The scaling of charging rate and cycle number of commercial batteries

Health management for commercial batteries is crowded with a variety of great issues, among which reliable cycle-life prediction tops. By identifying the cycle life of commercial batteries with different charging histories in fast-charging mode, we reveal that the average charging rate c and the resulted cycle life N of batteries obey c = c0Nb, where c0 is a limiting charging rate and b is an electrode-dependent constant. This c-N law, resembling the classic stress versus cycle number relationship (the S-N curve or Wohler curve) of solids subject to cyclic loading, could be applicable to most batteries. Such a scaling law, in combination with a physics-augmented machine-learning algorithm, could foster the predictability of battery life with high fidelity. The scaling of charging rate and cycle number may pave the way for cycle-life prediction and the directions of optimization of advanced batteries.