We present a physics-informed neural network modeling approach for missing physics estimation in cumulative damage models. This hybrid approach is designed to merge physics-informed and data-driven layers within deep neural networks. The result is a cumulative damage model in which physics-informed layers are used to model relatively well understood phenomena and data-driven layers account for hard-to-model physics. A numerical experiment is used to present the main features of the proposed framework. The test problem consists of predicting corrosion-fatigue of an Al 2024-T3 alloy used on panels of aircraft wings. Besides cyclic loading, panels are also subjected to saline corrosion. In this case, physics-informed layers implement the well-known Walker model for crack propagation, while data-driven layers are trained to compensate the bias in damage accumulation due to the corrosion effects. The physics-informed neural network is trained using full observation of inputs (far-field loads, stress ratio, and a corrosivity index defined per airport) and very limited observation of outputs (crack length at inspection for only a small portion of the fleet). Results show that the physics-informed neural network is able to learn how to compensate the missing physics of corrosion in the original fatigue model. Predictions from the hybrid model can be used in fleet management, for example, to prioritize inspection across the fleet or forecast ahead of time the number of planes with damage above a threshold.