An I-integral method for the crack-tip intensity factor in ferromagnetic materials with domain switching

An I-integral method is developed to calculate the crack-tip stress intensity factors (SIFs) in the ferromagnetic thin plate subjected to the external loads. The value of I-integral is not affected by the integral area size, the magnetization distributions or domain walls, which shows the applicability to the large-scale domain switching. Based on the stress and magnetic field obtained from phase-field simulations, the I-integral method is successfully employed to obtain the crack-tip intensity factors and decouples different modes of the crack-tip intensity factors in ferromagnetic thin plates with an impermeable edge crack under different mechanical and/or magnetic loadings. The influence of domain switching on the SIFs is investigated for different loadings. It is found that domain switching under a constant stress loading increases the crack-tip intensity factors, whereas domain switching decreases the crack-tip intensity factors under a constant strain loading. The results indicate that the domain switching-induced shielding or anti-shielding of a crack in ferromagnetic materials with an impermeable edge crack is dependent on the loading condition.