Erosion prediction for downhole tools

Downhole monitoring systems are described. The systems include a downhole string disposed in a borehole, the string having a downhole tool and the borehole has fluid therein. A sacrificial electrical sensor element is arranged in or on the string. The sacrificial electrical sensor element includes magnetic material at least partially exposed to the fluid and at least one coil arranged in magnetic communication with the magnetic material. A controller is configured to provide an electrical current into the coil, measure an electrical property of the coil that is based on the magnetic material in magnetic communication with the coil, and determine a wear state of the downhole tool based on the measured electrical property.