Analysis of an orthotropic strip containing multiple defects bonded between two piezoelectric layers

Nourazar, M.; Ayatollahi, M.

doi:10.1007/s00707-015-1559-0

Cited by 3 publications

(5 citation statements)

References 18 publications

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“…As for Equation (6), this represents a Hilbert problem, and the Plemelj function for two collinear cracks is stated by…”

Section: Evaluation Of Sifs At Crack Tips Via the Complex Functions A...mentioning

confidence: 99%

“…There are many achievements of SIFs. [6][7][8][9] Muskelishvili 10 proposed the theoretical solution of the elastic plane problem with collinear cracks by using complex functions, which have been extensively employed by other scholars. Tafreshi 11 presented a new analytical expression relating the J-integral and SIFs for a crack through exploiting the complex function approach.…”

Section: Introductionmentioning

confidence: 99%

“…There are many achievements of SIFs 6–9 . Muskelishvili 10 proposed the theoretical solution of the elastic plane problem with collinear cracks by using complex functions, which have been extensively employed by other scholars.…”

Section: Introductionmentioning

confidence: 99%

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Theoretical analysis of two cracks in sandstone under the simultaneous action of pressure and shear stress

Huang

Wang

Zhou

et al. 2023

Fatigue Fract Eng Mat Struct

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The cracked rock mass could slide along the weak side under the action of compressive loads and shear loads in landslides; thus, the stability evaluation of the crack in rock mass media is of particular importance. The formulas of stress intensity factors (SIFs) for each crack tip are theoretically derived by implementing complex function theory. The results of the analytical solutions are then compared with the predicted results of the finite element analysis via ABAQUS software, revealing a slight relative error. Photo elastic experiment and static compression tests are conducted to verify the correctness of theoretical results. The obtained results reveal that the internal pressure leads to the increasing SIFs of mode II at crack tips. Further, the larger the difference between the horizontal and vertical compressive stresses, the more likely the occurrence of shear failure in the cracked rock mass. For the two cracks, the most dangerous point is the inner crack tip of the longer crack. K E Y W O R D S collinear cracks, digital image correlation, static compression test, stress intensity factor Highlights • Theoretical formulas of SIFs for two cracks under pressure and shear stress were proposed. • The theoretical results were verified by finite element, and they have a good agreement. • The influences of different factors on the SIFs at crack tip were discussed. • High-speed camera and DIC method were used to analyze the fracture model and strain field.

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“…As for Equation (6), this represents a Hilbert problem, and the Plemelj function for two collinear cracks is stated by…”

Section: Evaluation Of Sifs At Crack Tips Via the Complex Functions A...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Theoretical analysis of two cracks in sandstone under the simultaneous action of pressure and shear stress

Huang

Wang

Zhou

et al. 2023

Fatigue Fract Eng Mat Struct

View full text Add to dashboard Cite

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“…The numerical results demonstrate that the positive charge can prevent the crack propagation, and the material with smaller thickness and stronger rigidity can be selected to better resist the fracture. Nourazar et al [15,16] investigated the fracture analysis of non-ideal piezoelectric coatings and orthotropic strips with multiple defects. Used the dislocation method, the problem was reduced to a singular integral equation and the effects of the non-ideal bonding coefficient, the defect geometry and coating properties on the stress intensity factor and the annular stress of the cavity were discussed numerically.…”

Section: Introductionmentioning

confidence: 99%

Interaction between Screw Dislocation and Interfacial Crack in Fine-Grained Piezoelectric Coatings under Steady-State Thermal Loading

2021

Applied Sciences

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The mechanical behavior of fine-grained piezoelectric/substrate structure with screw dislocation and interface edge crack under the coupling action of heat, force and electricity are studied. Using the mapping function method, firstly, the finite area plane is transformed into the right semi-infinite plane, then the expression of the temperature field is given with the help of the complex function, and then the temperature field of the problem is achieved. By constructing the general solution of the governing equation with temperature function, the analytical expression of the image force is derived. Finally, the effects of material parameters, temperature gradient, coating thickness and crack size on image force are analyzed by numerical examples. The results show that the temperature gradient has a very significant effect on the image force, and thicker coating is conducive to the stability of dislocation and interface crack.

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“…e numerical results showed that the residual stress had a significant effect on the piezoelectric nanomaterials, and the piezoelectric nanomaterials had stronger electromechanical coupling compared to the classical fracture mechanics. Nourazar and Ayatollahi [15] examined the effects of multiple interface cracks in orthotropic-strip-bonded bi-piezoelectric strips, and the results reflected the crack size had a great influence on the intensity factor and the hoop stress of the cavities. Tian and Rajapakse [16] studied a penny-shaped interface crack of double piezoelectric materials, and the Hankel integral transformation method was used to establish a mixed boundaryvalue problem corresponding to an interface crack.…”

Section: Introductionmentioning

confidence: 99%

Research on Multiple Griffith Cracks at the Interface of Fine‐Grained Piezoelectric Coating/Substrate

Liu

2019

Mathematical Problems in Engineering

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The behavior of a fine-grained piezoelectric coating/substrate with multiple Griffith interface cracks under electromechanical loads is investigated. In this work, double coupled singular integral equations are proposed to solve the fracture problems. Both the singular integral equation and single-valued conditions are simplified into an algebraic equation and solved by numerical calculation. Thereby, the intensity factors of electric displacement and stress obtained are used to obtain the expression of the energy release rate. Furthermore, numerical results of the energy release rate with material parameters are demonstrated. Based on the obtained results, it could be concluded that the energy release rate is closely related to the size of the interface cracks and the mechanical-electrical loading. For a bimaterial structure, the fine-grained piezoelectric structure exhibited better material performance compared to the large one.

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Analysis of an orthotropic strip containing multiple defects bonded between two piezoelectric layers

Cited by 3 publications

References 18 publications

Theoretical analysis of two cracks in sandstone under the simultaneous action of pressure and shear stress

Theoretical analysis of two cracks in sandstone under the simultaneous action of pressure and shear stress

Interaction between Screw Dislocation and Interfacial Crack in Fine-Grained Piezoelectric Coatings under Steady-State Thermal Loading

Research on Multiple Griffith Cracks at the Interface of Fine‐Grained Piezoelectric Coating/Substrate

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