Non‐local stress and electric displacement solution of a 3D semi‐permeable rectangular crack in infinite orthotropic piezoelectric materials

Purpose Based on the non-local piezoelectricity theory, this paper is concerned with two collinear permeable Mode-I cracks in piezoelectric materials subjected to the harmonic stress wave. The paper aims to discuss this issue. Design/methodology/approach According to the Fourier transformation, the problem is formulated into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. Findings Finally, the dynamic non-local stress and the dynamic non-local electric displacement fields near the crack tips are obtained. Numerical results are provided to illustrate the effects of the distance between the two collinear cracks, the lattice parameter and the circular frequency of the incident waves on the entire dynamic fields near the crack tips, which play an important role in designing new structures in engineering. Originality/value Different from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack tips in piezoelectric materials. It is found that the maximum stress and maximum electric displacement can be used as a fracture criterion.

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The Non-Local Theory Solution of a Crack in the Functionally Graded Piezoelectric Materials Subjected to the Harmonic Anti-Plane Shear Stress Waves

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.353-358.258 ◽

2007 ◽

Vol 353-358 ◽

pp. 258-262

Author(s):

Zhen Gong Zhou ◽

Lin Zhi Wu

Keyword(s):

Shear Stress ◽

Piezoelectric Materials ◽

Electric Displacement ◽

Stress Waves ◽

Functionally Graded ◽

Local Theory ◽

Plane Shear ◽

Functionally Graded Piezoelectric Materials ◽

Non Local ◽

Functionally Graded Piezoelectric

In this paper, the non-local theory of elasticity was applied to obtain the dynamic behavior of a Griffith crack in functionally graded piezoelectric materials under the harmonic anti-plane shear stress waves. The problem can be solved with the help of a pair of dual integral equations. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips, thus allows us to use the maximum stress as a fracture criterion.

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

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x19873425 ◽

2019 ◽

Vol 30 (20) ◽

pp. 3100-3112

Author(s):

Hai-Tao Liu ◽

Wen-Juan Wu ◽

Jian-Guo Wu

Keyword(s):

Dynamic Stress ◽

Electric Displacement ◽

Local Stress ◽

Lattice Parameter ◽

Piezoelectric Medium ◽

Mode I ◽

Collinear Cracks ◽

Dual Integral Equations ◽

Crack Tips ◽

Non Local

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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The Higher Order Crack Tip Fields for Interfacial Crack between Linear Functionally Graded and Homogeneous Piezoelectric Materials

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1015.97 ◽

2014 ◽

Vol 1015 ◽

pp. 97-100

Author(s):

Yao Dai ◽

Xiao Chong ◽

Ying Chen

Keyword(s):

Piezoelectric Materials ◽

Electric Displacement ◽

Interfacial Crack ◽

Crack Tip ◽

Higher Order ◽

Functionally Graded ◽

Linear Functions ◽

Intensity Factors ◽

Crack Tip Fields ◽

Functionally Graded Piezoelectric Materials

The higher order crack-tip fields for an anti-plane crack situated in the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The mechanical and electrical properties of the FGPMs are assumed to be linear functions of y perpendicular to the crack. The crack surfaces are supposed to be insulated electrically. By using the method of eigen-expansion, the higher order stress and electric displacement crack tip fields for FGPMs and HPMs are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.

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The Non-Local Theory Solution of a Crack in the Functionally Graded Piezoelectric Materials Subjected to the Harmonic Anti-Plane Shear Stress Waves

Key Engineering Materials - Progresses in Fracture and Strength of Materials and Structures ◽

10.4028/0-87849-456-1.258 ◽

2007 ◽

pp. 258-262

Author(s):

Zhen Gong Zhou ◽

Lin Zhi Wu

Keyword(s):

Shear Stress ◽

Piezoelectric Materials ◽

Stress Waves ◽

Functionally Graded ◽

Local Theory ◽

Plane Shear ◽

Functionally Graded Piezoelectric Materials ◽

Non Local ◽

Functionally Graded Piezoelectric ◽

Theory Solution

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Fundamental solutions of two 3D rectangular semi-permeable cracks in transversely isotropic piezoelectric media based on the non-local theory

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-09-2019-0169 ◽

2020 ◽

Vol 16 (6) ◽

pp. 1497-1520

Author(s):

Haitao Liu ◽

Liang Wang

Keyword(s):

Electric Displacement ◽

Transversely Isotropic ◽

Elastic Behavior ◽

Classical Solutions ◽

Local Theory ◽

Dual Integral Equations ◽

Piezoelectric Media ◽

Content Type ◽

Present Solution ◽

Non Local

PurposeThe paper aims to present the non-local theory solution of two three-dimensional (3D) rectangular semi-permeable cracks in transversely isotropic piezoelectric media under a normal stress loading.Design/methodology/approachThe fracture problem is solved by using the non-local theory, the generalized Almansi's theorem and the Schmidt method. By Fourier transform, this problem is formulated as three pairs of dual integral equations, in which the elastic and electric displacements jump across the crack surfaces. Finally, the non-local stress and the non-local electric displacement fields near the crack edges in piezoelectric media are derived.FindingsDifferent from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack edges in piezoelectric media.Originality/valueAccording to the literature survey, the electro-elastic behavior of two 3D rectangular cracks in piezoelectric media under the semi-permeable boundary conditions has not been reported by means of the non-local theory so far.

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