Elastic layer model for application to crack propagation problems in timber engineering
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A fracture mechanics model for analysis of crack initiation and propagation in wood is defined and applied. The model has the advantage of being simple, yet it enables reasonably general and accurate analysis commonly associated with more complex models. The present applied calculations are made by means of the finite element method and relate to progressive cleavage fracture along grain. The calculations concern a tapered double cantilever beam specimen and an end-notched beam. Comparisons are made of experimental test results. The fracture properties of the wood are modelled by means of a very thin linear elastic layer located along the crack propagation path. The properties of the layer are such that the strength and fracture energy of the wood are represented correctly. This makes a single linear elastic calculation sufficient for strength prediction. Both crack development and pre-existing cracks can be analyzed. Both material strength and fracture energy and stiffness are taken into account, their relative influence on structural strength being different for different elements. The fracture layer is in the finite element context represented by joint elements. Propagation of a crack can be analyzed either by a series of elastic calculations corresponding to different crack lengths or by use of a finite element code for non-linear analysis. The computational results include sensitivity analysis with respect to the influence of the various material parameters on structural strength.