Size effects in plain-weave Astroquartz® deployable thin shells

The general scaling trend for brittle materials, in which the strength increases when the sample size decreases, is reversed in plain-weave laminates of Astroquartz (R) and cyanate ester resin. Specifically, both the shear stiffness and the compressive strength decrease for test samples with widths smaller than 15 times the wavelength of the fabric, and observations at the microscale explain this behavior. The derived scaling is applied to the analysis of a deployable thin shell forming a 90 circle corner hinge with five cutouts on each side. The cutouts leave narrow strips of material with width as small as one fabric wavelength, forming structural ligaments whose strength and stiffness are subject to strong size-scaling effects. A numerical simulation of the folding process followed by a failure analysis is presented, using two alternative material models and failure criteria. The size independent model predicts that the structure will remain damage-free after it is folded and deployed, whereas the size-scaled model predicts that failure will occur. The correctness of the size-scaled model prediction is verified by measuring localized damage in a physical prototype, using x-ray CT scans.