Study On The Fracture And Fatigue Problems In Piezoelectric Materials By Boundary Element Method

Piezoelectric materials are widely used in the various intelligent composite materials and structures because of the effect of piezoelectricity.But the low fracture toughness and brittleness of most of the piezoelectric specimens make them easily produce cracks and other defects during processing,preparation and service,eventually resulting in greatly reducing the actual service life.Therefore,it is of great value and academic significance to study the fracture properties of the piezoelectric materials and to predict the residual life of piezoelectric structures.In this paper,the corresponding dual boundary element?dual BEM?program is developed to solve the problem of fracture and fatigue in piezoelectric materials.There are extended or modified several computational methods of fracture parameter at the crack tip,and then proposed a new fracture criterion to numerical analysis crack propagation path based on different electric boundary condition and predict the fatigue life of piezoelectric materials under the cyclic mechanical or electrical loading.The specific research contents are as follows:?1?To research the fracture problem in piezoelectric materials,the modified crack closure integral method?MCCI?is proposed to improve the calculational precision of fracture parameter based on the features of the discontinuous 1/4 crack tip element.The interaction integral method?I-integral?is here extended to boundary element application,whice has been realized the high precision calculation of the piezoelectric fracture parameters.Using displacement extrapolation,J integral method,MCCI and interaction integral method,the field intensity factors of piezoelectric cracks were numerically calculated and compared with analytical results to verified the accuracy of these numerical methods.?2?Based on the new fracture parameters?the hoop mechanical strain energy release rate _MG^??,the max_M^?G fracture criterion is proposed to analyze the initiation force of piezoelectric cracks under different electric boundary conditions,and compared with the experimental data to study the effectiveness of various electric boundary conditions.The subroutine module of crack progation is developed by adding the new crack element at the crack tip to realize simulation of crack propagation.The max hoop stress intensity factor criterion K_??and the maxG_M^?criterion are selected to numerically simulate the propagation paths of piezoelectric cracks under various loads,and compared with the existing results?3?By considering the small scale plastic yielding and electric yielding at the crack tip,a subroutine module of the fatigue crack propagation is developed based on the classical Paris formula in which the control parameters numerically calculated by the I-integral are modifed.The Paris formula of piezoelectric materials under the cyclic electrical loading is fitted by combining the existing experimental data and the corresponding fracture parameters calculated by the BEM to predict fatigue life of piezoelectric specimens,and compared to show their applicability.