  Composite structures must endure a great variety of multi-axial stress states
during their lifespan while guaranteeing their structural integrity and
functional performance. Understanding the fatigue behavior of these materials,
especially in the presence of notches that are ubiquitous in structural design,
lies at the hearth of this study which presents a comprehensive investigation
of the fracturing behavior of notched quasi-isotropic [+45/90/$-$45/0]$_{s}$
and cross-ply [0/90]$_{2s}$ laminates under multi-axial quasi-static and
fatigue loading.
  The investigation of the S-N curves and stiffness degradation, and the
analysis of the damage mechanisms via micro-computed tomography clarified the
effects of the multi-axiality ratio and the notch configuration. Furthermore,
it allowed to conclude that damage progression under fatigue loading can be
substantially different compared to the quasi-static case.
  Future efforts in the formulation of efficient fatigue models will need to
account for the transition in damaging behavior in the context of the type of
applied load, the evolution of the local multi-axiality ratio, the structure
size and geometry, and stacking sequence. By providing important data for model
calibration and validation, this study represents a first step towards this
important goal.
