Sensitivity of predicted stresses in thick-walled steel/ceramics spherical FGM-structures to parameter uncertainties

Abstract

The reliability of strength-predictions for devices of functionally graded materials (FGMs) depends both on appropriate homogenization schemes and the accuracy of the basic material data. Whereas there exist many studies on proper homogenization techniques for various FGMs, the question for the required precision of the material data has been addressed to a significantly lesser extent; almost all of the few available studies on this issue focus on the statics and dynamics of beams and (thin-walled) FGM-plates and FGM-shells. Indeed, the values of the material parameters of FGM-constituents given in even quite recent publications may vary – depending on the specific material considered – noticeably. Moreover, caused by the manufacturing process, the actual volume fractions of the constituents will deviate to some extent from the designed ones. Hence, it is the aim of the present investigation to study the influence of parameter uncertainties on the forecasted behavior of thick-walled hollow spherical FGM-structures under both internal pressure and homogeneous heating, taking also uncertainties caused by the manufacturing process into account. Of course, the maximum stresses to be expected are the most critical ones from an engineering point of view. Since statistical information about the scattering of the relevant data is hardly obtainable in practice, the study is based on maximum intervals of published parameter values. Specifically, numerical results are given for a spherical pressure vessel of steel/ceramics FGM. Power-law grading is presupposed, and both Voigt and Reuss rule – representing the extremum cases - for Young’s modulus are considered; Poisson’s ratio and the coefficient of thermal expansion are presumed to follow the rule of mixtures. The main findings are as follows. First, both the forecasted maximum and minimum stresses always are related with the bounds of all the individual parameter intervals. Second, scattering ranges of the material data may cause much larger expectation ranges for the maximum stresses (in percentages). Third, the influence of manufacturing uncertainties is less pronounced than that of – particularly – uncertain Young’s moduli and coefficients of thermal expansion. Fourth, consideration of the scattering of the stress distributions due to material data uncertainties may noticeably predominate over the question for the most appropriate homogenization scheme(s); hence, application of sophisticated and computationally expensive homogenization procedures seems meaningful only if the material data are available with quite high accuracy.