An analytical model for the fracture behavior of the flexible lithium-ion batteries under bending deformation

To understand the influence of the bending deformation on the stress evolution and crack propagation in nano flexible electrode during electrochemical cycling, an analytical model is developed based on core-shell structure in a cylindrical electrode. In the model, the analytical solution of stress specialized for the cylindrical electrode in the process of bending deformation and phase transformation is clarified. Further, the weight function is utilized to calculate the time-dependent stress intensity factor by combining the stress profiles as found in the analytical work. Thus, the behavior of the preexisting center and edge cracks in the electrode is discussed to investigate the effect of the initiation position on crack propagation. It is found that cracks tend to spread more easily in the early stages of discharging process due to the larger slope of the SIF curve within small edge cracks. Further, an analytical fracture mechanics study is presented and the formula of critical size for the flexible electrode is derived based on Griffith criterion, below which the crack does not spread under the superposition of the diffusion stress and the bending stress. In the light of the fracture mechanics study of the flexible electrode, the present work sheds some light on stress engineering and structural design of durable flexible lithium-ion batteries.