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.

Problem 1: Airy Stress Function Method.- Problem 2: Westergaard Method for a Crack Under Concentrated Forces.- Problem 3: Westergaard Method for a Periodic Array of Cracks Under Concentrated Forces.- Problem 4: Westergaard Method for a Periodic Array of Cracks Under Uniform Stress.- Problem 5: Calculation of Stress Intensity Factors by the Westergaard Method.- Problem 6: Westergaard Method for a Crack Under Distributed Forces.- Problem 7: Westergaard Method for a Crack Under Concentrated Forces.- Problem 8: Westergaard Method for a Crack Problem.- Problem 9: Westergaard Method for a Crack Subjected to Shear Forces.- Problem 10: Calculation of Stress Intensity Factors by Superposition.- Problem 11: Calculation of Stress Intensity Factors by Integration.- Problem 12: Stress Intensity Factors for a Linear Stress Distribution.- Problem 13: Mixed-Mode Stress Intensity Factors in Cylindrical Shells.- Problem 14: Photoelastic Determination of Stress Intensity Factor KI.- Problem 15: Photoelastic Determination of Mixed-Mode Stress Intensity Factors KI and KII.- Problem 16: Application of the Method of Weight Function for the Determination of Stress Intensity Factors.- Problem 17: Approximate Determination of the Crack Tip Plastic Zone for Mode-I and Mode-II Loading.- Problem 18: Approximate Determination of the Crack Tip Plastic Zone for Mixed-Mode Loading.- Problem 19: Approximate Determination of the Crack Tip Plastic Zone According to the Tresca Yield Criterion.- Problem 20: Approximate Determination of the Crack Tip Plastic Zone According to a Pressure Modified Mises Yield Criterion.- Problem 21: Crack Tip Plastic Zone According to Irwin’s Model.- Problem 22: Effective Stress Intensity factor According to Irwin’s Model.- Problem 23: Plastic Zone at the Tip of a Semi-Infinite Crack According to the Dugdale Model.- Problem 24: Mode-III Crack Tip Plastic Zone According to the Dugdale Model.- Problem 25: Plastic Zone at the Tip of a Penny-Shaped Crack According to the Dugdale Model.- Problem 26: Calculation of Strain Energy Release Rate from Load — Displacement — Crack Area Equation.- Problem 27: Calculation of Strain Energy Release Rate for Deformation Modes I, II and III.- Problem 28: Compliance of a Plate with a Central Crack.- Problem 29: Strain Energy Release Rate for a Semi-Infinite Plate with a Crack.- Problem 30: Strain Energy Release Rate for the Short Rod Specimen.- Problem 31: Strain Energy Release Rate for the Blister Test.- Problem 32: Calculation of Stress Intensity Factors Based on Strain Energy Release Rate.- Problem 33: Critical Strain Energy Release Rate.- Problem 34: Experimental Determination of Critical Stress Intensity Factor KIc.- Problem 35: Experimental Determination of KIc.- Problem 36: Crack Stability.- Problem 37: Stable Crack Growth Based on the Resistance Curve Method.- Problem 38: Three-Point Bending Test in Brittle Materials.- Problem 39: Three-Point Bending Test in Quasi Brittle Materials.- Problem 40: Double-Cantilever Beam Test in Brittle Materials.- Problem 41: Design of a Pressure Vessel.- Problem 42: Thermal Loads in a Pipe.- Problem 43: J-integral for an Elastic Beam Partly Bonded to a Half-Plane.- Problem 44: J-integral for a Strip with a Semi-Infinite Crack.- Problem 45: J-integral for Two Partly Bonded Layers.- Problem 46: J-integral for Mode-I.- Problem 47: J-integral for Mode III.- Problem 48: Path Independent Integrals.- Problem 49: Stresses Around Notches.- Problem 50: Experimental Determination of JIc from J — Crack Growth Curves.- Problem 51: Experimental Determination of J from Potential Energy — Crack Length Curves.- Problem 52: Experimental Determination of J from Load-Displacement Records.- Problem 53: Experimental Determination of J from a Compact Tension Specimen.- Problem 54: Validity of JIc and KIc Tests.- Problem 55: Critical Crack Opening Displacement.- Problem 56: Crack Opening Displacement Design Methodology.- Problem 57: Critical Fracture Stress of a Plate with an Inclined Crack.- Problem 58: Critical Crack Length of a Plate with an Inclined Crack.- Problem 59: Failure of a Plate with an Inclined Crack.- Problem 60: Growth of a Plate with an Inclined Crack Under Biaxial Stresses.- Problem 61: Crack Growth Under Mode-II Loading.- Problem 62: Growth of a Circular Crack Loaded Perpendicularly to its Cord by Tensile Stress.- Problem 63: Growth of a Circular Crack Loaded Perpendicular to its Cord by Compressive Stress.- Problem 64: Growth of a Circular Crack Loaded Parallel to its Cord.- Problem 65: Growth of Radial Cracks Emanating from a Hole.- Problem 66: Strain Energy Density in Cuspidal Points of Rigid Inclusions.- Problem 67: Failure from Cuspidal Points of Rigid Inclusions.- Problem 68: Failure of a Plate with a Hypocycloidal Inclusion.- Problem 69: Crack Growth From Rigid Rectilinear Inclusions.- Problem 70: Crack Growth Under Pure Shear.- Problem 71: Critical Stress in Mixed Mode Fracture.- Problem 72: Critical Stress for an Interface Crack.- Problem 73: Failure of a Pressure Vessel with an Inclined Crack.- Problem 74: Failure of a Cylindrical bar with a Circular Crack.- Problem 75: Failure of a Pressure Vessel Containing a Crack with Inclined Edges.- Problem 76: Failure of a Cylindrical Bar with a Ring-Shaped Edge Crack.- Problem 77: Stable and Unstable Crack Growth.- Problem 78: Dynamic Stress Intensity Factor.- Problem 79: Crack Speed During Dynamic Crack Propagation.- Problem 80: Rayleigh Wave Speed.- Problem 81: Dilatational, Shear and Rayleigh Wave Speeds.- Problem 82: Speed and Acceleration of Crack Propagation.- Problem 83: Stress Enhanced Concentration of Hydrogen around Crack Tips.- Problem 84: Subcritical Crack Growth due to the Presence of a Deleterious Species.- Problem 1: Estimating the Lifetime of Aircraft Wing Stringers.- Problem 2: Estimating Long Life Fatigue of Components.- Problem 3: Strain Life Fatigue Estimation of Automotive Component.- Problem 4: Lifetime Estimates Using LEFM.- Problem 5: Lifetime of a Gas Pipe.- Problem 6: Pipe Failure and Lifetime Using LEFM.- Problem 7: Strain Life Fatigue Analysis of Automotive Suspension Component.- Problem 8: Fatigue Crack Growth in a Center-Cracked Thin Aluminium Plate.- Problem 9: Effect of Crack Size on Fatigue Life.- Problem 10: Effect of Fatigue Crack Length on Failure Mode of a Center-Cracked Thin Aluminium Plate.- Problem 11: Crack Propagation Under Combined Tension and Bending.- Problem 12: Influence of Mean Stress on Fatigue Crack Growth for Thin and Thick Plates.- Problem 13: Critical Fatigue Crack Growth in a Rotor Disk.- Problem 14: Applicability of LEFM to Fatigue Crack Growth.- Problem 15: Fatigue Crack Growth in the Presence of Residual Stress Field.- Problem 16: Fatigue Crack Growth in a Plate Containing an Open Hole.- Problem 17: Infinite Life for a Plate with a Semi-Circular Notch.- Problem 18: Infinite Life for a Plate with a Central Hole.- Problem 19: Crack Initiation in a Sheet Containing a Central Hole.- Problem 20: Inspection Scheduling.- Problem 21: Safety Factor of a U-Notched Plate.- Problem 22: Safety Factor and Fatigue Life Estimates.- Problem 23: Design of a Circular Bar for Safe Life.- Problem 24: Threshold and LEFM.- Problem 25: Safety Factor and Residual Strength.- Problem 26: Design of a Rotating Circular Shaft for Safe Life.- Problem 27: Safety Factor of a Notched Member Containing a Central Crack.- Problem 28: Safety Factor of a Disk Sander.- Problem 29: Short Cracks and LEFM Error.- Problem 30: Stress Ratio effect on the Kitagawa-Takahashi diagram.- Problem 31: Susceptibility of Materials to Short Cracks.- Problem 32: The effect of the Stress Ratio on the Propagation of Short Fatigue Cracks in 2024-T3.- Problem 33: Crack Growth Rate During Irregular Loading.- Problem 34: Fatigue Life Under two-stage Block Loading.- Problem 35: The Application of Wheeler’s Model.- Problem 36: Fatigue Life Under Multiple-Stage Block Loading.- Problem 37: Fatigue Life Under two-stage Block Loading Using Non-Linear Damage Accumulation.- Problem 38: Fatigue Crack Retardation Following a Single Overload.- Problem 39: Fatigue Life of a Pipe Under Variable Internal Pressure.- Problem 40: Fatigue Crack Growth Following a Single Overload Based on Crack Closure.- Problem 41: Fatigue Crack Growth Following a Single Overload Based on Crack-Tip Plasticity.- Problem 42: Fatigue Crack Growth and Residual Strength of a Double Edge Cracked Panel Under Irregular Fatigue Loading.- Problem 43: Fatigue Crack Growth Rate Under Irregular Fatigue Loading.- Problem 44: Fatigue Life of a Pressure Vessel Under Variable Internal Pressure.- Problem 45: Equibiaxial Low Cycle Fatigue.- Problem 46: Mixed Mode Fatigue Crack Growth in a Center-Cracked Panel.- Problem 47: Collapse Stress and the Dugdale’s Model.- Problem 48: Torsional Low Cycle Fatigue.- Problem 49: Fatigue Life Assessment of a Plate Containing Multiple Cracks.- Problem 50: Fatigue Crack Growth and Residual Strength in a Simple MSD Problem.