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EXACT SOLUTION FOR ORTHOTROPIC MATERIALS WEAKENED BY DOUBLY PERIODIC CRACKS OF UNEQUAL SIZE UNDER ANTIPLANE SHEAR 被引量:4
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作者 Junhua Xiao Chiping Jiang 《Acta Mechanica Solida Sinica》 SCIE EI 2009年第1期53-63,共11页
Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique,... Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods. 展开更多
关键词 orthotropic material a doubly periodic array of cracks antiplane shear boundary value problem stress intensity factor effective modulus
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THE PERIODIC CRACK PROBLEM IN BONDED PIEZOELECTRIC MATERIALS 被引量:4
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作者 Ding Shenghu Li Xing 《Acta Mechanica Solida Sinica》 SCIE EI 2007年第2期171-179,共9页
The problem of a periodic array of parallel cracks in a homogeneous piezoelectric strip bonded to a functionally graded piezoelectric material is investigated for inhomogeneous continuum. It is assumed that the materi... The problem of a periodic array of parallel cracks in a homogeneous piezoelectric strip bonded to a functionally graded piezoelectric material is investigated for inhomogeneous continuum. It is assumed that the material inhomogeneity is represented as the spatial variation of the shear modulus in the form of an exponential function along the direction of cracks. The mixed boundary value problem is reduced to a singular integral equation by applying the Fourier transform, and the singular integral equation is solved numerically by using the Gauss-Chebyshev integration technique. Numerical results are obtained to illustrate the variations of the stress intensity factors as a function of the crack periodicity for different values of the material inhomogeneity. 展开更多
关键词 periodic array of parallel crack functionally graded piezoelectric material singular integral equation Gauss-Chebyshev integration technique
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Interaction between collinear periodic cracks in an infinite piezoelectric body
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作者 崔之健 胡洪平 杨峰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第7期863-870,共8页
The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping tec... The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping technique, the general periodic solutions for collinear cracks are obtained. The stress intensity factors and the size of saturation strips are derived analytically, and their dependencies on the ratio of the periodicity on the half-length of the crack are analyzed in detail. Numerical results show the following two facts. (1) When h/l 〉 4.0, the stress intensity factors become almost identical to those of a single crack in an infinite piezoelectric body. This indicates that the interaction between cracks can be ignored in establishing the criterion for the crack initiation in this case. (2) The speed of the saturation strip size of periodic cracks approaching that of a single crack depends on the electric load applied at infinity. In general, a large electric load at infinity is associated with a slow approaching speed. 展开更多
关键词 collinear periodic crack stress intensity factor saturation strips ratio of periodicity to half-length of crack approaching speed
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PERIODICAL INTERFACIAL CRACKS IN ANISOTROPIC ELASTOPLASTIC MEDIA
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作者 肖万伸 周建平 唐国金 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第11期1342-1347,共6页
By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by me... By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by means of definite integral transformation into a group of singular equations. Closed form of its solution was obtained and three corresponding problems of isotropic bimaterial, of a single anisotropic material and of a bimaterial of isotropy- anisotropy were treated as the specific cases. The plastic zone length of the crack tip and crack openning displacement ( COD) decline as the smaller yield limit of the two bonded materials rises, and they were also determined by crack length and the space between two neighboring cracks . In addition , COD also relates it with moduli of the materials . 展开更多
关键词 periodical crack interfacial crack anisotropic elastoplastic fracture of bi-rnaterial antiplane problem Dugdale-Barenblatt (D-B ) model crack openning displacement (COD)
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STRESS ANALYSIS FOR AN INFINITE STRIP WEAKNED BY PERIODIC CRACKS
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作者 陈宜周 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第11期1298-1303,共6页
Stress analysis for an infinite strip weakened by periodic cracks is studied. The cracks were assumed in a horizontal position, and the strip was applied by tension “ p ' in y_ direction. The boundary value... Stress analysis for an infinite strip weakened by periodic cracks is studied. The cracks were assumed in a horizontal position, and the strip was applied by tension “ p ' in y_ direction. The boundary value problem can be reduced into a complex mixed one. It is found that the EEVM ( eigenfunction expansion variational method) is efficient to solve the problem. The stress intensity factor at the crack tip and the T _stress were evaluated. From the deformation response under tension the cracked strip can be equivalent to an orthotropic strip without cracks. The elastic properties in the equivalent orthotropic strip were also investigated. Finally, numerical examples and results were given. 展开更多
关键词 eigenfunction expansion variational method periodic crack stress intensity factor T- stress
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Fracture of films caused by uniaxial tensions:a numerical model 被引量:1
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作者 Chenxue JIA Zihao WANG +2 位作者 Donghui ZHANG Taihua ZHANG Xianhong MENG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第12期2093-2108,共16页
Surface cracks are commonly observed in coatings and films.When structures with coatings are subject to stretching,opening mode cracks are likely to form on the surface,which may further lead to other forms of damage,... Surface cracks are commonly observed in coatings and films.When structures with coatings are subject to stretching,opening mode cracks are likely to form on the surface,which may further lead to other forms of damage,such as interfacial delamination and substrate damage.Possible crack forms include cracks extending towards the interface and channeling across the film.In this paper,a two-dimensional numerical model is proposed to obtain the structural strain energy at arbitrary crack lengths for bilayer structures under uniaxial tension.The energy release rate and structural stress intensity factors can be obtained accordingly,and the effects of geometry and material features on fracture characteristics are investigated,with most crack patterns being confirmed as unstable.The proposed model can also facilitate the analysis of the stress distribution in periodic crack patterns of films.The results from the numerical model are compared with those obtained by the finite element method(FEM),and the accuracy of the theoretical results is demonstrated. 展开更多
关键词 surface crack numerical model stress intensity factor periodic crack finite element method(FEM)
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Very-High-Cycle-Fatigue of in-service air-engine blades,compressor and turbine 被引量:4
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作者 SHANYAVSKIY A A 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2014年第1期19-29,共11页
In-service Very-High-Cycle-Fatigue(VHCF)regime of compressor vane and turbine rotor blades of the Al-based alloy VD-17and superalloy GS6K,respectively,was considered.Surface crack origination occurred at the lifetime ... In-service Very-High-Cycle-Fatigue(VHCF)regime of compressor vane and turbine rotor blades of the Al-based alloy VD-17and superalloy GS6K,respectively,was considered.Surface crack origination occurred at the lifetime more than 1500 hours for vanes and after 550 hours for turbine blades.Performed fractographic investigations have shown that subsurface crack origination in vanes took place inspite of corrosion pittings on the blade surface.This material behavior reflected lifetime limit that was reached by the criterion VHCF.In superalloy GS6K subsurface fatigue cracking took place with the appearance of flat facet.This phenomenon was discussed and compared with specimens cracking of the same superalloy but prepared by the powder technology.In turbine blades VHCF regime appeared because of resonance of blades under the influenced gas stream.Both cases of compressor-vanes and turbine blades in-service cracking were discussed with crack growth period and stress equivalent estimations.Recommendations to continue aircrafts airworthiness were made for in-service blades. 展开更多
关键词 SUBSURFACE fatigue crack Al-alloy SUPERALLOY RESONANCE quantitative fractography crack growth period stress level
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