PSI - Issue 2_B

David Taylor / Procedia Structural Integrity 2 (2016) 1999–2005 Author name / Structural Integrity Procedia 00 (2016) 000–000

2005

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4. Discussion This approach has allowed us to investigate the relationship between L and a microstructural distance d , an activity which is theoretically difficult when applied to real materials because of the difficulty of capturing all aspects of the crack growth process and associated mechanics. By considering some simplified microstructures it’s possible to show that the use of an FFM prediction with the assumption of constant L works well, and furthermore that the value of L is proportional to the value of d . This provides some insight into why the same approach is often successful for many real materials. In these three cases L was found to be of the same order of magnitude as d , but in the case of the microstructure with uncracked ligaments L could be significantly greater than d . Had we assumed a much larger number of uncracked ligaments – say 100 – then L would have been a correspondingly larger multiple. This goes some way towards explaining why L>>d for fibre composite materials, which use this mechanism. It may also explain why L>>d in amorphous polymers. Many such polymers (for example PMMA) form features at the crack tip called crazes, in which unbroken fibrils span the crack, functioning as uncracked ligaments. There can be several thousand such fibrils in a craze, each of the order of 10nm thick (McLeish et al 1989). This paper has considered one particular phenomenon – the small crack effect whereby K c decreases with crack length – which previous work has shown can be well predicted by FFM, though not, of course, by traditional LEFM. Though this is just one of several phenomena which FFM can predict (others include notch radius effects, notch size effects and interface cracking) the short crack effect is fundamental to behaviour in these other cases. For example the fact that short cracks propagate more easily than long ones is the reason why small cracks form during the loading of notches, and can become non-propagating at sub-critical loads. So I am sure that it would be possible to extend this same approach, i.e. the use of model microstructures, to investigate the application of FFM to other problems in fracture mechanics. References Kasiri, S., Taylor, D., 2008. A critical distance study of stress concentrations in bone. J.Biomechanics 41, 603-609. McLeish, T.C.D., Plummer, C.J.G., Donald, A.M., 1989. Crazing by disentanglement: non-diffusive reputation. Polymer 30, 1651-1655 Murakami,Y., 1987. Stress intensity factors handbook. Pergamon, Oxford UK. Nalla, R., Kinney, J., Krusic, J., Ritchie, R.O., 2004. Effect of aging on the toughness of human cortical bone: evaluation by R curves. Bone 34, 1240-1246. Ritchie, R.O., Knott, J.F., Rive, J.R., 1973. On the relationship between critical tensile stress and fracture toughness in mild steel. Journal of the Mechanics and Physics of Solids 21, 395-410. Taylor, D., 2006. The Theory of Critical Distances Applied to the Prediction of Brittle Fracture in Metallic Materials. Structural Integrity & Durability 1, 145-154. Taylor, D., 2007. The Theory of Critical Distances: A New Perspective in Fracture Mechanics. Publ Elsevier, Oxford, UK Weissgraeber, P., Leguillon, P., Becker, W., 2016. A review of finite fracture mechanics: crack initiation at singular and non-singular stress raisers. Arch Appl Mech 86, 375-401 Westergaard, H.M., 1939. Bearing pressures and cracks. Journal of Applied Mechanics A 49-53.