A complete thermo-mechanical model for the simulation of the inertia w
elding process of two similar parts is described. The material behavio
ur is represented by an incompressible viscoplastic Norton-Hoff law in
which the theological parameters are dependent on temperature. The fr
iction law was determined experimentally and depends on the prescribed
pressure and the relative rotating velocity between the two parts. Th
e mechanical problem is solved considering the virtual work principle
including inertia terms. The computation of the three components of th
e velocity field such as radial, longitudinal and rotational velocity,
in an axisymmetric approximation allows to take into account the tors
ional effects. The domain is updated based on a Lagrangian formulation
. The non-linear heat transfer equation with boundary conditions (conv
ection, radiation and friction flux) is solved separately for each tim
e step. Error estimators on mechanical and thermal computation are dev
ised to adapt the mesh in an automatic way. Finally, numerical results
concerning evolution of parts shape, strain, temperature, rotating ve
locity, upsetting are compared with actual industrial welds.