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A penny-shaped crack IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SOLID:MODES Ⅱ AND Ⅲ PROBLEMS

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Acta Mechanica Sinica 1999年第1期15卷 52-58页

作者：陈伟球丁皓江 Department of Civil Engineering Zhejiang UniversityHangzhou 310027China

An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solution of three-dimensional piezoelasticity and the four harmonics involved are represented by one complex potential.Previous results in potential theory are then utilized to obtain the exact solution that is expressed in terms of elementary functions.Comparison is made between the current results with those published and good agreement is obtained.

关键词： transversely isotropic piezoelectric material general solution potential theory penny-shaped crack modes Ⅱ and Ⅲ

A penny-shaped crack IN A MAGNETOELECTROELASTIC LAYER UNDER RADIAL SHEAR IMPACT LOADING

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Acta Mechanica Solida Sinica 2007年第3期20卷 275-282页

作者： Feng Wenjie Nie Hui Han Xu Department of Engineering Mechanics Shijiazhuang Railway Institute Shijiazhuang 050043 China State Key Lab Adv Design ＆ Manufacture Vehicle Bo Hunan University Changsha 410082 China

This paper analyzes the dynamic magnetoelectroelastic behavior induced by a pennyshaped crack in a magnetoelectroelastic layer. The crack surfaces are subjected to only radial shear impact loading. The Laplace and Hankel transform techniques are employed to reduce the problem to solving a Fredholm integral equation. The dynamic stress intensity factor is obtained and numerically calculated for different layer heights. And the corresponding static solution is given by simple analysis. It is seen that the dynamic stress intensity factor for cracks in a magnetoelectroelastic layer has the same expression as that in a purely elastic material. And the influences of layer height on both the dynamic and static stress intensity factors are insignificant as h/a 〉 2.

关键词： magnetoelectroelastic layer penny-shaped crack impact stress intensity factor Hankel transform Laplace transform

TORSIONAL IMPACT RESPONSE OF A penny-shaped crack IN A FUNCTIONAL GRADED STRIP

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Applied Mathematics and Mechanics(English Edition) 2004年第12期25卷 1398-1404页

作者：冯文杰李向国王守东 Department of Mechanics and Engineering Science Shijiazhuang Railway Institute Shijiazhuang 050043 P.R.China Department of Resource and Information University of Petroleum Beijing 102200 P.R.China

The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived.And it is shown that, as crack driving force, they are equivalent for the present crack problem. Investigated are the effects of material nonhomogeneity and (strip's) highness on the dynamic fracture behavior. Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus, and that the dynamic behavior varies little with the adjusting of the strip's highness.

关键词： dynamic stress intensity factor torsional impact penny-shaped crack functionally graded strip integral transform energy density factor

penny-shaped crack IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC MATERIALS

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Acta Mechanica Sinica 1994年第1期10卷 49-60页

作者：王子昆 Department of Engineering Mechanics Xi'an Jiaotong University Xi'an 710049 China

Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the dis- placement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another form of the general solution is obtained under cylindrical coordi- nate system by introducing three quasi-harmonic functions into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore, the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The results show that the stress and the electric displacement components near the crack tip have (r^(-1/2)) singularity.

关键词： piezoelectric material mechanical-electric coupling penny-shaped crack

Exact 3D Thermoelastic Solutions for a penny-shaped crack in an Infinite Magnetoelectric Medium

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Transactions of Nanjing University of Aeronautics and Astronautics 2014年第2期31卷 109-117页

作者： Chen Weiqiu Department of Engineering Mechanics Zhejiang University Hangzhou 310027 P.R. China

Exact solutions of three-dimensional(3D)crack problems are much less in number than those of two-dimensional ones,especially for multi-field coupling media exhibiting a certain kind of material anisotropy.An exact3Dthermoelastic solution has been reported for a uniformly heated penny-shaped crack in an infinite magnetoelectric space,with impermeable electromagnetic conditions assumed on the crack faces.Exact 3Dsolutions for the penny-shaped crack subjected to uniform or point temperature load are further presented here when the crack faces are electrically and magnetically permeable.The solutions,obtained by the potential theory method,are exact in the sense that all field variables are explicitly derived and expressed in terms of elementary functions.Along with the previously reported solution,the limits or bounds of the stress intensity factor at the crack-tip for a practical crack can be identified.

关键词： Exact three-dimensional solution General solution Magnetoelectric material penny-shaped crack Potential theory method

A penny-shaped crack IN AN INFINITE PIEZOELECTRIC BODY UNDER ANTISYMMETRIC POINT LOADS

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2001年第2期2卷 26-31页

作者：侯鹏飞丁皓江关富玲 Centre for Spatial Structures College of Architectural Engineering Zhejiang University Hangzhou China Institute of Geotechnical Engineering College of Architectural Engineering Zhejiang University Hangzhou China

In this study, Fabrikant(1989, 1991)’s new results in potential theory were used to obtain the exact and complete solution for the problem of a penny-shaped crack in an infinite transversely isotropic piezoelectric body subjected to antisymmetric point loads (point charges and normal point forces); then the complete solution for the problem of one-sided loading of a penny-shaped crack was obtained by the superposition of the symmetric loading solution in Chen and Shioya (1999) and the antisymmetric one presented here; and then the reciprocity theorem of piezoelectric media was used to deal with the problem of interaction between arbitrarily located point forces and a point charge with a penny-shaped crack and obtained the exact expressions of the crack faces’ normal displacement in terms of elementary functions and some non-singular integrals; and finally obtained the normal displacement of the positive and negative faces of the crack under many loading cases as shown in figures for an infinite PZT-4 piezoelectric ceramic body weakened by a penny-shaped crack.

关键词： transversely isotropic piezoelectric body penny-shaped crack point force point charge

THREE-DIMENSIONAL INTERACTIONS OF A penny-shaped crack IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

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THREE-DIMENSIONAL INTERACTIONS OF A PENNY-SHAPED CRACK IN A ...

Fracture of two three-dimensional parallel internal cracks in brittle solid under ultrasonic fracturing

2013全国压电和声波理论及器件技术研讨会

作者： Su-ming XIONG Peng-fei HOU Fan PENG College of Electrical Engineering Zhejiang University Department of Engineering Mechanics Hunan University

Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a penny-shaped crack in a transversely isotropic piezoelectric space interacting with various stress and charge sources:force dipoles,electric dipoles and moments.Locations and orientations of these resultant sources with respect to the crack are arbitrary.Such stress and charge sources may model defects like vacancies,foreign particles,and dislocations.Numerical results are presented at last.

关键词： piezoelectric space penny-shaped crack resultant source intensity factor

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Journal of Rock Mechanics and Geotechnical Engineering 2022年第3期14卷 757-769页

作者： Haijun Wang Hanzhang Li Lei Tang Xuhua Ren Qingxiang Meng Chun Zhu State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Nanjing Hydraulic Research InstituteNanjing210029China School of Earth Sciences and Engineering Hohai UniversityNanjing210098China

Similar to hydraulic fracturing(HF), the coalescence and fracture of cracks are induced within a rock under the action of an ultrasonic field, known as ultrasonic fracturing(UF). Investigating UF is important in both hard rock drilling and oil and gas recovery. A three-dimensional internal laser-engraved crack(3D-ILC) method was introduced to prefabricate two parallel internal cracks within the samples without any damage to the surface. The samples were subjected to UF. The mechanism of UF was elucidated by analyzing the characteristics of fracture surfaces. The crack propagation path under different ultrasonic parameters was obtained by numerical simulation based on the Paris fatigue model and compared to the experimental results of UF. The results show that the 3D-ILC method is a powerful tool for UF research.Under the action of an ultrasonic field, the fracture surface shows the characteristics of beach marks and contains powder locally, indicating that the UF mechanism includes high-cycle fatigue fracture, shear and friction, and temperature load. The two internal cracks become close under UF. The numerical result obtained by the Paris fatigue model also shows the attraction of the two cracks, consistent with the test results. The 3D-ILC method provides a new tool for the experimental study of UF. Compared to the conventional numerical methods based on the analysis of stress-strain and plastic zone, numerical simulation can be a good alternative method to obtain the crack path under UF.

关键词： Three-dimensional internal laser-engraved crack(3D-ILC) Interaction of cracks Ultrasonic fatigue penny-shaped crack Fracture mechanics High-cycle fatigue

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Applied Mathematics and Mechanics(English Edition) 2001年第12期22卷 1429-1435页

作者：吕念春程靳程云虹屈德志 Department of Astronautics and Mechanics Harbin Institute of Technology Harbin 150001 P R China Department of Civil Engineering Northeastern University Shenyang 110006 P R China Compressive Vessel Manufacturer of Constructive Installation Group Company of Daqing Daqing 163711 P R China

By the theory of complex functions, a penny-shaped crack on axially symmetric propagating problems for composite materials, was studied. The general representations of the analytical solutions with arbitrary index of self-similarity, were presented for fracture elastodynamics problems on axially symmetry by the ways of self-similarity under the ladder-shaped loads. The problems dealt with can be transformed into Riemann-Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov-Sobolev, the solutions of arbitrary complicated problems can be obtained.

关键词： penny-shaped crack axially symmetric composite materials analytical solutions