A numerical investigation of the statistical size effect in non-crimp fabric laminates under homogeneous compressive loads

The compressive strength of fiber reinforced composites is typically limited by a shear localization phenomenon known as microbuckling and is very sensitive to local imperfections of fiber alignment. Local misalignments act as randomly distributed flaws and introduce a dependence of the compressive strength on the size of material volume element under consideration. For homogeneously loaded material elements, weakest-link theory in combination with a Weibull power law is a frequently employed statistical model for microbuckling strength. This implies a dependence of strength on the size of volume under consideration. The present contribution investigates the strength-size relation for a non-crimp fabric via a numerical approach. Characteristics of the misalignment flaws used in simulations are derived from a comprehensive data set collected via large-scale measurements of roving dislocations on dry fiber material. Predictions resulting from the weakest-link Weibull theory are compared against strength-size statistics gathered by numerical analysis. In this manner, the size effects in single plies and laminates are quantified. The main findings are that weakest-link Weibull theory is well suited to predict size related strength loss in individual plies. However, it is also found that when plies are bonded to form laminates, misalignments in individual plies are mitigated in a way that is inconsistent with the weakest-link assumption. In all situations considered here, the strength loss expected from weakest-link Weibull theory was outweighed by a strength increase due to the mitigation effect when the volume was increased by adding extra layers to a laminate.

Automated summary

The compressive strength of fiber reinforced composites is often limited by microbuckling, which is influenced by local misalignments and flaws in the material. Weakest-link Weibull theory is commonly used to predict strength loss in individual plies, but misalignments in laminates may be mitigated in a way that contradicts weakest-link assumptions. Additionally, adding extra layers to a laminate can result in a strength increase that outweighs the strength loss predicted by Weakest-link Weibull theory.