Strength criteria for wood under the conditions of complex stressed state
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STRENGTH CRITERIA FOR WOOD UNDER THE CONDITIONS OF COMPLEX STRESSED STATE A. Seweryn and M. Romanovych
UDC 539.3
We propose strength criteria for wood under the conditions of complex stressed state. Various modes of fracture of wood, such as fracture along and across tracheids, crushing across tracheids, and buckling of tracheids, are analyzed. The local conditions of fracture of wood taking into account the action of normal and tangential stresses in the critical plane are formulated. The accumulated numerical results are in good agreement with the experimental data.
Strength analyses of anisotropic materials are most often carried out by using hypotheses formulated in the form of equations whose left-hand sides contain polynomials of the components of the stress tensor. The indicated “polynomial” criteria have the following common disadvantage: The empirical relations used in these criteria do not take into account the entire variety of the types of fracture. Thus, the Tsai–Hill hypothesis [1, 2] generalizing the Huber–Mises hypothesis of strength [3, 4] to the anisotropic case is fairly reliable for the case of plastic strains but inapplicable to the case of brittle fracture. In order to take into account the influence of the sign of normal stresses on the strength of anisotropic materials, Hoffman [5] and Tsai and Wu [6] added the linear part of these stresses to the Tsai – Hill criterial relation. However, even in this case, the hypotheses mentioned above describe the strength of materials for different mechanisms of fracture by a single limiting curve. It is also quite strange that, for the strength analysis of materials carried out according to the Hoffman and Tsai– Wu hypotheses in the case of biaxial tension, one must know a constant determined from the tests by uniaxial compression. Moreover, the “polynomial” criteria contain numerous constants whose relationship to the microstructure of the material is sometimes unclear. Nevertheless, these hypotheses are extensively used for the strength analysis of wood in the uniaxial stressed state [7–12]. The aim of the present work is to develop the strength criteria for wood under the conditions of complex stressed state by taking into account the specific features of its structure. In these criteria, the critical state of a body will be determined via the components of the stress tensor at the point of possible crack initiation. The range of applicability of these criteria is restricted to the case of small stress gradients. On the microlevel, wood is regarded as an elastic orthotropic body with three axes of orthotropy R, T, and L. The axes R and T are oriented in the cross section of a specimen and L is directed along its axis (Fig. 1a). In this case, wood is formed by separate cells. The the axial cells (tracheids) located along the trunk of a tree constitute the main part of softwood (Fig. 1b). The radial cells (rays) much smaller in size are located between the tracheids in the plane perpendicular to the trunk (along the rays going from the center of the
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