Crack Opening Potential Drop Research Articles

Strip-saturation model for arbitrary polarized electro-elastic material weakened by an eccentrically situated anti-plane semi-permeable crack

A strip-saturation model is studied to observe the effect of changing polarization axis on an electro-elastic strip, weakened by an eccentrically situated anti-plane semipermeable crack. The model is modified by considering that the saturated limit of electric displacement over rims of the saturation zone is quadratic interpolating polynomial times. The proposed model is formulated and then solved by using the Fourier integral transform technique and integral equations method. Closed-form analytic expressions are derived for developed saturation zone and fracture parameters viz. electric crack condition parameter, crack-sliding displacement, crack-opening potential drop, field intensity factors, energy release rate, etc. The influence of poling angle, prescribed electro-mechanical loadings, crack length, and material constants on fracture parameters are presented and analyzed graphically.

Magnetic-yielding zone model for assessment of two mode-III semi-permeable collinear cracks in piezo-electro-magnetic strip

A magnetic-yielding zone model for an infinitely long piezo-electro-magnetic strip weakened by two mode-III semi-permeable collinear cracks is proposed. Fourier series method and integral equation technique are adopted to solve the problem. The closed-form analytical expressions are obtained for several fracture parameters, namely crack opening potential drop, crack-sliding displacement, crack opening induction drop, intensity factors, and energy release rates. Also, the explicit analytical expressions are derived for developed magnetic-yielding zones. An illustrative numerical study is presented for poled BaTiO3-CoFe2O4 material to observe the impact of inter-crack distance, volume fraction, prescribed loadings, electro-magnetic crack-face boundary conditions on fracture parameters.

A novel method for measuring AFO stiffness using motion capture

A mathematical strip-saturation model is proposed to analyze the influence of changing poling direction on two hairline electrically semi-permeable collinear cracks embedded in a piezoelectric strip. The remote boundaries of the piezoelectric strip are subjected to anti-plane mechanical and in-plane electrical loads. Fourier series method is applied to transform the model into triple series equations which are then reduced to singular integral equations using the integral equation technique. The closed-form analytical expressions are derived for saturation zones length, crack-sliding displacement (CSD), crack opening potential drop (COPD), intensity factors (IFs), and energy release rate (ERR). Influence of the poling angle on CSD, COPD, and ERR are shown graphically for various cracked piezoelectric ceramics. In addition, the numerical study is also presented for analyzing the effect of inter-crack distance and prescribed electrical and mechanical loadings on the fracture parameters. All graphical results are analyzed and compared.

Electric and magnetic poling effects on two equal collinear semi‐permeable cracks in magneto‐electro‐elastic materials

AbstractIn this paper, the problem of two equal collinear semi‐permeable cracks is analytically studied for two‐dimensional arbitrarily polarized magneto‐electro‐elastic materials. The electric and magnetic poling directions make arbitrary angles with the crack line. Stroh's formalism and complex variable methodology are utilized to reduce the problem into non‐homogeneous Riemann–Hilbert problem. This numerical problem is then comprehended with the Riemann–Hilbert way to obtain the stress, electric displacement, and magnetic induction components at any point in the domain. The explicit expressions for the crack opening displacement, crack opening potential drop, crack opening induction drop, and the intensity factors are derived. A numerical contextual analysis is displayed for the composite. The numerical examination demonstrates that the change in electric/magnetic poling directions influences the different crack parameters.

Poling angle effect on two mode-III semi-permeable collinear cracks in a piezoelectric strip: Strip-saturation model

A mathematical strip-saturation model is proposed to analyze the influence of changing poling direction on two hairline electrically semi-permeable collinear cracks embedded in a piezoelectric strip. The remote boundaries of the piezoelectric strip are subjected to anti-plane mechanical and in-plane electrical loads. Fourier series method is applied to transform the model into triple series equations which are then reduced to singular integral equations using the integral equation technique. The closed-form analytical expressions are derived for saturation zones length, crack-sliding displacement (CSD), crack opening potential drop (COPD), intensity factors (IFs), and energy release rate (ERR). Influence of the poling angle on CSD, COPD, and ERR are shown graphically for various cracked piezoelectric ceramics. In addition, the numerical study is also presented for analyzing the effect of inter-crack distance and prescribed electrical and mechanical loadings on the fracture parameters. All graphical results are analyzed and compared.

Magneto-electro-elastic analysis for two mode-III semi-permeable collinear cracks in piezo-electro-magnetic strip

A mode-III crack problem for piezo-electro-magnetic strip weakened by two transversely oriented semi-permeable collinear cracks under out-of-plane shear stress and in-plane electric-displacement and magnetic induction is addressed. The problem is formulated and then solved using Fourier series method and integral equation technique. Closed-form analytic expressions are derived for various fracture parameters viz. crack sliding displacement, crack opening potential drop, crack opening induction drop, field intensity factors and energy release rates. Numerical case study is presented graphically for BaTiO3-CoFe2O4 piezo-electro-magnetic material to show the influence of inter-crack distance, volume fractions and electro-magnetic crack-face boundary conditions on crack sliding displacement, crack opening potential drop, crack opening induction drop and energy release rates. Moreover, the effect of prescribed mechanical loadings as well as electro-magnetic loadings on energy release rates are also presented graphically. Results obtained are presented graphically, analyzed and concluded.

A Study of Crack-Face Boundary Conditions for Piezoelectric Strip Cut Along Two Equal Collinear Cracks

AbstractA problem of two equal, semi-permeable, collinear cracks, situated normal to the edges of an infinitely long piezoelectric strip is considered. Piezoelectric strip being prescribed out-of-plane shear stress and in-plane electric-displacement. The Fourier series and integral equation methods are adopted to obtain analytical solution of the problem. Closed-form analytic expressions are derived for various fracture parameters viz. crack-sliding displacement, crack opening potential drop, field intensity factors and energy release rate. An numerical case study is considered for poled PZT–5H, BaTiO3 and PZT–6B piezoelectric ceramics to study the effect of applied electro-mechanical loadings, crack-face boundary conditions as well as inter-crack distance on fracture parameters. The obtained results are presented graphically, discussed and concluded.

A Mode-III strip saturation model for two collinear semi-permeable cracks in a piezoelectric media

In this paper, a mode-III strip-saturation model is proposed for a piezoelectric ceramic plate weakened by two equal collinear, semi-permeable hairline cracks. A mathematical model is obtained using Stroh’s formalism and solved using matrix Hilbert problem. Analytic closed form expressions are derived for various fracture parameters such as crack sliding displacement, crack opening potential drop, field intensity factor and energy release rate. An illustrative numerical case study is presented for impermeable, semi-permeable and permeable crack face boundary conditions for different piezoceramics. The results obtained are presented graphically, discussed and concluded. It is observed that the model proposed is capable of crack arrest under small-scale electric saturation.

Strip-electro-mechanical yield model for transversely situated two semi-permeable collinear cracks in piezoelectric strip

A strip-electro-mechanical model is proposed for two semi-permeable collinear cracks, symmetrically situated and transversely oriented in a poled piezoelectric strip. The remote boundary of the strip is subjected to mode-III stress and in-plane electric-displacement. Fourier series method together with integral equation method is employed to obtain the analytic solution. Expressions are derived for crack-sliding displacement, crack opening potential drop, intensity factors and energy release rate. Also, explicit expressions for developed slide-yield and saturation zones are derived. An illustrative case study is presented for poled PZT-5H, BaTiO3, PZT-6B and PZT-7A piezoelectric ceramics to study the capability of the strip-electro-mechanical yield model for the crack arrest. Results obtained are graphically presented, discussed and concluded.

A Modified Strip-Yield-Saturation-Induction Model Solution for Cracked Piezoelectromagnetic Plate

A strip-yield-saturation-induction model is proposed for an impermeable crack embedded in piezoelectromagnetic plate. The developed slide-yield, saturation, and induction zones are arrested by distributing, respectively, mechanical, electrical, and magnetic loads over their rims. Two cases are considered: when saturation zone exceeds induction zone and vice-versa. It is assumed that developed slide-yield zone is the smallest because of the brittle nature of piezoelectromagnetic material. Fourier integral transform technique is employed to obtain the solution. Closed form analytic expressions are derived for developed zones lengths, crack sliding displacement, crack opening potential drop, crack opening induction drop, and energy release rate. Case study presented for BaTiO3–CoFe2O4 shows that crack arrest is possible under small-scale mechanical, electrical, and magnetic yielding.

A mathematical strip-induction-saturation model for an off-centric semipermeable crack in a piezoelectromagnetic strip

A mode-III problem of strip-induction-saturation model is considered for a transversely isotropic piezoelectromagnetic strip weakened by a semipermeable non-centric crack. Three cases are considered: when the developed induction zone is larger, smaller and equal to the saturation zone. Fourier integral transform is used to reduce the problem into Fredholm integral equations of the second kind and solve numerically. Closed-form analytic expressions are derived for developed zones, field intensity factors, crack sliding displacement, crack opening induction drop, crack opening potential drop, local and global energy release rates. An illustrative numerical example is considered for a poled cracked narrow BaTiO3–CoFe2O3 strip to show the effect of prescribed loading combinations and developed zone length on the aforementioned fracture parameters. Results obtained are presented graphically, analyzed and concluded.

Mathematical model of electrical and mechanical yielding for piezoelectric strip weakened by a non-centric semi-permeable crack

A mathematical strip-electro-elastic yielding model solution is obtained for a long and narrow piezoelectric strip weakened by a non-centric, semi-permeable, mode-III crack. The crack is oriented parallel and situated asymmetrically with respect to the edges of the strip. Fourier cosine integral transform technique is adopted to solve the problem. Three different cases are considered: when developed saturation zone is bigger, smaller or equal to the developed slide-yield zone. Closed-form analytic expressions are derived for developed zones lengths, crack sliding displacement, crack opening potential drop, field intensity factors and energy release rate. A numerical case study is presented for poled BaTiO3 piezoelectric ceramic which affirms that proposed model is capable of crack arrest under small-scale mechanical and electrical yielding.

Two semi-permeable equal collinear cracks weakening a piezoelectric plate - A study using complex variable technique

In this paper, a mode-I crack problem is address for a piezoelectric plate cut along two-equal-collinear semi-permeable cracks. The plate being subjected to combined in-plane mechanical and electric displacement loads, respectively. Problem is formulated using Stroh formalism and solved using complex variable technique. Closed form expressions are derived for crack opening displacement, crack opening potential drop, field intensity factors, mechanical and total energy release rates. Theoretical derivations are validated by exact solutions existing in literature. Numerical examples considered for poled ceramics PZT-4, PZT-5H, and PZT-7A show the effect of applied mechanical and electrical displacement loadings on field intensity factors, mechanical and total energy release rates. Moreover, the effect of inter-crack distance as well as different types of crack-face electric boundary conditions on field intensity factors, mechanical and total energy release rates are presented graphically, discussed, and concluded.

A study on influence of poling direction on piezoelectric plate weakened by two collinear semi-permeable cracks

A study on the influence of change in poling direction is carried out for mechanical and electric strip-yield model for a transversely isotropic piezoelectric plate cut along two equal collinear semi-permeable straight hairline cracks. Two cases are considered, when the developed saturation zone is bigger or smaller than mechanical yield zone. The Stroh formalism and complex variable technique are employed to obtain the solution. The effect of change in poling direction is studied on crack opening displacement, crack opening potential drop and energy release rate. Also, a study is carried out on the suitability of crack closure for different piezoelectric ceramics. The obtained results are presented graphically and discussed.

A mathematical strip-saturation model for a piezoelectric plane weakened by two collinear equal cracks

A plane problem for a poled transversely isotropic piezoelectric plane cut along two equal collinear straight cracks is considered. It is assumed that the electrical yielding occurs at the continuations of the cracks due to the applied mechanical and electrical loadings. We model these crack continuations as the zones with constant cohesive saturation limit electrical displacement. The Stroh formalism and a complex variable technique are adopted to obtain the analytic solution of the problem. Closed-form expressions are derived for the developed saturation zone length, the crack opening displacement, the crack opening potential drop, the stress intensity factors, and the energy release rate. A qualitative numerical case study is presented for ceramics PZT-4, PZT-5H, and BaTiO3 to study the effects of various parameters as follows: developed saturation zone length and prescribed load, stress intensity factor, energy release rate, and crack opening displacement on crack growth resistance. The energy release rate and the stress intensity factor variations are investigated with respect to the inter-crack distance. The results obtained are presented graphically and discussed.

Strip-electromechanical model solution for piezoelectric plate cut along two semi-permeable collinear cracks

A strip electric saturation and mechanical yielding model solution is proposed for a piezoelectric plate cut along two equal collinear semi-permeable mode-I cracks with electrical polarization reaching a saturation limit and normal stress reaching a yield stress along a line segment in front of the cracks. By using Stroh formalism and complex variable technique, we derived the analytical solution for the field quantities. Three different situations are investigated when developed electrical saturation zone is bigger/smaller or equal to the developed mechanical yield zone. Numerical results show that the effect of different electric boundary conditions on the crack opening displacement and crack opening potential drop is significant and should not be ignored. The influence of electric load displacement on the energy release rate is also investigated for PZT-4, PZT-5H and BaTiO3 ceramics, and it may assists for the correct choosing of ceramic for specific job.