A mold assembly includes an injection mold configured to receive a woven preform. The preform has a principal direction with at least one edge extending substantially along the principal direction. The mold assembly is configured to allow the impregnation of the preform with a resin injected into the mold. The mold assembly further includes a removable longitudinal element for the injection mold, wherein said longitudinal element is configured to cooperate with the preform and conformed as a profiled member configured to be arranged in contact with the mold along at least the segment of the edge of the preform in order to prevent the pinching of free fibers extending from the edge of the preform between the two parts of the mold.