D.H. Lammlein PhD Dissertation - Vanderbilt University

contact. The contact area can include all or part of the surface and the nature of this
contact can be stick, slip, or stick/slip.
In the case of a stick condition (µ=1), the power is equivalent to that necessary for
interfacial shearing of the material in the vicinity of the tool. For a finite area dA at the
tool surface at a centroid radius, r, from the tool rotational axis; the corresponding, heat
input is:
dq = ω⋅τ yield ⋅r ⋅dA (1.3)
where ω is the radial velocity of the tool and τ yield is the shear strength of the weld
material. The shear strength of the material is obtained from the yield strength of the
material by applying the von Mises yield criterion in uniaxial tension and pure shear (as
is the case for the weld material at the tool surface):
=
σ yield
τ
yield 3
The yield strength is strongly dependent on temperature and to a lesser extent, strain rate.
This relationship will be discussed to a great extent in the material thermal properties
section.
For a slip or frictional (µτ yield , one must differ to the first case as interfacial shearing will occur.
Schmidt et al. define an additional variable, the contact state variable (δ), for the
slip/stick contact condition:
δ = Vmatrix / Vtool
9