Studies On Effects Of Surface Maxwell Stress On Fracture Of Piezoelectric Materials

Due to their extensive applications in various fields of engineering,the investigation of fracture behaviors in piezoelectric materials is of great importance,and has received much attentions in the past decades.Based on Stroh formulism,the fracture of single crack,multiple cracks as well as interface cracks are studied.Analytical solutions and numerical results are given to discuss the effect of electromechanical loadings and material constants.And the effect of electrostatic stress on the surface of piezoelectric solids,which is also known as Maxwell stress,is explored.The main works of this dissertation are summarized as follows:(1)Utilizing dislocation theory and electric dislocation,the solution of strip Dielectric Breakdown(DB)model containing semi-permeable crack is given.The variation of electric displacement inside crack is explained.Compared with strip Polarization Saturation(PS)model,DB model is essentially analogous.It is found that the influence of Maxwell stress on the surfaces of crack and matrix is significant,especially in prediction of field intensity factors and the size of electric yielding zone.(2)The interaction between multiple cracks is discussed in the models of two collinear cracks and periodic cracks,respectively.Same solution is obtained with conformal mapping and function substitution method.The tendency of crack propagation also depend on the relation between dielectric constants inside cracks and outside piezoelectric matrix.(3)Approximate analytical solution of periodic interface cracks in bi-materials is obtained using conformal mapping,then verified with numerical integral in function substitution method.The results reveal that the electric displacement is constant,while the field intensity factors are related to the size of cracks,loadings and dielectric constants.