  A new cohesive phase-field (CPF) interface fracture model is proposed on the
basis of the Euler-Lagrange equation of the phase-field theory and the
interface fracture energy check w.r.t. that of the cohesive zone model. It
employs an exponential function for the interpolation of fracture energy
between the bulk phase and the interface, while the effective interface
fracture energy $\tilde{G}_i$ is derived in such a way that the integrated
phase-field fracture energy across the diffusive interface region remains
consistent with the sharp interface fracture energy $G_i$ defined in the
classical cohesive zone model. This consistency is the key to ensure that the
numerical results remain insensitive to the choice of length-scale parameters,
particularly the regularized interface thickness $L$ and the regularized
fracture surface thickness $b$. By employing this energy consistency check,
various CPF interface models in the literature are reviewed. Besides the
length-scale insensitivity, the proposed CPF interface model offers further
advantages. Thanks to the fact that the exponential interpolation function can
be obtained conveniently from the relaxation solution of an Allen-Cahn
equation, the proposed CPF model is advantageous over other models with high
flexibility in handling structures containing complicated interface topology.
In order to demonstrate this merit and to check the length-scale insensitivity
in multiphysics context, the proposed CPF interface model is employed further
to derive a thermodynamically consistent chemo-mechanical model relevant to
Lithium-ion battery materials. Finite element simulation results of the
concurrent bulk and interface fracture in polycrystalline electrode particles,
reconstructed from images with segmented interfaces, confirm the expected
computational advantages and the length-scale insensitivity in chemo-mechanical
context.
