A theoretical analysis of interface debonding for coated sphere with functionally graded interphase

We present a novel nonlinear cohesive law for coated sphere with functionally graded interphase (FGI). It is derived from the van der Waals interaction accounting for the interface debonding of the coated sphere subjected to radial tensile loading. The present analytical results show that: (1) Higher values of the interphase radius r_b lead to a higher interface strength and a higher debonding strain; (2) a higher Young's modulus E_f and the Poisson's ratio v_f of the sphere lead to a lower interface strength and a smaller debonding strain; (3) large values of the index n and the inner Young's modulus E_a of FGI as well as the Poisson's ratio v_m of the entire coat improve the interface strength and reduce the debonding strain; (4) the sphere radius r_a and the outer coat radius r_c can not only improve but also reduce the interface strength and the debonding strain, respectively. The established analytical solutions should be of great help for understanding the mechanical properties of the coated sphere and sphere-reinforced composites, designing microcomposites and microelectromechanical systems.