##
**A novel analytical model and energy analysis of thermal stresses in two-phase composites.**
*(English)*
Zbl 1284.74025

Summary: This paper deals with analytical modelling of thermal stresses in a multi-particle-matrix system with isotropic spherical particles. These particles are periodically distributed in an isotropic infinite matrix. This model system which is characterized by microstructural parameters (particle volume fraction, particle radius) is applicable to two-phase composites of a precipitate-matrix type with isotropic phases. The thermal stresses originate during a cooling process due to a difference in thermal expansion coefficients. The analytical modelling which is based on fundamental equations of solid continuum mechanics represents a combination of different mathematical procedures applied to equilibrium and compatibility equations. This novel analytical model is compared with that which is based on mathematical procedures applied to the equilibrium equations only. The energy analysis of both analytical models which is applied to the SiC-\(\mathrm{Al}_{2}\mathrm{O}_{3}\) composite is presented.

Full Text:
DOI

### References:

[1] | Fanelli M (1986) Thermal stresses in plane elasticity: numerical solutions based only on harmonic functions. Meccanica 21:210–215 · Zbl 0612.73008 |

[2] | Martínez F, Quintanilla R (1998) On the incremental problem in thermoelasticity with microstructure. Meccanica 33:601–604 · Zbl 0941.74017 |

[3] | Suvorov AP, Dvorak GJ (2001) Optimal design of prestressed laminate/ceramic plate assemblies. Meccanica 36:87–109 · Zbl 1005.74052 |

[4] | Ieşan D, Nappa L (2004) Thermal stresses in plane strain of porous elastic solids. Meccanica 39:125–138 · Zbl 1075.74034 |

[5] | Drozdov AD, Dorfmann A (2004) A constitutive model in finite viscoelasticity of particle-reinforced rubbers. Meccanica 39:245–270 · Zbl 1089.74016 |

[6] | Vena P (2005) Thermal residual stresses in graded ceramic composites: a microscopic computational model versus homogenized models. Meccanica 40:163–179 · Zbl 1098.74014 |

[7] | Kulchytsky-Zhyhailo R, Matysiak JS, Perkowski DM (2007) On displacements and stresses in a semi-infinite laminated layer: comparative results. Meccanica 42:117–126 · Zbl 1162.74342 |

[8] | Meijer G, Ellyin F, Xia Z (2000) Aspects of residual thermal stress/strain in particle reinforced metal matrix composites. Composites: Part B 31:29–37 |

[9] | Ceniga L (2008) A new analytical model for thermal stresses in multi-phase materials and lifetime prediction methods. Acta Mech Sin 24:189–206 · Zbl 1257.74044 |

[10] | Ceniga L (2008) Thermal stresses in model materials. J Therm Stresses 31:728–758 · Zbl 1257.74044 |

[11] | Ceniga L (2010) Analytical model of thermal stresses in two- and three-component materials. Int J Eng Sci 48:290–311 · Zbl 1213.80007 |

[12] | Ceniga L (2007) Thermal stresses in isotropic multi-particle-envelope-matrix system. Application to SiC-YbN20-Si3N4 ceramics. In: Caruta BM (ed) New developments in material science research, 1st edn. Nova Science Publishers, New York, pp 139–180 |

[13] | Ceniga L (2010, in press) New analytical model of thermal stresses and analytical fracture mechanics in two-component materials. Application to two-component ceramics. In: Dimitriou E, Petralia M (eds) Ceramic Matrix Composites. Nova Science Publishers, New York, · Zbl 1231.80004 |

[14] | Ceniga L (2008) Analytical models of thermal stresses in composite materials I. Nova Science Publishers, New York · Zbl 1257.74044 |

[15] | Ceniga L (2007) Analytical models of thermal stresses in composite materials II. Nova Science Publishers, New York |

[16] | Mizutani T (1996) Residual strain energy in composites containing particles. J Mater Sci 11:483–494 |

[17] | Li S, Sauer RA, Wang G (2007) The Eshelby tensors in a finite spherical domain–part I: Theoretical formulations. J Appl Mech 74:770–783 |

[18] | Li S, Sauer RA, Wang G (2007) The Eshelby tensors in a finite spherical domain–part II: Applications to homogenization. J Appl Mech 74:784–797 |

[19] | Kushch VI (1985) Elastic equilibrium of a medium with periodically arranged spherical inclusions. Prikl Mekh 21:18–27 |

[20] | Kushch VI (2004) Stress concentration at an interacting spherical inclusions in a transversely isotropic body. Int Appl Mech 40:893–899 · Zbl 1128.74014 |

[21] | Kushch VI (2004) Effective elastic moduli of periodic granular composite with transversely isotropic phases. Int Appl Mech 40:1042–1049 · Zbl 1122.74328 |

[22] | Wu Y, Dong Z (1995) Three-dimensional finite element analysis of composites with coated spherical inclusions. Mater Sci Eng A 203:314–323 |

[23] | Sangani AS, Mo G (1997) Elastic interactions in particulate composites with perfect as well as imperfect interfaces. J Mech Phys Solids 45:2001–2031 · Zbl 0977.74513 |

[24] | Brdička M, Samek L, Sopko B (2000) Mechanics of continuum. Academia, Prague |

[25] | Skočovský P, Bokuvka O, Palček P (1996) Materials science. EDIS, Žilina |

[26] | Rektorys K (1973) Review of applied mathematics. SNTL, Prague · Zbl 0324.65049 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.