The influence of the surface effect on the nanosized spherical void growth in a rigidperfectly plastic material is analyzed and the mechanism of the nanosized void growth with high triaxiality is given. Based on the Rice and Tracey model for a macro void growth, the present model is proposed to account for the nanosized void growth under a uniform remote strain rate field with consideration on the surface effect. It is concluded that the surface effect yields an evident resistant influence on the nanosized void growth. That is, this influence decays as the void radius increases. With high triaxiality, the nanosized void growth is divided into two stages： the initial stage and the mature stage. At the first stage, the void grows slowly and the influence of surface effect is relatively weak, whereas at the second stage, the influence is significant and the void grows drastically.
The present investigation of the crack problem in piezoelectric materials is performed based on the non-local theory. After some manipulations, the impermeable crack, the permeable crack （the crack gap is full of NaCI solution）, and the semi-permeable crack （the crack gap is full of air or silicon oil） are reduced to a uniform formulation by assuming the normal electric displacement on the crack surfaces to be an unknown variable. Thus, a triple integral equation with the unknown normal electric displacement is established. By using the Newton iterative method and solving the triple integral equation, it is found that the normal electric displacement on the crack surfaces is no longer a constant as determined by previous studies, rather, it depends upon the remote combined electromechanical loadings. Numerical results of the stresses and electric displacement fields show that there are no singularities at the crack tips so that the stresses remain finite. It is of great significance that the concrete electric boundary condition on the crack surfaces exerts significant influence on the near-tip fields and in this way plays an important role in evaluating the crack stability in the non-local piezoelectric materials. More specifically, the impermeable crack model always overestimates the finite stresses at the crack tips, whereas the permeable crack model always underestimates them.
Q. Li Y. Chen School of Aerospace, Xi’an Jiao-Tong University,710049 Xi’an, China
A permeable interface crack between elastic dielectric material and piezoelectric material is studied based on the extended Stroh＇s formalism. Motivated by strong engineering demands to design new composite materials, the authors perform numerical analysis of interface crack tip singularities and the crack tip energy release rates for 35 types of dissimilar bimaterials, respectively, which are constructed by five kinds of elastic dielectric materials： Epoxy, Polymer, Al2O3, SiC, and Si3N4 and seven kinds of practical piezoelectric ceramics： PZT-4, BaTiO3, PZT-5H, PZT-6B, PZT-TA, P-7, and PZT-PIC 151, respectively. The elastic dielectric material with much smaller permittivity than commercial piezoelectric ceramics is treated as a special transversely isotropic piezoelectric material with extremely small piezoelectricity. The present investigation shows that the structure of the singular field near the permeable interface crack tip consists of three singularities： r^-1/2±iε and r^-1/2, which is quite different from that in the impermeable interface crack. It can be concluded that different far field loading cases have significant influence on the near-tip fracture behaviors of the permeable interface crack. Based on the present theoretical treatment and numerical analysis, the electric field induced crack growth is well explained, which provides a better understanding of the failure mechanism induced from interface crack growth in elastic dielectric/piezoelectric bimaterials.
By modeling metal as a special piezoelectric material with extremely small piezoelectricity and extremely large permittivity, we have obtained the analytical solutions for an interracial permeable crack in metal/piezoelectric bimaterials by means of the generalized Stroh formalism. The analysis shows that the stress fields near a permeable interracial crack tip are usually with three types of singularities： r^-1/2±iε and r^-1/2. Further numerical calculation on the oscillatory index ε are given for 28 types of metal/piezoelectric bimaterials combined by seven commercial piezoelectric materials： PZT-4, BaTiO3, PZT-5H, PZT-6B, PZT-7A, P-7 and PZT-PIC 151 and four metals： copper, silver, lead and aluminum, respectively. The explicit expressions of the crack tip energy release rate （ERR） and the crack tip generalized stress intensity factors （GSIF） are obtained. It is found that both the ERR and GSIF are independent of the electric displacement loading, although they seriously depends on the mechanical loadings.
