## Mechanics of Fretting FatigueFailures of many mechanical components in service result from fatigue. The cracks which grow may either originate from some pre-existing macroscopic defect, or, if the component is of high integrity but highly stressed, a region of localized stress concentration. In turn, such concentrators may be caused by some minute defect, such as a tiny inclusion, or inadvertent machining damage. Another source of surface damage which may exist between notionally 'bonded' components is associated with minute relative motion along the interface, brought about usually be cyclic tangential loading. Such fretting damage is quite insidious, and may lead to many kinds of problems such as wear, but it is its influence on the promotion of embryo cracks with which we are concerned here. When the presence of fretting is associated with decreased fatigue performance the effect is known as fretting fatigue. Fretting fatigue is a subject drawing equally on materials science and applied mechanics, but it is the intention in this book to concentrate attention entirely on the latter aspects, in a search for the quantification of the influence of fretting on both crack nucleation and propagation. There have been very few previous texts in this area, and the present volume seeks to cover five principal areas; (a) The modelling of contact problems including partial slip under tangentialloading, which produces the surface damage. (b) The modelling of short cracks by rigorous methods which deal effectively with steep stress gradients, kinking and closure. (c) The experimental simulation of fretting fatigue. |

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### Contents

Introduction | 1 |

Basic Contact Mechanics | 9 |

22 Plane problems formulation | 14 |

23 Plane problems solutions | 20 |

232 Indentation by a rigid flatended punch | 25 |

233 Indentation by a wedge | 26 |

234 Indentation by a punch producing constant pressure | 27 |

24 Axisymmetric problems formulation | 28 |

523 Real rough surfaces | 110 |

524 Stresses under rough contacts | 111 |

53 Friction | 113 |

54 The influence of surface treatments | 122 |

The Analysis of Cracks | 127 |

62 Analysis of plane cracks | 134 |

63 Partially closed cracks | 143 |

64 Three dimensional cracks | 149 |

25 Axisymmetric problems solutions | 31 |

252 Indentation by a rigid flatended punch | 34 |

253 Indentation by a cone | 35 |

254 Indentation by a punch producing constant pressure | 36 |

Contacts under Partial Slip | 41 |

32 Contact of cylinders under partial slip | 44 |

33 Contact of spheres under partial slip | 49 |

34 Load variation and history dependence | 53 |

35 The effect of bulk stress | 60 |

Advanced Contact Mechanics | 65 |

43 Twisting contacts | 78 |

homogeneous bodies | 82 |

441 Numerical solution of integral equations | 83 |

442 Influence function methods | 85 |

443 Other techniques | 88 |

45 Numerical methods layered problems | 89 |

Mechanics of Surfaces | 95 |

52 Contact of rough surfaces | 99 |

521 Regular roughness | 100 |

522 Random rough surfaces | 105 |

Fretting Fatigue Tests | 153 |

72 Bridgetype tests | 154 |

73 Test geometry the avoidance of singularities | 158 |

74 Fretting tests based on the Hertzian contact | 162 |

Analysis of crack propagation | 169 |

82 Analysis of fretting fatigue cracks | 175 |

821 Twodimensional analysis | 179 |

822 Threedimensional analysis | 184 |

83 Crack arrest in fretting fatigue | 187 |

Analysis of crack initiation | 195 |

92 Crack initiation in fretting | 197 |

93 The bulk approach to initiation analysis | 201 |

94 Local modelling of crack initiation | 205 |

941 Asperity passing model | 207 |

942 Persistent slip band model | 210 |

Conclusions | 215 |

Kernels for a dislocation in a halfplane | 219 |

References | 221 |

233 | |

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### Common terms and phrases

arise asperity contact axi-symmetric behaviour boundary bulk stress bulk tension Chapter closure coefficient of friction components compressive configuration constant contact geometry contact patch contact problems contacting bodies crack faces crack growth rate crack initiation crack length crack propagation damage described dislocation effect elastically similar experimental Figure finite element method fracture mechanics fretting fatigue fretting fatigue cracks fretting problems geometry give given half-plane hence Hertzian contact Indentation influence function integral equation intensity factor range ISBN material Mindlin mode normal load obtained occurs parameter partial slip plain fatigue plane plane strain plasticity Poisson's ratio possible predict region relative displacement relative slip residual stress rigid rough surfaces shear force shear stress shear traction distribution shown in fig singular sliding slip amplitude slip zones Solid Mechanics solution specimen stick zone strain stress intensity factor surface displacements tangential displacement tangential force tangential loading technique tensile tests zero

### Popular passages

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