Effect of graded interphase on the coefficient of thermal expansion for composites with spherical inclusions

The paper is concerned with the quantitative characterisation of the effective coefficient of thermal expansion for a particulate composite containing spherical inclusions surrounded by an interphase zone, whose properties are graded in the radial direction. A thermo-elastic problem of uniform heating is studied for a single hollow spherical inclusion embedded in a finite matrix assuming power-law variation of the thermo-elastic properties. An exact solution of the problem is derived using hypergeometric functions. The effective coefficient of thermal expansion is determined in closed form for composites with graded interphase zone around hollow and solid inclusions, as well as for the case of void in a graded matrix. Numerical results highlighting the effect of the interphase properties on the coefficient of thermal expansion for different volume fractions of inclusions are presented and discussed.