Ebook: Problems of Fracture Mechanics and Fatigue: A Solution Guide

On Fracture Mechanics A major objective of engineering design is the determination of the geometry and dimensions of machine or structural elements and the selection of material in such a way that the elements perform their operating function in an efficient, safe and economic manner. For this reason the results of stress analysis are coupled with an appropriate failure criterion. Traditional failure criteria based on maximum stress, strain or energy density cannot adequately explain many structural failures that occurred at stress levels considerably lower than the ultimate strength of the material. On the other hand, experiments performed by Griffith in 1921 on glass fibers led to the conclusion that the strength of real materials is much smaller, typically by two orders of magnitude, than the theoretical strength. The discipline of fracture mechanics has been created in an effort to explain these phenomena. It is based on the realistic assumption that all materials contain crack-like defects from which failure initiates. Defects can exist in a material due to its composition, as second-phase particles, debonds in composites, etc. , they can be introduced into a structure during fabrication, as welds, or can be created during the service life of a component like fatigue, environment-assisted or creep cracks. Fracture mechanics studies the loading-bearing capacity of structures in the presence of initial defects. A dominant crack is usually assumed to exist.

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The complexity surrounding the subjects of fracture mechanics and fatigue and the difficulties experienced by academics, researchers and engineers in comprehending the use of different approaches/solutions necessitated the writing of this book. The book, written by a selection of 15 world experts provides a step by step solution guide for a 139 problems. In its unique form, the book can provide valuable information for a selection of problems which cover the most important aspects of both fracture mechanics and fatigue. The use of references, theoretical background and accurate explanations allow the book to work on its own or as complementary material to other related titles.

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The complexity surrounding the subjects of fracture mechanics and fatigue and the difficulties experienced by academics, researchers and engineers in comprehending the use of different approaches/solutions necessitated the writing of this book. The book, written by a selection of 15 world experts provides a step by step solution guide for a 139 problems. In its unique form, the book can provide valuable information for a selection of problems which cover the most important aspects of both fracture mechanics and fatigue. The use of references, theoretical background and accurate explanations allow the book to work on its own or as complementary material to other related titles.
Content:
Front Matter....Pages i-xxv
Front Matter....Pages 1-1
Airy Stress Function Method....Pages 3-9
Westergaard Method for a Crack Under Concentrated Forces....Pages 11-15
Westergaard Method for a Periodic Array of Cracks Under Concentrated Forces....Pages 17-20
Westergaard Method for a Periodic Array of Cracks Under Uniform Stress....Pages 21-23
Calculation of Stress Intensity Factors by the Westergaard Method....Pages 25-29
Westergaard Method for a Crack Under Distributed Forces....Pages 31-32
Westergaard Method for a Crack Under Concentrated Forces....Pages 33-37
Westergaard Method for a Crack Problem....Pages 39-40
Westergaard Method for a Crack Subjected to Shear Forces....Pages 41-43
Calculation of Stress Intensity Factors by Superposition....Pages 45-48
Calculation of Stress Intensity Factors by Integration....Pages 49-51
Stress Intensity Factors for a Linear Stress Distribution....Pages 53-56
Mixed-Mode Stress Intensity Factors in Cylindrical Shells....Pages 57-61
Problem 16: Application of the Method of Weight Function for the Determination of Stress Intensity Factors....Pages 63-64
Approximate Determination of the Crack Tip Plastic Zone for Mode-I and Mode-II Loading....Pages 65-68
Approximate Determination of the Crack Tip Plastic Zone for Mixed-Mode Loading....Pages 69-72
Approximate Determination of the Crack Tip Plastic Zone According to the Tresca Yield Criterion....Pages 75-79
Approximate Determination of the Crack Tip Plastic Zone According to a Pressure Modified Mises Yield Criterion....Pages 81-82
Front Matter....Pages 83-89
Crack Tip Plastic Zone According to Irwin’s Model....Pages 91-94
Effective Stress intensity Factor According to Irwin’ Model....Pages 1-1
Plastic Zone at the Tip of a Semi-Infinite Crack According to the Dugdale Model....Pages 95-97
Mode-III Crack Tip Plastic Zone According to the Dugdale Model....Pages 99-101
Plastic Zone at the Tip of a Penny-Shaped Crack According to the Dugdale Model....Pages 103-105
Calculation of Strain Energy Release Rate from Load — Displacement — Crack Area Equation....Pages 107-111
Calculation of Strain Energy Release Rate for Deformation Modes I, II and III....Pages 113-115
Compliance of a Plate with a Central Crack....Pages 117-120
Strain Energy Release Rate for a Semi-Infinite Plate with a Crack....Pages 121-125
Strain Energy Release Rate for the Short Rod Specimen....Pages 127-130
Strain Energy Release Rate for the Blister Test....Pages 131-134
Calculation of Stress Intensity Factors Based on Strain Energy Release Rate....Pages 135-137
Critical Strain Energy Release Rate....Pages 139-141
Crack Stability....Pages 143-146
Stable Crack Growth Based on the Resistance Curve Method....Pages 147-153
Three-Point Bending Test in Brittle Materials....Pages 155-160
Three-Point Bending Test in Quasi Brittle Materials....Pages 161-162
Double-Cantilever Beam Test in Brittle Materials....Pages 163-168
Front Matter....Pages 169-172
Design of a Pressure Vessel....Pages 173-176
Thermal Loads in a Pipe....Pages 177-181
J-integral for an Elastic Beam Partly Bonded to a Half-Plane....Pages 183-187
J-integral for a Strip with a Semi-Infinite Crack....Pages 1-1
J-integral for Two Partly Bonded Layers....Pages 189-192
J-integral for Mode-I....Pages 193-195
J-integral for Mode-III....Pages 197-200
Path Independent Integrals....Pages 201-205
Stresses Around Notches....Pages 207-209
Experimental Determination of JIc from J — Crack Growth Curves....Pages 211-218
Experimental Determination of J from Potential Energy — Crack Length Curves....Pages 219-222
Experimental Determination of J from Load — Displacement Records....Pages 223-228
Experimental Determination of J from a Compact Tension Specimen....Pages 229-231
Validity of JIc and KIc Tests....Pages 233-237
Critical Crack Opening Displacement....Pages 239-241
Crack Opening Displacement Design Methodology....Pages 243-245
Critical Fracture Stress of a Plate with an Inclined Crack....Pages 247-249
Critical Crack Length of a Plate with an Inclined Crack....Pages 251-252
Failure of a Plate with an Inclined Crack....Pages 253-256
Growth of a Plate with an Inclined Crack Under Biaxial Stresses....Pages 257-260
Front Matter....Pages 263-268
Crack Growth Under Mode-II Loading....Pages 269-272
Growth of a Circular Crack Loaded Perpendicularly to its Cord by Tensile Stress....Pages 273-275
Growth of a Circular Crack Loaded Perpendicularly to its Cord by Compressive Stress....Pages 277-282
Growth of a Circular Crack Loaded Parallel to its Cord....Pages 1-1
Growth of Radial Cracks Emanating from a Hole....Pages 283-285
Strain Energy Density in Cuspidal Points of Rigid Inclusions....Pages 287-289
Failure from Cuspidal Points of Rigid Inclusions....Pages 291-292
Failure of a Plate with a Hypocycloidal Inclusion....Pages 293-296
Crack Growth From Rigid Rectilinear Inclusions....Pages 297-300
Crack Growth Under Pure Shear....Pages 301-303
Critical Stress in Mixed Mode Fracture....Pages 305-307
Critical Stress for an Interface Crack....Pages 309-313
Failure of a Pressure Vessel with an Inclined Crack....Pages 315-317
Failure of a Cylindrical Bar with a Circular Crack....Pages 319-325
Failure of a Pressure Vessel Containing a Crack with Inclined Edges....Pages 327-331
Failure of a Cylindrical Bar with a Ring-Shaped Edge Crack....Pages 333-337
Stable and Unstable Crack Growth....Pages 339-341
Dynamic Stress Intensity Factor....Pages 343-346
Crack Speed During Dynamic Crack Propagation....Pages 347-349
Rayleigh Wave Speed....Pages 351-354
Front Matter....Pages 355-357
Dilatational, Shear and Rayleigh Wave Speeds....Pages 359-363
Speed and Acceleration of Crack Propagation....Pages 365-367
Stress Enhanced Concentration of Hydrogen Around Crack Tips....Pages 369-372
Subcritical Crack Growth due to the Presence of a Deleterious Species....Pages 1-1
Front Matter....Pages 373-375
Estimating the lifetime of aircraft wing stringers....Pages 377-382
Estimating long life fatigue of components....Pages 385-395
Strain life fatigue estimation of automotive component....Pages 397-401
Lifetime estimates using LEFM....Pages 403-403
Lifetime of a gas pipe....Pages 405-408
Pipe failure and lifetime using LEFM....Pages 409-412
Strain life fatigue analysis of automotive suspension component....Pages 413-418
Fatigue crack growth in a center-cracked thin aluminium plate....Pages 419-421
Effect of crack size on fatigue life....Pages 423-425
Effect of fatigue crack length on failure mode of a center-cracked thin aluminium plate....Pages 427-430
Crack propagation under combined tension and bending....Pages 431-437
Influence of mean stress on fatigue crack growth for thin and thick plates....Pages 439-440
Critical fatigue crack growth in a rotor disk....Pages 441-443
Applicability of LEFM to Fatigue Crack Growth....Pages 445-447
Fatigue crack growth in the presence of residual stress field....Pages 449-452
Fatigue crack growth in a plate containing an open hole....Pages 453-454
Front Matter....Pages 455-456
Infinite life for a plate with a semi-circular notch....Pages 457-460
Infinite Life for a plate with a central hole....Pages 461-464
Crack Initiation in a sheet containing a central hole....Pages 467-468
Inspection Scheduling....Pages 403-403
Safety Factor of a U-Notched Plate....Pages 469-471
Safety Factor and Fatigue Life Estimates....Pages 473-475
Design of a circular bar for safe life....Pages 477-480
Threshold and LEFM....Pages 483-486
Safety Factor and Residual Strength....Pages 487-490
Design of a rotating circular shaft for safe life....Pages 491-494
Safety factor of a notched member containing a central crack....Pages 495-496
Safety Factor of a Disk Sander....Pages 497-500
Short Cracks and LEFM Error....Pages 501-503
Stress Ratio effect on the Kitagawa-Takahashi diagram....Pages 505-507
Susceptibility of Materials to Short Cracks....Pages 509-517
The effect of the Stress Ratio on the Propagation of Short Fatigue Cracks in 2024-T3....Pages 519-526
Crack Growth rate during irregular loading....Pages 529-532
Fatigue life under two-stage block loading....Pages 533-537
The Application of Wheeler’s Model....Pages 539-542
Fatigue Life Under Multiple-Stage Block Loading....Pages 543-548
Front Matter....Pages 551-552
Fatigue Life Under two-stage Block Loading Using Non-Linear Damage Accumulation....Pages 553-554
Fatigue Crack Retardation Following a Single Overload....Pages 555-557
Fatigue Life of a Pipe Under Variable Internal Pressure....Pages 559-561
Fatigue Crack Growth Following a Single Overload Based on Crack Closure....Pages 403-403
Fatigue Crack Growth Following a Single Overload Based on Crack-Tip Plasticity....Pages 563-564
Fatigue Crack Growth and Residual Strength of a Double Edge Cracked Panel Under Irregular Fatigue Loading....Pages 565-567
Fatigue Crack Growth Rate Under Irregular Fatigue Loading....Pages 569-572
Fatigue Life of a Pressure Vessel Under Variable Internal Pressure....Pages 573-574
Equibiaxial Low Cycle Fatigue....Pages 575-577
Mixed Mode Fatigue Crack Growth in a Center-Cracked Panel....Pages 579-582
Collapse Stress and the Dugdale’s Model....Pages 583-584
Torsional Low Cycle Fatigue....Pages 585-587
Fatigue Life Assessment of a Plate Containing Multiple Cracks....Pages 589-591
Fatigue Crack Growth and Residual Strength in a Simple MSD Problem....Pages 593-595
Back Matter....Pages 597-599
....Pages 601-606