In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane...In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.展开更多
Two equal collinear cracks with coalesced interior electric saturation zones are analytically studied for two-dimensional (2D) arbitrary polarized semipermeable piezo- electric media based on a modified strip saturate...Two equal collinear cracks with coalesced interior electric saturation zones are analytically studied for two-dimensional (2D) arbitrary polarized semipermeable piezo- electric media based on a modified strip saturated model. The strip saturated model is modified here by varying the strip saturated constant electric displacement condition to the polynomially varying electric displacement conditions. Based on the linear, quadratic, and cubic electric displacement conditions on the inner and outer saturated zones, dif- ferent modified strip saturated models are proposed and studied for two equal collinear cracks. With the Stroh formalism and the complex variable technique, these fracture problems are reduced into different types of non-homogeneous Riemann Hilbert problems in unknown generalized complex potential functions. These mathematical problems are then solved with the Riemann-Hilbert approach to obtain the stress and electric displace- ment components at any point of the domain. The explicit expressions for the outer saturated zone length, the crack opening potential (COP), the crack opening displace- ment (COD), and the local intensity factors (LIFs) are derived. A numerical study is presented for the modified strip saturated model in 2D arbitrary polarized semiperme- able PZT-4 material. The obtained results are compared with those of the strip saturated model, and the effects of the polynomially varying saturation condition on the saturated zones and the applied electrical loadings are presented.展开更多
基金ministry of Human Resource Development for the financial support
文摘In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.
文摘Two equal collinear cracks with coalesced interior electric saturation zones are analytically studied for two-dimensional (2D) arbitrary polarized semipermeable piezo- electric media based on a modified strip saturated model. The strip saturated model is modified here by varying the strip saturated constant electric displacement condition to the polynomially varying electric displacement conditions. Based on the linear, quadratic, and cubic electric displacement conditions on the inner and outer saturated zones, dif- ferent modified strip saturated models are proposed and studied for two equal collinear cracks. With the Stroh formalism and the complex variable technique, these fracture problems are reduced into different types of non-homogeneous Riemann Hilbert problems in unknown generalized complex potential functions. These mathematical problems are then solved with the Riemann-Hilbert approach to obtain the stress and electric displace- ment components at any point of the domain. The explicit expressions for the outer saturated zone length, the crack opening potential (COP), the crack opening displace- ment (COD), and the local intensity factors (LIFs) are derived. A numerical study is presented for the modified strip saturated model in 2D arbitrary polarized semiperme- able PZT-4 material. The obtained results are compared with those of the strip saturated model, and the effects of the polynomially varying saturation condition on the saturated zones and the applied electrical loadings are presented.
