  Large-scale simulations of thermal welding of polymers are performed to
investigate the rise of mechanical strength at the polymer-polymer interface
with the welding time. The welding process is in the core of integrating
polymeric elements into devices as well as in thermal induced healing of
polymers; processes that require development of interfacial strength equal to
that of the bulk. Our simulations show that the interfacial strength saturates
at the bulk shear strength much before polymers diffuse by their radius of
gyration. Along with the strength increase, the dominant failure mode changes
from chain pullout at the interface to chain scission as in the bulk. Formation
of sufficient entanglements across the interface, which we track using a
Primitive Path Analysis is required to arrest catastrophic chain pullout at the
interface. The bulk response is not fully recovered until the density of
entanglements at the interface reaches the bulk value. Moreover, the increase
of interfacial strength before saturation is proportional to the number of
interfacial entanglements between chains from opposite sides.
