Field intensity factors around inclusion corners in 0–3 and 1–3 composites subjected to thermo-mechanical loads

详细信息    查看全文

• 作者：Xuecheng Ping ; Mengcheng Chen ; Yihua Xiao…
• 关键词：Composites ; Inclusion ; Thermo ; mechanical load ; Singular stress ; Numerical eigensolution
• 刊名：International Journal of Mechanics and Materials in Design
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：12
• 期：1
• 页码：121-139
• 全文大小：1,117 KB
• 参考文献：Barut, A., Guven, I., Madenci, E.: Analysis of singular stress fields at junctions of multiple dissimilar materials under mechanical and thermal loading. Int. J. Solids Struct. 38, 9077–9109 (2001)CrossRef MATH
  Budiansky, B.: On the elastic moduli of some heterogeneous materials. J. Mech. Phys. Solids 13, 223 (1965)CrossRef
  Buryachenko, V.A.: Micromechanics of Heterogeneous Materials. Springer, New York (2007)CrossRef MATH
  Buryachenko, V.A., Bechel, V.T.: A series solution of the volume integral equation for multiple inclusion interaction problems. Compos. Sci. Technol. 60, 2465–2469 (2000)CrossRef
  Chen, D.H.: Analysis of singular stress field around the inclusion corner tip. Eng. Fract. Mech. 49, 533–546 (1994)CrossRef
  Chen, D.H., Nisitani, H.: Singular stress fields near the corner of the corner of jointed dissimilar materials. J. Appl. Mech. 60, 607–613 (1993a)CrossRef MATH
  Chen, D.H., Nisitani, H.: Singular stress field in jointed materials due to thermal residual stress. Trans. JSME Ser. A 59, 1937–1941 (1993b)CrossRef
  Chen, M.C., Ping, X.C.: A novel hybrid finite element analysis of inplane singular elastic field around inclusion corner-tips in elastic media. Int. J. Solids Struct. 46, 2527–2538 (2009a)CrossRef MATH
  Chen, M.C., Ping, X.C.: Analysis of the interaction within a rectangular array of rectangular inclusions using a new hybrid finite element method. Eng. Fract. Mech. 76, 580–593 (2009b)CrossRef
  Chen, M.C., Ping, X.C.: Analysis of singular thermal stress fields around corner tips of inclusions. Chin. J. Solids Mech. 32, 314–318 (2011)
  Chen, M.C., Sze, K.Y.: A novel hybrid finite element analysis of bimaterial wedge problems. Eng. Fract. Mech. 68, 1463–1476 (2001)CrossRef
  Dong, C.Y., Cheung, Y.K., Lo, S.H.: A regularized domain integral formulation for inclusion problems of various shapes by equivalent inclusion method. Comput. Methods Appl. Mech. Eng. 191, 3411–3421 (2002)CrossRef MATH
  Dong, C.Y., Lo, S.H., Cheung, Y.K.: Stress analysis of inclusion problems of various shapes in an infinite anisotropic elastic medium. Comput. Methods Appl. Mech. Eng. 192, 683–696 (2003)CrossRef MATH
  Dong, C.Y., Zhang, G.L.: Boundary element analysis of three dimensional nanoscale inhomogeneities. Int. J. Solids Struct. 50, 201–208 (2013)CrossRef
  Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. R. Soc. Lond. A 241, 376–396 (1957)CrossRef MathSciNet MATH
  Ghosh, S., Mukhopadhyay, S.N.: A material based finite element analysis of heterogeneous media involving Dirichlet tessellations. Comput. Methods Appl. Mech. Eng. 104, 211–247 (1993)CrossRef MATH
  Gong, S.X., Meguid, S.A.: Interacting circular inhomogeneities in plane elastostatics. Acta Mech. 99, 49–60 (1993a)CrossRef MATH
  Gong, S.X., Meguid, S.A.: On the elastic fields of an elliptical inhomogeneity under plane deformation. Proc. R. Soc. Lond. A 443, 457–471 (1993b)CrossRef MATH
  Hill, J.R.: A self consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213–222 (1965)CrossRef
  Kattis, M.A., Meguid, S.A.: On the partly bonded thermoelastic circular inhomogeneity. J. Appl. Mech. 62, 535–537 (1995)CrossRef MathSciNet MATH
  Kröner, E.: Berechnung der elastischen Kongstanten des Vielkristalls aus den Kongstanten des Einkristalls. Z. Phys. 151, 504–518 (1958)CrossRef
  Kushch, V.I., Shmegera, S.V., Buryachenko, V.A.: Interacting elliptic inclusions by the method of complex potentials. Int. J. Solids Struct. 42, 5491–5512 (2005)CrossRef MATH
  Lee, J., Choi, S., Mal, A.: Stress analysis of an unbounded elastic solid with orthotropic inclusions and voids using a new integral equation technique. Int. J. Solids Struct. 38, 2789–2802 (2001)CrossRef MATH
  Luo, J.C., Gao, C.F.: Stress field of a coated arbitrary shape inclusion. Meccanica 46, 1055–1071 (2011)CrossRef MathSciNet MATH
  Madenci, E., Shkarayev, S., Sergeev, B.: Thermo-mechanical stresses for a triple junction of dissimilar materials: global–local finite element analysis. Theor. Appl. Fract. Mech. 30, 103–117 (1998)CrossRef
  Meguid, S.A., Hu, G.D.: A new finite element for treating plane thermomechanical heterogeneous solids. Int. J. Numer. Methods Eng. 44, 567–585 (1999)CrossRef MathSciNet MATH
  Meguid, S.A., Zhu, Z.H.: A new finite element for treating inhomogenous solids. Int. J. Numer. Methods Eng. 38, 1579–1592 (1995a)CrossRef MATH
  Meguid, S.A., Zhu, Z.H.: Stress distribution in dissimilar materials containing inhomogeneities near the interface using a novel finite element. Finite Elem. Anal. Des. 20, 283–298 (1995b)CrossRef MATH
  Mori, T., Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metal. 21, 571–574 (1973)CrossRef
  Munz, D., Yang, Y.Y.: Stress singularities at the interface in bonded dissimilar materials under mechanical and thermal loads. J. Appl. Mech. 59, 857–881 (1992)CrossRef
  Mura, T.: Micromechanics of Defects in Solids. Martinus Nijhoff Publishers, Dordrecht (1987)CrossRef
  Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. P. Noordhoff, Groningen (1953)MATH
  Nakamura, T., Suresh, S.: Effects of thermal residual stresses and fiber packing on deformation of metal-matrix composites. Acta Metal. Mater. 41, 1665–1681 (1993)CrossRef
  Nakasone, Y., Nishiyama, H., Nojiri, T.: Numerical equivalent inclusion method: a new computational method for analyzing stress fields in and around inclusions of various shapes. Mater. Sci. Eng. A 285, 229–238 (2000)CrossRef
  Nemat-Nasser, S., Muneo, H.: Micromechanics: Overall Properties of Heterogeneous Materials. Elsevier, Amsterdam (1999)
  Noda, N.A., Hayashida, H., Tomari, K.: Interaction among a row of ellipsoidal inclusions. Int. J. Fract. 102, 371–392 (2000a)CrossRef
  Noda, N.A., Takase, Y.: Intensity of singular stress at the fiber end in a hexagonal array of fibers. Int. J. Solids Struct. 42, 4890–4908 (2005)CrossRef MATH
  Noda, N.A., Takase, Y., Chen, M.C.: Generalized stress intensity factors in the interaction between two fibers in matrix. Int. J. Fract. 103, 19–39 (2000b)CrossRef
  Noda, N.A., Takase, Y., Hamashima, T.: Generalized stress intensity factors in the interaction within a rectangular array of rectangular inclusions. Arch. Appl. Mech. 73, 311–322 (2003)CrossRef MATH
  Noda, N.A., Shirao, R., Li, J., Sugimoto, J.S.: Intensity of singular stress fields causing interfacial debonding at the end of a fiber under pullout force and transverse tension. Int. J. Solids Struct. 44, 4472–4491 (2007)CrossRef MATH
  Singh, I.V., Mishra, B.K., Bhattacharya, S.: XFEM simulation of cracks, holes and inclusions in functionally graded materials. Int. J. Mech. Mater. Des. 7, 199–218 (2011)CrossRef
  Sze, K.Y., Wang, H.T.: A simple finite element formulation for computing stress singularities at bimaterial interfaces. Finite Elem. Anal. Des. 35, 97–118 (2000)CrossRef MATH
  Thomson, R.D., Hancock, J.W.: Local stress and strain fields near a spherical elastic inclusion in a physically deforming matrix. Int. J. Fract. 24, 209–228 (1984)CrossRef
  Tian, L., Rajapakse, R.K.N.D.: Elastic field of an isotropic matrix with a nanoscale elliptical inhomogeneity. Int. J. Solids Struct. 44, 7988–8005 (2007)CrossRef MATH
  Tiwary, A., Hu, C., Ghosh, S.: Numerical conformal mapping method based Voronoi cell finite element model for analyzing microstructures with irregular heterogeneities. Finite Elem. Anal. Des. 43, 504–520 (2007)CrossRef MathSciNet
  Tsukrov, I., Novak, J.: Effective elastic properties of solids with defects of irregular shapes. Int. J. Solids Struct. 391, 1539–1555 (2002)CrossRef
  Williams, M.L.: Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 19, 526–528 (1952)
  Xu, L.M., Fan, H., Sze, K.Y., Li, C.: Elastic property prediction by finite element analysis with random distribution of materials for heterogeneous solids. Int. J. Mech. Mater. Des. 3, 319–327 (2006)CrossRef
  Zou, W.N., He, Q.C., Huang, M.J., Zheng, Q.S.: Eshelby’s problem of non-elliptical inclusions. J. Mech. Phys. Solids 58, 346–372 (2010)CrossRef MathSciNet MATH
  
• 作者单位：Xuecheng Ping (1)
  Mengcheng Chen (2)
  Yihua Xiao (1)
  Qing Wang (1)
  
  1. School of Mechanical and Electronical Engineering, East China Jiaotong University, Nanchang, 330013, Jiangxi, China
  2. School of Civil Engineering, East China Jiaotong University, Nanchang, 330013, Jiangxi, China
  
• 刊物类别：Engineering
• 刊物主题：Mechanical Engineering
  Engineering Design
  Continuum Mechanics and Mechanics of Materials
  Materials Science
  
• 出版者：Springer Netherlands
• ISSN：1573-8841

文摘

A super inclusion corner apex element for polygonal inclusions in 0–3 and 1–3 composites is developed by using numerical stress and displacement field solutions based on an ad hoc finite element eigenanalysis method. Singular stresses near the apex of inclusion corner under thermo-mechanical loads can be obtained by using a super inclusion corner apex element in conjunction with hybrid-stress elements. The validity and the applicability of this technique are established by comparing the present numerical results with the existing solutions and the conventional finite element solutions. As examples of applications, a square array of square inclusions in 0–3 composites and a rectangular array of rectangular inclusions in 1–3 composites are considered. All numerical examples show that the present numerical method yields satisfactory solutions with fewer elements and is applicable to complex problems such as multiple singular points or fields in composite materials. Keywords Composites Inclusion Thermo-mechanical load Singular stress Numerical eigensolution