Preface ....................................................... XI
Acknowledgements ............................................. XIII
Disclaimer .................................................... XIV
1 Introduction ................................................. 1
1.1 Objectives of Bonded Repairs and an Overview of the
Repair Process .......................................... 1
1.1.1 Structural assessment ............................ 3
1.1.2 Repair design .................................... 3
1.1.3 Installation of the repair ....................... 7
1.2 Objectives of This Book ................................. 8
1.3 Review of Past and Current Work on Design and Analysis
of Bonded Repair ........................................ 8
1.4 Basic Elements of Fracture Mechanics Theory ............ 10
2 Theory of Bonded Doublers and Bonded Joints ................. 16
2.1 Introduction ........................................... 16
2.2 Stress Analysis of Two-Sided Doublers and Double-
trap Joints ............................................ 17
2.2.1 Elastic analysis of two-sided doublers and
double-strap joints ............................. 17
2.2.2 Elastic-plastic analysis of two-sided doublers
and double-strap joints ......................... 23
2.2.3 Peel stresses in two-sided doublers and double
-strap joints .................................... 28
2.3 Stress Analysis of One-Sided Bonded Double and Single
Strap Joints ........................................... 31
2.3.1 Stage Г. Solution for bending moment at ends
and middle of overlap ........................... 33
2.3.2 Stage II: Solution for induced adhesive peel
stresses ........................................ 38
2.3.3 Stage III: Solution for induced adhesive shear
stresses ........................................ 45
2.4 Consideration of Other Important Effects in Bonded
Doublers and Joints ................................... 50
2.4.1 Stress-free condition at the adhesive ends ...... 51
2.4.2 Corner singularity .............................. 53
2.4.3 Stress concentration in adherends ............... 59
2.4.4 Triaxial stresses and plastic yielding .......... 62
2.5 Failure Criteria for Bonded Doublers and Joints ........ 65
3 Fundamental Concept of Crack Patching ....................... 69
3.1 Introduction ........................................... 69
3.2 Formulation and Notation ............................... 71
3.3 Symmetric or Fully Supported One-Sided Repairs ......... 73
3.3.1 Stage I: Load attraction by patch ............... 73
3.3.2 Stage II: Stress intensity factor ............... 80
3.3.3 The effect of plastic adhesive .................. 82
3.3.4 The effect of finite crack size ................. 83
3.3.5 The effect of mixed mode loading ................ 86
3.4 One-Sided Repairs ...................................... 87
3.5 Thermal Stresses ....................................... 92
3.6 Summary ................................................ 94
4 Mathematical Theory of Supported One-Sided Crack Patching
or Two-Sided Crack Patching ................................ 95
4.1 Introduction ........................................... 95
4.2 Stage I: Load Attraction ............................... 95
4.2.1 Equivalent inclusion method ..................... 97
4.2.2 Inclusion problem with polynomial
eigenstrains .. .................................100
4.2.3 Solution of the load attraction problem ........ 107
4.2.4 Load attraction with thermal effects ........... 110
4.3 Stage II: Fracture Analysis ........................... 115
4.3.1 Cracked sheet displacements and stresses ....... 118
4.3.2 Composite patch displacements and stresses ..... 122
4.3.3 Stress intensity factor evaluation ............. 130
4.4 Numerical Illustrations ............................... 131
4.5 Thermal Constraints ................................... 138
4.6 Summary ............................................... 145
5 Approximate Theory of Unsupported One-Sided Crack
Patching ................................................... 146
5.1 Introduction .......................................... 146
5.2 Stage I: Geometrically Linear Analysis ................ 147
5.2.1 Inclusion with constant eigencurvature ......... 147
5.2.2 Geometrically linear analysis of polygonal
patch .......................................... 152
5.3 Geometrically Nonlinear Analysis of Stage I ........... 159
5.3.1 Thermal stresses in polygonal patch ............ 162
5.3.2 Patch spanning across the entire plate's
width under purely mechanical loading .......... 176
5.3.3 Polygonal patch under combined thermo-
mechanical loading ............................. 183
5.4 Stage II: Fracture Analysis Using Crack-bridging
Model ................................................. 189
5.4.1 Determination of spring constants .............. 192
5.4.2 Fracture analysis by crack-bridging model ...... 197
5.4.3 Numerical solutions of integral equations ...... 201
5.4.4 Illustrative examples .......................... 205
5.5 Thermal Residual Stresses Resulting from Bonding ...... 209
5.5.1 Rose's or Barneveld-Fredell's curing model ..... 209
5.5.2 Duong and Yu's curing model .................... 209
5.5.3 Wang and Erjavec's curing model ................ 210
5.6 Characterization of Fatigue Crack Growth in
One-Sided Patching .................................... 214
5.7 Summary ............................................... 214
6 Analytical Approach to Repairs of Corrosion Grind-Outs ..... 216
6.1 Introduction .......................................... 216
6.2 Fundamental Concepts .................................. 216
6.2.1 Eshelby solution for elliptical
inhomogeneities ................................ 217
6.2.2 Analytical solution of elliptical patches ...... 220
6.2.3 Formulas for a special case of an elliptical
isotropic patch with a Poisson's ratio same
as skin ........................................ 224
6.3 General Solution of Polygon-Shaped Patches ............ 229
6.3.1 Polygonal inhomogeneity with variable
stiffness ...................................... 229
6.3.2 Repair over an elliptical grind-out ............ 232
6.4 Summary ............................................... 247
7 Bond-line Analysis at Patch Ends ........................... 248
7.1 Introduction .......................................... 248
7.2 One-Dimensional Analysis of Tapered Patches and
Doublers .............................................. 248
7.2.1 Mathematical formulation and two-step
solution method ................................ 249
7.2.2 Solution for nonlinear moment distribution
along the joint ............................... 249
7.2.3 Solutions for peel and shear stresses in the
adhesive ....................................... 253
7.2.4 Numerical examples ............................. 261
7.3 One-Dimensional Analysis of Tapered Patches and
Doublers Including Effects of Thermal Mismatch and
Adhesive Plasticity ................................... 270
7.3.1 Extension to include the effect of thermal
mismatch ....................................... 271
7.3.2 Extension to include the effect of adhesive
plasticity ..................................... 276
7.4 Approximate Method for Adhesive Stresses at Patch
End in a One-Sided Repair ............................ 277
7.5 Approximate Method for Adhesive Stresses at Patch
End in a Two-Sided Repair ............................ 278
7.6 Summary ............................................... 279
8 Fatigue Crack Growth Analysis of Repaired Structures ....... 280
8.1 Introduction .......................................... 280
8.2 Crack-Closure Analysis of Repaired Cracks ............. 281
8.2.1 Crack closure of repaired cracks under small-
scale yielding ................................. 281
8.2.2 Crack closure of repaired cracks under
large-scale yielding ........................... 284
8.3 Overload Effect and Validation Using Finite Element
Method ................................................ 289
8.4 Comparison with Experimental Results .................. 292
8.5 Summary ............................................... 299
9 Preliminary Design Approach for Crack Patching ............. 300
9.1 Introduction .......................................... 300
9.2 Basic Analysis Methods Used in the Preliminary
Design Approach ....................................... 300
9.1 Introduction .......................................... 300
9.2.1 Analysis method for a repair subjected only to
mechanical loads ............................... 301
9.2.2 Analysis method for a repair subjected to
thermo-mechanical loads ........................ 304
9.3 Design Criteria ....................................... 310
9.3.1 Design criteria for cracked skin ............... 311
9.3.2 Design criteria for patch ...................... 312
9.3.3 Design criteria for adhesive ................... 313
9.4 Material Selection .................................... 314
9.4.1 Patch materials ................................ 314
9.4.2 Adhesive materials ............................. 315
9.5 Preliminary Design Procedure .......................... 320
9.5.1 Design procedure for a repair subjected only
to mechanical loads ............................ 323
9.5.2 Design procedure for a repair subjected to
thermo-mechanical loads ........................ 325
9.6 An Illustrative Example Using Design Process .......... 332
9.6.1 Loading conditions ............................. 333
9.6.2 Design parameters ............................. 333
9.7 Summary ............................................... 335
10 A Preliminary Design Approach for Corrosion Repairs ........ 336
10.1 ntroduction ........................................... 336
10.2 Basic Analysis Methods Used in the Preliminary Design
Approach .............................................. 337
10.2.1 Analysis method for a repair subjected only to
mechanical loads ............................... 337
10.2.2 Analysis method for a repair subjected to
thermo-mechanical loads ............................... 340
10.3 Design Criteria ....................................... 345
10.3.1 Design criteria for corroded skin or substrate . 345
10.3.2 Design criteria for patch ...................... 345
10.3.3 Design criteria for adhesive ................... 346
10.4 Preliminary Design Procedure .......................... 346
10.5 Summary ............................................... 348
11 Experimental Verifications of Analytical Methods ........... 349
11.1 Introduction .......................................... 349
11.2 Fatigue Crack Growth Tests and Method Validation ...... 350
11.2.1 Fatigue crack growth tests ..................... 350
11.2.2 Characterization of fatigue crack growth in
one-sided and two-sided repairs ............... 351
11.2.3 Fatigue crack growth analysis .................. 360
11.2.4 Comparison between analytical predictions and
test results ................................... 362
11.3 Load Attraction Tests and Method Validation ........... 374
11.3.1 Load attraction tests .......................... 374
11.3.2 Comparison between analytical prediction and
test results ................................... 376
11.4 Summary ............................................... 377
12 Repair of Sonic Fatigue .................................... 382
12.1 Introduction .......................................... 382
12.2 Structural Response to Acoustic Loading ............... 386
12.3 Analysis of Damped Repairs ............................ 387
12.3.1 Dynamic analysis of layered beams .............. 387
12.3.2 Influence of structural damping ................ 388
12.3.3 Static and dynamic responses of damped repair .. 390
12.3.4 Stresses and stress intensity factors in the
repaired skin ...................................391
12.4 Fatigue Crack Growth Analysis ......................... 393
12.5 Optimization of Damped Repairs ........................ 395
12.6 An Illustrative Example ............................... 395
13 Repair Analysis Methods Accounting for Secondary Effects ... 402
13.1 Effect of Tapering on Load Attraction of Bonded
Patches ............................................... 402
13.2 Effect of Patches in Proximity on Load Attraction ..... 406
13.3 Effect of Adherend Shear Deformation on Repair
Efficiency ............................................ 412
14 Concluding Remarks ...................................... 419
Appendix: Introduction to CRAS Software ...................... 421
References .................................................... 442
Index ......................................................... 456
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