Modelling Log-End Cracks Due to Growth Stresses: Calculation of the Elastic Energy Release Rate
Résumé
The occurrence of log-end cracks, due to the release of growth stress pre-existing in the standing tree, causes severe damage at the early stage of wood transformation. A mechanical model based on Griffith's theory for elastic-fragile materials has been developed to explain the observed patterns: a crack can only progress when the elastic energy release rate (G) exceeds the toughness (Gc) of the material for the given fracture mode and orientation. At each stage of the crack propagation, G was calculated using the finite-element method. The influence of various parameters related to the rigidity components, the initial growth stress field or the crack geometry has been investigated, based on a set of experimental data gathered on a population of Eucalyptus. In all cases the high G values just after crack initiation are followed by a marked decrease until the periphery has been reached. Their order of magnitude for a typical log is similar to Gc values measured independently on similar material, thus supporting the validity of the approach.
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