Predicting failure in textile composites using the Binary Model with gauge-averaging

First introduced over a decade ago, the Binary Model has evolved into a computationally efficient tool for predicting the properties of textile composites. Key to the formulation is the question of what details of the textile composite and the distributions of stress, strain, temperature, etc., are necessary and sufficient to represent the physics of the problem adequately and to ensure useful engineering predictions. This paper is concerned specifically with the prediction of the ultimate strength in cases where failure follows a single substantial local damage event, such as the rupture or kinking of a tow or the creation of a shear band mediated by matrix damage, without further increase in the external load. The accuracy of predictions is assessed for some triaxially braided carbon/epoxy composites. A gauge length is introduced that is suggested by the micromechanics of the failure mechanisms. Predictions are made by reference to strains that are averaged over a volume whose sides are commensurate with this gauge, but nevertheless retain spatial variations associated with the textile architecture. Failure criteria for tow rupture and matrix shear failure are taken from a single un-notched tensile test; the calibrated model then successfully predicts the failure mechanism (matrix shear or fiber rupture) and ultimate strength in un-notched and open-hole tension tests for any orientation of the textile fabric relative to the load axis, as well as bending and simple shear tests. The successful predictions are made using strains calculated for an entirely elastic representation of the material, which is possible because of the brittle character of the stress–strain curves. Predictions are also attempted using strains computed under the assumption that the textile material is homogeneous. These predictions are significantly inferior.