Highly curved composite laminates used at the junction between two perpendicular panels experience unfolding failure. Unfolding failure is a delamination which occurs in the curved composite laminates, when they are loaded under the bending moment, trying to flatten the curvature which induces out-of-plane stresses, causing different plies to separate. The interlaminar tensile strength is determined empirically by means of a four-point bending test on L-shaped unidirectional (UD) samples. Notwithstanding, many studies have noticed that four-point bending test, applied to curved multidirectional (MD) composite laminates, experience unfolding failure that may be caused by both interlaminar and intralaminar stresses. In the first stage, an intralaminar crack is formed which, under a certain level of interlaminar stresses, propagates as a delamination [1]. The present work is focused on analyzing the two failure mechanisms occurring in curved laminates, using both numerical and experimental study. At first, since UD curved laminates undergo pure interlaminar failure, the delamination at the interfaces is modelled using cohesive elements and the behavior is analyzed. Since delamination propagation is very unstable, a control algorithm explained in [2] is used to capture these instabilities and displacement jumps. While the ILTS problem is subjected to load control, the algorithm uses special auxiliary nodes to load the model under displacement control with the crack tip opening displacements. Subsequently, MD curved laminates undergo both intralaminar and interlaminar failures. For modelling intralaminar failure, a phase-field fracture method in terms of UMAT/HETVAL subroutine available from [3], further developed for orthotropic material behavior is employed to demonstrate these matrix-dominated intra laminar failures in 0°/90° cross-ply and quasi-isotropic curved laminates. Furthermore, the study is extended to more complicated finite element models, combining both phase field and interfacial cohesive damage methodologies to demonstrate the interaction between these two failure mechanisms.