Monotonic and Fatigue Behaviour of Double Shear Bolted Joints: Experimental and Numerical Studies

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Monotonic and Fatigue Behaviour of Double Shear Bolted

Joints: Experimental and Numerical Studies

Lucas Fernandes Rodrigues Coelho da Silva

Advisor: Abílio M. P. de Jesus

Co-advisors: Vitor M. G. Gomes & José A. F. O. Correia

June 2020

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Abstract

Racking systems are usually built using thin steel plates with different surface finishing including zinc coating and zinc plus paint coating. These structures when used in automatic storage systems tend to be loaded 24 hours a day, 7 days a week in which due to the cyclic nature of loadings, tend to raise fatigue issues.

Double shear bolted joints are typically used in racking system. In industrial environment, bolts are not always properly tightened resulting in snug tight bolts. Properly preloaded bolts transmit forces by friction, but that is not what happens in the snug tight case. In this case, the behaviour of the double shear joints becomes more unpredictable, include their fatigue performance.

A significant program of monotonic and fatigue tests was performed in order to investigate the behaviour of double shear bolted joints. Different conditions were analysed including bolts arrangement, stress R-ratio, bolt preload, surface finishing and hole preparation. The obtained fatigue data were analyzed with the help of PROFATIGUE software and using statistical procedure of ASTM E739, in order to obtain S-N curves.

This work revealed some discrepancies between Eurocode 3 suggested S-N curves and obtained experimental data. Snug tight bolts presented an average fatigue strength of 114 MPa at 2E6 cycles while preloaded bolts presented an average fatigue strength at 2E6 cycles of 108 MPa.

Numerical damage models were developed in order to model the monotonic behaviour of the bolted joints. The models predicted ultimate loads and maximum displacements with good accuracy. The numerical models were also able to predict damage initiation, damage evolution and fracture locus according to the experimental data.

Crack growth simulations were modeled using software Franc3D . Postulated initial Central and throughR

thickness cracks were analysed with snug tight and preloaded bolted joints. The cracks were submitted to fatigue loads with maximum load of 150 MPa and stress R-ratio equal to 0.1. The main objective of these simulations were to grow the cracks from its initial size until the critical stress intensity factors making it possible to evaluate the critical crack size and number of cycles to reach it.

Franc3D simulations showed that preloaded connections have bigger critical crack sizes and stand almost three times more cycles than snug tight connections. This result showed the importance of properly loaded bolted joints as it gives maintenance crews more time to replace the cracked parts and avoid catastrophic failures that leads to time and money losses.

Keywords: Bolted Connections; Monotonic Static Behaviour; Fatigue Behaviour; S-N Curves; Numerical Analysis; Ductile Damage; Fatigue Crack Growth.

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Acknowledgement

The author express his gratitude to the FASTCOLD RFCS European Project (Grant Agreement No. 745982). Shelter S.A (Prokopis Tsintzos and Markos Mezari) is particularly acknowledged for the material supply. The SciTech (Science and Technology for Competitive and Sustainable Industries) RD project NORTE-01-0145-FEDER-000022 co-financed by Programme Operational Regional do Norte ("NORTE2020") through Fundo Europeu de Desenvolvimento Regional (FEDER) and the Portuguese Science Foundation (FCT) through the post-doctoral grant SFRH/BPD/107825/2015 are also acknowledged for their financial aid. Additionaly, the author would like to thank the support given by the Construction Institute (IC) of the University of Porto, Portugal.

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Nomenclature

α Threshold parameter for normalized variable

σ Stress

σa Alternate stress

σm Average stress

σmin Minimum stress

σmax Maximum stress

σt True stress

∆σ Stress range

∆σr Stress range at mechanical part

∆σc Fatigue strenght at 2.106 cycle (fatigue class)

∆ Strain range

∆K Stress intensity factor range

∆Kth Fatigue crack growth threshold

Strain

t True strain

γ Walker’s exponent

µslipav g Average value of slip factor

µslip Slip factor

µc Characteristic slip factor

η Triaxiality

Ab Bolt area

b Material constant for S-N curve B Threshold for lifetime

C Materials constant for crack growth equation C0 Material constant for S-N curve

C” Calibration coefficient.

D Threshold parameter for stress level

D1 Minor diameter

D2 Pitch diameter

D3 Major diameter

Dbolt Bolt diameter

Dw Bolt head diameter

F Axial fore

Fp Preload applied to the bolt

Fslip Load applied by the test machine on slip tests

H Height of the thread

kb Bolt stiffness

km Equivalent stiffness

Kc Material toughness

m Material’s exponent for crack growth equation Mclamping Clamping torque

nbolt Number of bolts

nshear Number of shear planes

N Number of cycles

Nf Number of cycles for failure

p Hidrostatic pressure

P Pitch

Pf Probability of failure for a specimen

q Equivalent Von Mises stress

Q External load

Qb Load on bolts

Qm Load on members

Qmin Minimum load

Qmax Maximum load

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Sf Stress range for failure

Se Stress range for endurance limit

S Standard deviation S2 _Variance Sf Safety factor Sy Yield strength Su Ultimate strength T Torque X Independent variable Y Dependent variable

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List of Figures

Figure 1: Automated storage and retrieval system for warehouse . . . 1

Figure 2: Cracks near bolt holes . . . 1

Figure 3: Bolted joints applied to racking systems . . . 2

Figure 4: Schematic of void nucleation, growth and coalescence leading to fracture [2] . . . 3

Figure 5: Schematic graphic of the relation between fracture strain and stress triaxiality [3] . . . 4

Figure 6: Typical fatigue loading . . . 5

Figure 7: Typical Wöhler curve for steels . . . 5

Figure 8: Different fatigue regimes. Adapted from [4] . . . 6

Figure 9: The three fundamental pure cracking modes . . . 7

Figure 10: Eucode 3 detail categories for bolted joints . . . 8

Figure 11: Bolt nomenclature . . . 9

Figure 12: M20 bolt thread nomenclature: A)Bolt shank B)Thread dimensions . . . 10

Figure 13: Schematic image of a bolted joint . . . 11

Figure 14: Double shear bolted joint . . . 11

Figure 15: Geometry of specimens for slip tests (left) and slip tests setup (right) . . . 14

Figure 16: Geometry of the 1+1 specimen used in static monotonic tests, with photo of the experimental setup . . . 16

Figure 17: Geometry of the 4+4 specimen used in static monotonic tests, with photo of the experimental setup . . . 17

Figure 18: Geometry of specimens for static tests: A) 1+1 bolted joint B)4+4 bolted joint . . . 17

Figure 19: Results for monotonic static tests for uncoated single bolted jointS with 2mm plates: A) Snug tight; B) Preloaded . . . 18

Figure 20: Results for monotonic static tests for uncoated single bolted joints with 3mm plate: A) Snug tight; B) Preloaded . . . 19

Figure 21: Results for monotonic static tests for uncoated multiple bolted joints with 2mm plates: A) Snug tight; B) Preloaded . . . 19

Figure 22: Results for monotonic static tests for uncoated multiple bolted joints with 3mm plates: A) Snug tight; B) Preloaded . . . 20

Figure 23: Results for monotonic static tests for zinc coated single bolted joints with 2mm plates: A) Snug tight; B) Preloaded . . . 20

Figure 24: Results for monotonic static tests for zinc coated single bolted joints with 3 mm plates: A) Snug tight; B) Preloaded . . . 21

Figure 25: Results for monotonic static tests for zinc coated multiple bolted joints with 2mm plates: A) Snug tight; B) Preloaded . . . 21

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Figure 26: Results for monotonic static tests for zinc coated multiple bolted joint with 3 mm plate: A)

Snug tight B) Preloaded . . . 22

Figure 27: Results for monotonic static tests for zinc plus paint coated single bolted joints with 2mm plates: A) Snug tight; B) Preloaded . . . 22

Figure 28: Results for monotonic static tests for zinc plus paint coated single bolted joints with 3 mm plates: A) Snug tight; B) Preloaded . . . 23

Figure 29: Results for monotonic static tests for zinc plus paint coated multiple bolted joint with 2 mm plate: A) Snug tight B) Preloaded . . . 23

Figure 30: Results for monotonic static tests for zinc plus paint coated multiple bolted joints with 3 mm plates: A) Snug tight; B) Preloaded . . . 24

Figure 31: 1/4 Finite element model and mesh for 1+1 bolted joint . . . 26

Figure 32: 1/4 Finite element model and mesh for 4+4 bolted joint . . . 27

Figure 33: Detail of the mesh refinement on central plates around the hole border: A) 1+1 bolted joint model; B) 4+4 bolted joint model . . . 27

Figure 34: Boundary conditions applied to 1/4 finite element model for 1+1 bolted joint . . . 28

Figure 35: Boundary conditions applied to 1/4 finite element model for 4+4 bolted joint . . . 29

Figure 36: Bolt preload application . . . 29

Figure 37: True and Engineering stress-strain curve for Bolt ,S355MC and S350GD steels . . . 30

Figure 38: Plastic strain - triaxility curve for steel S355MC and proposed curve for S350GD . . . 31

Figure 39: Material behaviour with damage and without damage [17] . . . 31

Figure 40: Load-displacement curves for snug-tight bolts. Experimental and numerical results for S355MC. 32 Figure 41: Comparison of maximum loads between experimental and numerical results for S355MC snug tight bolted joints. . . 33

Figure 42: Load-displacement curves for preloaded bolts. Experimental and numerical results for S355MC. 33 Figure 43: Comparison between maximum load for experimental and numerical results for S355MC preloaded bolted joints. . . 34

Figure 44: Damage initiation locus for snug tight bolted connection. Numerical example from SMC3 specimen . . . 34

Figure 45: Damage initiation locus for preloaded bolted connection. Numerical example from SMC3 specimen . . . 35

Figure 46: Stress distribution around bolt hole [18]: A) Snug tight bolt B) Preloaded bolt . . . 35

Figure 47: Damage location [18]: A) Snug tight bolt; B) Preloaded bolt . . . 35

Figure 48: Load-displacement curves for snug-tight bolts. Experimental and numerical results for S350 with zinc coating . . . 36

Figure 49: Comparison between maximum load for experimental and numerical results for S350GD with zinc coating and snug tight bolt . . . 36

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Figure 50: Load-displacement curves for preloaded bolts. Experimental and numerical results for S350 with zinc coating . . . 37 Figure 51: Comparison between maximum load for experimental and numerical results for S350GD with

zinc coating and preloaded bolt . . . 38 Figure 52: Load-displacement curves for snug-tight bolts. Experimental and numerical results for S350GD

with zinc plus paint coating . . . 38 Figure 53: Comparison between maximum load for experimental and numerical results for S350GD with

zinc plus paint coating and snug-tight bolt . . . 39 Figure 54: Load-displacement curves for preloaded bolts. Experimental and numerical results for S350GD

with zinc plus paint coating . . . 39 Figure 55: Comparison between maximum load for experimental and numerical results for S350GD with

zinc plus paint coating and preloaded bolt . . . 40 Figure 56: Geometries of test fatigue specimens (dimension in mm): (a) single connection (width = 80mm);

(b) multiple connection (width = 130mm); (c) single connection (Width = 70mm). All plate thicknesses were 2mm and total length of 500 mm for single connections and 600 mm for multiple connections . . . 43 Figure 57: Comparison between S-N curve obtained from ASTM E379 for preloaded bolts and Eurocode

3 class 112. . . 44 Figure 58: Comparison between S-N curve obtained from ASTM E379 for snug tight bolts and EuroCode3

class 90. . . 44 Figure 59: Comparison of the hole quality between : A) Punched Hole B) Drilled hole . . . 45 Figure 60: Comparison between S-N curve obtained from ASTM E379 for multiple bolts joints with snug

tight bolts and Eurocode 3 class 90. . . 46 Figure 61: Probabilistic S-N field obtained from ProFatigue software for single bolt connection with snug

tight bolts . . . 47 Figure 62: Weibul field for single bolt connection with snug tight bolts: comparison with multiple bolt

joints and reduced cross section single bolt joints. . . 48 Figure 63: Probabilistic S-N field obtained from ProFatigue software for multiple bolt connection with

snug tight bolts . . . 49 Figure 64: Weibul field for multiple connection with snug tight bolts: comparison with Eurocode3 class 90. 49 Figure 65: Weibul S-N field obtained from ProFatigue software for single bolt preloaded connection . . . 50 Figure 66: Weibul S-N field for single bolt connection with preloaded bolts: comparison with Eurocode3

Class 112 . . . 50 Figure 67: Comparison between S-N curve obtained from ASTM E379 for single bolted joints snug tight

bolts and Eurocode 3 class 90 and Eurocode 3 class 90 new suggestion. . . 51 Figure 68: Comparison between S-N curve obtained from ASTM E379 for multiple bolted joints with snug

tight bolts and Eurocode 3 class 90 and Eurocode 3 class 90 new suggestion. . . 51 Figure 69: Comparison between S-N curve obtained from ASTM E379 for preloaded bolts and Eurocode

3 class 112 and Eurocode 3 class 112 new suggestion. . . 52 Figure 70: Fractured single Snug Tight specimens with their locations in S-N curve . . . 53

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Figure 71: Fractured single Preloaded specimen with its respectively point in S-N curve . . . 54 Figure 72: Fractured multiple snug tight specimens . . . 54 Figure 73: Scanning Electron Microscope image of a fracture surface for a snug tight bolt. Crack initiation

and hole punching areas (specimen 1) . . . 55 Figure 74: Scanning Electron Microscope image of failure modes for a snug tight bolt. Failure by ductile

fracture (specimen 1) . . . 56 Figure 75: Scanning Electron Microscope image of failure modes for snug tight bolt. Detail of ductile

fracture zone (specimen 1) . . . 56 Figure 76: Scanning Electron Microscope image of failure modes. Detail of crack initiation zone (specimen

2) . . . 57 Figure 77: Scanning Electron Microscope image of failure modes. Detail of ductile fracture zone (specimen

2). . . 58 Figure 78: Scanning Electron Microscope image of failure modes. Hole and crack initiation zone (specimen

3). . . 59 Figure 79: Scanning Electron Microscope image of failure modes. Ductile fracture zone (specimen 3). . . 59 Figure 80: Scanning Electron Microscope image of failure modes. Detail of ductile fracture zone (specimen

3). . . 60 Figure 81: Scanning Electron Microscope image of failure modes. Crack initiation zone (specimen 6). . . 61 Figure 82: Scanning Electron Microscope image of failure modes. Ductile fracture zone (specimen 6). . . 61 Figure 83: Linear regression with experimental results for R = 0 and R = 0.25 to obtain parameter γ for

Walker equation . . . 62 Figure 84: Franc3D model for single bolt connection model: A) Submodel; B) Full model . . . 63 Figure 85: Franc3D sub model generated from single bolt connection model with center crack location . 64 Figure 86: Franc3D sub model initial mesh generated from single bolt connection model with center crack:

A) Superior view; B) Lateral view . . . 65 Figure 87: Crack front evolution and mode I stress intensity factors for center crack with snug tight bolts 65 Figure 88: Mode II and III stress intensity factors for center crack with snug tight bolts . . . 66 Figure 89: Mode I stress intensity factor in function of crack size evaluated on crack center (mid thickness)

for snug tight bolts . . . 66 Figure 90: Mode II and III stress intensity factor in function of crack size evaluated on crack center (mid

plate thickness) for snug tight bolts . . . 67 Figure 91: Crack size in function of number of cycles to crack to reach the critical crack size for snug tight

joints . . . 67 Figure 92: Crack front templates and mode I stress intensity factors for center crack with preloaded bolts 68 Figure 93: Modes II and III stress intensity factors for center crack with preloaded bolts . . . 68 Figure 94: Mode I stress intensity factor in function of crack size evaluated on crack center for preloaded

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Figure 95: Mode II and III stress intensity factor in function of crack size evaluated on crack center for preloaded bolts . . . 69 Figure 96: Crack size in function of number of cycles to crack to reach the critical crack size for preloaded

joints . . . 70 Figure 97: Franc3D sub model generated from single bolt connection model with through thickness crack

location . . . 70 Figure 98: Franc3D sub model initial mesh generated from single bolt connection model with through

thickness crack: A) Superior view; B) Lateral view . . . 71 Figure 99: Crack front templates and mode I stress intensity factors for through thickness crack with snug

tight bolts . . . 71 Figure 100: Mode II and mode III stress intensity factors for through thickness crack with snug tight bolts 72 Figure 101: Mode I stress intensity factor in function of crack size evaluated on crack center (mid thickness)

for snug tight bolts . . . 72 Figure 102: Mode II and III stress intensity factor in function of crack size evaluated on crack center (mid

thickness) for snug tight bolts . . . 73 Figure 103: Crack size in function of number of cycles to crack to reach the critical crack size for snug tight

joints . . . 73 Figure 104: Crack front templates and mode I stress intensity factors for through thickness crack with

preloaded bolts . . . 74 Figure 105: Mode II and III stress intensity factors for through thickness crack with preloaded bolts . . . 74 Figure 106: Mode I stress intensity factor in function of crack size evaluated on crack center for preloaded

bolts . . . 75 Figure 107: Mode II and III stress intensity factor in function of crack size evaluated on crack center for

preloaded bolts . . . 75 Figure 108: Crack size in function of number of cycles for the through thickness crack to reach the critical

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List of Tables

Table 1: Triaxiality for different stress conditions . . . 4

Table 2: Chemical Composition of S355MC and S350GD . . . 13

Table 3: Mechanical Properties of S355MC and S350GD . . . 13

Table 4: Average sliding forces (FslipAV G), average slip factors (µslipAV G), characteristic slip values (µc) and respective coefficient of variations (CoV ) obtained from the slip tests, for the three investigated surface treatments. . . 14

Table 5: Slip factors (µslipAV G) obtained from the slip and static/monotonic tests. . . 15

Table 6: Average dimensions (mm) of test specimens . . . 18

Table 7: Average maximum load and displacement of test specimens with its standard deviation . . . . 24

Table 8: Overview of numerical and experimental results and its errors for S355MC uncoated . . . 40

Table 9: Overview of numerical and experimental results and its errors for S350GD with zinc plus paint coated . . . 41

Table 10: Overview of numerical and experimental results and its errors for S350GD zinc coated . . . 41

Table 11: Overview of the performed test Matrix. . . 42

Table 12: Equations for function f (R) . . . 43

Table 13: Parameters obtained from ProFatigue for single bolt connection with snug tight bolt . . . 46

Table 14: Parameters obtained from ProFatigue for multiple bolt connection with snug tight bolt . . . 48

Table 15: Parameters obtained from ProFatigue for single bolted preloaded connection . . . 48

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1 Introduction

Automated storage and retrieval systems are computer-controlled systems that, as the names says, store and retrieve goods in warehouses (see Figure 1). They are usually applied in situations a high volume of good are being moved, and reliability is critical due to the high economical impact of any failures.

Figure 1: Automated storage and retrieval system for warehouse

Recently with the development of ecommerce industries such as Alibaba and Amazon the need and use for automated storage and retrieval systems have increased. Most of these structures tend to be loaded 24 hours a day, 7 days a week. A fatigue failure (Figure 2) in a storage and retrieval system may lead to huge losses, because of that reliability is a paramount in this type of structures. Due to the long periods associate to intensive moving loads, these structures are very likely subjected to fatigue failures. Studies are developed in this area aiming at designing increasingly reliable structures .

Figure 2: Cracks near bolt holes

Racking system are usually built using thin steel plates with different surface finishing including zinc coating or zinc plus paint coating. Double shear bolted joints are a common types used in racking systems. In racking construction environment, not always the bolts are properly preloaded, the concept of snug tight bolts being adopted. Properly loaded bolts would transmit forces by friction but that is not what happens in the snug tight case. In this case, the behaviour of the double shear joints becomes more unpredictable.

According to AISC [1] a snug tight bolt is a bolt that have been tightened enough that it can’t be removed without a wrench. Also when all the plates that compose the joint are pulled firm into contact by the bolts. The snug tight level of the bolted joint depends on the person who is tightening the bolt, so it can be concluded that there is a human factor involved in snug tight concept. In this work the level for snug tight is going to be considered as 25% of the preloaded level. The snug tight condition is then considered as 25% of 70% of the bolt ultimate force.

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FASTCOLD stands for Fatigue Strength of Cold-formed Structural Steel Details. It is a 42 month long research project funded by Research Fund for Coal and Steel (RFCS) of the European Commission. The main objective of this project is to develop fatigue design rules for cold formed steel members and their connections, with specific focus to applications to the logistic industry.

Since FASTCOLD project aims at cold formed steel structures it generates technical knowledge of general validity on the topic of cold-formed steels. It also assess the possibility of extending the fatigue design approach of Eurocode 3 to cold-formed structural steels as it is currently done for hot-rolled steels.

This work intends to analyse the monotonic and fatigue behaviour of double shear bolted joints used in racking system under preload and snug tight conditions (see Figure 3). Experimental and numerical procedures were developed in order to better understand the behaviour of these joints. The obtained data will be treated under statistical models and the results will be compared to design codes and other literature. Numerical simulations have been developed in order to better understand the monotonic and fatigue behaviour of bolted joints with snug tight and preloaded bolts.

Figure 3: Bolted joints applied to racking systems

Monotonic static simulations were performed in order to evaluated maximum loads and displacements of the joints. It also was used to evaluate the fracture modes observed in experimental tests. Fatigue crack growth simulations were able to evaluate critical crack sizes and numbers of cycles to failure giving an opportunity to compare behaviours of snug tight and preloaded bolted joints.

This work will be divided in seven main parts: introduction, literature review, monotonic experimental tests and results, numerical models for monotonic static tests, fatigue experimental tests and results, fatigue numerical results and conclusions.

The literature review part will approach topics as fatigue, bolts and damage of metallic materials. This section aims to give an overview of the subjects covered in this work.

The obtained experimental results and tests descriptions will be analysed on "monotonic experimental tests and results". The numerical models for monotonic static tests is addressed on section 4 with numerical models mesh, geometry, boundary conditions and the numerical results obtained.

The fatigue topics are addressed on sections 5 and 6. Experimental details and results for fatigue tests can be found on section 5. The numerical model for fatigue tests is addressed on section 6 with numerical models mesh, geometry, boundary conditions and the numerical results obtained.

Finally the conclusions can be analysed on section 7. This section resumes all the conclusions that are reached in this work and suggestions for future works. Following the conclusions the references used in this work and the appendix with resume of all experimental tests.

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2 Literature Review

The following subsections will give an overview of the subjects that are covered in this work. Fatigue, bolts, bolted joints and monotonic ductile failure are the topics that are going to be discussed.

2.1 Monotonic Ductile Failure

The main mechanism that leads to fracture of ductile materials is due to the nucleation, growth and coalescence of voids. Figure 4 shows the schematic of the damage mechanism. The voids typically nucleates around impurities or inclusions in the matrix of the material. These voids tends to grow when the material is submitted to loads. The voids then starts to act as a notch and leads to stress concentration and the strain localisation. Finally some necking starts to happen between voids and once they coalescence the fracture happens.

Figure 4: Schematic of void nucleation, growth and coalescence leading to fracture [2]

The plastic deformation on the onset of damage is function of stress triaxiality and stress rate as can be analysed from Equation (1).

pl_D(η, 0pl) (1)

η = −p/q (2)

The triaxiality can be evaluated from Equation (2) Where η is the triaxiality, p is the hidrostatic pressure and q is equivalent Von Mises stress. Table shows examples of values of triaxiality for specimens under different stress conditions.

The typical fracture Strain-Stress triaxility curve is an negative exponential that when the stress triaxility increases the fracture plastic strains decreases. This effect can be analysed from the schematic Figure 5, as the notch radius decrease, modifying the triaxiality the fracture strain decreases.

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Table 1: Triaxiality for different stress conditions

Stress state Principal Stress p q η

Uniaxial Tension σ1> 0; σ2= σ3= 0 σ1/3 σ1 1/3

Uniaxial Compression σ1< 0; σ2= σ3= 0 σ1/3 |σ1| -1/3

Equibiaxial Tension σ1= σ2; σ3= 0 2σ1/3 σ1 2/3

Pure Shear σ1= −σ2; σ3= 0 0 σ1/3 0

Figure 5: Schematic graphic of the relation between fracture strain and stress triaxiality [3]

2.2 Fatigue

Fatigue is the damage mechanism caused by cyclic loading that leads to crack initiation and growth. The fatigue phenomenon can be divided in two main phases: crack initiation and crack growth.

When a mechanical part is submitted to loadings that is not constant in time this part may initiate a crack. Once the crack initiates it tends to grow until the stress intensity factor exceeds the fracture toughness for that material. When the fracture toughness is exceeded, the crack will grow unstable and the mechanical part will fail.

Figure 6 shows a typical fatigue loading, where σa is the alternate stress; σm is the average mean stress; σmin and

σmax are the minimum and maximum stresses; ∆σ is the stress range. We can also define the stress R-ratio according

to Equation (3).

R = σmin σmax

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Fatigue usually can be analysed according two different regimes: low cycle fatigue and high cycle fatigue. Low cycle fatigue is governed by deformation range (∆) and plasticity behaviour while high cycle fatigue is governed by stress range (∆σ) and elastic behaviour.

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Figure 6: Typical fatigue loading

2.2.1 High cycle Fatigue

About 150 years ago Wöhler started analysing the failure of railroad axles and initiate the study of fatigue. Nowadays the approach for evaluating high cycle fatigue is called Wöhler method or S-N method. Figure 7 shows the Wöhler curve, or S-N curve, that is obtained from the fatigue test of different specimens with the same stress R-ratio and different stress ranges. The parameter Sf is the stress range leading to a fatigue failure for a certain fatigue life N

(cycles); Sethe stress range for endurance limit i.e. the stress range corresponding to infinite life. Thus the endurance

limit is the stress limit range below which the fatigue failure will not occur. The S-N curve can be expressed by the Equation 4, where b and C0 are materials constants. Many factors can influence the life of a mechanical part such as surface finishing, temperature, grain size, stress multiaxiality, stress volume, residual stresses, etc

Figure 7: Typical Wöhler curve for steels

N × S_fb = C0 (4)

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other words the S-N method should only be applied to mechanical parts without cracks, and complete/total failure without considering crack size or predefined crack initiation criterion is envisaged. The remaining fatigue life of cracked compounds should be modelled using a fracture mechanics approach

2.2.2 Fatigue Crack Growth

As previously discussed, the crack initiation is controlled by the stress range (∆σ) or the strain range (∆); on other hand the fatigue crack growth process is controlled by the stress intensity factor range, ∆K. The crack growth can be divided into three main phases as shown in Figure 8. The first phase happens when ∆K is closer to the crack propagation threshold and the crack growth is very slow. The second phase happens when ∆Kth < ∆K and

Kmax < Kc and the crack growth is considered stable. The third and final phase happens when Kmax approaches Kc

and the crack growth becomes unstable.

Figure 8: Different fatigue regimes. Adapted from [4]

The main relation proposed for crack growth description was developed by Paris and Erdogan [5] and can be described by Equation (6). Where the parameters C and m are material properties.

da

dN = C.∆K

m ₍₅₎

In order to account for the stress R-ratio effect, Walker [6] suggested a modification of the equation proposed by Paris and Erdogan, where γ is a new material property:

da dN = C. _∆K (1 − R)γ) m = C(∆Kef f)m (6)

Cracks can grow under 3 fundamental modes. Mode I refers to the crack opening, mode II refers to shearing deformation mode and mode III happens when the crack is under tearing. The three pure modes are shown in Figure 9.

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Figure 9: The three fundamental pure cracking modes

2.2.3 Eurocode 3

Eurocode 3 [7] is the design code adopted in Europe for metallic structures which includes methods for the fatigue resistance assessment of structural components. The methods described in it are based on fatigue tests with large scale specimens. These tests include effects of imperfections from different sources such as: geometry or structural imperfections, material production or execution such as residual stresses. The methods available in Eurocode 3 are applicable to all grades of structural and stainless steels.

The fatigue strength is represented by S-N curves and can be obtained from Equation (7) for number of cycles N ≤ 5 × 106 and the different detail categories presented in the Eurocode 3. In the Equation (7) ∆σc stands for the

fatigue strength associated to each detail category, ∆σR is the stress range applied to the mechanical part and NRis

the number of cycles that the part can endure.

∆σm_R.NR= ∆σmc .2.10

6_{with m = 3} ₍₇₎

This research aims to study double shear bolted joints so two detail categories fatigue classes are of interest: 112 and 90. Figure 10 extracted from Eurocode 3 shows the 2 detail categories and its characteristics. Category 112 is applied to double covered symmetrical joint with preloaded high strength bolts. Category 90 is applied for double covered joints with non preloaded injection bolts; this category will be used to compare with the behaviour of snug tight bolted joints since it behaves similarly to non preloaded injection bolts.

Eurocode 3[7] suggests two different ways to calculate the stress range ∆σ as can be seen on Figure 10. For preloaded bolts Eurocode 3 suggests that ∆σ should be calculated at the gross cross section, while for non preloaded bolts, ∆σ should be calculated on the net cross section.

2.2.4 Statistical Analysis of Fatigue Data

In order to analyse experimental fatigue data it is necessary to apply statistical procedures. These procedures have the main objective of provide a S-N curve that relates stress range with number of cycles to failure. Also, the statistical procedures provide confidence bands that can be used to evaluate the reliability of the design.

2.2.5 ProFatigue Software

ProFatigue is a software [8] that uses statistical tools to provide an estimation of parameters used in regression probabilistic Weibull fatigue model. Tipically it can be applied on fatigue approaches based on stresses or strains. It

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Figure 10: Eucode 3 detail categories for bolted joints

is important to highlight that ProFatigue software considers the effect of run-out specimens, i.e. non-failed tests in the evaluation of parameters. The Weibull distribution model is described by Equations (8) and (9).

Pf(N, ∆σ) = 1 − exp[−(

V − λ δ )

β_] ₍₈₎

V = (logN − B)(log∆σ − D); V ≥ λ to f ailure (9)

Where Pf is the probability of failure for a specimen, N is the number of cycles, ∆σ is the stress level, B is the

threshold for lifetime, D is the threshold parameter for stress level (endurance fatigue limit) and λ is the threshold parameter for the normalized variable V, also called location parameter, δ is the scale parameter and β the shape parameter.

2.2.6 ASTM E739 Standard

ASTM E739 [9] presents a standard practice for statistical analysis of linear or linearized stress-life and strain-life fatigue data. In other words, this practice makes possible to analyse fatigue experimental data under a linear regression in order to obtain S-N curves, its confidence interval and statistical indicators. The average S-N curve, considering a linear model, can be expressed as:

Y = A + B.X (10) X = log(∆σ) (11) Y = log(Nf) (12) A = Y + BX (13) B =Σ k i =1(Xi− X)(Yi− Y Σk i =1(Xi− X)2 (14) Xi= log(∆σi) (15)

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Yi= log(Nf i) (16)

Where ∆σ is the stress range and Nf is the number of cycles to fatigue failure. The dependent variable Y follows a

normal distribution. Parameters X and Y are average values of Xi and Yi obtained from the experimental values of

∆σiand Nf i. In ASTM E739 procedure no run-outs or suspended data are considered. Anyway if they are considered,

a conservative S-N curve will be computed. The rectilinear confidence bands are defined as:

Y = A + B.X ± α.S = (A ± α.S) + B.X (17)

Where α allows to state different probabilities of failure. For example α = 1 stands for a confidence interval of 68.2%, α = 2 stands for 95.4% and α = 3 is equal to 99% confidence.

The standard deviation can be evaluated as the square root of the variance S2_{, which is then given by:}

S2=Σ

k

i =1(Yi− A + B.Xi)2

k − 2 (18)

where k is the number of experimental points.

2.3 Bolts

Bolts are cylindrical mechanical components with an external male thread usually used to join mechanical parts transferring forces and moments. Figure 11 shows a bolt and name its nomenclature. One of main advantages of the use of bolts is to ease assembly of parts since it can be quickly applied or removed.

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Figure 12 shows the main dimensions on a M20 bolt where P is the distance between two consecutive crests or roots and is called pitch; D1is minor diameter; D2 is the pitch diameter; D3 is the major diameter and H is the height of

the thread.

Figure 12: M20 bolt thread nomenclature: A)Bolt shank B)Thread dimensions

Measure the load developed by a bolt is not a simple task but to measure the torque applied in it is simpler. Since the torque induces the preload on bolt if is possible to assume that the axial force Fp is controlled by the torque T .

The Equation (19) estimates Fp.

Fp=

kT D2

(19)

where k is a constant. However this relation depends on friction and their calibration by testing is essential.

2.3.1 Bolted Joints

When in need of a connection member that can be disassembled without being destroyed, bolted joints are a good solution. Bolted joints can stand traction, moments, shear loads and a combination of those without any problems. Figure 13 exemplifies a bolted joint connection, where Dw is the diameter of the bolt head and L the sum of all the

plates thickness.

The spring method allows to evaluate the stiffness of connection members. Equation 20 is used to calculate the equivalent stiffness km of a member, where k1, k2, k3...kn are the stiffness of each individual member that acts like

springs in series. 1 km = 1 k1 + 1 k2 + 1 k3 + ... + 1 kn (20)

2.3.2 Bolted Joints Under Monotonic Loading

In a situation where the bolted joint is submitted to an external load Q it is possible to evaluate the proportion of the load transferred by members (friction) and by bolts (bearing) according to Equations (21) and (22), where Qb is

the load transferred by bolts; Qmis the load transferred by members; kb is the bolt stiffness and kmis the equivalent

stiffness. Usually members tend to stand more than 80% of the load since the members are more stiff than the bolts.

Q = Qm+ Qb (21)

Qm= Qb

km

kb

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Figure 13: Schematic image of a bolted joint

When the bolted joint is under double shear, as shown in Figure 14 the bolt preload has a really important role on the behaviour of the joint. If the applied load is less than the friction force developed by the bolt preload there is no slip between the plates and the forces are transmitted by friction. The friction force (Ff r ic) is calculated by Equation

(23).

Figure 14: Double shear bolted joint

Ff r ic= Fp× µ (23)

Otherwise if the load Q is higher than the friction force, slip will happen and the forces will be transmitted by bearing. In this situation higher stress concentration will occur around the bolt hole and the failure of the plate will happen in this location. The same relation can be made for plates with low friction factor (µ), due to the low friction factor slip will occur and higher stress concentration will occur in the bolt hole.

2.3.3 Bolted Joints under Fatigue

Bolted connections that are submitted to traction loads that varies in time may be subjected to fatigue. Usually these loadings varies between zero and the maximum load Qmax. The alternate stress can be evaluated by Equation (25),

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where Ab is the bolt area projection. The average stress can be evaluated from Equation (26) where Qmin is the minimum load. Ab= D3× L (24) σa= Qb 2Ab (25) σm= Qb 2Ab +Qmin Ab × kb km+ kb (26)

It becomes possible to verify the safety factor (sf ) of the bolted joint using a failure criteria like Goodman, for example, with Equation (27). sf.σa Sy +sf.σm Su = 1 (27)

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3 Monotonic Experimental Tests and Results

In this chapter the materials, experimental setup and results obtained from the monotonic tests will be presented. This chapter will be divided in 5 sections: materials description, experimental details for monotonic slip tests, results for monotonic slip tests, experimental details for monotonic static tests and results for monotonic static tests. Monotonic static tests were performed until failure, monotonic slip tests were performed until slipping conditions area attained and they were used to evaluate slip factors (friction coefficients).

3.1 Materials Description

Monotonic static and slip tests were developed in order to analyse the behaviour of double shear bolted joints. Steels S355MC and S350GD were investigated. S355MC is a hot-rolled, low-alloy mild steel that combines high strength with outstanding formability. S355MC is easily galvanized and welded used for cold-forming profiles production. Usually replaces construction steel in situations where high strength is paramount importance. S350GD is a zinc coated mild steel obtained by hot-dip galvanization process with good corrosion resistance. The chemical composition for S355MC and S350GD steels can be observed in Table 2 in accordance to the EN 10149 [10] and EN 10346 [11] standards, respectively.

Table 2: Chemical Composition of S355MC and S350GD Chemical Composition (Max. %)

C Si Mn P S Al Nb V Ti

S355MC 0.12 0.50 1.5 0.025 0.02 0.015 0.09 0.2 0.15

S350GD 0.20 0.60 1.70 0.10 0.045 - - -

-Mechanical Properties of S355MC and S350GD steels can be evaluated from Table 3 where σY minstands for minimum

yield strength, σU for ultimate tensile strength and R for total elongation.

Table 3: Mechanical Properties of S355MC and S350GD σY min. (MPa) σU (MPa) R

S355MC ≥ 355 430 − 550 19%

S350GD ≥ 350 420 16%

3.2 Experimental Details for Monotonic Slip Tests

As described in the paper entitled "Monotonic and Fracture behaviours of bolted connections with distinct bolt preloads and surface treatments" by Gomes et al. [12] monotonic slip tests, in accordance to EN 1090-2, were performed. The main objective of the study was to evaluate slip factors for three different surface finishing conditions namely. The tests were conducted with preloaded bolts (70% Fu) and 5 repetitions for each surface finishing resulting in 15 tests.

The slip factor, in accordance to the EN1090-2 standard, is evaluated for a load leading to a slide of 0.15mm, measured with linear variable differential transformer (LVDT). Figure 15 shows the experimental setup for slip tests. Two blocks were fixed on middle plates with two LVDT in each and two stop plates fixed on cover plates. The slip factor values µslip and values for characteristic slip µc, were computed using Equations (28) and (29) for a confidence interval of

75%: µslip= Fslip nbolt× nshear× Fp (28) µc= µslipavg − 2.05 × Sµ (29)

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where Fslip is the load applied by the test machine leading to a 0.15 mm, nboltis the number of bolts, nshear is the

number of shear planes, Fpr eload is the preload applied to the bolted connection, µslipavg is the average value and

Sµ is the standard deviation of the slip factors obtained for all tests. The bolt preload is calculated, according to

EN 1090-2 [13], with Equation (30), where Mclamping is the clamping torque, dbolt is the bolt diameter and C” the

calibration coefficient.

Fpr eload=

Mclamping

C” × dbolt

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Figure 15: Geometry of specimens for slip tests (left) and slip tests setup (right)

In order to obtain the calibration coefficient C” a dedicated test was performed using a special load cell. Two preload levels were measured and the results confirmed a coefficient of calibration C” equal to 0.2 for M16 bolts .

3.3 Results for Monotonic slip tests

Sliding forces (Fslip) were measured in order to evaluate slip factors (µslip) according to Equation 28. Also the

characteristic slip values (µc) were obtained according to Equation 29. Table 4 summarize the obtained data from the

slip tests for all surface finishing considered in this study.

Table 4: Average sliding forces (FslipAV G), average slip factors (µslipAV G), characteristic slip values (µc) and

respective coefficient of variations (CoV ) obtained from the slip tests, for the three investigated surface treatments. Steel Grade Surface Treatment FslipAV G[kN ] µslipAV G µc CoV %

S355MC Without Coating 97.06 0.28 0.16 21.65

S350GD Zinc Coating 107.90 0.31 0.20 18.77

S350GD Zinc Plus Paint Coating 47.28 0.14 0.09 15.56

From the Table 4 it is possible to verify that the zinc coating presented the highest sliding force, more than twice the sliding force for zinc plus paint coating. Also, it is possible to verify that the coefficient of variation (CoV %) presented values higher than 15% for all surface treatments.

Friction coefficients were also evaluated from the load-displacement curves of the monotonic static tests to be presented in next section. The methodology for evaluating the static friction coefficients consisted in analysing the load peak or the curve slope variation. Table 5 overviews the results obtained for all surface treatments, bolt load conditions, bolt arrangements and plate thickness. It is possible to verify that uncoated surfaces have an higher friction coefficient than the zinc coating and zinc plus paint coating. This phenomenon can be explained by the fact that the surface finishing act like a lubricant lowering the friction coefficient. The monotonic static test yield average slip factors more consistent units than characteristic values from monotonic slip tests.

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Table 5: Slip factors (µslipAV G) obtained from the slip and static/monotonic tests.

Surface Treatment Without

Coating

Zinc Coating Zinc plus paint Coating Monotonic Slip Tests (EN1090) Preloaded Bolts (70%F u) 2+2 Bolts Slip Factor (µslipAV G) 0.28 0.31 0.14 Charact. Slip (µc) 0.16 0.20 0.09 Monotonic Static Tests

Snug Tight Bolts (25% × 70%F u) 1+1 Bolts 2mm 0.18 0.09 0.06 3mm 0.22 0.10 0.09 Monotonic Static Tests

Snug Tight Bolts (25% × 70%F u) 4+4 Bolts 2mm 0.17 0.15 0.08 3 mm 0.14 0.11 0.14 Monotonic Static Tests Preloaded Bolts (70%F u) 1+1 Bolts 2mm 0.17 0.15 0.08 3mm 0.16 0.14 0.10 Monotonic Static Tests Preloaded Bolts (70%F u) 4+4 Bolts 2mm 0.13 0.11 0.09 3 mm 0.14 0.13 0.10

Average Friction Coefficients from Monotonic Static Tests 0.17 0.12 0.10

3.4 Experimental details for Monotonic Static Tests

Monotonic static tests were performed on two different bolted joints setups: 1+1 and 4+4 bolts. Setup 1+1 is composed by 2 M16 (DIN933) bolts, 2 M16 (DIN125) washers, 2 M16 nuts (DIN938), 2 plates with dimensions 245 mm x 80 mm x 2 mm and two plates with dimensions 150 mm x 80 mm x 2 mm.In addition the experiments were also performed with plates of 3 mm thickness. Refer to Figure 16 for details about the single bolted joint used in the monotonic static tests.

The multiple bolts setup (4+4 bolts) is composed by 8 M16 bolts (DIN933), 8 M16 washer DIN125, 8 M16 nuts (DIN938), 2 plates with dimensions 295mm X 130mm X 2mm and two plates with dimensions 150mm X 80mm X 2mm. The experiments were also performed with plates of 3 mm thickness besides the 2 mm plates. Refer to Figure 17 for details about the multiple bolted joint used in the monotonic static tests.

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Figure 16: Geometry of the 1+1 specimen used in static monotonic tests, with photo of the experimental setup

Monotonic static tests were conducted in order to better understand the influence of geometry, surface treatments i.e. friction factor and bolt preload in the static behaviour and failure modes of double shear bolted joints. Several tests were performed with two different preload levels ( 70% Fuand 25% × 70% Fuwhere Fustands for bolt ultimate tensile

resistance), three surface finishing (uncoated, zinc coated and zinc plus paint coating). The tests were conducted with setups previously shown (1+1 Figure 16 and 4+4 Figure 36) with plates of 2 and 3 mm, resulting in a total of 72 monotonic static tests.

The two selected bolt preload levels were chosen in order to represent the state of preloaded bolts used in rack structures. The higher preload level (70% Fu) represent the recommended values in codes for high strength bolts. The

lower preload level (25% × 70% Fu) intends to represent the preload level often used in rack structures, known as snug

tight bolts. The bolted joints in the rack structures are often performed without torque control, using small diameter non-certified bolts and involving thin plates which make the preloaded high strength bolted joints less plausible and effective in these structures.

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Figure 17: Geometry of the 4+4 specimen used in static monotonic tests, with photo of the experimental setup

Figure 18: Geometry of specimens for static tests: A) 1+1 bolted joint B)4+4 bolted joint

Geometries data of the specimens used in tests can be analysed from Table 6 and Figure 18, where Dhole stands for

the plate hole diameters, e1 the end distance, e2 is the side distance to the edge of the plate. Parameters p1 and p2 represent the distance between the center of the holes. Table 6 shows the average dimensions for each of the specimens. As regards the specimen reference code, the first letter stands for the type of test (S-static) the second letter is the type of bolt arrangement (S-Single; M-Multiple), the third letter is the surface finishing condition (C-uncoated, Z-zinc and P-zinc plus paint coating) and the last digit stands for the plate thickness in mm. Each condition of Table 6 was performed for two bolts preloads above mentioned.

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Table 6: Average dimensions (mm) of test specimens

Specimen Material Thickness Width Dhole e1 e2sup e2inf p1 p2

SSC2 S355MC 2.00 80.00 18.03 35.01 40.00 - - -SSC3 S355MC 2.89 80.06 17.97 34.96 40.04 - - -SSZ2 S350GD 2.07 80.02 18.08 34.97 40.01 - - -SSZ3 S350GD 3.03 80.08 18.05 34.64 40.04 - - -SSP2 S350GD 2.50 80.30 17.65 34.94 40.15 - - -SSP3 S350GD 3.32 80.13 17.60 34.50 40.06 - - -SMC2 S355MC 2.06 130.03 17.90 34.94 40.06 40.12 50.01 50.07 SMC3 S355MC 3.09 129.98 17.97 34.97 40.09 40.09 50.02 50.04 SMZ2 S350GD 2.10 130.10 18.00 35.05 40.11 39.86 49.81 50.02 SMZ3 S350GD 3.09 130.23 17.95 35.08 40.25 40.01 49.99 50.08 SMP2 S350GD 2.40 130.32 17.65 35.02 40.18 40.15 49.82 49.95 SMP3 S350GD 3.31 130.40 17.57 34.86 40.31 40.22 49.70 49.95

3.5 Results for Monotonic Static Tests

In this section the results for monotonic static tests will be presented. Each test was repeated three times resulting in a total of 72 tests. Figure 19 shows the results for single uncoated bolted joints with 2 mm thickness plates. The average maximum force for snug tight bolted joints was 36.7kN while for preloaded bolts was 39kN .

Figure 19: Results for monotonic static tests for uncoated single bolted jointS with 2mm plates: A) Snug tight; B) Preloaded

Figure 20 shows the results for single uncoated bolted joints with 3 mm thickness plates. The average maximum force for snug tight bolted joints was 59kN while for preloaded bolts was 63kN . It was possible to verify that the increase of 1mm in the plate thickness increased the maximum load in over 60%. There was not a big difference in terms of maximum displacement between 2 mm and 3 mm thickness plates.

The results for the multiple bolted joints with uncoated finishing can be evaluated from Figures 21 and 22. The average maximum loads for the snug tight multiple bolted joint with 2mm plates is 100kN while for the same connection with preloaded bolts was 105kN . The results for preloaded bolts showed a huge variation in terms of maximum displacement. The results varied from 10.4mm to 16.3mm.

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Figure 20: Results for monotonic static tests for uncoated single bolted joints with 3mm plate: A) Snug tight; B) Preloaded

Figure 21: Results for monotonic static tests for uncoated multiple bolted joints with 2mm plates: A) Snug tight; B) Preloaded

Figure 22 shows the results for multiple bolt joints with 3mm plates. The average maximum load for snug tight is 154kN while for preloaded bolts is 161kN . The results for the maximum load are about 50% higher for 3mm plates than for the 2mm plates. The maximum displacement for preloaded bolts varied 3.4mm, from 17.36mm to 20.77mm.

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Figure 22: Results for monotonic static tests for uncoated multiple bolted joints with 3mm plates: A) Snug tight; B) Preloaded

The results for zinc coated bolted joints will be presented next. Particularly Figure 23 shows the results for single zinc coated bolted joints with 2 mm thick plates. The maximum load for snug tight and preloaded bolted joints are respectively 39.8kN and 42.8kN .

Figure 23: Results for monotonic static tests for zinc coated single bolted joints with 2mm plates: A) Snug tight; B) Preloaded

Figure 24 shows the results for single zinc coated bolted joints with 3mm plates. The average maximum load for snug tight is 55kN while for preloaded bolts is 56kN . The results for the maximum loads are about 40% higher for 3mm plates than 2mm plates. Preloaded bolts results showed maximum displacement from 25mm to 36mm.

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Figure 24: Results for monotonic static tests for zinc coated single bolted joints with 3 mm plates: A) Snug tight; B) Preloaded

The results for the multiple zinc coated bolted joint can be evaluated from Figures 25 and 26. The average maximum load for the snug tight multiple bolted joint with 2 mm plates is 101kN while for the same connection with preloaded bolts was 110kN . The results for preloaded bolts showed a huge variance in terms of maximum displacement. The results varied from 9 mm to 14 mm.

Figure 25: Results for monotonic static tests for zinc coated multiple bolted joints with 2mm plates: A) Snug tight; B) Preloaded

Figure 26 shows the results for multiple zinc coated bolted joints with 3 mm plates. The average maximum load for snug tight is 142.8kN while for preloaded bolts is 141.7kN . Differently from previous cases the average maximum load for snug tight is slightly higher than the one for preloaded bolts. The results for the maximum load are between 30% and 40% higher for 3 mm plates than 2 mm plates. Preloaded results showed maximum displacement from 16.8 mm to 20.5 mm.

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Figure 26: Results for monotonic static tests for zinc coated multiple bolted joint with 3 mm plate: A) Snug tight B) Preloaded

The following results refers to the tests with zinc plus paint coating. Figure 27 shows the results for single zinc plus paint coated bolted joints. The average maximum load for snug tight zinc plus paint coated with snug tight bolts is 37.9kN while for preloaded bolts is 39.8kN .

Figure 27: Results for monotonic static tests for zinc plus paint coated single bolted joints with 2mm plates: A) Snug tight; B) Preloaded

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Figure 28 shows the results for single zinc plus paint coated bolted joints with 3 mm plates. The average maximum load for snug tight is 52kN while for preloaded bolts is 55.4kN . The results for maximum load are about 37% higher for 3mm plates than for 2mm plates. Preloaded results showed maximum displacements from 34 mm to 35 mm.

Figure 28: Results for monotonic static tests for zinc plus paint coated single bolted joints with 3 mm plates: A) Snug tight; B) Preloaded

Figure 29 shows the results for zinc plus paint multiple coated bolted joints with 2mm plates. The average maximum load for snug tight is 100kN while for preloaded bolts is 99.9kN . Preloaded results showed maximum displacement of around 21mm while snug tight results showed a maximum displacement from 21.2 mm to 22.4 mm.

Figure 29: Results for monotonic static tests for zinc plus paint coated multiple bolted joint with 2 mm plate: A) Snug tight B) Preloaded

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The last available results are from zinc plus paint coated multiple bolted joints. The average maximum load for snug tight condition is 139kN and for preloaded condition is 140.3kN . The 3 mm bolted connection plates has a maximum load about 40% higher than the 2 mm bolted connection plates. The maximum displacement for snug tight condition is from 22.6 mm to 24.2 mm, while for preloaded condition is from 22.2 mm to 23.2 mm.

Figure 30: Results for monotonic static tests for zinc plus paint coated multiple bolted joints with 3 mm plates: A) Snug tight; B) Preloaded

Table 7: Average maximum load and displacement of test specimens with its standard deviation

Specimen Bolt Load Average Max. Load (N) St. Dev. (N) Average Max. Displacement (mm) St. Dev. (mm)

SSC2 Snug tight 36690 579 23.15 3.86 SSC2 Preloaded 39029 590 25.58 0.77 SSC3 Snug tight 59176 683 25.94 1.56 SSC3 Preloaded 63045 1108 21.42 1.18 SSZ2 Snug tight 39808 505 36.20 1.66 SSZ2 Preloaded 42842 1513 33.64 6.88 SSZ3 Snug tight 55157 584 32.00 4.01 SSZ3 Preloaded 56277 2837 30.92 5.59 SSP2 Snug tight 37962 717 33.17 2.75 SSP2 Preloaded 39845 338 37.00 1.51 SSP3 Snug tight 52085 416 34.74 1.10 SSP3 Preloaded 55448 432 34.33 0.69 SMC2 Snug tight 100570 745 23.70 0.24 SMC2 Preloaded 105098 5252 13.03 2.98 SMC3 Snug tight 154018 1218 23.96 0.54 SMC3 Preloaded 161661 689 19.40 1.80 SMZ2 Snug tight 101178 1567 21.28 0.72 SMZ2 Preloaded 110373 5173 11.30 2.77 SMZ3 Snug tight 142840 320 24.10 0.53 SMZ3 Preloaded 141709 2756 18.21 2.24 SMP2 Snug tight 100178 676 21.88 0.64 SMP2 Preloaded 99909 1143 21.14 0.36 SMP3 Snug tight 139165 1906 23.50 0.80 SMP3 Preloaded 140349 1892 22.74 0.39

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In conclusion, on average 3mm thick plates stand from 40% to 60% more loads than the 2mm thick bolted connections. When bolts are properly loaded (preloaded) they tend to withstand about 10% more load than the snug tight condition. Single bolted joints have a bigger maximum displacement than multiple bolted joints while single bolted joints, as expected, stand less than half of the maximum load of the multiple bolted connections.

Comparing the specimens with zinc coated and zinc plus paint coated with the same bolt arrangement and plate thickness it is possible to verify that the maximum load for zinc coated is higher. This can be explained by the fact that the friction factor is higher on zinc coated (0.12) than the zinc plus paint coated (0.10). It is possible to conclude that the friction factor plays an important role on the behaviour of the bolted joints.

Regarding the maximum displacement is possible to verify that the preloaded joints can withstand a smaller displacement that the snug tight ones. This phenomenon is more explicit on the multiple bolts connection where, for example, the maximum displacement for SMZ2 with snug tight bolts is 88% higher than the one with preloaded boats. This can be explained by the fact that preloaded bolt joints are more stiff and deform less with the same load.

The sliding zone can be analysed at the first 8 mm in all of the experimental tests. It is possible to verify that load is higher on preloaded bolted joint than the snug tight ones. For example on specimens SMZ2 its is not even possible to distinguish the sliding zone from the deformation zone on the load × displacement graphic. This can be explained by the fact that on preloaded bolted joints the load necessary to overcome the friction forces is higher than the one on snug tight bolted joints.

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4 Numerical Models for Monotonic Static tests

Finite element models were developed to simulate the monotonic behaviour of bolted joints under different conditions. The main goal of this study was to evaluate the maximum load ductility whose tests were presented in the previous chapter and fracture modes of the bolted joints. The obtained results were compared to the obtained results in the experimental tests presented in previous chapter. The commercial software Abaqus/CAE 2019 was used due to its capabilities and for being widely used in industries.

4.1 Geometry and Mesh

The 1+1 and 4+4 bolted joints were both modelled. Figures 31 and 32 shows the finite element models (mesh) for 1+1 and 4+4 configurations respectively. All the plates are meshed with C3D8 elements, a 8-noded 3D brick element. The bolts were meshed with C3D10 elements a 10-noded 3D tetrahedral element. Only 1/4 of the geometries were modeled in order to save computational cost. The bolt thread was simplified as a smooth cylinder. The washer and nuts were modelled as a unique slide attached to the bolt.

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Figure 32: 1/4 Finite element model and mesh for 4+4 bolted joint

A mesh refinement of the mesh was made around the bolt holes due to the fact that it is expected to have a stress concentration in this area. Figure 33 shows in detail the refinement around the bolt holes of the central plates of 1+1 and 4+4 finite element models. Both models have elements with minimum size of 0.66 mm located around the hole border.

Figure 33: Detail of the mesh refinement on central plates around the hole border: A) 1+1 bolted joint model; B) 4+4 bolted joint model

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The contact between plates (normal contact) was made using the default constraint enforcement method with surface-surface discretization method. The tangential behaviour used the penalty method for the friction formulation. The friction coefficient used was based on the data obtained from the monotonic slip tests for each surface finishing. The contact implementation will be further discussed in the following sections.

4.2 Boundary Conditions

In order to save the computational costs, symmetry was used in both models. This was possible due to the application of plane symmetry as boundary conditions in planes normal to X and Y. Figure 34 and 35 show the boundary conditions applied for 1+1 and 4+4 models respectively.

A displacement of 20mm was applied to the central plate end. The 20 mm was chosen because it was a larger displacement than any of the tested specimens could stand; in other words, it was expected that the fracture of the specimens would happen before that full displacement being applied.

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Figure 35: Boundary conditions applied to 1/4 finite element model for 4+4 bolted joint

The preload on bolt was applied using the "Bolt Load" option available in Abaqus/CAE. It is necessary to make a partition in the center of the bolt and specify an axis normal to the bolt load application. Figure 10 shows the bolt load application.

Figure 36: Bolt preload application

In order to apply contact in the model it was necessary firstly to identify the contact regions pairs. The following contact pairs were assumed in the model: I)cover plates and middle plate; II) bolt head and superior plate; III) nut and washer; IV) washer and inferior plate; V) bolt body and holes of the plates and washer. Also, in preloaded bolt condition it was necessary to apply contact between superior and inferior cover plates due to large deformations. The friction formulation was the penalty method. This method can be understood as the addition of an imaginary spring between the contact surfaces, where the penetration is inversely proportional to the spring stiffness. In other words, high spring stiffness leads to lower body penetration. The stiffness used was the Abaqus default. The discretization method applied was the "surface-surface".

The normal behaviour was enforced as "hard contact". In other words this could be considered as a penalty method with an infinite stiffness for the spring, leading to almost zero penetration between bodies.

4.3 Material behaviour Modeling

The S355MC and S350GD materials behaviours were modelled with elastoplastic behaviour, multi-linear isotropic hardening. The uniaxial engineering stress-strain curve was obtained by tensile tests performed in this research. Since it is expected large deformations in the modeling of fracture behaviour of bolted joints, it is necessary to use the real stress-strain curve. The transformation from engineering stress-strain curve to real stress-strain curve can be evaluated using Equations (31) and (32).

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t= ln(1 + ) (31)

σt= σ(1 + ) (32)

Figure 37 shows the real stress-strain for bolt, S355MC and S350GD steels.

Figure 37: True and Engineering stress-strain curve for Bolt ,S355MC and S350GD steels

4.4 Ductile Damage Modeling

The two main mechanisms of fracture of ductile metals are ductile criterion due to to the nucleation, growth and coalescence of voids and shear fracture due to shear band localization. For the bolted joints the ductile criterion was more appropriate. The ductile criterion was based on Bao and Wierzbicki (2004) [14] work and assumes that the plastic deformation on the onset of damage is function of stress triaxiality and stress rate as previously discussed. The plastic strain - triaxility curve obtained for S355 from Petr and Talja (2017) [15] can be evaluated from Figure 38. The Plastic strain - triaxility is an exponential curve that the critical plastic strain decreases as the triaxiality increases. Due to the lack of experimental data for S355GD triaxiality - plastic strain a curve was proposed based on S355MC experimental data. As seem on experimental data for monotonic static tests the specimens for S350GD showed a bigger maximum displacement than the specimens with S355. The suggested curve for S350GD is equal to S355 but displaced up 0.65 plastic strains units.

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Figure 38: Plastic strain - triaxility curve for steel S355MC and proposed curve for S350GD

Figure 39 shows the characteristic behaviour of a material undergoing damage. The damage can be analysed as degradation of elasticity or decreasing of yield strength (softening). In Figure 39 the dashed line represents the behaviour of the material without damage and the continuous line represents the material’s behaviour with damage. Parameters σY 0 and pl0 represent the stress and plastic strain at the onset of damage which are determined using

data of Figure 38.

Once the parameter D reaches its maximum value Dmaxon all integration points of an element that element is removed

from the mesh and the forces and stresses are redistributed on elements around it. For the analysed work the damage evolution is based on a critical energy release. The software user specify the fracture energy per unit of area G, once the fracture energy on the element is reached that element is removed from the mesh. For the simulations the fracture energy of 1.9 MN.m/m based X52 steel was used. In the absence of better data for S350GD fracture energy X52 steel properties were chosen due to similarities with S350GD steel. The properties were obtained from the book "Monotonic and ultra-low-cycle fatigue behaviour of pipeline steels: experimental and numerical approaches" [16].

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4.5 Results for Numerical Monotonic Static Tests

The following subsections will present the numerical results obtained for damage modelling. The results will be divided in three subsections referring for each material and surface finishing: S355MC non coated; S350GD with zinc coating and S350GD with zinc plus paint coating:

4.5.1 S355MC non Coated

Figure 40 shows the load-displacement curves for experimental tests and numerical obtained from software Abaqus for snug-tight bolted joints. First it is possible to analyse that the plate thickness increased the maximum load for single and multiple bolted connections as expected. For single bolt connection, the 3mm plates showed an increase on the maximum load of around 60% while in the multiple bolt connections the increase was around 50%.

The initial behaviour showed some discrepancies between numerical and experimental tests. This can be explained by the complexity of the friction phenomenon. A detailed analysis is necessary in order to better characterize this behaviour, but this is not the scope of this work.

Figure 40: Load-displacement curves for snug-tight bolts. Experimental and numerical results for S355MC. Regarding the damage, it is possible to verify that the numerical model represented the softening and load drop of all specimens with great accuracy. The biggest difference on failure displacement is from specimen SMC2 with 1.7mm from experimental to numeric results, but in general the experimental results exhibited high scatter in this result. Figure 41 shows the comparison of maximum load between experimental and numerical results, for snug tight bolts. The biggest error between experimental and numerical maximum load on snug tight bolted connections is 3.81% on SSC2 and the minimum error evaluated is 0.18% on SMC3. Figure 41 also shows the error bars based on three standard deviations of experimental results.

(47)

Figure 41: Comparison of maximum loads between experimental and numerical results for S355MC snug tight bolted joints.

Figure 42 shows the load-displacement curves for experimental tests and numerical results obtained from software Abaqus for preloaded bolted joints. Once again is possible to verify that as the plate thickness increased the maximum load. In this case, the increase was about 60% for both single and multiple bolt connections. It is also possible to verify that the bolt preload increased the maximum load compared to snug tight connections. This can be explained by the friction between the plates that tends to increase with the increase load on the bolts.

As expected, the results for preloaded bolt connections are not as precise as the results for snug tight bolted connections. This can be explained by the fact that friction plays a more important role in preloaded connections than in snug tight connections.

(48)

Figure 43 shows the comparison between maximum loads for preloaded bolt connections. The error for maximum loads are below 3% except for the connections SSC2 where the error is around 36%. This can be explained by the fact that the bolt preload leads to transverse deformation of the plates. Figure 43 also shows the error bars based on three standard deviations.

Figure 43: Comparison between maximum load for experimental and numerical results for S355MC preloaded bolted joints.

It was also possible to verify that the damage initiation location changed in a function of the bolt load. For snug tight bolted connection the damage took place on the hole border while on preloaded bolted connection the damage took place outside the border hole. This can be verified from Figures 44 and 45.

Monotonic and Fatigue Behaviour of Double Shear Bolted Joints: Experimental and Numerical Studies