Model for a piezoelectric strip of crack arrest subjected to Mode-I loadings

Purpose: In the present paper a crack arrest model is proposed for an infinitely long narrow poled piezoelectric strip embedded with a centrally situated finite hairline straight crack. Design/methodology/approach: The ceramic of the strip is assumed to be mechanically brittle and electrically ductile. Combined mechanical and electrical loads applied at the edge of the strip open the rims of the crack in mode-I deformations. Consequently a yield zone protrudes ahead of each tip of the crack. Under small scale yielding the yield zone are assumed to lie on the line segment along the axis of the crack. To arrest the crack from further opening the rims of the yield zones are subjected to normal, cohesive quadratically varying yield point stress. Two cases are considered: Case-I the edges of the strip are subjected to in-plane normal and in-plane electrical displacement and in Case-II the in-plane stresses and in-plane electrical field are applied on the edges of the strip. In each case problem is solved using Fourier transform method which finally reduces to the solution of integral equation. Findings: Analytic expressions are derived for stress intensity factor, yield zone, crack opening displacement, crack growth rate, variation of these quantities with respect to affecting parameters viz. width of the strip, yield zone length, crack length, material constants for different ceramics have been plotted. Research limitations/implications: The material of the strip is assumed mechanically brittle and electrically ductile consequently mechanically singularity is encountered first. The investigations in this paper are carried at this level. Also the crack yielding under the loads is considered small scale hence the yield zone is assumed to be lying on the line segment ahead of the crack. Practical implications: Piezoelectric ceramics are widely used as sensors and actuators, this necessity prompts the fracture study on such ceramics under different loading conditions. Originality/value: The paper gives an assessment of the quadratically varying load required to be prescribed on yield zones so as to arrest the opening of the crack. The investigations are useful to smart material design technology where sensors and actuators are manufactured.