The JKR Contribution

The correct solution to the problem of contact between elastic spheres with surface adhesion was obtained by Johnson, Kendall and Roberts 37 years later. This came about because Roberts and Kendall had both been supervised by Tabor while studying for doctorates in Cambridge, while Johnson had collaborated over many years with Tabor on the contact problems associated with friction and lubrication.  

Roberts,while observing the contact of rubber windscreen wiper blades on glass, had noticed that the contact spot was much larger than he expected from Hertz theory under dry conditions, yet approached the Hertz predictions rather precisely when wetted with soapy water. Kendall had been measuring the contact spot size between polymer, glass, and metal surfaces using optical and 

The solution came on a cold February night in 1970 when Roberts had visited Kendall in Derby where he was working on wheel to rail adhesion at British Railways Technical Centre. After discussing the problem over dinner, it 

Roberts and Kendall then did more experimental work on rubber/rubber and gelatin/poly(methyl methacrylate) contacts. These results fitted Equation (9.4) extremely well, as shown in Fig. 9.6, and allowed the work of adhesion to be scaled to the observations. It turned out later that a similar mathematical argument had been produced by Sperling in 1964, but he had found no experimental evidence to support his theory.  

From the contact spot size dj at zero load, where 

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