Thermal residual stresses in adhesively bonded in-plane functionally graded clamped circular hollow plates

Abstract

This study investigates the effects of in-plane compositional gradient exponent and direction on the thermal residual stress and deformations in adhesively bonded functionally graded clamped circular plates. The material composition was assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations in polar coordinates describing the two-dimensional thermo-elastic problem were discretized using finite-difference method, and the set of linear equations were solved using the pseudo-singular-value method. The material composition direction is designed as Ceramic-Metal (CM)–CM, CM–Metal-Ceramic (MC), MC–CM, and MC–MC for the inner and outer plates. The temperature decreased radially along the plates, but exhibited a sharp decrease across the adhesive layer. The compositional gradient exponent and direction affected evidently temperature levels and heat transfer period. The compressive radial and shear strains are more effective on the deformation in the adhesive layer and the plate regions near the plate–adhesive interfaces. The adhesive layer is subjected to considerable shear deformations. The equivalent strain and stresses are very low in a large region of the plates but exhibit sharp peaks on the plate regions near the plate–adhesive interfaces, and decrease towards the adhesive interfaces. These stress and strain peaks in the plates and adhesive layer are affected by the compositional gradient and direction. For an outer edge flux, the largest equivalent strain and stresses are observed in the CM–MC joint but the lowest levels occur in the MC–CM or secondly CM–CM joint. In addition, an inner edge flux results in the lowest and highest peak strains and stresses in the MC–CM and CM–MC joints, respectively. The MC–MC and CM–CM joints result in lower temperature, stress and strain levels around the adhesive layer and along the adhesive interfaces for outer and inner edge fluxes, respectively.