### Goran Iveti´c

PhD Thesis

## Residual Stress Effects on

## Fatigue Phenomena in

## Aerospace Structures

University of Pisa January 2010

### University of Pisa

Faculty of Engineering

Department of Aerospace Engineering ING-IND/04 Costruzioni e Strutture Aerospaziali

### PhD Thesis

### Residual Stress Effects on

### Fatigue Phenomena in Aerospace Structures

Thesis Advisor Candidate

Prof. Agostino Lanciotti Goran Iveti´c

January 2010

Il contenuto di questa relazione `e strettamente riservato, essendo presenti argomenti tutelati dalla legge come segreti. Pertanto tutti coloro che ne prendono conoscenza sono soggetti all’obbligo, sanzionato anche penalmente dagli articoli 325 e 623 del codice penale, di non divulgare e di non utilizzare le informazioni acquisite.

Za moju obitelj Alla mia famiglia

### Contents

Contents iv

List of Figures ix

List of Tables xvii

Nomenclature xix

Abstract xxii

Acknowledgments xxiv

I Residual Stresses and Fatigue - General 1

1 Introduction 2

1.1 Research Motivation . . . 3

1.2 Residual Stresses and Fatigue . . . 4

2 Residual Stress Measurement 7 2.1 Residual Stress Measurement Methods . . . 8

2.1.1 X-ray Diffraction and Neutron Diffraction . . . 8

2.1.2 Ultrasonic Method . . . 10

2.1.3 Hole Drilling Method . . . 10 iv

Contents

2.1.4 Ring Core Method . . . 10

2.1.5 Crack Compliance (Slitting) Method . . . 11

2.1.6 Sectioning Method . . . 12

2.1.7 Other Advanced Methods . . . 12

2.2 Measurement of Residual Stress in a Rectangular Butt-welded Panel . . . 13

2.2.1 Experimental Measurement of Residual Stress . . . 16

2.2.2 Numerical Valuation of the Used Measurement Method 19 2.2.3 Additional Effects Verified by the FEM model . . . . 26

2.2.4 Conclusions . . . 29

3 Residual Stresses and Fatigue in Integral Stiffened Panels 33 3.1 Introduction . . . 34

3.2 Experimental Activity . . . 34

3.2.1 Specimen Definition . . . 36

3.3 Experimental Analysis of Stress Distribution on the Panels . 39 3.4 Crack Propagation Tests . . . 48

3.4.1 Results . . . 51

3.5 Residual Stress Measurements in Stiffened Panels . . . 58

3.5.1 Residual Stress Results . . . 65

3.6 Concluding Remarks . . . 66

3.7 Residual Strength Tests . . . 75

4 FEM Evaluation of Crack Propagation in Residual Stress Field 78 4.1 Crack Propagation in Welded Panels . . . 79

4.1.1 Introduction . . . 79

4.1.2 FEM Model and Analysis . . . 80

4.1.3 Determination of Stress Intensity Factor for Symmetric Cracks . . . 81

4.1.4 Symmetric cracks - Residual Stress Redistribution . . 84

4.1.5 Determination of stress intensity factor for Asymmetric cracks . . . 85

4.1.6 Asymmetric cracks - Residual stress redistribution . . 88

Contents

4.1.7 Conclusions . . . 89

5 Numerical Evaluation of Additional Effects - Welding De-formations 100 5.1 Analysis of Out-of-plane Welding Deformations . . . 101

5.1.1 Introduction . . . 101

5.1.2 Literature overview . . . 102

5.1.3 FEM model . . . 103

5.1.4 FEM results . . . 106

5.1.5 Conclusions . . . 110

6 Numerical Evaluation of Additional Effects - Debonding 112 6.1 Crack Propagation in Bonded Panels . . . 113

6.1.1 Introduction . . . 113

6.1.2 Analysis procedure . . . 113

6.1.3 Material Model . . . 114

6.1.4 Model Geometry and Mesh definition . . . 115

6.1.5 Boundary Conditions and Load Definition . . . 116

6.1.6 Results . . . 116

6.1.7 Conclusions . . . 124

II Residual Stresses and Fatigue - Laser Shock Peening 125 7 Introduction 126 7.1 Principles of Laser Operation . . . 127

7.2 Laser Types . . . 128

7.2.1 The Nd:YAG Laser . . . 129

7.2.2 The Nd:Glass Laser . . . 129

8 Overview of LSP 130 8.1 History of LSP . . . 131

8.2 LSP Process Description . . . 131

8.2.1 Plasma models . . . 133

8.2.2 Shock wave propagation . . . 134

8.3 Current applications . . . 136 vi

Contents

8.4 Suggested applications and implementation . . . 136

9 Experimental evaluation of LSP treated thin sheets 138 9.1 Introduction . . . 139

9.2 Test matrix . . . 139

9.3 Residual stress measurements . . . 145

9.4 Fatigue tests . . . 150

10 Experimental evaluation of LSP treated thick plates 151 10.1 Introduction . . . 152

10.2 Test matrix . . . 152

10.3 Residual stress measurements . . . 152

10.4 Fatigue tests . . . 153

11 Material Models in Laser Shock Peening 164 11.1 Analysis procedure . . . 165

11.2 Material Model . . . 165

11.3 Load definition . . . 168

12 FEM Modelling of Laser Shock Peening in thin sheets 170 12.1 FEM analysis of LSP of Thin 2024-T351 Sheets . . . 171

12.1.1 Geometry and mesh definition . . . 171

12.1.2 Load definition . . . 172

12.1.3 Results . . . 172

12.2 Additional FEM analyses . . . 176

12.2.1 Boundary conditions considerations . . . 176

12.2.2 Mesh and loading definition . . . 179

12.2.3 Benchmark analysis . . . 180

12.2.4 Results . . . 183

12.3 Conclusions . . . 187

13 FEM Modelling of Laser Shock Peening in thick plates 189 13.1 Geometry and Mesh Definition . . . 190

13.2 Load Definition . . . 190

13.3 Definition of Material Constants and Results . . . 190

Contents

13.4 Conclusions . . . 196

14 Conclusions and Future Work 200

14.1 Conclusions . . . 201 14.2 Future work . . . 205

Bibliography 206

III Appendix 224

A. Publications List 225

B. Mechanical and Thermal Properties of 2219-T851 226

C. Laser Shock Peening - Literature Overview 228

### List of Figures

1.1 Residual stresses and temperatures during welding . . . 5 1.2 Residual stresses due to non uniform plastic deformation . . 6 2.1 Depth ranges of residual stress measurement techniques . . 9 2.2 Hole drilling method for residual stress measurement . . . . 11 2.3 Ring core method for residual stress measurement . . . 11 2.4 Crack compliance residual stress measurement setup . . . . 12 2.5 Longitudinal and transversal residual stress in a welded panel 14 2.6 Disposition of strain gauges for determination of residual

stress . . . 17 2.7 Panel sectioning using a mill saw . . . 18 2.8 Longitudinal residual stress distribution σy obtained

experi-mentally . . . 19 2.9 Locations of the thermocouples in the experimental analysis 21 2.10 Longitudinal residual distribution σy for the model with

zones with different mechanical properties . . . 22 2.11 Longitudinal residual stress σy distribution for different

mod-els analyzed . . . 25 2.12 Longitudinal residual stress σy distribution obtained

numer-ically . . . 26

List of Figures

2.13 The effect of the height of the panel (i.e. the distance of the cut from the path where the elastic strain is read), on the maximum values of longitudinal residual stress σy . . . 27

2.14 Stress redistribution due to lateral and central flaw propagation 31 2.15 Distribution of transversal residual stress σx along y-axis of

the panel . . . 32 2.16 Longitudinal residual stress distribution σy for full 150 step

analysis and for simplified, 2 step analysis . . . 32 3.1 Integral stiffeners manufactured by HSC, LBW and FSW . 35 3.2 DaToN panel geometry . . . 36 3.3 DaToN panels configurations and manufacturing technologies 38 3.4 Strain gauge map for stress distribution measurement . . . 39 3.5 Comparison of stress distribution in 6056 LBW2-PWHT

panel, half and fully clamped . . . 41 3.6 Stress distribution on pristine 6056 LBW2-PWHT panel,

flat side . . . 42 3.7 Stress distribution on pristine 6056 LBW2-PWHT panel,

stringer side . . . 42 3.8 Stress distribution on pristine 6056 panels, 80 MPa, flat side 44 3.9 Stress distribution on pristine 6056 panels, 80 MPa, stringer

side . . . 44 3.10 Stress distribution on pristine 6056 panels, 110 MPa, flat side 45 3.11 Stress distribution on pristine 6056 panels, 110 MPa, stringer

side . . . 45 3.12 Stress on panel 6056 LBW2-PWHT at different crack lengths,

110 MPa, flat side . . . 46 3.13 Stress on panel 6056 LBW2-PWHT at different crack lengths,

110 MPa, stringer side . . . 46 3.14 Stress distribution on 6056 cracked panels, flat side . . . 47 3.15 Stress distribution on 6056 cracked panels, stringer side . . 47 3.16 Geometry of the initial defect . . . 49 3.17 Servohydraulic machine and electronic device . . . 50 3.18 Crack propagation in 6056 panels: 80 MPa, R=0.1 . . . 52

List of Figures

3.19 Crack propagation in 6056 panels: 110 MPa, R=0.5 . . . 52

3.20 Crack propagation in 2024 panels: 80 MPa, R=0.1 . . . 53

3.21 Crack propagation in 2024 panels: 110 MPa, R=0.5 . . . 53

3.22 Crack propagation in panels in 6056 and 2024 at 80 MPa, R=0.1 . . . 54

3.23 Crack propagation in panels in 6056 and 2024 at 110 MPa, R=0.5 . . . 55

3.24 Crack propagation rate in panels in 6056 at 80 MPa, R=0.1 56 3.25 Crack propagation rate in panels in 6056 at 110 MPa, R=0.5 56 3.26 Crack propagation rate in 2024 panels at 80 MPa, R=0.1 . 57 3.27 Crack propagation rate in 2024 panels at 110 MPa, R=0.5 . 57 3.28 Comparison of 6056 and 2024 LBW1 and LBW2 panels at 80 MPa, R=0.1 . . . 59

3.29 Comparison of 6056 and 2024 LBW1 and LBW2 panels at 110 MPa, R=0.5 . . . 59

3.30 Crack propagation in panels 6056-T6 LBW2 (80 MPa, R=0.1), different initial crack positions . . . 60

3.31 Comparison of crack propagation rate of 6056-T6 LBW2 panels (80 MPa, R=0.1) . . . 60

3.32 Strain gauge map for residual stress measurement . . . 61

3.33 Saw cutting for residual stresses relax . . . 63

3.34 Residual stress measurement by mill cutting . . . 64

3.35 Residual stress distribution in panel 6056 LBW1 with zero crack length . . . 67

3.36 Residual stress distribution in panel 6056 LBW1 PWHT with zero crack length . . . 67

3.37 Residual stress distribution in panel 6056 LBW2 with zero crack length . . . 68

3.38 Residual stress distribution in panel 6056 LBW2 PWHT with zero crack length . . . 68

3.39 Residual stress distribution in panel 6056 FSW PWHT with zero crack length . . . 69

3.40 Residual stresses distributions in panel 2024 LBW1 with zero crack length . . . 69

List of Figures

3.41 Residual stresses distributions in panel 2024 LBW2 with zero crack length . . . 70 3.42 Residual stresses distributions in panel 2024 FSW with zero

crack length . . . 70 3.43 Relaxation of the residual stress: panel 6056 LBW2 . . . 71 3.44 Comparison of the skin residual stress in the panels 6056

LBW2-PWHT and 6056 FSW-PWHT . . . 73 3.45 Comparison of the crack propagation rate in the panels 6056

LBW2-PWHT and 6056 FSW-PWHT . . . 74 3.46 Load - displacement curve of residual strength tests . . . 76 4.1 FEM model used for simulating crack propagation . . . 91 4.2 Stress intensity factor due to residual stresses - COD vs.

Tada-Paris distribution . . . 92 4.3 The principle of virtual crack closure technique . . . 92 4.4 Stress intensity factor due to residual stresses - COD vs.

VCCT vs. Tada-Paris distribution . . . 93 4.5 FEM results - residual stress in analyzed panel, with zero

crack length . . . 93 4.6 Stress intensity factor due to residual stresses only - Weight

function results vs. Tada-Paris distribution . . . 94 4.7 Residual stress redistribution due to propagation of a

sym-metric crack . . . 94 4.8 FEM model used for simulating crack propagation in a two

butt-welds panel . . . 95 4.9 Residual stress in two-stringer panel: FEM results and

Tada-Paris approximation used for applying the weight function method . . . 96 4.10 Crack geometry and stress distribution . . . 96 4.11 Kres results for weight function for eccentric internal crack,

crack tip A- Contributions of two different stress distributions 97 4.12 Kres results for weight function for infinite plate, crack tip

A - Contributions of two different stress distributions and their sum . . . 97

List of Figures

4.13 Stress intensity factor due to residual stress in two-stringer panel, obtained using different techniques . . . 98 4.14 Redistribution of residual stress in two-stringer panel -

ex-perimental vs. analytic results distribution . . . 98 4.15 FEM results - redistribution of residual stress in two-stringer

panel vs. analytic results . . . 99 5.1 Possible shape changes in welded structures . . . 102 5.2 Boundary conditions considered . . . 106 5.3 Deformations of the panel in z-axis direction, boundary

conditions as in Figure 5.2(a) . . . 107 5.4 Deformations of the panel in z-axis direction, boundary

conditions as in Figure 5.2(b) . . . 108 5.5 Deformations of the panel in z-axis direction, boundary

conditions as in Figure 5.2(c) . . . 109 5.6 Distribution along x-axis of angular deformation around y-axis110 6.1 Boundary conditions at the first step of the mechanical analysis117 6.2 Boundary conditions at Step 2. Restrained movements shown118 6.3 Introduction of the initial defect . . . 118 6.4 Load step, with initial defect shown . . . 119 6.5 Debonding of a titanium doubler as the crack (red nodes)

propagates under it . . . 120 6.6 Cracking of an aluminium doubler . . . 120 6.7 Crack propagation in compressive residual stress field with

titanium doubler . . . 121 6.8 Residual stress distribution in loading direction in Al skin

and Ti doubler . . . 122 6.9 Stress intensity factor due to residual stresses in titanium

doublers . . . 123 6.10 Stress intensity factors due to residual stress and external

loading (residual stresses present in titanium doublers only) 123 6.11 Crack propagation rate in panels with Ti and Al doublers,

experimental results . . . 124

List of Figures

7.1 Principal components of a laser . . . 128

8.1 Comparison between LSP and LPwC . . . 132

8.2 In depth residual stresses obtained with Shot peening and Laser shock peening . . . 132

8.3 Correlation between laser power density and peek pressure . 135 8.4 Wave focusing effect . . . 136

9.1 Laser power effect . . . 141

9.2 Layer number effect . . . 141

9.3 Peen size effect . . . 142

9.4 Pulse duration effect . . . 142

9.5 Top material damping effect . . . 143

9.6 Ablative layer effect . . . 144

9.7 Specimen used by the Open University for residual stress measurements . . . 145

9.8 Residual stress distribution - unclad specimen 0.5-18-2 . . . 146

9.9 Residual stress distribution - unclad specimen 0.5-18-4 . . . 146

9.10 Residual stress distribution - unclad specimen 1-18-2 . . . . 147

9.11 Residual stress distribution - unclad specimen 1-18-4 . . . . 147

9.12 Residual stress distribution - clad specimen 0.5-18-2 . . . . 148

9.13 Residual stress distribution - clad specimen 0.5-18-4 . . . . 148

9.14 Residual stress distribution - clad specimen 1-18-2 . . . 149

9.15 Residual stress distribution - clad specimen 1-18-4 . . . 149

10.1 The geometry of the specimen for the residual stress mea-surement . . . 156

10.2 LSP treated specimens prior to residual stress measurement 157 10.3 Measurement points for the x-ray diffraction technique . . . 157

10.4 The setup of the hole drilling measurement of residual stress 158 10.5 Residual stress distribution for different LSP setups in LT direction . . . 159

10.6 The definition of peening sequence . . . 159

List of Figures

10.7 Distribution of residual stress for 4-18-3 LSP setup for x-ray diffraction, and hole drilling method, compared with

standard shot peening . . . 160

10.8 The geometry of the fatigue specimen . . . 161

10.9 Fatigue results, R=0.1 . . . 162

10.10 Fatigue results, R=-1 . . . 162

10.11 Fatigue results, R=-3 . . . 163

12.1 FEM model geometry, boundary conditions and peen line position . . . 171

12.2 Residual stress distributions along the depth of the peen, unclad 1-18-2 . . . 173

12.3 Residual stress distributions along the depth of the peen, unclad 1-18-4 . . . 174

12.4 Residual stress distributions along the depth of the peen, clad 1-18-2 . . . 175

12.5 The effect of the peening sequence on residual stress distri-bution along the surface of the peen . . . 176

12.6 The distribution of residual stress S22 along the surface of the peen for the case of 200% coverage . . . 177

12.7 The distribution of residual stress S22 along the surface of the peen for the case of 400% coverage . . . 178

12.8 Residual stress distributions along the depth of the peen . . 179

12.9 The distribution of residual stress S22 along the surface of the peen for three LSP setups . . . 180

12.10 Shock wave reaching an immovable boundary and a free boundary . . . 181

12.11 Two panel configuration with free back side . . . 181

12.12 Creation of spall . . . 182

12.13 Different process setups for the simple case without top-placed panel . . . 183 12.14 Boundary condition, number of layers and different material

model effects for the simple case without top-placed panel . 184 12.15 Different process setups for the case with top-placed panel . 185

List of Figures

12.16 Number of layers, different material model and different peening sequence effects for the case with top-placed panel . 187 13.1 The geometry of the FEM specimen with boundary

condi-tions and peen position . . . 191 13.2 FEM specimen for the evaluation of the geometry effect with

boundary conditions and peen position . . . 192 13.3 Residual stress distributions along the depth of the laser

peen - comparison between experimental and FEM results . 194 13.4 The effect of the presence of a radius . . . 195 13.5 The distribution of residual stress S22 along the surface of

the peen for the case of 300% coverage . . . 196 13.6 Residual stress distributions along the depth of the peen,

4-18-3 . . . 197 13.7 The effect of laser pulse durations on the distributions of

residual stresses . . . 198 13.8 Comparison between two laser settings . . . 198 13.9 The effect of the size of laser peens . . . 199

### List of Tables

3.1 Crack propagation test program . . . 48 3.2 Panel sectioning method . . . 61 5.1 Deformations and residual stresses present in different model

configurations . . . 111 6.1 Mechanical and thermal properties of materials at room

tem-perature used in the FEM analysis . . . 115 8.1 Comparison between Shot peening and Laser shock peening . 134 9.1 Effect of LSP parameters on the distribution of residual

stresses to be investigated . . . 140 9.2 LSP 2024-T351 thin sheets fatigue results . . . 150 10.1 Residual stresses obtained using x-ray diffraction measurement

technique for different LSP setups . . . 153 10.2 Specimen conditions for the fatigue tests of AA7050-T7451 . 154 10.3 Increase in fatigue life of LSP treated specimen for the same

stress level . . . 155 10.4 Increase in stress level of LSP treated specimen for the same

number of fatigue cycles (105_{) . . . 155}

List of Tables

11.1 Mechanical properties of 2024-T351 and 7050-T7451 . . . 166 11.2 Johnson-Cook parameters for 2024-T351 (T-3) and 7050-T7451167 11.3 EOS Properties of Al 2024 and 7050 . . . 168 12.1 Johnson-Cook parameters for clad layer . . . 172 13.1 Johnson-Cook parameters - parametric analysis . . . 193

### Nomenclature

a Crack length

A, B, C, n, m Johnson-Cook material constants A0 Elongation

c Inversion point

C0 Interpolation constant (Sound propagation velocity at standard

condi-tions)

d Height of the isolated area of the panel after sectioning E Young’s modulus

Em Internal energy per unit mass

F Vertical force between nodes at the crack front GI Mode I energy release rate

GIc Critical Mode I energy release rate

h(x, a) Weight function HEL Hugoniot’s elastic limit I0 Laser intensity

Kres Stress intensity factor due to residual stresses

Nomenclature p Plasma pressure P Pressure stress PH Hugoniot pressure S1 Interpolation constant T0 Reference temperature Tm Melting temperature

Up Material particle velocity

Us Shock velocity

v Vertical displacement between nodes in front of the crack W Width of the panel

xc Distance from the crack tip

Y , Yb Geometric functions

Zs Acoustic impedance

Greek letters

x - Transversal elastic strain

y - Longitudinal elastic strain

eq Equivalent plastic strain

p Plastic strain .

Strain rate

.

0 Strain rate under quasi-static loading

Γ0 Material constant (from Gr¨uneisen ratio)

λ, µ Lam´e constants

Nomenclature

ν Poisson’s ratio ρ0 Reference density

σ Flow stress in Johnson-Cook material model σ0 Maximum residual stress at welded centre line

σmax Maximum strength

σx - Transversal residual stress

σy - Longitudinal residual stress

σyield Yield stress

σy,dynamic Uniaxial dynamic yield stress

σy(x) Stress distribution acting on the x-axis in the uncracked state

τxy - Tangential stress

η Nominal compressive volumetric strain (1-ρ0/ρ)