Interval-Based Computation of the Uncertainty in the Mechanical Properties and the Failure Analysis of Unidirectional Composite Materials

Abstract

An interval-based method is presented to evaluate the uncertainty in the computed mechanical properties and the failure assessment of composite unidirectional (UD) laminates. The method was applied to two composite laminates: a carbon/epoxy and a glass/epoxy. The mechanical properties of the UD lamina were derived using simplified micromechanical equations. An uncertainty level of ±5% was assumed for the input properties of the constituents. The global minimum and maximum values of the properties were computed using an interval branch-and-bound algorithm. Interval arithmetic operations were used to evaluate the uncertainty in the Hashin-type failure criteria in a closed form. Using the closed-form uncertainties of intervals and sets of stresses obtained by finite element analysis, the uncertainty in the failure assessment was quantified for the two composite laminates. For the assumed uncertainty level of ±5%, the computed uncertainty for the mechanical properties ranges from 6.64% to 10.63% for the carbon/epoxy material and from 6.72% to 12.28% for the glass/epoxy material. For evaluating the uncertainty effect on the efficiency of failure criteria, a probability of failure function, which employs interval boundaries, was defined and proved capable of evaluating the whole spectrum of stresses.