J R Barber, Department of Mechanical Engineering, University of Michigan, MI

Frictional elastic systems under periodic loading History-dependence, non-uniqueness and energy dissipation
When May 19, 2014
from 02:00 PM to 03:00 PM
Where LR8, IEB Building, Engineering Science
Contact Name
Contact Phone 01865-283302
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Frictional systems exist throughout engineering, including applications in aero engines,
tectonic plates, bolted joints, etc. In many of these cases, the contact is nominally
stuck, but because of the elasticity of the material, there may be regions of microslip. If
the loading is periodic, this results in energy dissipation, reflected as apparent hysteretic
damping of the system, and also may cause the initiation of fretting fatigue cracks.
For many years, tribologists assumed that Melan’s theorem in plasticity could be extended
to frictional systems — i.e. that if there exists a state of residual stress associated
with frictional slip that is sufficient to prevent periodic slip in the steady state, then the
system will shake down, regardless of the initial conditions. However, we now know that
this is true if and only if there is no coupling between the normal and tangential loading
problems, as will arise notably in the case where contact occurs on a symmetry plane.
More recently, Ponter has shown that this is a special case of a more general theorem that
for uncoupled systems, the time-varying terms in the steady state are independent of initial
conditions, and this result applies even in the corresponding elastodynamic problem.
With sufficient clamping force, ‘complete’ contacts (i.e. those in which the contact
area is independent of the normal load) can theoretically be prevented from slipping, but
on the microscale, all contacts are incomplete because of surface roughness and some
microslip is inevitable. In this case, the local energy dissipation density can be estimated
from relatively coarse-scale roughness models, based on a solution of the corresponding
‘full stick’ problem.
If the system is coupled, the steady state generally depends on initial conditions and
hence the system must retain a ‘memory’ of these conditions, which resides in the tangential
displacements at nodes that are instantaneously stuck. When a stuck node starts to
slip, it can ‘exchange’ memory with one or more other nodes, but there is generally some
degradation. Thus, long term dependence on initial conditions even for coupled systems
generally depends on the existence of a set of nodes that never slip in the steady state.
However, we shall demonstrate simple cases where there exist more than one distinct
steady state even when this set is null.