Mixed mode fracture is a widely studied topic, while the coupling effects of mixed mode cracking are unclear. In this paper, elastic fracture behaviors and the coupling effects of the mixed mode cracks are studied in detail based on the finite element method, experimental study and linear elastic fracture mechanics. Results show that there always exist II-III coupling effects at the crack tips of mixed mode cracks, which have many effects on the crack tip field and crack propagation behavior. It is found that a mode II component at the tip of a mixed mode crack is the main reason for crack deflection, while the mode III components show no effect. For any mixed mode crack, mode II components at the crack tip can be divided as that by mode II loading which causes plane crack propagation, and by the coupling effect which causes spatial crack propagation. On this basis, a new fracture criterion suitable for any mixed mode crack is proposed, combined with the coupling effect and the linear elastic superposition principle. The research in this paper provides a solution to the problem of an II-III coupling effect in mixed mode fracture research and further promotes the development of fracture mechanics.

The failure probability of piston ring abrasion occupies the forefront in reciprocating compressor cylinder assembly. Due to the reciprocating friction between the piston ring and cylinder liner, the local vibration signal contains typical nonstationary characteristics with a seriously overlapped frequency band of impact signals, while the different featured signals are coupled with each other. Therefore, the identification of cylinder friction and abrasion fault modes has always been a hot and difficult problem in fault diagnosis of reciprocating compressors. In order to monitor the friction and abrasion between low linear speed nonmetallic piston ring and cylinder liner of reciprocating compressor in refinery and provide a theoretical basis for preventive maintenance, an analysis method based on VMD-multifractal spectrum was presented in this paper. First, the feasibility of the proposed method was proven based on the cylinder vibration experiment of a reciprocating compressor in the laboratory. Then, an in-service reciprocating compressor in a refinery was taken as the research object, from which the cylinder friction vibration signals were processed by using variational mode decomposition to obtain a band-limited intrinsic mode function (BLIMF). Multifractal detrended fluctuation analysis is employed in the final abrasion pattern identification. The results show that the proposed method based on VMD-multifractal spectrum analysis can effectively obtain the abrasion state of a piston ring, which can avoid blind overhaul or provide the basis for preventive maintenance and a practicable engineering route for the study of the piston ring abrasion degree.