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• Difference of damage modes caused by the boundary conditions of primary load-bearing yarns. • Straightening effect of braided yarns with undulations under low-velocity impact. • Variation of off-axial angles leading to the transition of failure modes. The sensitivity of off-axial angle on impact response was investigated by experimental and numerical methods in this work. Three types of braided laminates with different on/off-axial angles in terms of OA00, OA225 and OA45 were prepared and low-velocity impact tests with various energy levels were performed. Meso-level finite element model (FEM) was also developed to reveal impact damage initiation and development. We discovered that the boundary condition of primary load-bearing yarns depending on the off-axial angles caused the difference of structural deformation and stress distribution of braiding yarns during impact process. Due to the restriction of the pressurized tips, the straightening effect of primary load-bearing yarns with heavy waviness caused its out-of-plane movement and related main cracks in OA00 specimen. In addition, the matrix resin cracks were found at the edge of the specimen because of in-plane shear movement of braiding yarns. As for OA45 specimen, more evident bending deformation was observed, resulting in elevated tensile stress of braiding yarns on non-impact side. The variation of off-axial angle from 0 to 45 degree led to the failure mode transforming from the extensive matrix damage on specimen edge to the severe fiber breakage on non-impact side. As a medium off-axial angle, OA225 specimen exhibited a mixture failure mode to resist impact and achieved excellent performance with respect to higher peak force and delayed load dropping. [Display omitted] [ABSTRACT FROM AUTHOR]