Fracture Mechanics for a Mode Ⅲ Crack in a Piezoelectromagnetic Material

Analytical solutions for a Griffith crack inside an infinite piezoelectromagnetic medium under combined mechanical-electrical-magnetic loadings are formulated using integral transform method. The singular stress, electric and magnetic fields in the piezoelectromagnetic material are obtained by the theory of linear piezoelectromagneticity. Fourier transforms are used to reduce the mixed boundary value problems of the crack, which is assumed to be permeable, to dual integral equations. The solution of the dual integral equations is then expressed analytically. Expressions for strains, stresses, electric fields, electric displacements, magnetic fields and magnetic inductions in the vicinity of the crack tip are derived. Field intensity factors and energy release rate for piezoelectromagnetic material are obtained. The stresses, electric displacements and magnetic inductions at the crack tip show the traditional square root singularities; and the electric field intensity factor (EFIF) and the magnetic field intensity factor (MFIF) are always zero.     

A New Fracture Criterion for a Crack under Combined Mode Loading

A new fracture criterion was proposed, The physical explanation ot the criterion is that crack will propagate when the minimum strain energy-density in iso-hoop-stress curve reach a critical strength of the material considered. The resulting curve of critical fracture of mixed-mode cracks shows that the present fracture is efficient and more accurate than the previous criteria.