A Statistical Mesoscale Approach to Model the Size Effect on the Tensile Strength of Notched Woven Composites

The scaling of the strength of composite parts with part size is referred to as the size effect. In the presence of notches, stress concentration affects a portion of material that increases with the notch size. Furthermore, in woven composites, the notch and tow size can be comparable, thus demanding a mesoscale approach to properly capture the stress intensification. In this paper, a probabilistic mesoscale method to model the size effect in notched woven composites is presented. First, the stress distribution is estimated with a finite element model, calibrated on experimental Digital Image Correlation data. The FE model simulates the mesoscale heterogeneity of the woven reinforced material and replicates the local stress intensification at the tow level. Then, a three-parameter Weibull-based statistical model is introduced to model the probability of failure from the calculated stress distribution and the volume of the part. An equivalent stress is used to capture the relevant fiber and matrix failure modes and the maximum value within the specimen volume is the random variable of the model. The method is applied to open-hole tension tests of a woven twill carbon fiber-epoxy composite. Two specimen widths and three width-to-diameter ratios, from 3 to 12, are considered. Specimen width produced an observable size effect, whereas the variation of hole size in the range considered did not. The statistical model is found to accurately describe the experimental observations, efficiently replicating an inverse size effect, regardless of hole size, while wider specimens lead to a lower probability of failure.