On singular stress at the crack tip of a thick plate under in-plane loading

Abstract

By superposition of three asymptotic solutions, which collectively satisfy all the equilibrium and compatibility equations as well as boundary conditions, the three-dimensional crack tip stresses of a thick plate with a through-the-thickness cut are shown to be of square root singularity throughout the thickness. The near tip deformation is shown to be plane strain with stress intensity factor changing in the thickness direction. All components of the singular stresses vanish on plate surfaces. The profile of the stress intensity factor in the thickness direction cannot be determined by the asymptotic analysis alone.

An analysis of the effect of domain switching on fracture behavior of piezoelectric solids

“…Therefore, a negative E tends to open the crack while a positive E tends to close the crack. These results contradict the conclusions of Sun and Chang [9] for the cracks perpendicular to the original poling direction and to the direction of applied electric field. Hence, it appears that the original poling direction and the direction of applied electric field play a role when domain switching is considered.…”

“…The values of spontaneous strain ẽs and spontaneous polarization P s are 0.39% and 0.34 C m −2 , respectively. The critical energy values for the 90 • and 180 • domain switching are 1.05 and 1.36 MN m −2 , respectively [9]. In this work, fournode plain strain elements are employed.…”

“…Only the piezoelectric moduli e mkl vary with the domain switching. In addition, after domain switching the spontaneous stress and spontaneous polarization are included in the constitutive equations to account for the change of the crystal structure [7,9].…”

“…where the spontaneous strain ẽs and the spontaneous polarization P s are assumed to be material constants. The spontaneous polarization P s is used in the criterion [7,9]. The new piezoelectric constants e i jk are obtained from the coordinate transformation law, i.e.…”

“…Steinkoff [8] proposed a finiteelement model to study the typical behavior of ferroelastic, ferroelectric, and piezoelectric materials. Jiang [7] and Sun and Chang [9] presented a number of nonlinear finiteelement solutions that included the effect of domain switching in the analysis of the piezoelectric materials with cracks perpendicular to the poling direction. They found that a negative electric field increases the fracture toughness while a positive electric field leads to a reduction of fracture toughness.…”