The effects of cladding layers of rate-sensitive materials on the ductility and fracture strain of compressed rings are numerically investigated by using the finite element method (FEM) and employing the Johnson–Cook (J–C) model. The results show that ductility is governed by the behavior of the material that is located at the ring outer wall regardless of the volume fraction of the core and clad materials. However, as the number of layers increases, this influence becomes less noticeable. Moreover, as barreling increases at the outer wall and decreases at the inner wall, fracture strain increases. Furthermore, the effects of ring shape factor and bonding type of clad and core materials are numerically evaluated. The numerical results show that less force per unit volume is required to fracture narrower rings and that using a noise diffusion pattern at the interface of the materials is more suitable to simulate crack propagation in the compressed rings and functionally graded materials (FGMs). Additionally, delamination has a direct relation to layer thickness and can occur even in the presence of perfect bonding conditions owing to differences among the material and fracture parameters of laminated layers.