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1

Crack arrest saturation model under combined electrical and mechanical loadings

Bhargava R. R., Setia A.

Journal of Achievements in Materials and Manufacturing Engineering

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2009

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Vol. 37, nr 2

544-548

EN

Purpose: The investigation aims at proposing a model for cracked piezoelectric strip which is capable to arrest the crack. Design/methodology/approach: Under the combined effect of electrical and mechanical loadings applied at the edges of the strip, the developed saturation zone is produced at each tip of the crack. To arrest further opening of the crack, the rims of the developed saturation zones are subjected to in-plane cohesive, normal uniform constant saturation point electrical displacement. The problem is solved using Fourier integral transform method which reduces the problem to the solution of Fredholm integral equation of the second kind. This integral equation in turn is solved numerically. Findings: The expressions are derived for different intensity factors and energy release rate. A qualitative analysis of the parameters affecting the arrest of opening of the crack and fatigue crack growth with respect to strip thickness and material constants are presented graphically. Research limitations/implications: The investigations are carried out by considering the material electrical brittle. Consequently, the zones protrude along the straight lines ahead of the crack tips. And further, the small scale electrical yielding conditions are used. Practical implications: Piezoelectric materials are widely getting used nowadays, even in day to day life like piezoelectric cigarette lighter, children toys etc. And, its advance used in technology like transducers, actuators has been already in progress. So, the aspect of cracking of piezoelectric materials are of great practical importance. Originality/value: The piezoelectric material under the combined effect of electrical and mechanical loadings gives the assessment of electrical displacement which is required to arrest the crack. The various useful interpretations are also drawn from the graphs.

2

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

Bhargava R.R., Setia A.

Archives of Computational Materials Science and Surface Engineering

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2009

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Vol. 1, nr 1

5-12

EN

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.

3

Crack arrest model for a piezoelectric strip subjected to Mode-I loadings

Bhargava R. R., Setia A.

Journal of Achievements in Materials and Manufacturing Engineering

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2007

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Vol. 22, nr 2

19-22

EN

Purpose: The present paper aims at proposing a crack arrest model for an infinitely long narrow, poled ceramic strip weakened by a finite hairline straight crack when the edges of the strip are subjected to combined mechanical and electrical loads. Design/methodology/approach: (Model) As a consequence of loads the rims of crack open forming a yield zone ahead of each tip 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 presented when edges of the strip are subjected to: Case-I-in-plane stresses and electrical displacement or Case-II-in-plane stresses and in-plane electric field. Problems are solved using Fourier integral transform method. Findings: The stress intensity factor, yield zone length, crack opening displacement, crack growth rate have been calculated. Their variation with respect to affecting parameters viz. yield zone length, width of the strip, material constant, electrical and mechanical loads has been depicted graphically. 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 difference 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.

4

Crack arrest model for a piezoelectric strip subjected to Mode-I loadings

Bhargava R. R., Setia A.

Journal of Achievements in Materials and Manufacturing Engineering

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2007

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Vol. 20, nr 1-2

215-218

EN

Purpose: The present paper aims at proposing a crack arrest model for an infinitely long narrow, poled ceramic strip weakened by a finite hairline straight crack when the edges of the strip are subjected to combined mechanical and electrical loads. Design/methodology/approach: (Model) As a consequence of loads the rims of crack open forming a yield zone ahead of each tip 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 presented when edges of the strip are subjected to: Case-I-in-plane stresses and electrical displacement or Case-II-in-plane stresses and in-plane electric field. Problems are solved using Fourier integral transform method. Findings: The stress intensity factor, yield zone length, crack opening displacement, crack growth rate have been calculated. Their variation with respect to affecting parameters viz. yield zone length, width of the strip, material constant, electrical and mechanical loads has been depicted graphically. 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.