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Parametric study of composite bolted joint under compressive loading
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11th International Conference Interdisciplinarity in Engineering, INTER-ENG 2017, 5-6 October 11th International Conference Interdisciplinarity in Engineering, 2017, Tirgu-Mures, Romania INTER-ENG 2017, 5-6 October 2017, Tirgu-Mures, Romania
Parametric study of composite bolted joint under compressive
Parametric study of composite bolted joint2017, under compressive Manufacturing Engineering Society International Conference MESIC 2017, 28-30 June loading 2017, Vigoloading (Pontevedra), Spain a,
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Laxman V. Awadhania, *, Anand Bewoorb Costing models for capacity optimization Industry 4.0: Trade-off Laxman V. Awadhani *, AnandinBewoor Savitribai Phule Pune University, Pune, India between used and operational efficiency Scapacity avitribai Phule University, Pune, India Mechanical Engineering Department, Cummins College of Pune Engineering for Women, Savitribai Phule Pune University, Pune, India P
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Mechanical Engineering Department, Cummins College of Engineering for Women, Savitribai Phule Pune University, Pune, India P
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb Abstract a University of Minho, 4800-058 Guimarães, Portugal Abstract b Unochapecó, 89809-000 Chapecó, SC, Brazil Use of composite structures in various sectors is rapidly increasing. The composite materials are becoming very popular due to Use composite structures in high various sectorstois weight rapidly ratio, increasing. The composite materials are becoming very popular due to high ofstrength to weight ratio, stiffness low coefficient of friction, improved appearance etc. Extensive high strength to weight high stiffness to weight ratio, lowsubjected coefficient friction, improved etc. Extensive literature is available for ratio, the behavior of composite bolted joints to of tensile loading for theappearance aerospace structures. The literature is available theisbehavior of composite joints subjected tensile loading for the of aerospace structures. The work reported in this for paper an attempt to extend bolted the analytical model fortostudying the behaviour composite bolted joint Abstract work in this paper The is anmodel attempt to extend the analytical for studying of composite bolted joint under reported compressive loading. is capable of conducting the model parametric study onthe thebehaviour joint stiffness variation with respect under compressive The model4.0", is capable of conducting thesequence parametric on the joint stiffnessThe variation with respect to parameters suchloading. asofplate width, bolt diameter and processes stacking compressive loading. model is verified Under the concept "Industry production will beforstudy pushed to be increasingly interconnected, to parametersbased such as boltdesigned diameter stacking sequence for compressive loading. capacity The model is stiffness. verified experimentally. The on experiments toand study the effect of variation inIn the on the joint information aplate real width, timewere basis and, necessarily, much more efficient. thisparameters context, optimization experimentally. Thebidirectional experimentscarbon were fibre designed tocomposite study thelaminates effect ofwere variation in per the ASTM parameters on The the parameters joint stiffness. Unidirectional and epoxy tested D5961. viz. goes beyond the traditional aim of capacity maximization, contributing also foras organization’s profitability and value. Unidirectional and bolt bidirectional carbon fibre of epoxy composite laminates were as tested as per ASTM D5961. The parameters viz. stacking sequence, diameter, plate width the joint stiffness are identified significant. Indeed, lean management and continuous improvement approaches suggest capacity optimization instead of stacking sequence, bolt diameter,byplate widthB.V. of the joint stiffness are identified as significant. © 2018 The Authors. Published Elsevier maximization. The study of capacity optimization and costing models is an important research topic that deserves © 2018 The under Authors. Published by Elsevier B.V.committee Peer-review responsibility ofthe scientific of the 11th International Conference Interdisciplinarity in © 2018 The Authors. Published by Elsevier B.V. contributions from both the practical and theoretical This paperConference presents and discusses a mathematical Peer-review under responsibility ofthe scientific committeeperspectives. of the 11th International Interdisciplinarity in Engineering. Peer-review under responsibility of the scientific committee of the 11th International Conference Interdisciplinarity Engineering. model for capacity management based on different costing models (ABC and TDABC). A generic in model has been Engineering.
developed and it was used to analyze capacity and to design strategies towardsloading; the maximization Keywords: Characterization; Composite boltedidle joint; Analytical model; Joint stiffness; Compressive joint behavior. of organization’s Keywords: Characterization; Composite bolted joint; Analytical model; Jointefficiency stiffness; Compressive loading;and jointitbehavior. value. The trade-off capacity maximization vs operational is highlighted is shown that capacity optimization might hide operational inefficiency. © The Authors. Published by Elsevier B.V. 1. 2017 Introduction 1. Introduction Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. Use of composite structures in various sectors is rapidly increasing. The composite materials are becoming very Use ofdue composite variousratio, sectors is stiffness rapidly increasing. materials becoming very popular to high structures strength toinweight high to weight The ratio,composite low coefficient of are friction, improved Keywords: Cost Models; TDABC; Capacity; Efficiency popular due to highABC; strength to Capacity weight Management; ratio, high Idle stiffness toOperational weight ratio, low coefficient of friction, improved 1. Introduction
* Corresponding author. Tel.: +91-902-873-0691. * E-mail Corresponding author. Tel.: +91-902-873-0691. address:[email protected] The cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address:[email protected]
in modern production systems. In general, it is defined as unused capacity or production potential and can be measured 2351-9789© 2018 The Authors. Published by Elsevier B.V. 2351-9789© 2018 The Authors. Published by Elsevier B.V.hours Peer-review responsibility ofthe scientific committee of the 11th Conference in Engineering. in several under ways: tons of production, available of International manufacturing, etc. Interdisciplinarity The management of the idle capacity Peer-review underTel.: responsibility scientific committee of 741 the 11th International Conference Interdisciplinarity in Engineering. * Paulo Afonso. +351 253ofthe 510 761; fax: +351 253 604 E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 11th International Conference Interdisciplinarity in Engineering. 10.1016/j.promfg.2018.03.029
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appearance etc. The structures are built either by fastening or by bonding. The bonded joints are suitable for the light duty applications while the fastened joints are used for moderate and heavy duty applications. The bolted structures can be assembled or dismantled easily which facilitates the repairs. Due to cost and specialized needs for manufacturing, the applications of the composite structures were limited to aerospace industry. Presently composite bolted joints are extensively used in the modern machine structures in order to reduce the weight of the machines, reduce the energy requirement of the machine etc. The current applications of the composite bolted joint include secondary structures in the automobiles such as fairings on heavy duty trucks [15] or front or rear panels of bus which are subjected to compressive loadings due to weight. Extensive literature is available for studying the behavior of composite bolted joints subjected to tensile loading for the aerospace structures [1]. 1.1. Background Various researchers have analyzed the bolted joint using numerical analysis and experimental analysis for the characterization. The analytical model has been used by few researchers for the prediction of the performance of the composite bolted joint as well as investigating the parameters influencing the joint stiffness of composite bolted joint [1]. The performance of the composite bolted joint has been extensively studied for tensile loading, but compressive loading significantly not reported in the literature. The characterization studies based on analytical models from the literature for tensile loading included joint parameters such as length, width, edge distance, stacking sequence, bolt diameter, tightening torque, coefficient of friction, bolt-hole clearance etc. Hence the behavioral studies of composite bolted joint has been undertaken. 1.2. Literature Review The spring based analytical model to predict the stiffness of single- lap composite bolted joint includes a predictive method to consider the effect of secondary bending as a function of geometrical parameters, material elastic properties, stacking sequence, and load path eccentricity [2]. The analytical prediction for bolted joints in composites is being done in tensile loading for past few years. The criteria used were ‘Yamada–Sun failure criterion’ and the ‘Chang–Scott–Springer characteristic curve model’. As development progressed the methodology changed resulting in more accurate and precise results and predictions. Finite Element Analysis and software’s like ABAQUS are used. [4, 5, 6, 10] The researchers described the effect of parameters like stacking sequence, fastening torque, clearance between bolt and hole, bolt diameter, coefficient of friction, length, width, edge to diameter ratio and mating materials [3, 7, 8, 9, 12, 13, and 14]. The influence of specimen stacking sequences on the mean bearing strength, mean ultimate failure stress, failure displacement and bearing stiffness is found as specimens with [0/90] 2s stacking sequence have the maximum failure displacement and ultimate failure stress compared with the other stacking sequences. [11]. The work reported in this paper is an attempt to extend the analytical model for studying the behavior of composite bolted joint under compressive loading. The model is capable of conducting the parametric study on the joint stiffness variation with respect to parameters such as plate width, bolt diameter and stacking sequence for compressive loading. The model is validated experimentally. The experiments were designed to study the effect of variation in the parameters on the joint stiffness. Unidirectional and bidirectional carbon fiber epoxy composite laminates were tested as per ASTM D5961 [16]. The parameters such as bolt-hole clearance, length of plate and bolt preload were not included in the experimental studies. 1.3. Analytical Model An analytical model to predict the stiffness of single- lap composite bolted joint is proposed. The present analytical model is an extension of the model proposed by McCarthy [12]. The compressive loading may include the effect of buckling of the plates which is taken care in the experimentation by using a fixture to avoid the buckling.
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a
b
Fig. 1. (a) Single lap single bolted composite bolted joint; (b) Spring mass model of composite bolted joint [12].
The single-lap single-bolt composite joint shown in Fig. 1a may be represented by a system of masses and springs, as shown in Fig. 1b. The joint load is applied at mass 3 and reacted at the clamped end of the joint. 𝑀𝑀1 = mass of plate 1 𝑀𝑀3 = mass of plate 2 𝑀𝑀2 = mass of bolt 𝐾𝐾𝑏𝑏 = Stiffness of bolt 𝐾𝐾𝑝𝑝𝑝𝑝𝑝𝑝 = Stiffness of plates in longitudinal direction 𝐾𝐾𝑠𝑠ℎ−𝑝𝑝𝑝𝑝𝑝𝑝 = Stiffness of plate in shearing Considering that masses are free to move in the x-direction only, the system shown in leads to a system of linear equations of the form:
{F } [ M ]{x} + [ K ]{ x} =
(1)
For quasi-static loading, the accelerations can be neglected, leading to
[ K ]{ x} = {F }
(2)
Calculation of the displacements is straightforward by pre-multiplying the load vector F by the inverse of stiffness matrix K.
K pl 1 + K shear −K shear 0 K pl 1 + K bolt −K bolt 0
0 x1
− K shear K shear + K pl 2 − K pl 2 − K bolt K bolt + K pl 2 − K pl 2
0 − K pl 2 x2 = 0 K pl 2 x3 − F 0 x1
− K pl 2 x2 = K pl 2 x3
− K bolt c − K bolt u f + Ffricc K c+K u −F bolt f fricc bolt −F
(3)
(4)
2. Calculations of spring stiffness The composite plate stiffness, in each plate i, can be found considering a composite laminate subjected to uniform compressive load: K pli = E LciWci tci
(p
ci
− D 2)
(5)
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Where E Lc is the equivalent elasticity modulus in longitudinal direction calculated using the laminate theory. W c and t c are width and thickness of the composite plate respectively. Pc is the distance between the hole centre and the plate free end where load is applied, and D is the hole diameter. The shear stiffness K shear is found as the shear stiffness of the two composite plates in series.
1 1 K shear = + K sh − pl 1 K sh − pl 2
−1
(6)
The maximum value of friction forces that the joint can transmit, F fricc , is obtained considering the friction coefficient and the normal force produced by the bolt torque Ffricc = µ Ft
(7)
The stiffness included in bolt can be found as follows: K bolt=
1 K sh − b
+
1 K bend − b
+
1 K be − pl 1
+
1 Kϕ 1
+
1 K be − pl 2
+
Kϕ 2 1
−1
where, 𝐾𝐾𝑠𝑠ℎ−𝑏𝑏 is bolt shear stiffness given as: K sh − b =
3Gb Ab 4t
(8)
(9)
where, G b is bolt shear modulus and A b is cross section area of bolt. The bolt bending stiffness K bend-b is given by: K bend − b =
Eb t 4
(10)
Where, E b is the Young Modulus of bolt material. Bearing stiffness of plates is given by:
K be − pli = t EL ET
(11)
Where, 𝐸𝐸𝑇𝑇 is the equivalent elasticity modulus of composite plate in transverse direction. The secondary bending stiffness for each composite plate is: Kφ =
16 EI tt m L
(12)
where, t m is the load path eccentricity. MATLAB code is developed to identify influencing parameters on joint properties. Then 'Load vs. Displacement' curve is plotted. The inputs given to MATLAB code are given in Table1.
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Table 1. Input for the MATLAB code. Parameters
Values
Elasticity modulus in longitudinal direction (EL)
240 GPa
Elasticity modulus in transverse direction (ET)
70 GPa
Density
1800 g/cc
Filament diameter
7 micrometer
Number of layers
10
Poisson's ratio of fiber
0.25
Poisson's ratio of matrix
0.30
Flexural rigidity (EI)
4.267 Nmm2
Unidirectional fibre layup Bidirectional fibre layup [0/90] s
23.0245Nmm2
Clearance
0 micron to 200 micron
Tightening Torque
0 N-mm to 4000 N-mm
Coefficient of Friction
0.1 to 0.5
Specimen width
20 mm to 40 mm
Specimen length
75 mm to 195 mm
Specimen thickness
3 mm
Young's Modulus of bolt
117 GPa
Shear Modulus of bolt
43 GPa
Initially the load displacement curves for parametric variations were found out and from these graphs the joint stiffness was determined. By varying the plate width, the load displacement diagram is obtained as shown in Fig. 2. Load vs Displacement
w=20 mm
Load (N)
w=25 w=30 w=35 Displacement (mm)
w=40
Fig. 2. Load vs. Displacement Curves for different values of width.
From Fig. 2 it is observed that joint stiffness varies as the width varies. Similar graphs were plotted by varying bolt tightening torque, clearance, length of specimen, coefficient of friction and bolt diameter. From the loaddisplacement curves, the joint stiffness was calculated. The variation of the joint stiffness with respect to the various parameters is presented in Fig. 3 to 5. 3. Variation in Joint Stiffness for different parameters From Fig. 3(a) it is observed that joint stiffness varies as the width varies. It is observed that changing width from 20 mm to 40 mm, stiffness changes from 9882.6 N/mm to 13639 N/mm. Thus width is significant parameter
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From Fig. 3(b) it is observed that joint stiffness varies as the length varies. It is observed that changing length from 75 mm to 195 mm, stiffness changes from 15151.4 N/mm to 10078.4 N/mm. Hence length is also significant parameter. From Fig. 4(a) it is observed that joint stiffness negligibly varies as the coefficient of friction varies. It is observed that changing coefficient of friction from 0.1 to 0.5, stiffness changes from 12169.3 N/mm to 12026.7 N/mm. Therefore it is not significant parameter From Fig. 5(a) it is observed that joint stiffness negligibly varies as the Torque varies. It is observed that changing torque from 0 N-mm to 4000 N-mm, stiffness changes from 12202.5 N/mm to 11837.2 N/mm. Therefore bolt tightening torque is insignificant parameter in compressive loading. From Fig. 4(b) it is observed that joint stiffness varies as the clearance varies. It is observed that changing clearance from 0 to 200 micron stiffness changes from 11403.3N/mm to 12923.8 N/mm. Hence clearance has significant effect on joint stiffness. From Fig. 5(b) it is observed that joint stiffness varies as the Diameter varies. It is observed that changing diameter from 5 mm to 15 mm, stiffness changes from 9497.929N/mm to 9917 N/mm. Therefore bolt diameter is significant parameter.
b Joint Stiffness (N/mm)
Joint Stiffness (N/mm)
a
Length (mm)
Width (mm) Fig. 3. Joint Stiffness vs. (a)Width and (b) Length.
b Joint Stiffness (N/mm)
Joint Stiffness (N/mm)
a
Coeff. of friction
Clearance (micron)
Fig. 4 Joint Stiffness vs. Coefficient of friction and bolt hole clearance.
b
Joint Stiffness(N/mm)
Joint Stiffness (N/mm)
a
Torque N-mm
Diameter(mm)
Fig. 5. Joint Stiffness vs. (a) Tightening torque and (b) Bolt diameter.
4. Experimentation According to ASTM D 5961[16] the compression shear test was conducted. The experimental work is carried with the help of support fixture as shown in Fig. 6 (a) for holding the specimen between the flat circular plates of the
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UTM crossheads. The load range lies between 0 - 10 kN. For experimentation 18 tests are carried out according to Design of Experiment. Table 2. Details of specimen geometry. Specimen Type
Bolt diameter ‘d’ (mm)
Edge distance ‘e’ (mm)
Quantity (Nos.)
1
4
16
6
2
5
20
6
3
6
24
6
The parameters taken into account for the analytical parametric study for determining the joint stiffness of composite bolted joint are length of specimen, width of specimen, bolt-hole clearance, bolt tightening torque, coefficient of friction, bolt diameter. But only few of these mentioned parameters have a major impact on the joint stiffness as concluded from the observations made in previous article. The finalization of parameters in experimental parametric studies is mentioned further. Even though length of the specimen is found as a significant parameter in the analytical work, it is kept constant as per the guidelines of ASTM D5961. Width of composite specimen is also found as a significant parameter, but due to the limitations of the support fixture is kept constant. Bolt-hole clearance is significant parameter influencing joint stiffness. Neat Fit Case is considered for the experiment. Bolt diameter is a significant parameter in determining the joint stiffness. From the graphs plotted previously it can be noted that the joint stiffness increases as the bolt diameter increases. The bolt diameters selected for the parametric study are 4 mm, 5 mm & 6 mm. As there is no significant work done on varying loading rate, it is selected as the parameter in order to find out whether it is significant or insignificant parameter. The loading rates selected for the parametric study are 0.2mm/min, 2mm/min & 5mm/min. It is observed from the literature that stacking sequence has prominent effect on the joint stiffness as the different lay-up of fibers in the composite materials have a different load sustaining capability. So the stacking sequences selected for the parametric study are Unidirectional & Bidirectional [0/90] s fibre lay-up. The Load vs. Displacement curves are obtained on UTM for each 18 trials as per Design of Experiment. Fig. 7 shows the specimen after the testing which represents secondary bending failure in the compression test.
a
b
Fig. 6 Test fixture and Test specimen geometry.
a
b
Fig. 7 Specimen failures after compression test.
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5. Results and discussion The test results are represented in the form of joint stiffness variation with respect to the various parameters such as loading rate, bolt diameter and the unidirectional or bidirectional composite laminates.
a
b
K vs Loading Rate (D) 0.2LRUD 2LRUD 5LRUD
Joint stiffness (N/mm)
Joint stiffness (N/mm)
K vs Diameter (LR)
Diameter (mm)
4DUD 5DUD 6DUD Loading Rate (mm/min)
Fig. 8 (a) Comparison between Joint stiffness vs. Diameter for variable loading rate for Unidirectional layup; (b) – Comparison between Joint stiffness vs. loading rate for variable bolt diameter for Unidirectional layup.
From Fig. 8 (a) it is observed that for all loading rates of 0.2 mm/min, 2 mm/min and 5 mm/min joint stiffness increases as bolt diameter increases. From this Fig. 8 (b) it is observed that effect of loading rate on joint stiffness for bolt diameter 4mm is negligible. Whereas for bolt diameter of 5mm and 6mm effect of loading rate on joint stiffness is considerable.
a
0.2LRBD 2LRBD 5LRBD
Diameter (mm)
b
K vs Loading Rate (D) Joint stiffness (N/mm)
Joint stiffness (N/mm)
K vs Diameter (LR)
4DBD 5DBD 6DBD Loading rate (mm/min)
Fig. 9 (a) Comparison between Joint stiffness vs. Diameter for variable loading rate for Bidirectional layup; (b)– Comparison between Joint stiffness vs. Loading Rate for variable Diameter for Bidirectional layup.
From Fig. 9 (a), it is observed that for all loading rates of 0.2 mm/min, 2 mm/min and 5 mm/min joint stiffness increases as bolt diameter increases. This trend is similar in both unidirectional and bidirectional [0/90] s. . From Fig. 9 (b) it is observed that effect of loading rate on joint stiffness for bolt diameter 4mm and 5mm is negligible. But for bolt diameter of 6mm, effect of loading rate on joint stiffness is considerable. K vs D (0.2mm/min)
Unidirectional
Bidirectional
K vs D (2mm/min)
Unidirectional
Bidirectional
Joint Stiffness (N/mm)
Joint Stiffness (N/mm)
a
Diameter (mm)
Diameter (mm)
Fig. 10 (a) Comparison between unidirectional and bidirectional on joint stiffness for different diameters for loading rate 0.2 mm/min; (b) Comparison between unidirectional and bidirectional on joint stiffness for different diameters for loading rate 2 mm/min.
b
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K vs D (5mm/min) Joint Stiffness (N/mm)
a
Unidirectional
K vs Loading Rate (4 mm) Unidirectional
Bidirectional
Joint Stiffness (N/mm)
194 202
Diameter (mm)
Loading Rate (mm/min)
Fig. 11. (a) Comparison between unidirectional and bidirectional on joint stiffness for different diameters for loading rate 5 mm/min Comparison between unidirectional and bidirectional on joint stiffness for different loading rates for bolt diameter 4 mm.
K vs Loading Rate (5mm)
Bidirectional
Joint Stiffness (N/mm)
UNidirectional
Loading Rate (mm/min)
K vs Loading Rate (6mm)
Unidirectional
; (b)
b
Bidirectional
Joint Stiffness (N/mm)
a
b
Bidirectional
Loading Rate (mm/min)
Fig. 12. (a) Comparison between unidirectional and bidirectional on joint stiffness for different loading rates for bolt diameter 5 mm Comparison between unidirectional and bidirectional on joint stiffness for different loading rates for bolt diameter 6 mm.
; (b)
6. Conclusions In this work the analytical model for the parametric study of single bolted single lap composite bolted joint for the tensile loading has been extended to the compressive loading to identify the significant parameters of the joint stiffness. The experiments were designed to test the effect of the joint parameters such as bolt diameter, loading rate and unidirectional and bidirectional composite laminates. The analytical model used here can predict the influencing parameters; however, the joint stiffness obtained from the model does not match with the experimental value. The deviation in the joint stiffness could be because of buckling effect under compressive loading and non linear behavior of the joint. The model makes use of elements giving linear response. The model needs refinement in order to suit for the compressive loading. It is observed from the experimental results with increase in bolt diameter joint stiffness increases in both unidirectional and bi-directional [0/90] s specimen. In case of unidirectional specimen, effect of loading rate on joint stiffness for bolt diameter 4mm is negligible. Whereas for bolt diameter of 5mm and 6mm effect of loading rate on joint stiffness is considerable. In case of bi-directional [0/90] s specimen effect of loading rate on joint stiffness for bolt diameter 4mm and 5mm is negligible. While for bolt diameter of 6mm, effect of loading rate on joint stiffness is considerable. Acknowledgements This work was completed with the grants and facilities of PCCOE. Authors are thankful to this institute for extending this cooperation. References [1] D. Srinivasa , Thoppul, Joana Finegan,Ronald F. Gibson ,Mechanics of mechanically fastened joints in polymer–matrix composite structures – A review, Composites Science and Technology. 69 (2009) 301–329.
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[2] A. Olmedo, C. Santiuste, E. Barbero, An analytical model for the secondary bending prediction in single-lap composite bolted-joints, Composite Structures. 111 (2014) 354–361. [3] K. Gordon, S. Hallstro, Bearing strength of carbon fibre/epoxy laminates: effects of bolt-hole clearance, Composites. Part B Engineering. 35(4) (2004) 331–343 [4] B. Okutan, The effects of geometric parameters on the failure strength for pin-loaded multi-directional fiber-glass reinforced epoxy laminate, Composites. Part B 33 (2002) 567–578. [5] F. Nerilli, M. Marino, G. Vairo, A numerical failure analysis of multi-bolted joints in FRP laminates based on basalt fibers, Procedia Engineering. 109 (2015) 492 – 506. [6] N.K. Hassan, M.A. Mohamedient, S.H. Rizkallat, Finite element analysis of bolted connections for PFRP composites, Composites. Composites Part B: Engineering, 27(3-4) 1996, 339-349. [7] T. Dang Hoang, C. Herbelot , A. Imad, On failure mode analysis in a bolted single lap joint under tension-shearing, Engineering Failure Analysis. 24 (2012) 9–25. [8] M.A. McCarthy, V.P. Lawlor, W.F. Stanley, C.T. McCarthy, Bolt-hole clearance effects and strength criteria in single-bolt, single-lap, composite bolted joints, Composites Science and Technology. 62 (2002) 1415–1431. [9] M.A. McCarthy, C.T. McCarthy, G.S. Padhi, A simple method for determining the effects of bolt–hole clearance on load distribution in single-column multi-bolt composite joints, Composite Structures .73 (2006) 78–87. [10] Á. Olmedo, C. Santiuste, On the prediction of bolted single-lap composite joints, Composite Structures. 94 (2012) 2110–2117. [11] U.A. Khashaba, T.A. Sebaey, K.A. Alnefaie , Failure and reliability analysis of pinned-joints composite laminates: Effects of stacking sequences, Composites Part: B Engineering. 45(1) (2013) 1694–1703. [12] C.T. McCarthy, P.J. Gray, An analytical model for the prediction of load distribution in highly torqued multi-bolt composite joints, Composite Structures. 93 (2011) 287–298. [13] Y. Xiao, T. Ishikawa, Bearing strength and failure behavior of bolted composite joints (part I: Experimental investigation), Composites Science and Technology. 65 (2005) 1022–1031. [14] V.P. Lawlor, W.F. Stanley, M.A. McCarthy, Characterization of damage development in single shear bolted composite joints, Plastics, Rubber and Composites. 31 (2002) 126-133. [15] R.M. Wood, S.X.S. Bauer, Simple and Low-Cost Aerodynamic Drag Reduction Devices for Tractor-Trailer Trucks, SAE 2003-01-3377. [16] ASTM D 5961, Standard test method for bearing response of polymer matrix composite laminates.
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11th International Conference Interdisciplinarity in Engineering, INTER-ENG 2017, 5-6 October 11th International Conference Interdisciplinarity in Engineering, 2017, Tirgu-Mures, Romania INTER-ENG 2017, 5-6 October 2017, Tirgu-Mures, Romania
Parametric study of composite bolted joint under compressive
Parametric study of composite bolted joint2017, under compressive Manufacturing Engineering Society International Conference MESIC 2017, 28-30 June loading 2017, Vigoloading (Pontevedra), Spain a,
b
Laxman V. Awadhania, *, Anand Bewoorb Costing models for capacity optimization Industry 4.0: Trade-off Laxman V. Awadhani *, AnandinBewoor Savitribai Phule Pune University, Pune, India between used and operational efficiency Scapacity avitribai Phule University, Pune, India Mechanical Engineering Department, Cummins College of Pune Engineering for Women, Savitribai Phule Pune University, Pune, India P
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b P
Mechanical Engineering Department, Cummins College of Engineering for Women, Savitribai Phule Pune University, Pune, India P
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb Abstract a University of Minho, 4800-058 Guimarães, Portugal Abstract b Unochapecó, 89809-000 Chapecó, SC, Brazil Use of composite structures in various sectors is rapidly increasing. The composite materials are becoming very popular due to Use composite structures in high various sectorstois weight rapidly ratio, increasing. The composite materials are becoming very popular due to high ofstrength to weight ratio, stiffness low coefficient of friction, improved appearance etc. Extensive high strength to weight high stiffness to weight ratio, lowsubjected coefficient friction, improved etc. Extensive literature is available for ratio, the behavior of composite bolted joints to of tensile loading for theappearance aerospace structures. The literature is available theisbehavior of composite joints subjected tensile loading for the of aerospace structures. The work reported in this for paper an attempt to extend bolted the analytical model fortostudying the behaviour composite bolted joint Abstract work in this paper The is anmodel attempt to extend the analytical for studying of composite bolted joint under reported compressive loading. is capable of conducting the model parametric study onthe thebehaviour joint stiffness variation with respect under compressive The model4.0", is capable of conducting thesequence parametric on the joint stiffnessThe variation with respect to parameters suchloading. asofplate width, bolt diameter and processes stacking compressive loading. model is verified Under the concept "Industry production will beforstudy pushed to be increasingly interconnected, to parametersbased such as boltdesigned diameter stacking sequence for compressive loading. capacity The model is stiffness. verified experimentally. The on experiments toand study the effect of variation inIn the on the joint information aplate real width, timewere basis and, necessarily, much more efficient. thisparameters context, optimization experimentally. Thebidirectional experimentscarbon were fibre designed tocomposite study thelaminates effect ofwere variation in per the ASTM parameters on The the parameters joint stiffness. Unidirectional and epoxy tested D5961. viz. goes beyond the traditional aim of capacity maximization, contributing also foras organization’s profitability and value. Unidirectional and bolt bidirectional carbon fibre of epoxy composite laminates were as tested as per ASTM D5961. The parameters viz. stacking sequence, diameter, plate width the joint stiffness are identified significant. Indeed, lean management and continuous improvement approaches suggest capacity optimization instead of stacking sequence, bolt diameter,byplate widthB.V. of the joint stiffness are identified as significant. © 2018 The Authors. Published Elsevier maximization. The study of capacity optimization and costing models is an important research topic that deserves © 2018 The under Authors. Published by Elsevier B.V.committee Peer-review responsibility ofthe scientific of the 11th International Conference Interdisciplinarity in © 2018 The Authors. Published by Elsevier B.V. contributions from both the practical and theoretical This paperConference presents and discusses a mathematical Peer-review under responsibility ofthe scientific committeeperspectives. of the 11th International Interdisciplinarity in Engineering. Peer-review under responsibility of the scientific committee of the 11th International Conference Interdisciplinarity Engineering. model for capacity management based on different costing models (ABC and TDABC). A generic in model has been Engineering.
developed and it was used to analyze capacity and to design strategies towardsloading; the maximization Keywords: Characterization; Composite boltedidle joint; Analytical model; Joint stiffness; Compressive joint behavior. of organization’s Keywords: Characterization; Composite bolted joint; Analytical model; Jointefficiency stiffness; Compressive loading;and jointitbehavior. value. The trade-off capacity maximization vs operational is highlighted is shown that capacity optimization might hide operational inefficiency. © The Authors. Published by Elsevier B.V. 1. 2017 Introduction 1. Introduction Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. Use of composite structures in various sectors is rapidly increasing. The composite materials are becoming very Use ofdue composite variousratio, sectors is stiffness rapidly increasing. materials becoming very popular to high structures strength toinweight high to weight The ratio,composite low coefficient of are friction, improved Keywords: Cost Models; TDABC; Capacity; Efficiency popular due to highABC; strength to Capacity weight Management; ratio, high Idle stiffness toOperational weight ratio, low coefficient of friction, improved 1. Introduction
* Corresponding author. Tel.: +91-902-873-0691. * E-mail Corresponding author. Tel.: +91-902-873-0691. address:[email protected] The cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address:[email protected]
in modern production systems. In general, it is defined as unused capacity or production potential and can be measured 2351-9789© 2018 The Authors. Published by Elsevier B.V. 2351-9789© 2018 The Authors. Published by Elsevier B.V.hours Peer-review responsibility ofthe scientific committee of the 11th Conference in Engineering. in several under ways: tons of production, available of International manufacturing, etc. Interdisciplinarity The management of the idle capacity Peer-review underTel.: responsibility scientific committee of 741 the 11th International Conference Interdisciplinarity in Engineering. * Paulo Afonso. +351 253ofthe 510 761; fax: +351 253 604 E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 11th International Conference Interdisciplinarity in Engineering. 10.1016/j.promfg.2018.03.029
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appearance etc. The structures are built either by fastening or by bonding. The bonded joints are suitable for the light duty applications while the fastened joints are used for moderate and heavy duty applications. The bolted structures can be assembled or dismantled easily which facilitates the repairs. Due to cost and specialized needs for manufacturing, the applications of the composite structures were limited to aerospace industry. Presently composite bolted joints are extensively used in the modern machine structures in order to reduce the weight of the machines, reduce the energy requirement of the machine etc. The current applications of the composite bolted joint include secondary structures in the automobiles such as fairings on heavy duty trucks [15] or front or rear panels of bus which are subjected to compressive loadings due to weight. Extensive literature is available for studying the behavior of composite bolted joints subjected to tensile loading for the aerospace structures [1]. 1.1. Background Various researchers have analyzed the bolted joint using numerical analysis and experimental analysis for the characterization. The analytical model has been used by few researchers for the prediction of the performance of the composite bolted joint as well as investigating the parameters influencing the joint stiffness of composite bolted joint [1]. The performance of the composite bolted joint has been extensively studied for tensile loading, but compressive loading significantly not reported in the literature. The characterization studies based on analytical models from the literature for tensile loading included joint parameters such as length, width, edge distance, stacking sequence, bolt diameter, tightening torque, coefficient of friction, bolt-hole clearance etc. Hence the behavioral studies of composite bolted joint has been undertaken. 1.2. Literature Review The spring based analytical model to predict the stiffness of single- lap composite bolted joint includes a predictive method to consider the effect of secondary bending as a function of geometrical parameters, material elastic properties, stacking sequence, and load path eccentricity [2]. The analytical prediction for bolted joints in composites is being done in tensile loading for past few years. The criteria used were ‘Yamada–Sun failure criterion’ and the ‘Chang–Scott–Springer characteristic curve model’. As development progressed the methodology changed resulting in more accurate and precise results and predictions. Finite Element Analysis and software’s like ABAQUS are used. [4, 5, 6, 10] The researchers described the effect of parameters like stacking sequence, fastening torque, clearance between bolt and hole, bolt diameter, coefficient of friction, length, width, edge to diameter ratio and mating materials [3, 7, 8, 9, 12, 13, and 14]. The influence of specimen stacking sequences on the mean bearing strength, mean ultimate failure stress, failure displacement and bearing stiffness is found as specimens with [0/90] 2s stacking sequence have the maximum failure displacement and ultimate failure stress compared with the other stacking sequences. [11]. The work reported in this paper is an attempt to extend the analytical model for studying the behavior of composite bolted joint under compressive loading. The model is capable of conducting the parametric study on the joint stiffness variation with respect to parameters such as plate width, bolt diameter and stacking sequence for compressive loading. The model is validated experimentally. The experiments were designed to study the effect of variation in the parameters on the joint stiffness. Unidirectional and bidirectional carbon fiber epoxy composite laminates were tested as per ASTM D5961 [16]. The parameters such as bolt-hole clearance, length of plate and bolt preload were not included in the experimental studies. 1.3. Analytical Model An analytical model to predict the stiffness of single- lap composite bolted joint is proposed. The present analytical model is an extension of the model proposed by McCarthy [12]. The compressive loading may include the effect of buckling of the plates which is taken care in the experimentation by using a fixture to avoid the buckling.
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a
b
Fig. 1. (a) Single lap single bolted composite bolted joint; (b) Spring mass model of composite bolted joint [12].
The single-lap single-bolt composite joint shown in Fig. 1a may be represented by a system of masses and springs, as shown in Fig. 1b. The joint load is applied at mass 3 and reacted at the clamped end of the joint. 𝑀𝑀1 = mass of plate 1 𝑀𝑀3 = mass of plate 2 𝑀𝑀2 = mass of bolt 𝐾𝐾𝑏𝑏 = Stiffness of bolt 𝐾𝐾𝑝𝑝𝑝𝑝𝑝𝑝 = Stiffness of plates in longitudinal direction 𝐾𝐾𝑠𝑠ℎ−𝑝𝑝𝑝𝑝𝑝𝑝 = Stiffness of plate in shearing Considering that masses are free to move in the x-direction only, the system shown in leads to a system of linear equations of the form:
{F } [ M ]{x} + [ K ]{ x} =
(1)
For quasi-static loading, the accelerations can be neglected, leading to
[ K ]{ x} = {F }
(2)
Calculation of the displacements is straightforward by pre-multiplying the load vector F by the inverse of stiffness matrix K.
K pl 1 + K shear −K shear 0 K pl 1 + K bolt −K bolt 0
0 x1
− K shear K shear + K pl 2 − K pl 2 − K bolt K bolt + K pl 2 − K pl 2
0 − K pl 2 x2 = 0 K pl 2 x3 − F 0 x1
− K pl 2 x2 = K pl 2 x3
− K bolt c − K bolt u f + Ffricc K c+K u −F bolt f fricc bolt −F
(3)
(4)
2. Calculations of spring stiffness The composite plate stiffness, in each plate i, can be found considering a composite laminate subjected to uniform compressive load: K pli = E LciWci tci
(p
ci
− D 2)
(5)
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Where E Lc is the equivalent elasticity modulus in longitudinal direction calculated using the laminate theory. W c and t c are width and thickness of the composite plate respectively. Pc is the distance between the hole centre and the plate free end where load is applied, and D is the hole diameter. The shear stiffness K shear is found as the shear stiffness of the two composite plates in series.
1 1 K shear = + K sh − pl 1 K sh − pl 2
−1
(6)
The maximum value of friction forces that the joint can transmit, F fricc , is obtained considering the friction coefficient and the normal force produced by the bolt torque Ffricc = µ Ft
(7)
The stiffness included in bolt can be found as follows: K bolt=
1 K sh − b
+
1 K bend − b
+
1 K be − pl 1
+
1 Kϕ 1
+
1 K be − pl 2
+
Kϕ 2 1
−1
where, 𝐾𝐾𝑠𝑠ℎ−𝑏𝑏 is bolt shear stiffness given as: K sh − b =
3Gb Ab 4t
(8)
(9)
where, G b is bolt shear modulus and A b is cross section area of bolt. The bolt bending stiffness K bend-b is given by: K bend − b =
Eb t 4
(10)
Where, E b is the Young Modulus of bolt material. Bearing stiffness of plates is given by:
K be − pli = t EL ET
(11)
Where, 𝐸𝐸𝑇𝑇 is the equivalent elasticity modulus of composite plate in transverse direction. The secondary bending stiffness for each composite plate is: Kφ =
16 EI tt m L
(12)
where, t m is the load path eccentricity. MATLAB code is developed to identify influencing parameters on joint properties. Then 'Load vs. Displacement' curve is plotted. The inputs given to MATLAB code are given in Table1.
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Table 1. Input for the MATLAB code. Parameters
Values
Elasticity modulus in longitudinal direction (EL)
240 GPa
Elasticity modulus in transverse direction (ET)
70 GPa
Density
1800 g/cc
Filament diameter
7 micrometer
Number of layers
10
Poisson's ratio of fiber
0.25
Poisson's ratio of matrix
0.30
Flexural rigidity (EI)
4.267 Nmm2
Unidirectional fibre layup Bidirectional fibre layup [0/90] s
23.0245Nmm2
Clearance
0 micron to 200 micron
Tightening Torque
0 N-mm to 4000 N-mm
Coefficient of Friction
0.1 to 0.5
Specimen width
20 mm to 40 mm
Specimen length
75 mm to 195 mm
Specimen thickness
3 mm
Young's Modulus of bolt
117 GPa
Shear Modulus of bolt
43 GPa
Initially the load displacement curves for parametric variations were found out and from these graphs the joint stiffness was determined. By varying the plate width, the load displacement diagram is obtained as shown in Fig. 2. Load vs Displacement
w=20 mm
Load (N)
w=25 w=30 w=35 Displacement (mm)
w=40
Fig. 2. Load vs. Displacement Curves for different values of width.
From Fig. 2 it is observed that joint stiffness varies as the width varies. Similar graphs were plotted by varying bolt tightening torque, clearance, length of specimen, coefficient of friction and bolt diameter. From the loaddisplacement curves, the joint stiffness was calculated. The variation of the joint stiffness with respect to the various parameters is presented in Fig. 3 to 5. 3. Variation in Joint Stiffness for different parameters From Fig. 3(a) it is observed that joint stiffness varies as the width varies. It is observed that changing width from 20 mm to 40 mm, stiffness changes from 9882.6 N/mm to 13639 N/mm. Thus width is significant parameter
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From Fig. 3(b) it is observed that joint stiffness varies as the length varies. It is observed that changing length from 75 mm to 195 mm, stiffness changes from 15151.4 N/mm to 10078.4 N/mm. Hence length is also significant parameter. From Fig. 4(a) it is observed that joint stiffness negligibly varies as the coefficient of friction varies. It is observed that changing coefficient of friction from 0.1 to 0.5, stiffness changes from 12169.3 N/mm to 12026.7 N/mm. Therefore it is not significant parameter From Fig. 5(a) it is observed that joint stiffness negligibly varies as the Torque varies. It is observed that changing torque from 0 N-mm to 4000 N-mm, stiffness changes from 12202.5 N/mm to 11837.2 N/mm. Therefore bolt tightening torque is insignificant parameter in compressive loading. From Fig. 4(b) it is observed that joint stiffness varies as the clearance varies. It is observed that changing clearance from 0 to 200 micron stiffness changes from 11403.3N/mm to 12923.8 N/mm. Hence clearance has significant effect on joint stiffness. From Fig. 5(b) it is observed that joint stiffness varies as the Diameter varies. It is observed that changing diameter from 5 mm to 15 mm, stiffness changes from 9497.929N/mm to 9917 N/mm. Therefore bolt diameter is significant parameter.
b Joint Stiffness (N/mm)
Joint Stiffness (N/mm)
a
Length (mm)
Width (mm) Fig. 3. Joint Stiffness vs. (a)Width and (b) Length.
b Joint Stiffness (N/mm)
Joint Stiffness (N/mm)
a
Coeff. of friction
Clearance (micron)
Fig. 4 Joint Stiffness vs. Coefficient of friction and bolt hole clearance.
b
Joint Stiffness(N/mm)
Joint Stiffness (N/mm)
a
Torque N-mm
Diameter(mm)
Fig. 5. Joint Stiffness vs. (a) Tightening torque and (b) Bolt diameter.
4. Experimentation According to ASTM D 5961[16] the compression shear test was conducted. The experimental work is carried with the help of support fixture as shown in Fig. 6 (a) for holding the specimen between the flat circular plates of the
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UTM crossheads. The load range lies between 0 - 10 kN. For experimentation 18 tests are carried out according to Design of Experiment. Table 2. Details of specimen geometry. Specimen Type
Bolt diameter ‘d’ (mm)
Edge distance ‘e’ (mm)
Quantity (Nos.)
1
4
16
6
2
5
20
6
3
6
24
6
The parameters taken into account for the analytical parametric study for determining the joint stiffness of composite bolted joint are length of specimen, width of specimen, bolt-hole clearance, bolt tightening torque, coefficient of friction, bolt diameter. But only few of these mentioned parameters have a major impact on the joint stiffness as concluded from the observations made in previous article. The finalization of parameters in experimental parametric studies is mentioned further. Even though length of the specimen is found as a significant parameter in the analytical work, it is kept constant as per the guidelines of ASTM D5961. Width of composite specimen is also found as a significant parameter, but due to the limitations of the support fixture is kept constant. Bolt-hole clearance is significant parameter influencing joint stiffness. Neat Fit Case is considered for the experiment. Bolt diameter is a significant parameter in determining the joint stiffness. From the graphs plotted previously it can be noted that the joint stiffness increases as the bolt diameter increases. The bolt diameters selected for the parametric study are 4 mm, 5 mm & 6 mm. As there is no significant work done on varying loading rate, it is selected as the parameter in order to find out whether it is significant or insignificant parameter. The loading rates selected for the parametric study are 0.2mm/min, 2mm/min & 5mm/min. It is observed from the literature that stacking sequence has prominent effect on the joint stiffness as the different lay-up of fibers in the composite materials have a different load sustaining capability. So the stacking sequences selected for the parametric study are Unidirectional & Bidirectional [0/90] s fibre lay-up. The Load vs. Displacement curves are obtained on UTM for each 18 trials as per Design of Experiment. Fig. 7 shows the specimen after the testing which represents secondary bending failure in the compression test.
a
b
Fig. 6 Test fixture and Test specimen geometry.
a
b
Fig. 7 Specimen failures after compression test.
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5. Results and discussion The test results are represented in the form of joint stiffness variation with respect to the various parameters such as loading rate, bolt diameter and the unidirectional or bidirectional composite laminates.
a
b
K vs Loading Rate (D) 0.2LRUD 2LRUD 5LRUD
Joint stiffness (N/mm)
Joint stiffness (N/mm)
K vs Diameter (LR)
Diameter (mm)
4DUD 5DUD 6DUD Loading Rate (mm/min)
Fig. 8 (a) Comparison between Joint stiffness vs. Diameter for variable loading rate for Unidirectional layup; (b) – Comparison between Joint stiffness vs. loading rate for variable bolt diameter for Unidirectional layup.
From Fig. 8 (a) it is observed that for all loading rates of 0.2 mm/min, 2 mm/min and 5 mm/min joint stiffness increases as bolt diameter increases. From this Fig. 8 (b) it is observed that effect of loading rate on joint stiffness for bolt diameter 4mm is negligible. Whereas for bolt diameter of 5mm and 6mm effect of loading rate on joint stiffness is considerable.
a
0.2LRBD 2LRBD 5LRBD
Diameter (mm)
b
K vs Loading Rate (D) Joint stiffness (N/mm)
Joint stiffness (N/mm)
K vs Diameter (LR)
4DBD 5DBD 6DBD Loading rate (mm/min)
Fig. 9 (a) Comparison between Joint stiffness vs. Diameter for variable loading rate for Bidirectional layup; (b)– Comparison between Joint stiffness vs. Loading Rate for variable Diameter for Bidirectional layup.
From Fig. 9 (a), it is observed that for all loading rates of 0.2 mm/min, 2 mm/min and 5 mm/min joint stiffness increases as bolt diameter increases. This trend is similar in both unidirectional and bidirectional [0/90] s. . From Fig. 9 (b) it is observed that effect of loading rate on joint stiffness for bolt diameter 4mm and 5mm is negligible. But for bolt diameter of 6mm, effect of loading rate on joint stiffness is considerable. K vs D (0.2mm/min)
Unidirectional
Bidirectional
K vs D (2mm/min)
Unidirectional
Bidirectional
Joint Stiffness (N/mm)
Joint Stiffness (N/mm)
a
Diameter (mm)
Diameter (mm)
Fig. 10 (a) Comparison between unidirectional and bidirectional on joint stiffness for different diameters for loading rate 0.2 mm/min; (b) Comparison between unidirectional and bidirectional on joint stiffness for different diameters for loading rate 2 mm/min.
b
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K vs D (5mm/min) Joint Stiffness (N/mm)
a
Unidirectional
K vs Loading Rate (4 mm) Unidirectional
Bidirectional
Joint Stiffness (N/mm)
194 202
Diameter (mm)
Loading Rate (mm/min)
Fig. 11. (a) Comparison between unidirectional and bidirectional on joint stiffness for different diameters for loading rate 5 mm/min Comparison between unidirectional and bidirectional on joint stiffness for different loading rates for bolt diameter 4 mm.
K vs Loading Rate (5mm)
Bidirectional
Joint Stiffness (N/mm)
UNidirectional
Loading Rate (mm/min)
K vs Loading Rate (6mm)
Unidirectional
; (b)
b
Bidirectional
Joint Stiffness (N/mm)
a
b
Bidirectional
Loading Rate (mm/min)
Fig. 12. (a) Comparison between unidirectional and bidirectional on joint stiffness for different loading rates for bolt diameter 5 mm Comparison between unidirectional and bidirectional on joint stiffness for different loading rates for bolt diameter 6 mm.
; (b)
6. Conclusions In this work the analytical model for the parametric study of single bolted single lap composite bolted joint for the tensile loading has been extended to the compressive loading to identify the significant parameters of the joint stiffness. The experiments were designed to test the effect of the joint parameters such as bolt diameter, loading rate and unidirectional and bidirectional composite laminates. The analytical model used here can predict the influencing parameters; however, the joint stiffness obtained from the model does not match with the experimental value. The deviation in the joint stiffness could be because of buckling effect under compressive loading and non linear behavior of the joint. The model makes use of elements giving linear response. The model needs refinement in order to suit for the compressive loading. It is observed from the experimental results with increase in bolt diameter joint stiffness increases in both unidirectional and bi-directional [0/90] s specimen. In case of unidirectional specimen, effect of loading rate on joint stiffness for bolt diameter 4mm is negligible. Whereas for bolt diameter of 5mm and 6mm effect of loading rate on joint stiffness is considerable. In case of bi-directional [0/90] s specimen effect of loading rate on joint stiffness for bolt diameter 4mm and 5mm is negligible. While for bolt diameter of 6mm, effect of loading rate on joint stiffness is considerable. Acknowledgements This work was completed with the grants and facilities of PCCOE. Authors are thankful to this institute for extending this cooperation. References [1] D. Srinivasa , Thoppul, Joana Finegan,Ronald F. Gibson ,Mechanics of mechanically fastened joints in polymer–matrix composite structures – A review, Composites Science and Technology. 69 (2009) 301–329.
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[2] A. Olmedo, C. Santiuste, E. Barbero, An analytical model for the secondary bending prediction in single-lap composite bolted-joints, Composite Structures. 111 (2014) 354–361. [3] K. Gordon, S. Hallstro, Bearing strength of carbon fibre/epoxy laminates: effects of bolt-hole clearance, Composites. Part B Engineering. 35(4) (2004) 331–343 [4] B. Okutan, The effects of geometric parameters on the failure strength for pin-loaded multi-directional fiber-glass reinforced epoxy laminate, Composites. Part B 33 (2002) 567–578. [5] F. Nerilli, M. Marino, G. Vairo, A numerical failure analysis of multi-bolted joints in FRP laminates based on basalt fibers, Procedia Engineering. 109 (2015) 492 – 506. [6] N.K. Hassan, M.A. Mohamedient, S.H. Rizkallat, Finite element analysis of bolted connections for PFRP composites, Composites. Composites Part B: Engineering, 27(3-4) 1996, 339-349. [7] T. Dang Hoang, C. Herbelot , A. Imad, On failure mode analysis in a bolted single lap joint under tension-shearing, Engineering Failure Analysis. 24 (2012) 9–25. [8] M.A. McCarthy, V.P. Lawlor, W.F. Stanley, C.T. McCarthy, Bolt-hole clearance effects and strength criteria in single-bolt, single-lap, composite bolted joints, Composites Science and Technology. 62 (2002) 1415–1431. [9] M.A. McCarthy, C.T. McCarthy, G.S. Padhi, A simple method for determining the effects of bolt–hole clearance on load distribution in single-column multi-bolt composite joints, Composite Structures .73 (2006) 78–87. [10] Á. Olmedo, C. Santiuste, On the prediction of bolted single-lap composite joints, Composite Structures. 94 (2012) 2110–2117. [11] U.A. Khashaba, T.A. Sebaey, K.A. Alnefaie , Failure and reliability analysis of pinned-joints composite laminates: Effects of stacking sequences, Composites Part: B Engineering. 45(1) (2013) 1694–1703. [12] C.T. McCarthy, P.J. Gray, An analytical model for the prediction of load distribution in highly torqued multi-bolt composite joints, Composite Structures. 93 (2011) 287–298. [13] Y. Xiao, T. Ishikawa, Bearing strength and failure behavior of bolted composite joints (part I: Experimental investigation), Composites Science and Technology. 65 (2005) 1022–1031. [14] V.P. Lawlor, W.F. Stanley, M.A. McCarthy, Characterization of damage development in single shear bolted composite joints, Plastics, Rubber and Composites. 31 (2002) 126-133. [15] R.M. Wood, S.X.S. Bauer, Simple and Low-Cost Aerodynamic Drag Reduction Devices for Tractor-Trailer Trucks, SAE 2003-01-3377. [16] ASTM D 5961, Standard test method for bearing response of polymer matrix composite laminates.