Strip-saturation model for piezoelectric plane weakened by two collinear cracks with coalesced interior zones

Bhargava, Rama; Jangid, Kamlesh

doi:10.1016/j.apm.2012.09.026

Cited by 21 publications

(8 citation statements)

References 11 publications

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“…where Π = Π 4 Π 4 − Π 44 Π , * = −Π 44 + Π 4 4 . The solution of Equation 16 together with single-valuednes condition of the mechanical displacement is:…”

Section: Solution For Modified Strip Saturated Modelsmentioning

confidence: 99%

“…For providing the analytical solution of semipermeable two collinear cracks of equal/unequal lengths based on strip saturation model, they implemented the complex variable approach of Collins [2] and Theocaris. [13] Closed form expressions of saturated zone length, local intensity factor, COP and COD were obtained for two collinear cracks problems based on different strip saturation models such as strip electro-mechanical yielding model, [14] strip electromechanical semipermeable model, [15] strip saturation model with coalesced interior zones [16,17] and mode-III strip saturation semipermeable model. [18] Fan et al [19] extended the fracture mechanics study based on PS model to a semipermeable crack in three dimensional piezoelectric media.…”

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confidence: 99%

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Analytical solution for two equal collinear modified strip saturated cracks in 2‐D semipermeable piezoelectric media

2019

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An analytical solution and study is presented for two equal collinear cracks in 2‐D semipermeable piezoelectric media based on modified strip saturation models. The constant saturated condition defined in strip saturation model is modified here by considering the symmetric and polynomial varying saturation conditions. These proposed saturated conditions are multiplicative of saturated electric displacement value and polynomial (constant to cubic order) of a variable defined as ratio of distance of a point on saturated zone length to the extended half‐crack length. Moreover, these are interpolated on the basis of possible saturated values near the crack‐tips and zone tips. To present the analytical study, a problem of two cracks of equal length situated in series is considered in 2‐D arbitrary polarized infinite piezoelectric domain subjected to semipermeable crack‐face and electromechanical loading conditions. Applying the extended Stroh formalism and complex variable approach, these problems are mathematically modeled into non‐homogeneous Riemann Hilbert problems in terms of unknown complex functions representing stress and electric displacement components at any point within the domain. Using Muskhelishvili [1] and Collin's [2] mathematical techniques, these complex functions are obtained from the developed non‐homogeneous Riemann Hilbert problems. Hence, the explicit expressions for saturated zone lengths (inner and outer), crack opening potentials (COPs), crack opening displacements (CODs) and local stress intensity factors (LSIFs) are obtained. Further, the impact of polynomial varying saturated conditions is highlighted on these fracture parameters with respect to inter crack space distance, crack‐face conditions, polarization angle by presenting the numerical applications in infinite 2‐D PZT‐4 media.

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“…where Π = Π 4 Π 4 − Π 44 Π , * = −Π 44 + Π 4 4 . The solution of Equation 16 together with single-valuednes condition of the mechanical displacement is:…”

Section: Solution For Modified Strip Saturated Modelsmentioning

confidence: 99%

mentioning

confidence: 99%

Analytical solution for two equal collinear modified strip saturated cracks in 2‐D semipermeable piezoelectric media

2019

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“…They implemented the complex variable approach for finding the yielding zone lengths. Thereafter, Bhargava and Jangid [13] extended SS model to study the semipermeable two collinear cracks in an infinite 2-D piezoelectric media. They applied the complex variable technique to obtain the analytical expressions for saturated zone lengths, Crack Opening Displacement (COD), Crack Opening Potential (COP) and Local Stress Intensity Factors (LSIFs).…”

Section: Introductionmentioning

confidence: 99%

Simplified numerical algorithms for generalized strip saturated two equal collinear cracks in piezoelectric media using distributed dislocation technique

Sharma

Singh²,

Bui

2023

Z Angew Math Mech

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In this paper, we present the distributed dislocation technique (DDT) based numerical algorithms to study the generalized strip saturated (GSS) models for two equal collinear cracks in 2‐D finite and infinite piezoelectric media. Numerical studies for particular cases such as linear, quadratic and cubic strip saturated models are simulated by considering their equivalent forms based on the principle of superposition. Two equal collinear cracks problem and its particular case of coalesced zones are considered in 2‐D semipermeable piezoelectric media under arbitrary poling direction and in‐plane electromechanical loadings. The results of saturated zone lengths (inner and outer) and local stress intensity factors (at inner and outer tips) are evaluated numerically for infinite and finite domain problems. The results of infinite domain obtained using DDT are compared with the reference analytical solutions. A good agreement of the results shows the efficacy of the proposed algorithms based on DDT for solving GSS two equal collinear cracks problems in 2‐D finite/infinite piezoelectric media.

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“…Because piezoelectric medium is usually brittle and contain many cracks, the investigation of fracture problems in a piezoelectric medium has been actively studied by Bhargava and Jangid (2013), Chen et al (2014), Liu et al (2016), Monfared and Ayatollahi (2017), Sharma et al (2016), Yu et al (2018), Zhang and Wang (2018), Zhao et al (2014Zhao et al ( , 2018, and Zhou et al (2007b). For example, a stripsaturation model is proposed (Bhargava and Jangid, 2013) for a transversely isotropic piezoelectric plane weakened by two collinear equal cracks. By using the precise integration algorithm (PIA) and the approach of dual vector form, the elastodynamic axisymmetric response of the multi-layered transversely isotropic piezoelectric medium is explored by Liu et al (2016).…”

Section: Introductionmentioning

confidence: 99%

Dynamic non-local stress analysis of two collinear semi-permeable mode-I cracks in a piezoelectric medium

Liu

2019

Journal of Intelligent Material Systems and Structures

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This article investigates the dynamic non-local stress analysis of two collinear semi-permeable mode-I cracks in a piezoelectric medium under the harmonic waves by using the generalized Almansi theorem and the Schmidt method. Based on the Fourier transform technique, this problem is formulated into coupled dual integral equations. The dynamic stress and the dynamic electric displacement fields at the crack tips are obtained by solving the derived dual integral equations. Numerical examples are provided to show the effects of the crack length, the distance between the two collinear cracks, the lattice parameter, the electric permittivity of the air inside the crack, and the characteristics of the harmonic wave on the dynamic stress field and the dynamic electric displacement field near the crack tips. The dynamic stress and electric displacement decrease with increasing the distance between two collinear cracks and lattice parameter in a piezoelectric medium. Meanwhile, the dynamic field will impede or enhance crack propagation in piezoelectric medium depending on the circular frequency of the incident wave. Different from the classical solutions, the present solutions exhibit no stress and electric displacement singularities at the crack tips. This work is expected to be helpful for theoretical modeling of piezoelectric medium at nanoscale.

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Strip-saturation model for piezoelectric plane weakened by two collinear cracks with coalesced interior zones

Cited by 21 publications

References 11 publications

Analytical solution for two equal collinear modified strip saturated cracks in 2‐D semipermeable piezoelectric media

Analytical solution for two equal collinear modified strip saturated cracks in 2‐D semipermeable piezoelectric media

Simplified numerical algorithms for generalized strip saturated two equal collinear cracks in piezoelectric media using distributed dislocation technique

Dynamic non-local stress analysis of two collinear semi-permeable mode-I cracks in a piezoelectric medium

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