The nondestructive evaluation of closed cracks is a challenging subject in ultrasonic testing. Recently, nonlinear ultrasonic phased array with fixed-voltage fundamental wave amplitude difference (fixed-voltage FAD) has been proposed as a practical approach. In this study, the maximum incident wave amplitude, which is one of the most critical parameters in closed-crack imaging, was investigated. First, a theoretical model was formulated to explicitly show the essence of the fundamental principle of FAD and the advantage of fixed-voltage FAD over different-voltage FAD. In experiments, the authors imaged a closed fatigue crack using a nonlinear ultrasonic phased array with fixed-voltage FAD while varying the incident wave amplitude. It was found that when the incident wave amplitude was sufficiently high, the nonlinear image visualized the closed crack tip, which could not be visualized in linear images. In addition, the incident-wave-amplitude dependence of the nonlinear responses was quantified. It was found that different parts within a single fatigue crack showed different nonlinear behaviors. This suggests that fixed-voltage FAD is useful not only for practical application of closed crack imaging but also for examining the nonlinear dynamics at various parts of closed cracks with a high spatial resolution.