)
Cyclic stress (MPa)
120 120
100 cycles 10000 cycles 100000 cycles 300000 cycles 500000 cycles 700000 cycles 750000 cycles 793000 cycles
80
40
0 0.0
0.1
0.2
0.3
100 cycles 10000 cycles 100000 cycles 300000 cycles 500000 cycles 1000000 cycles 1200000 cycles 1255000 cycles
80
40
0.4
0 0.0
0.1
0.2
0.3
0.4
Displacement (mm)
Displacement (mm)
Fig. 12 Typical hysteresis loops of CFRP/Al electromagnetic riveted specimen under four different stress levels 3.3.3. Fracture analysis The failure mode of fatigue specimens under each stress level was all ruptured at the Al sheet. Fig. 13 shows the typical fatigue fracture appearance of CFRP/Al electromagnetic riveted lap joints. It could be seen that there were three typical zones 16
on fracture surface. In the zone 1, the black oxide and microcracks (zone 4) confirmed that this area (around the hole of Al sheet) was crack initiation zone. These characteristics were caused by the fretting wear between Al sheet and rivet under cyclic loading. In the zone 2, the fatigue lines (beach markings) and fatigue striations (zone 5) were observed, demonstrating that this area was fatigue propagation zone. In addition, the crack propagation direction was usually perpendicular to the fatigue lines. Therefore, it could be deduced that the cracks direction was propagated along both width and thickness of the Al sheet. This result was consistent with the previous theoretic description [28]. Because the asymmetry of the riveted lap specimens under shear loading usually sustained a combination effect of bending and axial loading. This would further increase the stress distribution in the width and thickness direction. In the zone 3, the various size tensile dimples (zone 6) were observed, illustrating that this area was fatigue final fracture zone and the failure mode was ductile fracture. Consequently, according to the above analysis, it could be verified that cracks firstly initiated around the hole of Al sheet, then propagated from there to both sides until the one side of Al sheet could not sustain the cyclic loading, and final break occurred. As a whole, the fatigue failure mode was consistent with above microstructure analysis that the hole of Al sheet was the most vulnerable position.
17
Fig. 13 The typical fatigue fracture appearance of CFRP/Al electromagnetic riveted lap joints 4. Conclusion This paper comprehensively investigated the fatigue behavior of CFRP/Al electromagnetic riveted joints to guarantee secure and reliable engineering application. The microstructure observation, quasi-static shear and fatigue experiments were carried out. Based on the above results and discussions, the main conclusions were drawn as following: (1) Joint cross-section microstructure observations showed that the hole in the Al sheet occurred severe plastic deformation, indicating that this area was the most vulnerable. In addition, no obvious microcracks or defects were observed in the CFRP sheet. This demonstrated that EMR technique was suitable for composite joining. (2) The CFRP/Al electromagnetic riveted joints showed stable shear properties. The shear failure mode was bending of the Al sheet and damage of the CFRP sheet. Specifically, the damage mechanisms of CFRP sheets were fiber broken and layer separation. (3) The fatigue data were analyzed statistically by Weibull distribution. The S-N curves for different reliability levels were obtained. The S-N curves with higher reliability level (R=90%) were recommended to design the automobile and airplane for higher security. (4) Hysteresis loop analysis showed that the specimens exhibited stable performance in the ahead about 90% of the fatigue cycles. This further suggested that the joints had no obvious flaw after EMR. (5) The failure mode of fatigue specimens was ruptured at the Al sheet. The 18
fracture analysis demonstrated that cracks firstly initiated around the hole of Al sheet, then propagated from there to both sides until the one side of Al sheet could not bear the cyclic loading, and final break occurred. Acknowledgement This project is supported by National Natural Science Foundation of China (No. 51405149) and the State Key Program of National Natural Science Foundation of China (No. 61232014).
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[19] Zhang X, Li CF. The effect of loading rate on deformation of TA1 titanium alloy bars subjected to electromagnetic heading. Materials Science & Engineering A 2017; 679: 511-519. [20] Calabrese L, Proverbio E, Di Bella G, Galtieri G, Borsellino C. Failure behaviour of SPR joints after salt spray test. Engineering Structures 2015; 82: 33-43. [21] Han L, Thornton M, Shergold M. A comparison of the mechanical behaviour of self-piercing riveted and resistance spot welded aluminium sheets for the automotive industry. Materials and Design 2010; 31: 1457-67. [22] Sakin R, Ay I. Statistical analysis of bending fatigue life data using Weibull distribution in glass-fiber reinforced polyester composites. Materials and Design 2008; 29: 1170-1181. [23] Zhao YX, Liu HB. Weibull modeling of the probabilistic S-N curves for rolling contact fatigue. International Journal of Fatigue 2014; 66: 47-54. [24] Selmy AI, Azab NA, Abd El-baky MA. Flexural fatigue characteristics of two different types of glass fiber/epoxy polymeric composite laminates with statistical analysis. Composites Part B: Engineering 2013; 45: 518-527. [25] Khashaba UA. Fatigue and reliability analysis of unidirectional GFRP composites under rotating bending loads. Journal of Composite Materials 2003; 37: 317-31. [26] Plaine AH, Suhuddin UFH, Alcantara NG, Santos JF. Fatigue behavior of frictionspot welds in lap shear specimens of AA5754 and Ti6Al4V alloys. International Journal of Fatigue 2016; 91:149-57. [27] Boni L, Lanciotti A, Polese C. Some contraindications of hole expansion in riveted joints. Engineering Failure Analysis 2014; 46: 140-156. [28] Adid A, Jeong J, Pluvinage G. Three-dimensional finite element analysis of tensile-shear spot-welded joints in tensile and compressive loading conditions. Strength of materials 2004; 36: 353-364.
21
Figure captions Fig. 1 Geometry dimensions of the riveted specimens Fig. 2 The schematic of electromagnetic riveting: (a) electromagnetic setup; (b) riveting process Fig. 3 The diagram of the electromagnetic riveting equipment Fig. 4 Schematic of rivet driven head dimensions Fig. 5 Fatigue test process for CFRP/Al electromagnetic riveted joint Fig. 6 Microstructure observation in the section of CFRP/Al riveted joint and typical areas Fig. 7 The shear load-displacement curves of CFRP/Al electromagnetic riveted lap specimens Fig. 8 The shear failure appearance of CFRP/Al electromagnetic riveted lap joints: (a) driven head side; (b) manufactured head side Fig. 9 Weibull probability plot for CFRP/Al electromagnetic riveted joints under Fig. 10 The relationship between MTTF and CV under four maximum cyclic stresses Fig. 11 S-N curves for different reliability levels Fig. 12 Typical hysteresis loops of CFRP/Al electromagnetic riveted specimen under four different stress levels Fig. 13 The typical fatigue fracture appearance of CFRP/Al electromagnetic riveted lap joints
22
Table captions Table 1 Mechanical properties of 2A10 aluminum alloy rivet and 5182 aluminum alloy sheet Table 2 Properties of carbon fiber composite laminate Table 3 Fatigue test results for CFRP/Al electromagnetic riveted specimens
23
Electromagnetic riveting Driven head
Al
Rivet shaft
CFRP Manufactured head
185.5 MPa 172.2 MPa 159.0 MPa 145.7 MPa
0.5
In In [R(t)]
0.0 -0.5 -1.0 -1.5 -2.0
y=4.41x-57.22
-2.5 y=2.46x-29.94
y=6.73x-93.95
11.5
Reliability R=10% R=36.8% R=50% R=90%
190
180
Related formula -0.1503 SM=1227.0Nf -0.1293 SM=904.0Nf -0.1216 SM=809.3Nf -0.0928 SM=533.7Nf
170
160
150
y=8.04x-108.78
-3.0 11.0
Maximum cyclic stress (MPa)
200 1.0
12.0
12.5
In (t)
13.0
13.5
14.0
140 0.0
2.0x10
5
4.0x10
5
6.0x10
5
8.0x10
5
1.0x10
6
Fatigue life
Microcracks
1.2x10
6
1.4x10
6
Highlights The microstructural characteristics of CFRP/Al electromagnetic riveted joints were obtained.
The quasi-static shear behaviors for CFRP/Al electromagnetic riveted joints were investigated.
Two-parameters Weibull distribution was employed to analyze statistically fatigue results.
The hysteresis loop and fatigue fracture appearances were analyzed.
24
S0142-1123(17)30363-8 http://dx.doi.org/10.1016/j.ijfatigue.2017.08.026 JIJF 4451
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
25 April 2017 16 August 2017 27 August 2017
Please cite this article as: Jiang, H., Luo, T., Li, G., Zhang, X., Cui, J., Fatigue life assessment of electromagnetic riveted carbon fiber reinforce plastic/aluminum alloy lap joints using Weibull distribution, International Journal of Fatigue (2017), doi: http://dx.doi.org/10.1016/j.ijfatigue.2017.08.026
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.
Fatigue life assessment of electromagnetic riveted Carbon Fiber Reinforce Plastic/Aluminum alloy lap joints using Weibull distribution Hao Jiang1, Tong Luo1, Guangyao Li1, 2, Xu Zhang3, Junjia Cui1, 2* 1 State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China 2 Joint Center for Intelligent New Energy Vehicle, Shanghai, 200092, China 3 College of Mechanical and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, 411100, China ABSTRACT Electromagnetic riveting (EMR) has received increasing attention as a new kind of riveting technique in engineering industry. In this paper, EMR process was used to connect carbon fiber reinforced plastics (CFRP) and aluminum alloy (Al) hybrid joints. The mechanical behaviors (including static and fatigue properties) of the electromagnetic riveted lap joints were comprehensively investigated. The microstructure observation and the mechanical property tests were conducted to evaluate the joints performance. The mechanical test results showed that the failure modes of shear specimens were bending of the Al sheet and damage of the CFRP sheet, which was caused by rivet squeezing effect under static loading. However, the failure mode of fatigue specimens under each stress level was all ruptured at the Al sheet and the fracture analysis showed that cracks firstly initiated around the hole of Al sheet. This was caused by the fretting wear between Al sheet and rivet under cyclic loading. Two-parameter Weibull distribution was employed to analyze statistically fatigue cycles results. The S-N curves were drawn for different reliability levels (10%, 36.8%, 50% and 90%) for engineering applications. In addition, Hysteresis loop analysis implied that the specimens had no obvious flaw after EMR. Keywords: Electromagnetic riveting; Carbon fiber Reinforced Plastics; Weibull distribution; Fatigue behaviors; *
Corresponding author: Tel.:+86 731 88664001 ; Fax:+86 731 88822051 ; Email: [email protected] 1
1. Introduction Lightweight materials such as composites and aluminum alloys have been increasingly applied in engineering applications (e.g. automotive, railway and aerospace fields) due to their light weight and superior mechanical properties. Therefore, the demands of advance joining techniques for dissimilar materials are becoming more apparent, especially metal and nonmetal materials. Due to the great differences of material properties, only mechanical joining methods (e.g. riveting [1] and bolting [2, 3]) and adhesive bonding [4] can be competent for this challenging task. Among them, adhesive bonding process takes longer time (requiring surface preparation and curing) and consumes more energy [5]. Bolting joints are prone to loose and bolting process counts against automated assembly. Conversely, riveting joints are more stable and reliable, as well as riveting process is simple and efficient [6]. Consequently, riveting techniques have been widely used in aircraft fuselage [7], automotive frame [8] and bridge structures [9]. However, composite sheets are liable to damage due to inhomogeneous hole expansion under the conventional riveting process (pneumatic riveting and hydraulic riveting), which would further reduce the joining quality [10]. Compared to conventional riveting process [11], electromagnetic riveting (EMR) is a relatively new riveting technology based on mutually exclusive magnetic pulse force, which has advantages of high-speed loading, larger impact force, deformation stability and uniform hole expansion. Many studies [12-14] have also been conducted experimentally and numerically on the joining strength of the electromagnetic riveted joints. For example, Repetto et al. [12] firstly proposed a finite element mode for electromagnetic riveting which simultaneously took thermal and dynamic effects into account. Reinhal et al. [13] presented a new rivet die, which could produce high quality and crack free riveted joints. Li et al. [14] found that the fatigue properties of EMR joints were about 1-3 times higher than that of regular pressure riveted joints. In addition, adiabatic shear band (ASB) is one of the most significant microstructure deformation behaviors during EMR, which has a direct influence on the microstructure properties of the rivet. For microscopic characteristics, Deng et al. [15] 2
discovered that the twinning deformation was primary grain evolution mechanism inside the ASB of Ti Grade 1 rivet in low voltage electromagnetic riveting. Zhang et al. [16] explored the microstructural evolution of Al-Cu alloy bars using electromagnetic upsetting, and the results showed that dynamic nucleation particles and equiaxed recrystallization grains were generated in ASBs. Note that aforementioned works mainly focused on the metal connection performances. The fatigue strength of joining structures with metal and nonmetal materials recently gained increasing attention in manufacturing industry for guaranteeing safe and reliable applications. However, few studies have been reported on fatigue reliability of EMR joints so far. This paper aimed to investigate fatigue behaviors of electromagnetic riveted lap joints comprehensively. Firstly, microstructures on the joint interface were characterized by metallographic observations. The shear properties under quasi-static loading were tested and the maximum shear loads were obtained to determine fatigue dynamic loads. After that, the fatigue tests were conducted to evaluate fatigue life. The fatigue data were statistically analyzed by using two parameters Weibull distribution, and hysteresis loops of whole fatigue test process were also presented. Finally, the fracture appearances of fatigue specimens were observed. 2. Experimental materials and methods 2.1. Sample preparation In this study, the riveted specimens were constructed by CFRP sheets and 5182 T6 aluminum alloy sheets with 2A10 aluminum alloy rivets. It can be seen from Fig. 1 that 5182 T6 aluminum alloy sheet with size of 140 × 40 mm and thickness of 1.8 mm was placed in the upper, while CFRP sheet with size of 140 × 40 mm and thickness of 2.5 mm was put in the bottom (close to manufactured head). The overlap area was designed as 40 × 40 mm. The riveted holes placed in the center of this area, and its diameter was set to 5.1 mm. Finally, the rivet with diameter of 5.0 mm and length of 11.0 mm was accordingly selected.
3
Fig. 1 Geometry dimensions of the riveted specimens The CFRP sheets were manufactured by Toray T300 unidirectional carbon fiber and epoxy resin (resin content about 40%) using an autoclave. Those laminates were obtained overlaying 17 layers with thickness of 0.15 mm per layer, the laying orientation of which was 0°/90° in this research. The curing cycle were composed of three stages. The first stage heated up to 60° and kept for half an hour. The second stage kept the temperature at 90° for half an hour. The third stage heated up to 130° and kept for about 2 hours. Mechanical properties of Al and CFRP are presented in Table 1 and Table 2, respectively. Table 1 Mechanical properties of 2A10 aluminum alloy rivet and 5182 aluminum alloy sheet Aluminum alloy
Density (g/cm3)
Tensile strength (MPa) 400
Tensile modulus (GPa) 73.8
Poisson ratio
2.7
Yield strength (MPa) 250
2A10 5182
2.8
150
225
70
0.33
0.33
Table 2 Properties of carbon fiber composite laminate Fiber
Fiber
Fiber
Fiber
Tensile
Tensile
Ply
Resin
density
modulus
strength
density
strength
modulus
thickness
content
(g/cm3)
(GPa)
(MPa)
(g/cm3)
(MPa)
(GPa)
(mm)
(%)
1.76
230
3530
1.76
911
76
0.2
40
Considering of both material properties and machining accuracy, Al and CFRP sheets were perforated using different methods. Specifically, Wire Cut Electrical Discharge Machining was used to cut Al sheets. Drilling machine with the spindle 4
speed of 1500 RPM and feed rate of 1.5 mm/min were used to drilling CFRP sheets. In addition, the burrs around holes were removed. 2.2. Electromagnetic riveting The schematic of the electromagnetic riveting process is presented in Fig. 2. It mainly consists of two parts: electromagnetic equipment and riveting die. The electromagnetic equipment is used to provide riveting energy, while the riveting die is used to join the sheets. In detail, Capacitors firstly get charged to a predetermine discharge energy. When closing the switch, the stored energy is discharged through the plate copper coil. This causes the driver plate (copper with high conductivity) further producing reverse eddy current. Consequently, a repulsive magnetic force quickly forms between the coil and driver plate, and accelerates the punch to impact the rivets. Fig. 2 (b) shows the rivet forming process. It can be seen that the rivet driven head is upset like drum shape and locks the two sheets with manufactured head.
Fig. 2 The schematic of electromagnetic riveting: (a) electromagnetic setup; (b) riveting process 5
The EMR experiments were carried out by a PS 48-16 electromagnetic forming (EMF) machine (produced by PST company), as shown in Fig. 3. This machine has maximum discharge energy of 48 kJ and maximum capacitance of 408 μF. Higher discharge energies always lead to larger impact force, so the diameter of the driven head increased and the height of that decreased with the increasing of discharge energies. According to previous studies [17], the dimensions of driven head had significant influence on the mechanical properties. The previous results showed that normalized dimension D/D0 (D is the diameter of rivet driven head and D0 is the diameter of rivet shaft as shown in Fig. 4) of 1.5 was the optimal one. Therefore, after a series of process parameters experiments, discharge energy of 5 kJ was selected for electromagnetic riveting in this paper.
Fig. 3 The diagram of the electromagnetic riveting equipment
Fig. 4 Schematic of rivet driven head dimensions 6
2.3. Mechanical property test and microstructure observations Quasi-static shear and fatigue tests were conducted using Instron 5985 universal testing machine and Instron 8801 Electro-hydraulic servo fatigue machine, respectively. Six quasi-static shear specimens were tested under a loading velocity of 2 mm/min. The fatigue tests were applied under a load of sinusoidal wave shape, a frequency of 20 Hz and a stress ratio (R=minimum stress/maximum stress) of 0.1. The maximum cyclic stresses were determined by certain percentages of the maximum quasi-static shear stress. In this paper, four different maximum cyclic stress levels (55%, 60%, 65% and 70%) were adopted and six fatigue specimens were tested at each maximum stress. Taking the bend of specimens into consideration, the aluminum balance plates which had the same thickness of riveted sheets were assembled during fatigue tests as shown in Fig. 5. To avoid slippage during the tests, the clamping area on the CFRP side was roughen by sandpaper. Besides, the quasi-static shear specimens were gripped through the same way.
Fig. 5 Fatigue test process for CFRP/Al electromagnetic riveted joint The specimens after EMR were firstly split along the axis. After that, the section of specimens was mechanically polished and etched by Keller solution (2.5 ml HNO3, 1.5 ml HCL, 1 ml HF, and 95 ml H2O). Then the solution of 10 ml HNO3 and 40 ml H2O was used to remove corrosion products on the surface of etched specimens. Metallographic characterizations were carried out with a Leica optical microscope. 7
Static and fatigue rupture appearances were characterized with FEI QUANTA 200 Scanning Electron Microscope after cleaning up by ultrasonic cleaning machine. 3. Results and discussion 3.1. Microstructure The microstructural characteristics had greatly influence on fatigue properties of joining joints. In order to gain insight into the performances of CFRP/Al electromagnetic riveted specimens, microstructure observation of the joints was conducted. Fig. 6 shows the section metallographical structure of CFRP/Al electromagnetic joint. It could be seen that the rivet driven head and manufactured head locked the sheets, and the rivet shaft fitted tightly with CFRP and Al sheets. In the Al sheet part, the expansion degree of rivet shaft was relatively larger and Al sheet produced severe plastic deformation in zone 5. Furthermore, according to Manes’s study [18], it easily produced contact stress concentration in this area. This suggested that this part was relatively vulnerable. In the CFRP sheet part, the expansion of the rivet shaft in CFRP sheet was homogeneous. The matrix cracks and delamination in CFRP sheet were not observed. This demonstrated that this part was correspondingly secure and EMR technique was suitable for composite joining. In addition, the symmetric distribution of ASBs was clearly observed and divided the driven head into four zones: small deformation zone (zone 1), mixed deformation zone (zone 2), adiabatic shear band (zone 3) and large deformation zone (zone 4). In the zone 3, it could be found that the width of ASBs was about 100 μm. Moreover, the dynamic plastic deformation behaviors resulted in the grains elongating to threadiness. In the zone 1, the gains had little deformation and nearly kept original size. This was due to the material plastic flow in this zone was restricted by the friction effect between the punch and the driven head [19]. In the zone 2, the microstructure deformation was the most severe, and the grains were obviously distorted and elongated. The phenomenon was caused by the multiple effect of three-dimensional comprehensive stress and shear deformation [19]. In the zone 4, the material could flow toward the horizontal direction. Consequently, the grains in this area only had a certain degree of deformation. In general, although severe microstructure deformation 8
existed in the rivet driven head, no obvious defects were found.
Fig. 6 Microstructure observation in the section of CFRP/Al riveted joint and typical areas 3.2. Shear behaviors Three repeated shear tests for CFRP/Al electromagnetic riveted specimens were conducted under quasi-static loading. Fig. 7 presents the shear load-displacement curves. It could be clearly seen that the repeatability of results was excellent. The maximum shear load of the six specimens was about 5.50 kN and the complete failure location was around 11 mm. In particular, it could be seen that all the curves could be 9
obviously divided into two stages: elastic and plastic stages. At the elastic stage (0-1mm), the curves were linear increase. During this linear process, the shear load was caused by the extrusion pressure between hole wall and rivet as well as friction resistance between CFRP and Al sheets. At the plastic stage (characterized by reduction of curves slope at around 1 mm), it was observed that the shear load first increased to the maximum value at around 5 mm and then decreased. This illustrated the joints became damaged progressively. The phenomenon resulted from bending effect (the asymmetric construction of the riveted lap joint caused the torque) of the sheets in the lapping zone [20]. In this stage, the shear load was only offered by the damage resistance of CFRP and Al sheets.
Shear load (kN)
6 Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6
4
2
0 0
3
6
9
12
Displacement (mm)
Fig. 7 The shear load-displacement curves of CFRP/Al electromagnetic riveted lap specimens Fig. 8 shows the shear failure appearance of CFRP/Al electromagnetic riveted lap joints. This was a typical failure behavior of riveted joints which was referred to as unbuttoning phenomenon [21]: the rivet manufactured head locked CFRP sheet and broke away from Al sheet. In addition, bending of the Al sheet and damage of the CFRP sheet were obviously observed. Specifically, It could be clearly seen that there were two typical failure mechanisms of CFRP sheets: fiber broken and layer separation. The fibers around the hole suffered squeezing of the rivet in the shear test process. Therefore, a number of 0° and 90° fiber layers were separated as well as many carbon fibers were broken. 10
Fig. 8 The shear failure appearance of CFRP/Al electromagnetic riveted lap joints: (a) driven head side; (b) manufactured head side 3.3. Fatigue behaviors 3.3.1. Statistics analysis Two-parameter Weibull distribution function was adopted to analyze statistically fatigue cycles due to the simple function and calculation, accurate failure analysis and suitable for data analysis of small samples [22-24]. The probability density function f(t) and corresponding cumulative distribution function F(t) are expressed as following Eq. (1) and Eq. (2), respectively.
t f (t )
1
t exp
t F (t ) 1 exp
(1)
(2)
where β and η are the shape and scale parameter, respectively; t is the random variable value and represents the fatigue life in this paper. The reliability function R(t) is defined as Eq. (3). 11
t R(t ) exp
(3)
By taking the natural logarithm twice on both sides of Eq. (3), the following Eq. (4) is obtained.
InIn
1 In(t ) In R(t )
(4)
It can be observed that the relationship between InIn[1/R(t)] and In(t) is linear. The substituted reliability Ṙ(t) is calculated by a proliferation function of Eq. (5).
i 0.3 R (t i ) 1 n 0.4
（i=1, 2, …, n）
(5)
where i and n are the failure sequence number and the total number of specimens, respectively. Weibull probability plot can be obtained from fatigue results. The shape parameter β and scale parameter η can be calculated by the linear slope and intercept. Consequently, Weibull mean life (mean time to failure, MTTF), standard deviation (SD) and coefficient of variation (CV) can be calculated from following Eq. (6), Eq. (7) and Eq. (8), respectively. 1 E (T ) t f (t )dt 1 0
2 1 SD(T ) 2 1 2 1
CV
SD(T ) ) E (T )
2 1 2 1 1 1 1
(6)
(7)
(8)
where is Г the gamma function [25]. Table 3 shows the fatigue results of the CFRP/Al electromagnetic riveted specimens under four different maximum cyclic stress levels and corresponding InIn[1/R(t)] and In(t) are also presented. Fig. 9 shows the Weibull probability plot for the specimens under different maximum cyclic stress levels. The value of the shape parameter β and scale parameter η was obtained by linear regression. Furthermore, MTTF values and CV values were obtained from Eq. (6)-(8). The specific Weibull 12
parameters results are shown in Table 4. The relationship between MTTF and CV under four different maximum cyclic stress levels is presented in Fig. 10. CV is a non-dimensional parameter which represents the volatility of the fatigue data under a certain stress level. It could be observed that the CV value under maximum cyclic stress of 185.5 MPa was the highest. This demonstrated that the performance of CFPR/Al electromagnetic riveted specimens under high dynamic loading fluctuated greater than that under low dynamic loading. Table 3 Fatigue test results for CFRP/Al electromagnetic riveted specimens Maximum cyclic stress (MPa)
185.5
172.2
159.0
145.7
Fatigue life (cycles)
InIn[1/R(t)]
In(t)
77519
-2.150
11.26
131610
-1.566
11.79
154120
-0.607
11.95
210111
-0.142
12.26
221531
0.269
12.31
223826
0.792
12.32
287520
-2.150
12.57
361046
-1.566
12.80
364164
-0.607
12.81
371601
-0.142
12.83
420501
0.269
12.95
563409
0.792
13.24
571770
-2.150
13.26
640425
-1.566
13.37
695238
-0.607
13.45
736251
-0.142
13.51
793356
0.269
13.58
804120
0.792
13.60
948968
-2.150
13.76
956202
-1.566
13.77
968595
-0.607
13.78
1256031
-0.142
13.95
1138042
0.269
14.04
1278542
0.792
14.06
13
1.0
185.5 MPa 172.2 MPa 159.0 MPa 145.7 MPa
0.5
In In [R(t)]
0.0 -0.5 -1.0 -1.5 -2.0
y=4.41x-57.22
-2.5 y=2.46x-29.94
y=6.73x-93.95 y=8.04x-108.78
-3.0 11.0
11.5
12.0
12.5
13.0
13.5
14.0
In (t)
Fig. 9 Weibull probability plot for CFRP/Al electromagnetic riveted joints under different maximum cyclic stress levels Table 4 Weibull parameters for four maximum cyclic stress levels Maximum cyclic stress (MPa)
Shape parameter
Scale parameter
η
Mean fatigue life （cycles）
Coefficient of variation
β
185.5 172.2 159.0 145.7
2.46 4.41 8.04 6.73
193055 431515 751518 1155312
171226 393328 707907 1078484
0.8616 0.6346 0.5382 0.5824
SM=185.5 MPa
Coefficient of Variation
0.8
SM=172.2 MPa SM=159.0 MPa
SM=145.7 MPa
0.4
0.0
171226
393328
707907
1078484
Mean fatigue life (cycles)
Fig. 10 The relationship between MTTF and CV under four maximum cyclic stresses Based on the above results of Weibull distribution analysis, the fatigue life of different reliability at a certain stress level can be calculated by Eq. (9). N Rx [ In( Rx )]1 / 14
(9)
where NRx is the fatigue life with x% reliability. In this study, Reliability of 10%, 36.8% (corresponding characteristic life), 50% and 90% were taken into account, respectively. In addition, the fatigue life was fitted by the following power function [26]:
S M a( N f ) b
(10)
where SM and Nf are the maximum cyclic stress and fatigue life, respectively; a and b are constants, which can be obtained using the least square method. Fig. 11 depicts the S-N curves of CFRP/Al electromagnetic riveted specimens under four different reliability levels. These curves could predict the possibility of fatigue life according to the reliability levels, which were desired by the engineering applications. Especially, the S-N curves with higher reliability level (R=90%) were recommended to design the automobile and airplane for higher security. In general, the prospective fatigue cycles are lower for higher security levels [26].
Maximum cyclic stress (MPa)
200
Reliability R=10% R=36.8% R=50% R=90%
190
180
Related formula -0.1503 SM=1227.0Nf -0.1293 SM=904.0Nf -0.1216 SM=809.3Nf -0.0928 SM=533.7Nf
170
160
150
140 0.0
2.0x10
5
4.0x10
5
5
6.0x10 8.0x10
5
1.0x10
6
1.2x10
6
1.4x10
6
Fatigue life
Fig. 11 S-N curves for different reliability levels 3.3.2. Hysteresis loop analysis Fig. 12 shows typical hysteresis loops of CFRP/Al electromagnetic riveted specimen under four different stress levels. It could be observed that the variation law of hysteresis loops was similar under four stress levels. In particular, at the early fatigue test stage, the slope of hysteresis loops had small increases. This implied that the stiffness of the specimens increased at this stage, and the phenomenon was caused by fastener tightening effect and hole wall hardening effect under dynamic loading 15
[27]. At the medium fatigue test stage, it could be observed that the displacement increased with the fatigue cycles, illustrating that the riveted hole gradually expanded by the cyclic loading. At the final fatigue test stage, the slope of hysteresis loops dramatically decreased. This illustrated that the specimens lost the fastener tightening and occurred failure causing by the further hole expansion. In general, the hysteresis loops recorded the state of specimens during the fatigue test process. The specimens exhibited stable performance in the ahead about 90% of the fatigue cycles, while lost stability in the remaining fatigue cycles. This further implied that the specimens had no obvious flaw after EMR and the crack initiation process consumed most of the fatigue cycles. 200
Stress level 102.0 MPa 160
120
100 cycles 1000 cycles 10000 cycles 100000 cycles 150000 cycles 190000 cycles 200000 cycles 210000 cycles
80
40
Cyclic stress (MPa)
Cyclic stress (MPa)
160
0.2
0.3
0.4
120
100 cycles 10000 cycles 100000 cycles 200000 cycles 300000 cycles 350000 cycles 360000 cycles 371000 cycles
80
40
0 0.1
Stress level 94.7 MPa
0
0.5
0.1
0.2
Displacement (mm)
0.3
0.4
0.5
Displacement (mm) 160
160
Stress level 80.2 MPa
Stress level 87.4 MPa
Cyclic stress (MPa)
Cyclic stress (MPa)
120 120
100 cycles 10000 cycles 100000 cycles 300000 cycles 500000 cycles 700000 cycles 750000 cycles 793000 cycles
80
40
0 0.0
0.1
0.2
0.3
100 cycles 10000 cycles 100000 cycles 300000 cycles 500000 cycles 1000000 cycles 1200000 cycles 1255000 cycles
80
40
0.4
0 0.0
0.1
0.2
0.3
0.4
Displacement (mm)
Displacement (mm)
Fig. 12 Typical hysteresis loops of CFRP/Al electromagnetic riveted specimen under four different stress levels 3.3.3. Fracture analysis The failure mode of fatigue specimens under each stress level was all ruptured at the Al sheet. Fig. 13 shows the typical fatigue fracture appearance of CFRP/Al electromagnetic riveted lap joints. It could be seen that there were three typical zones 16
on fracture surface. In the zone 1, the black oxide and microcracks (zone 4) confirmed that this area (around the hole of Al sheet) was crack initiation zone. These characteristics were caused by the fretting wear between Al sheet and rivet under cyclic loading. In the zone 2, the fatigue lines (beach markings) and fatigue striations (zone 5) were observed, demonstrating that this area was fatigue propagation zone. In addition, the crack propagation direction was usually perpendicular to the fatigue lines. Therefore, it could be deduced that the cracks direction was propagated along both width and thickness of the Al sheet. This result was consistent with the previous theoretic description [28]. Because the asymmetry of the riveted lap specimens under shear loading usually sustained a combination effect of bending and axial loading. This would further increase the stress distribution in the width and thickness direction. In the zone 3, the various size tensile dimples (zone 6) were observed, illustrating that this area was fatigue final fracture zone and the failure mode was ductile fracture. Consequently, according to the above analysis, it could be verified that cracks firstly initiated around the hole of Al sheet, then propagated from there to both sides until the one side of Al sheet could not sustain the cyclic loading, and final break occurred. As a whole, the fatigue failure mode was consistent with above microstructure analysis that the hole of Al sheet was the most vulnerable position.
17
Fig. 13 The typical fatigue fracture appearance of CFRP/Al electromagnetic riveted lap joints 4. Conclusion This paper comprehensively investigated the fatigue behavior of CFRP/Al electromagnetic riveted joints to guarantee secure and reliable engineering application. The microstructure observation, quasi-static shear and fatigue experiments were carried out. Based on the above results and discussions, the main conclusions were drawn as following: (1) Joint cross-section microstructure observations showed that the hole in the Al sheet occurred severe plastic deformation, indicating that this area was the most vulnerable. In addition, no obvious microcracks or defects were observed in the CFRP sheet. This demonstrated that EMR technique was suitable for composite joining. (2) The CFRP/Al electromagnetic riveted joints showed stable shear properties. The shear failure mode was bending of the Al sheet and damage of the CFRP sheet. Specifically, the damage mechanisms of CFRP sheets were fiber broken and layer separation. (3) The fatigue data were analyzed statistically by Weibull distribution. The S-N curves for different reliability levels were obtained. The S-N curves with higher reliability level (R=90%) were recommended to design the automobile and airplane for higher security. (4) Hysteresis loop analysis showed that the specimens exhibited stable performance in the ahead about 90% of the fatigue cycles. This further suggested that the joints had no obvious flaw after EMR. (5) The failure mode of fatigue specimens was ruptured at the Al sheet. The 18
fracture analysis demonstrated that cracks firstly initiated around the hole of Al sheet, then propagated from there to both sides until the one side of Al sheet could not bear the cyclic loading, and final break occurred. Acknowledgement This project is supported by National Natural Science Foundation of China (No. 51405149) and the State Key Program of National Natural Science Foundation of China (No. 61232014).
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[9] Abílio MP, António LL, José AFO. Fatigue of riveted and bolted joints made of puddle iron-An experimental approach. Journal of Constructional Steel Research 2015; 104: 81-90. [10] Cao ZQ, Cardew-Hall M. Interference-fit riveting technique in fiber composite laminates. Aerospace Science and Technology 2006; 10: 327-330. [11] Aman F, Cheraghi SH, Krishnan KK, Lankarani H. Study of the impact of riveting sequence, rivet pitch, and gap between sheets on the quality of riveted lap joints using finite element method. The International Journal of Advanced Manufacturing Technology 2013; 67: 545-562. [12] Repetto EA, Radovitzky R, Ortiz M, Lundquist RC, Sandstrom DR. A Finite Element Study of Electromagnetic Riveting. ASME, Journal of Manufacturing Science and Engineering 1999; 121: 61-68. [13] Reinhal PG, Ghassaei S, Choo V. An analysis of rivet die design in electromagnetic riveting. ASME, Journal of Vibration Acoustics Stress and Reliability in Design 1988; 110: 65-69. [14] Li GY, Jiang H, Zhang X, Cui JJ. Mechanical properties and fatigue behavior of electromagnetic riveted lap joints influenced by shear loading. Journal of Manufacturing Processes 2017; 26: 226-239. [15] Deng JH, Tang C, Fu MW, Zhan YR. Effect of discharge voltage on the deformation of Ti grade 1 rivet in electromagnetic riveting. Materials science and engineering: A 2014; 591: 26-32. [16] Zhang X, Cui JJ, Li GY. Microstructural mechanism in adiabatic shear bands of Al-Cu alloy bars using electromagnetic impact upsetting. Materials Letters 2017; 194: 62-65. [17] Skorupa M, Skorupa A, Machniewicz T, Korbel A. Effect of production variables on the fatigue behaviour of riveted lap joints. International Journal of Fatigue 2010; 32: 996-1003. [18] Manes A, Giglio M, Vigano F. Effect of riveting process parameters on the local stress field of a T-joint. International Journal of Mechanical Sciences 2011; 53: 1039-1049. 20
[19] Zhang X, Li CF. The effect of loading rate on deformation of TA1 titanium alloy bars subjected to electromagnetic heading. Materials Science & Engineering A 2017; 679: 511-519. [20] Calabrese L, Proverbio E, Di Bella G, Galtieri G, Borsellino C. Failure behaviour of SPR joints after salt spray test. Engineering Structures 2015; 82: 33-43. [21] Han L, Thornton M, Shergold M. A comparison of the mechanical behaviour of self-piercing riveted and resistance spot welded aluminium sheets for the automotive industry. Materials and Design 2010; 31: 1457-67. [22] Sakin R, Ay I. Statistical analysis of bending fatigue life data using Weibull distribution in glass-fiber reinforced polyester composites. Materials and Design 2008; 29: 1170-1181. [23] Zhao YX, Liu HB. Weibull modeling of the probabilistic S-N curves for rolling contact fatigue. International Journal of Fatigue 2014; 66: 47-54. [24] Selmy AI, Azab NA, Abd El-baky MA. Flexural fatigue characteristics of two different types of glass fiber/epoxy polymeric composite laminates with statistical analysis. Composites Part B: Engineering 2013; 45: 518-527. [25] Khashaba UA. Fatigue and reliability analysis of unidirectional GFRP composites under rotating bending loads. Journal of Composite Materials 2003; 37: 317-31. [26] Plaine AH, Suhuddin UFH, Alcantara NG, Santos JF. Fatigue behavior of frictionspot welds in lap shear specimens of AA5754 and Ti6Al4V alloys. International Journal of Fatigue 2016; 91:149-57. [27] Boni L, Lanciotti A, Polese C. Some contraindications of hole expansion in riveted joints. Engineering Failure Analysis 2014; 46: 140-156. [28] Adid A, Jeong J, Pluvinage G. Three-dimensional finite element analysis of tensile-shear spot-welded joints in tensile and compressive loading conditions. Strength of materials 2004; 36: 353-364.
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Figure captions Fig. 1 Geometry dimensions of the riveted specimens Fig. 2 The schematic of electromagnetic riveting: (a) electromagnetic setup; (b) riveting process Fig. 3 The diagram of the electromagnetic riveting equipment Fig. 4 Schematic of rivet driven head dimensions Fig. 5 Fatigue test process for CFRP/Al electromagnetic riveted joint Fig. 6 Microstructure observation in the section of CFRP/Al riveted joint and typical areas Fig. 7 The shear load-displacement curves of CFRP/Al electromagnetic riveted lap specimens Fig. 8 The shear failure appearance of CFRP/Al electromagnetic riveted lap joints: (a) driven head side; (b) manufactured head side Fig. 9 Weibull probability plot for CFRP/Al electromagnetic riveted joints under Fig. 10 The relationship between MTTF and CV under four maximum cyclic stresses Fig. 11 S-N curves for different reliability levels Fig. 12 Typical hysteresis loops of CFRP/Al electromagnetic riveted specimen under four different stress levels Fig. 13 The typical fatigue fracture appearance of CFRP/Al electromagnetic riveted lap joints
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Table captions Table 1 Mechanical properties of 2A10 aluminum alloy rivet and 5182 aluminum alloy sheet Table 2 Properties of carbon fiber composite laminate Table 3 Fatigue test results for CFRP/Al electromagnetic riveted specimens
23
Electromagnetic riveting Driven head
Al
Rivet shaft
CFRP Manufactured head
185.5 MPa 172.2 MPa 159.0 MPa 145.7 MPa
0.5
In In [R(t)]
0.0 -0.5 -1.0 -1.5 -2.0
y=4.41x-57.22
-2.5 y=2.46x-29.94
y=6.73x-93.95
11.5
Reliability R=10% R=36.8% R=50% R=90%
190
180
Related formula -0.1503 SM=1227.0Nf -0.1293 SM=904.0Nf -0.1216 SM=809.3Nf -0.0928 SM=533.7Nf
170
160
150
y=8.04x-108.78
-3.0 11.0
Maximum cyclic stress (MPa)
200 1.0
12.0
12.5
In (t)
13.0
13.5
14.0
140 0.0
2.0x10
5
4.0x10
5
6.0x10
5
8.0x10
5
1.0x10
6
Fatigue life
Microcracks
1.2x10
6
1.4x10
6
Highlights The microstructural characteristics of CFRP/Al electromagnetic riveted joints were obtained.
The quasi-static shear behaviors for CFRP/Al electromagnetic riveted joints were investigated.
Two-parameters Weibull distribution was employed to analyze statistically fatigue results.
The hysteresis loop and fatigue fracture appearances were analyzed.
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