A General Strength Theory for Composite Materials Based on Dual Kriging Interpolation

Abstract

Failure behaviour of composite materials presents several characteristics which depend on the materials selected, the manufacturing process used and the state of stress or strain. An important number of strength criteria have been applied to model failure in the last two decades. Each criterion is different and can be used to fit particular experimental results. Up to now, there is no general and systematic approach to describe the failure of composite materials. In this study, a general strength theory based on dual kriging is proposed to model the failure behaviour of composite materials. The theoretical background of the method is first presented, then its application to model failure of composite materials is demonstrated on two examples: a graphite-epoxy composite and paperboard. The mathematical expression of the criterion can be obtained either through a parametric or an implicit formulation. The parametric formulation is used to predict three-dimensional failure envelopes of graphite-epoxy fabrics and paperboard. The method shows an excellent agreement with available experimental data. Different types of interpolating functions, can be used such as polynomials or trigonometric functions. The results obtained are compared with the tensor quadratic, tensor cubic and parametric criteria. The model can be improved when a nugget effect is added in the kriging equations: the interpolating function does no longer fit the data points. This approach permits incorporating the effect of measurements errors in the interpolation procedure. The intensity of the nugget effect is usually chosen to be proportional to the variance error. The uncertainty of the measurements is thus reflected on the shape of the failure envelope. Note that general tensor polynomial criteria can be derived as a limit case of this approach, and additional experimental data incorporated in the model to refine its accuracy. The proposed methodology can be used as a general and systematic tool to model effectively a great variety of failure behaviours.