Crack analysis of circular bars reinforced by a piezoelectric layer under torsional transient loading

Bagheri, R.; Hassani, Alireza

doi:10.1007/s00419-019-01527-y

Cited by 15 publications

(2 citation statements)

References 23 publications

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“…At this section of the paper, torsional rigidity of an isotropic bar with an orthotropic layer weakened by a Volterra‐type screw dislocation under time‐dependent loading,

M false(t false) = M_{0} H false(t false)

, is analyzed. The torsional rigidity is obtained by the following formula as

M (t) = D (t) α = \int_{0}^{2 π} \int_{0}^{R_{2}} r^{2} τ_{θ z} (r, θ, t) d r d θ

in which

τ_{θ z} false(r, θ, t false)

is the stress component obtained in Equation and

M (t)

is the transient external moment. Upon Substituting Equation into Equation the torsional rigidity is determined as follows

D = D_{0} - \frac{1}{2} μ (R_{1}^{2} - a^{2}) \frac{b_{z} (t)}{α}

in which

D_{0} = \frac{1}{2} π (μ R_{1}^{4} + G_{r z} (R_{2}^{4} - R_{1}^{4}))

where D 0 is the torsional rigidity in an intact bar with an orthotropic layer subjected to transient torsion.…”

Section: General Formulationmentioning

confidence: 99%

Analytical solutions for multiple mode III cracks in a cylindrical bar with an orthotropic coating under dynamic loading

Karimi

Hassani

2020

Z Angew Math Mech

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This study presents an analytical formulation for a cylindrical bar, with an orthotropic layer, containing multiple mode III cracks under time-dependent torsion. The transient response to a dislocation cut with time-dependent Burgers vector is obtained in the cross-section of the cylindrical bar, with an orthotropic layer, with the help of the Fourier and Laplace transform. The dislocation solution is used to drive a group of singular integral equations for the study of circular domains with the orthotropic coating containing smooth radial cracks under transient torsional loading. The singular integral equations are evaluated numerically to calculate the torsional rigidity of the domain, and the dynamic stress intensity factors at the singular crack tips. Finally, there are several examples to illustrate the effect of the orthotropic coating on the dynamic stress intensity factors and torsional rigidity of the domain under consideration. K E Y W O R D Scylindrical bar, distributed dislocation method, dynamic stress intensity factor (DSIF), orthotropic coating, torsional transient loading

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“…At this section of the paper, torsional rigidity of an isotropic bar with an orthotropic layer weakened by a Volterra‐type screw dislocation under time‐dependent loading,

M false(t false) = M_{0} H false(t false)

, is analyzed. The torsional rigidity is obtained by the following formula as

M (t) = D (t) α = \int_{0}^{2 π} \int_{0}^{R_{2}} r^{2} τ_{θ z} (r, θ, t) d r d θ

in which

τ_{θ z} false(r, θ, t false)

is the stress component obtained in Equation and

M (t)

is the transient external moment. Upon Substituting Equation into Equation the torsional rigidity is determined as follows

D = D_{0} - \frac{1}{2} μ (R_{1}^{2} - a^{2}) \frac{b_{z} (t)}{α}

in which

D_{0} = \frac{1}{2} π (μ R_{1}^{4} + G_{r z} (R_{2}^{4} - R_{1}^{4}))

where D 0 is the torsional rigidity in an intact bar with an orthotropic layer subjected to transient torsion.…”

Section: General Formulationmentioning

confidence: 99%

Analytical solutions for multiple mode III cracks in a cylindrical bar with an orthotropic coating under dynamic loading

Karimi

Hassani

2020

Z Angew Math Mech

Self Cite

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“…Using the functionally graded materials as interface layer, the stress concentration caused by the discontinuity of material properties at the interface can be deleted [3]. The crack problem for functionally graded materials is considered in many literatures [4][5][6][7][8][9][10][11][12][13][14]. Liu and colleagues [15][16][17] studied the axisymmetric frictionless contact and the torsional problem using the linear multi-layer model to simulate the functionally graded interfacial layer with arbitrarily varying material properties along the thickness direction.…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric contact problem of piezoelectric coating-substrate system with functionally graded piezoelectric interfacial layer

Zang

Liu

2023

Mathematics and Mechanics of Solids

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In this paper, the electromechanical response of piezoelectric coating-functionally graded piezoelectric (FGP) interfacial layer–piezoelectric substrate system under the rigid spherical punch is considered. It is assumed that the piezoelectric coating and piezoelectric substrate are connected by the FGP interfacial layer which is simulated by a multi-layer model. The axisymmetric frictionless contact problem of piezoelectric coating–substrate system with FGP interfacial layer is formulated in terms of singular integral equation with the method of transfer matrix and Hankel integral transform technique. The effect of the gradient of material properties on the stress components and electric displacement components in piezoelectric coating–substrate system is gained by solving the equation numerically. The present results could serve as a useful reference for the design of piezoelectric coating–substrate system.

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Analytical solutions of multiple cracks and cavities in a rectangular cross-section bar coated by a functionally graded layer under torsion

2021

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Crack analysis of circular bars reinforced by a piezoelectric layer under torsional transient loading

Cited by 15 publications

References 23 publications

Analytical solutions for multiple mode III cracks in a cylindrical bar with an orthotropic coating under dynamic loading

Analytical solutions for multiple mode III cracks in a cylindrical bar with an orthotropic coating under dynamic loading

Axisymmetric contact problem of piezoelectric coating-substrate system with functionally graded piezoelectric interfacial layer

Analytical solutions of multiple cracks and cavities in a rectangular cross-section bar coated by a functionally graded layer under torsion

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