A new analytical model for thermal stresses in multi-phase materials and lifetime prediction methods

Abstract

Based on the fundamental equations of the mechanics of solid continuum, the paper employs an analytical model for determination of elastic thermal stresses in isotropic continuum represented by periodically distributed spherical particles with different distributions in an infinite matrix, imaginarily divided into identical cells with dimensions equal to inter-particle distances, containing a central spherical particle with or without a spherical envelope on the particle surface. Consequently, the multi-particle-(envelope)-matrix system, as a model system regarding the analytical modelling, is applicable to four types of multi-phase materials. As functions of the particle volume fraction v, the inter-particle distances d ₁, d ₂, d ₃ along three mutually perpendicular axes, and the particle and envelope radii, R ₁ and R ₂, respectively, the thermal stresses within the cell, are originated during a cooling process as a consequence of the difference in thermal expansion coefficients of phases represented by the matrix, envelope and particle. Analytical-(experimental)-computational lifetime prediction methods for multi-phase materials are proposed, which can be used in engineering with appropriate values of parameters of real multi-phase materials.