Micromechanics Investigation on defects in piezoelectric and elastic solids
Date of Issue2006
School of Mechanical and Aerospace Engineering
The emerging technologies of smart materials and structures have found increasing applications in diverse engineering branches such as aerospace, mechanical, manufacturing and civil engineering, etc. Piezoelectric materials are ideal candidates for functional (smart) materials, and have been a primary focus of attention in the realization of smart (adaptive) structure systems. Due to the fact that piezoelectric materials are very brittle, to find better employment of piezoelectric materials depends on the better understanding of mechanical failure mechanism of piezoelectric materials. Micro-crack is one of the most commonly encountered defects leading to mechanical failure, and it plays an important part in fracture processes. During the entire fracture procedure of a crack, Zener-Stroh crack mechanism controls the initial stage of crack growth and propagation. When the micro-crack is stressed after its propagation, Griffith crack mechanism controls the crack to final fracture. Investigation on Zener-Stroh crack and Griffith crack can help to understand how a crack initiates and gradually grows and find out which cracks constitute an obvious risk for fracture and which do not. In the current research, the physical problems on micro-cracks near a coated inclusion in piezoelectric materials are investigated; both Zener-Stroh crack and Griffith crack mechanism are studied for the existing micro-cracks. Accordingly, three specific problems, viz, a screw dislocation interacting with a coated inclusion; a Zener-Stroh crack interacting with a coated inclusion and a Griffith crack interacting with a coated inclusion in piezoelectric solids, are analyzed in detail. In the study, three dissimilar material phases are involved: the matrix, the inclusion and the coating layer. All the three materials are piezoelectric and with different material constants. The solutions for the two crack problems begin with the derivation of stress and electric displacement fields of a screw piezoelectric dislocation in relevant three phase piezoelectric structures. Explicit closedform analytical solutions are obtained by using the complex variable method. The image force acting on the screw dislocation is calculated by using the generalized Peach-Koehler formula. Numerical examples for different material constant combinations are performed. Following this work, the obtained single screw dislocation solution is used as Green's function to simulate the crack with the application of distributed dislocation method. The crack problems are formulated into a set of singular integral equations and solved with comprehensive numerical methods. The stress and electric displacement intensity factors are derived and expressed in terms of dislocation density functions. The influences of material properties of the inclusion and the coating layer and defects location are studied in numerical examples in detail. Besides the above solved physical problems, the interaction between an edge dislocation with an interfacial void (the centre of void is at the interface of a bi-material structure) is also studied. The existing void is simulated by distributing continuous dislocations in mathematical sense and the resulting singular integral equations are solved by GaussJacobi quadrature. The image forces on the dislocation are discussed in numerical examples with the influence of material properties and dislocation positions. It is found that an oscillatory characteristic exists with the existence of interfacial void when the dislocation is very close to the void.
DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics
Nanyang Technological University