Analytical Solution of an Arbitrary-location Through Crack Emanating from a Nano-hole in Magneto-electro-elastic Materials
With the development of engineering technology and materials science,pure elastic materi-als can no longer meet the application needs of materials in industrial manufacturing.Magneto-electro-elas-tic(MEE)materials have more complex internal structures compared to classical elastic materials,and the methods for solving mechanical and physical performance are more difficult compared to classical elastic materials.Therefore,the mode Ⅲ fracture behavior of MEE materials with nano-defects(pores and cracks)is investigated in this study.Based on the Gurtin-Murdoch surface theory and conformal mapping theory,the mode Ⅲ fracture properties of MEE materials containing an arbitrary-location through crack emanating from a nano-hole under anti-plane mechanical loading,in-plane electrical loading,and in-plane magnetic loading are studied.The accurate solution of the MEE field in the matrix is obtained using the MEE theory and the far-field loading conditions.Analytical expressions for the MEE field intensity factors of the tips at both ends of the through crack,assuming that the surface of nano-defects is magneto-electric impermeable,are given.The proposed method is validated through a comparison with existing research.The effects of crack location,crack interaction,and the application of multiple physical loads on the di-mensionless MEE field strength factors are discussed.The results show that the dimensionless MEE field intensity factors exhibit a significant size effect.The surface effect of nano-defects on the MEE tip fields of the cracks is constrained by the crack location.The dimensionless MEE field intensity factors are signifi-cantly affected by the ratio of the through crack length to the applied MEE loads.The results obtained in this study provide a theoretical basis for the experiments and numerical simulations of the mode Ⅲ fracture behavior of an arbitrary-location through crack emanating from a nano-hole in MEE materials.
MEE materialsmultiple nano-defectsthrough crack emanating from nano-holesize effectcrack location
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