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The J -integral based criterion is widely used in elastic–plastic fracture mechanics. However, it is not rigorously applicable when plastic unloading appears during crack propagation. One difficulty is that the energy density with plastic unloading in the J -integral cannot be defined unambiguously. In this paper, we alternatively start from the analysis on the power balance, and propose a surface-forming energy release rate (ERR), which represents the energy available for separating the crack surfaces during the crack propagation and excludes the loading-mode-dependent plastic dissipation. Therefore the surface-forming ERR based fracture criterion has wider applicability, including elastic–plastic crack propagation problems. Several formulae are derived for calculating the surface-forming ERR. From the most concise formula, it is interesting to note that the surface-forming ERR can be computed using only the stress and deformation of the current moment, and the definition of the energy density or work density is avoided. When an infinitesimal contour is chosen, the expression can be further simplified. For any fracture behaviors, the surface-forming ERR is proven to be path-independent, and the path-independence of its constituent term, so-called J s -integral, is also investigated. The physical meanings and applicability of the proposed surface-forming ERR, traditional ERR, J s -integral and J -integral are compared and discussed. Besides, we give an interpretation of Rice paradox by comparing the cohesive fracture model and the surface-forming ERR based fracture criterion. [ABSTRACT FROM AUTHOR]

The low fracture toughness of the widely used piezoelectric and ferroelectric materials in technological applications raises a big concern about their durability and safety. Up to now, the mechanisms of electric-field induced fatigue crack growth in those materials are not fully understood. Here we report experimental observations that alternative electric loading at high frequency or large amplitude gives rise to dramatic temperature rise at the crack tip of a ferroelectric solid. The temperature rise subsequently lowers the energy barrier of materials for domain switch in the vicinity of the crack tip, increases the stress intensity factor and leads to unstable crack propagation finally. In contrast, at low frequency or small amplitude, crack tip temperature increases mildly and saturates quickly, no crack growth is observed. Together with our theoretical analysis on the non-linear heat transfer at the crack tip, we constructed a safe operating area curve with respect to the frequency and amplitude of the electric field, and validated the safety map by experiments. The revealed mechanisms about how electro-thermal-mechanical coupling influences fracture can be directly used to guide the design and safety assessment of piezoelectric and ferroelectric devices. [ABSTRACT FROM AUTHOR]