1 Some Fundamentals
1.1 Fretting in Practice
1.2 Basics, Equilibrium and 'Coupling' 1.3 Friction
1.4 Contact Requirements
1.5 Classes of Contact 1.6 Methods of Solution
1.7 Shakedown
1.8 Three Dimensional Aspects
2 Plane Elasticity and Half-Plane Contacts
2.1 Airy Stress Functions and the Half-Plane 2.2 Integral Equation Formulation
2.3 Solution
2.3.1 Cauchy Equations of the First Kind 2.3.2 Cauchy Equations of the Second Kind
2.3.3 Numerical Solutions
2.4 Mossakovskii-Barber Procedure 2.4.1 Normal Loading Problem
2.4.2 Application of a Shear Force
2.4.3 Influence of Bulk Tension 2.4.4 Application of a Moment
2.5 Solutions Based on Dislocations
2.6 Summary
3 Williams' Solution
3.1 Introduction
3.2 Antiplane Loading
3.3 General Loading
3.4 Crack Tip and Incomplete Contact Edge Solution
3.5 Bonded Wedges
3.6 Sliding Wedges
4 Half Plane Partial Slip Contact Problems
4.1 Introduction
4.2 The Normal Load Problem for Asymmetrical Contacts 4.3 The Sequence of Loading
4.3.1 Sequential Loading (Constant Normal Load)
4.3.2 Proportional Loading
4.3.3 Two-Stage Proportional Loading
4.3.4 Application to a Hertzian Geometry
4.4 The Effect of Differential Bulk Tension
4.4.1 Tangential Load and Moderate Differential Bulk Tension
4.4.2 Bulk Tension Dominated Partial Slip Problems
4.5 Periodic Loading
4.6 More General Loading Scenarios
4.7 General Cyclic Proportional Loading
4.7.1 The Permanent Stick Zone
4.7.2 Mapping between the Normal and Tangential Problems
4.7.3 Example - Tilted Wedge
4.8 Partial Slip Solutions Based on Dislocations
4.8.1 Glide Dislocation Solutions
4.8.2 Example Problem - Cattaneo-Mindlin Problem
4.8.3 Large Bulk Tension Problems
4.9 Antiplane Loading
5 Complete Contacts and their Behaviour
5.1 General Frictional Response - square contacting element
5.2 Finite Slip Zones 5.3 Cracks at Contact Edges
5.4 References
6 Representation of Half-plane Contact Edge Behaviour by Asymptotes
6.1 Introduction
6.2 Basic Solution
6.3 Partial Slip: constant normal load
6.4 Partial Slip: varying normal load .
6.5 References
7 Crack Propagation, Nucleation and Nucleation Modelling
7.1 Introduction
7.2 Notch and Critical Distance Methods
7.3 Critical Plane Methods 7.4 Short Crack Methods
7.5 Wear and Corrosion
8 Experiments to Measure Fretting Fatigue Strength
8.1 Fundamental and Historic Considerations
8.2 Single Actuator Experimental Apparatus
8.3 Two Actuator Experimental Apparatus 8.4 Further Developments
8.5 Concluding Remarks
About the Author: David Hills read Engineering Science at the University of Oxford, and after a short period in industry did a PhD at what was then Trent Polytechnic, where he was made a lecturer. In 1983 he spent a very educational year at the University of Michigan with Maria Comninou and Jim Barber. In 1984 he secured an appointment in the department in which he had incepted, together with a Fellowship at Lincoln College. He has retained these positions, working mainly on fretting, fretting fatigue and contact problems generally.
Hendrik N. Andresen graduated from the Technical University of Berlin with a master's degree in 2017 and began his DPhil studies at the University of Oxford under the supervision of Prof David A. Hills in the field of contact mechanics the same year. During his studies he gained invaluable professional experience in the automotive and aerospace industries and participated in an exchange programme with the University of Michigan. In 2019 he was a stipendiary lecturer at Lincoln College. He is now pursuing a career in intellectual property law in Berlin.
