Elastic field in composite cylinders made of functionally graded coatings

In this paper, the elastic field is studied in a composite cylinder made of heterogeneous coatings. The coating layers are such that the mechanical properties of the entire composite structure change across the radius. Thus, both Young’s modulus and Poisson’s ratio vary continuously in coatings across the radius. The effect of varying Young’s modulus has been shown to be significant on the elastic field in these types of composites. Herein, it is shown that varying Poisson’s ratio also plays an important role in the stress and strain distribution and should be considered in the design process especially in carbon coated titanium cylinders, where Poisson’s ratio changes between zero and a half in the structure. In addition, variation of Poisson’s ratio across the radius not only changes the elastic field, but also different spatial variations of Poisson’s ratio lead to distinct hoop stresses and radial displacements for a coated cylinder. The effects of Poisson’s ratio variation on the elastic field in thick composite cylinders are also studied. Two closed form expressions are derived for the normalized hoop stresses at the inner and outer surfaces of thick-walled coated cylinders. It is found that the effect of varying Poisson’s ratio on the normalized hoop stress in thick-walled coated cylinders is also important and the maximum hoop stress changes dramatically for thicker cylinders.