  Vortex breaking has been traditionally studied for nonuniform critical
current densities, although it may also appear due to nonuniform pinning force
distributions. In this article we study the case of a
high-pinning/low-pinning/high-pinning layered structure. We have developed an
elastic model for describing the deformation of a vortex in these systems in
the presence of a uniform transport current density $J$ for any arbitrary
orientation of the transport current and the magnetic field. If $J$ is above a
certain critical value, $J_c$, the vortex breaks and a finite effective
resistance appears. Our model can be applied to some experimental
configurations where vortex breaking naturally exists. This is the case for
YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) low angle grain boundaries and films on vicinal
substrates, where the breaking is experienced by Abrikosov-Josephson vortices
(AJV) and Josephson string vortices (SV), respectively. With our model, we have
experimentally extracted some intrinsic parameters of the AJV and SV, such as
the line tension $\epsilon_l$ and compared it to existing predictions based on
the vortex structure.
