  Disc warping, and possibly disc breaking, has been observed in protoplanetary
discs around both single and multiple stars. Large warps can break the disc,
producing multiple observational signatures. In this work, we use comparisons
of disc timescales to derive updated formulae for disc breaking, with better
predictions as to when and where a disc is expected to break and how many
breaks could occur. Disc breaking is more likely for discs with small inner
cavities, cooler temperatures, and steeper power-law profiles, such that thin,
polar-aligning discs are more likely to break. We test our analytic formulae
using 3D grid-based simulations of protoplanetary discs warped by the
gravitational torque of an inner binary. We reproduce the expected warp
behaviors in different viscosity regimes and observe disc breaking at locations
in agreement with our derived equations. As our simulations only show disc
breaking when disc viscosity is low, we also consider a viscous criterion for
disc breaking, where rapid alignment to the precession vector can prevent a
break by reducing the maximum misalignment between neighboring rings. We apply
these results to the GW Orionis circumtriple disc, and find that the precession
induced from the central stars can break the disc if it is relatively thin. We
expect repeated or multiple disc breaking to occur for discs with sufficiently
steep power law profiles. We simulate a polar-aligning disc around an eccentric
binary with steep power-law profiles, and observe two separate breaking events
at locations in rough agreement with our analytical predictions.
