Glass-fiber-polymer-composites are common composite types that can achieve optimum strength or desired mechanical properties for different applications by altering various parameters such as angular alignment of fibers. Fracture in these types of composites involves a combination of different mechanisms such as matrix crack, fiber breakage, delamination, and fiber debonding from the matrix. This paper presents an empirical investigation of the first mode failure mechanisms in glass/epoxy composite beams with different fiber angles by means of nondestructive electromechanical impedance measurements, force-displacement diagrams and observations. For this purpose, after fabricating beam specimens and attaching the piezoelectric sensor on them, the impedance spectra of the beams are compared with the reference beam spectrum during the elongation and crack opening process. Continuous and rapid crack growth was recognized by spatial and temporal synchronization of impedance data, visual observations of calibration indices on the beam specimen during the crack opening, and recorded movies of the tests and force-displacement diagrams. Studying the beam data with different angles arrangement revealed that the sample 0-90 was more stable during crack growth with fewer force variations. Also, the dominant mode of failure in this sample was the matrix fracture. This study showed that the electromechanical impedance measurement can be used as an effective tool for detecting the initiation and propagation of cracks in this type of composite beams due to high sensitivity at different stages of crack growth.