Elasto-plastic solution for thick-walled spherical vessels with an inner FGM layer

Purely elastic, partially and fully plastic stress states in a thick-walled spherical pressure vessel with an inner functionally graded material (FG) coating subjected to internal and external pressures are developed analytically in this paper. The modulus of elasticity and the uniaxial yield limit of the FG coating layer are considered to vary nonlinearly through the thickness. Using Tresca’s yield criterion and ideal plastic material behavior, the plastic model is established. Under pressure loading, the scenario in which the plastic deformation starts from inner surface of FG coating layer is taken into account. Having increased the pressure loading, it is assumed that the FG coating layer becomes fully plastic and the yielding commences subsequently at the inner surface of homogenous part. Essentially, the variation of FG parameters in the radial direction is properly adjusted in order to achieve the stated yielding scenario. Furthermore, axisymmetric finite element model is performed to validate the accuracy of the analytical results. It is concluded that the elastic and plastic response of the spherical pressure vessel are influenced by grading parameters and coating behavior.