Antiplane mechanical and inplane electric time-dependent load applied to two coplanar cracks in piezoelectric ceramic material

• Published in: Theoretical and applied fracture mechanics Vol. 33; no. 3; pp. 173 - 184
• Main Authors: Chen, Z.T., Worswick, M.J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.06.2000; Elsevier
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Cross-disciplinary physics: materials science; rheology; Dielectric, piezoelectric, ferroelectric and antiferroelectric materials; Dielectrics, piezoelectrics, and ferroelectrics and their properties; Elasticity and anelasticity; Elasticity and anelasticity, stress-strain relations; Exact sciences and technology; Materials science; Niobates, titanates, tantalates, pzt ceramics, etc; Physics; Treatment of materials and its effects on microstructure and properties; Fourier transformation; Singular equation; Insulators; Numerical method; Antiplane strain; Piezoceramic materials; Crack propagation; Vibrations; Time dependence; Cracks; Numerical computation; Integral equations; Electric fields; Dynamic response; Stress wave; Elastic material; Dynamic loads; Cauchy problem; Electric charges; Stress intensity factors; Plane strain; Mechanical load; Crack length; Boundary-value problems; Laplace transformation; Applied load; Cauchy integral; Electromechanical properties
• ISSN: 0167-8442; 1872-7638
• DOI: 10.1016/S0167-8442(00)00012-4

This work is concerned with the dynamic response of two coplanar cracks in a piezoelectric ceramic under antiplane mechanical and inplane electric time-dependent load. The cracks are assumed to act either as an insulator or as a conductor. Laplace and Fourier transforms are used to reduce the mixed boundary value problems to Cauchy-type singular integral equations in Laplace transform domain. A numerical Laplace inversion algorithm is used to determine the dynamic stress and electric displacement factors that depend on time and geometry. A normalized equivalent parameter describing the ratio of the equivalent magnitude of electric load to that of mechanical load is introduced in the numerical computation of the dynamic stress intensity factor (DSIF) which has a similar trend as that for the pure elastic material. The results show that the dynamic electric field will impede or enhance crack propagation in a piezoelectric ceramic material at different stages of the dynamic electromechanical load. Moreover, the electromechanical response is greatly affected by the ratio of the crack length to the ligament between the cracks. The stress and electric displacement intensity factor can be combined by the energy density factor or function to address the fracture of piezoelectric materials under the combined influence of electromechanical loading.