  This paper identifies two ways to extract the energy (or power) flowing into
a crack tip during propagation based on the power balance of areas enclosed by
a stationary contour and a comoving contour. It is very interesting to find a
contradiction that two corresponding energy release rates (ERRs), a
surface-forming ERR and a local ERR, are different when stress singularity
exists at a crack tip. Besides a rigorous mathematical interpretation, we
deduce that the stress singularity leads to an accompanying kinetic energy at
the crack tip. The local ERR represents the driving force to overcome the
surface energy and the accompanying kinetic energy, while the surface-forming
ERR represents the driving force to overcome the surface energy only. Their
advantages and disadvantages are discussed. We recommend using the
surface-forming ERR based fracture criterion for a crack propagation in
elastic-plastic materials, since it has a wide applicability and concise
formulae which are easy to compute among all energy based criteria.
