Bayesian estimation of single ply anisotropic elastic constants from spherical indentations on multi-laminate polymer-matrix fiber-reinforced composite samples

In this paper, the application of a recently formulated two-step Bayesian framework to the estimation of effective anisotropic elastic constants of single plies within a multi-laminate polymer matrix composite is demonstrated, while using previously reported spherical indentation measurements within singular plies. Experimental spherical indentation measurements within the epoxy/fiber plies are inherently noisy due to local variation of the fiber volume fraction underneath the indenter. This paper demonstrates that the usage of a two-step Bayesian framework enables the extraction of reliable point estimates (and associated distributions) for the effective elastic constants from indentation modulus measurements conducted within single plies at different angles to the fiber orientations. The first step of the two-step Bayesian framework establishes the effective elastic indentation modulus of a single ply as a function of its intrinsic elastic stiffness parameters and the angle between the indentation direction and the fiber orientation using a database of suitable finite element simulations. The second step involves the calibration of the indentation measurements from a given set of multi-laminate samples to the reduced-order model established in the first step. The second step is accomplished by sampling the posterior distribution of the single ply elastic parameters via Monte Carlo Markov Chain methods. This new framework is demonstrated in this study for an IM7/977-3 carbon fiber/epoxy multi-laminate sample.