D.H. Lammlein PhD Dissertation - Vanderbilt University

(1.11)
where r p is the probe (pin) radius, h is the probe height, is the average shear stress
over the probe surface, µ is the coefficient of friction, F is the translational force during
welding, and λ is the thread helix angle. The remaining terms are defined as follows:
Russell et al. [12] estimate the contribution of the probe to the total heat
generation near the interface to be approximately 2% using equation (1.7) and assuming
the contact shear stress to be 5% of its room temperature value (taking into account
material softening with temperature and strain). Simar et al. [8] estimate 12% for this
same value. These analytically calculated probe contributions are tool geometry,
material, and parameter dependent, as are the empirical values.
Debate exists over the predominant nature of the tool interface contact
condition, particularly for the shoulder, and how best to model it. Schmidt et al. [24]
assume full shoulder contact with a constant frictional coefficient over the shoulder
surface. Under these conditions, slip occurs where the frictional shearing does not
exceed the shear yield strength of the material, and stick occurs elsewhere. Colgrove et
al. [22] use a stick condition with an artificially small contact radius and achieve good
agreement with experiment. The authors however concede this approach to be physically
unrealistic. Its use is justified as a simplification. The authors state that a slip condition
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