Deformation fracture criterion for bodies with V-notches under the conditions of longitudinal shear
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DEFORMATION FRACTURE CRITERION FOR BODIES WITH V-NOTCHES UNDER THE CONDITIONS OF LONGITUDINAL SHEAR M. P. Savruk, A. M. Osechko, and V. E. Panasyuk
UDC 539.375
The force fracture criterion is especially extensively used for the analysis of the limiting equilibrium of bodies with V-notches. In this case, the critical stress intensity factor depends on the opening angle of the notch. We propose a deformation fracture criterion containing only standard characteristics of the material, i.e., the yield strength and crack resistance. The criterion is developed on the basis of the closed solution of the elastoplastic problem for an infinite wedge under the conditions of longitudinal shear.
In order to determine the limiting equilibrium of bodies with V-notches, as in the case of cracked bodies, it is customary to use force, deformation, and energy fracture criteria. In the case of symmetric loads, the force criterion is used especially extensively [1–6]. According to this criterion, the stress intensity factor K possesses a power singularity at the angular point and reaches the critical value K c corresponding to the onset of fracture. However, the indicated critical value depends on the opening angle of the notch β (K C = K C (β )) and, hence, is not a characteristic of the material. This conclusion also follows from the theory of dimensionalities because the dimensionality of the stress intensity factor at the tip of the notch depends on the angle β. This situation explains the necessity of application of the deformation criterion (based on the analysis of the opening displacement at the notch tip) whose dimensionality is independent of β. To find the ultimate loads for bodies with Vnotches, it is also customary to use the Novozhilov criterion [7] based on the evaluation of the mean maximum stresses normal to the axis of symmetry of the notch in a small interval near the notch tip comparable with the atomic sizes. Different researchers established the relationships between the critical stress intensity factors for bodies with V-notches K c ( β ) and bodies with cracks K c either according to the theory of dimensionalities [6] or by using the Novozhilov criterion [4]. In order to determine the onset of local fracture, it is also possible to use the energy criteria [8, 9]. A deformation fracture criterion whose criterial equations contain only standard characteristics of the material, namely, its yield strength and crack resistance, is developed for bodies with Vnotches under the conditions of plane stressed state [10] and plane deformation [11]. In what follows, we propose a similar deformation criterion for the case of longitudinal shear and perform its experimental verification. Plastic Zone Near a V-Notch In a cylindrical coordinate system ( r, θ, z ), we consider an infinite wedge with opening angle β < π occupying the region 0 ≤ r < ∞,
–π +
β β < θ < π – , 2 2
– ∞ < z < ∞.
(1)
Karpenko Physicomechanical Institute, Ukrainian National Academy of Sciences, Lviv. Translated from Fizyko-Khimichna Mekhanika Materi
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