The only engineering materials with both high strength and toughness, and with densities less than 1000 kg m-3 , are natural materials (woods) and some plastics. Cellular structures such as the octet lattice, when made from periodic arrangements of strong, low-density metallic trusses, are known to have high specific strengths and elastic moduli. However, much less is known of their resistance to fracture. Here we investigate the fracture toughness of a Ti-6Al-4V alloy octet-lattice truss structure manufactured using a 'snap-fit' method. The samples had densities between 360 and 855 kg m-3 (relative densities of 8-19%) and free truss lengths between 4 and 15 mm. Their fracture resistance was determined using the J-integral compliance method applied to single-edge notched bend specimens. The toughness is shown to increase linearly with the relative density and with the square root of the cell size, while the strength was confirmed to scale only with relative density and the strength of the solid. A moderate increase in resistance with crack length (an R-curve effect) was seen for the higher relative density and larger cell size samples. With a fracture toughness between 2 and 14 MPa m 1/2 and a compressive strength between 20 and 70 MPa, these structures offer a new lightweight engineering material solution for use at temperatures up to 450C.
A key aspect of the longitudinal tensile failure of composites is the stress redistribution that occurs around broken fibres. Work on this topic has focussed mainly on the stress field surrounding a single broken fibre; however, this is an important limitation as unstable failure in carbon fibre bundles occurs when a cluster of about 16 or more broken fibres is formed.Therefore, we have developed a detailed Finite Element (FE) model to investigate how stress redistribution varies with the number of broken fibres in a cluster. The results show that both the recovery length and stress concentration factor increase significantly with increasing number of broken fibres in a cluster. We have also developed an analytical model, suitable to be included in existing or new fibre bundle models, that captures how the recovery length and stress concentration factor vary with the broken cluster size, and validated its predictions against our FE simulations. Finally, we extended our FE model to predict the survival probability of fibre bundles using Monte Carlo simulations, and found that these predictions were in good agreement with experimental and analytical results on microcomposites.
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