Determination of the Stress Intensity Factor for a Transverse Shear Crack in a Beam Specimen
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DETERMINATION OF THE STRESS INTENSITY FACTOR FOR A TRANSVERSE SHEAR CRACK IN A BEAM SPECIMEN P. S. Kun’,1, 2 S. T. Shtayura,1 and T. M. Lenkovs’kyi1
UDC 539.421.2
By the method of superposition of stressed states, we deduce a formula for the stress intensity factor KІІ under the conditions of transverse shear of an I-beam specimen. The comparison of the results of calculations with the theoretical data obtained earlier by the finite-element method reveals their satisfactory convergence within a broad range of relative crack lengths. Keywords: I-beam specimen, transverse shear, stress-intensity factor, crack resistance, superposition method, finite-element method.
Unlike the well-studied mechanism of normal tension (mode I), the experimental simulation of the process of propagation of fatigue cracks of transverse shear (mode II) requires high attention to the development of new special specimens and certain schemes and conditions of loading, which would guarantee the long-term stability of crack propagation and the correctness of the obtained results [1–4]. For this purpose, we designed an I-beam specimen and proposed it for the investigation of the static and cyclic crack resistance of structural materials by using the corresponding scheme of cantilever bending (Fig. 1) [5]. For the subsequent use of this specimen, it is necessary to deduce the formulas for the mode II stress intensity factor (SIF) K II valid for a given loading scheme. In order to determine the SIF K II , we use an approximate approach proposed in [6], based on the applica-
tion of the method of superposition of stressed states, and extensively applied in the linear fracture mechanics. The problem of determination of the stressed state near the crack tip in a beam specimen weakened by a lateral longitudinal crack under the conditions of cantilever bending by a force P (Fig. 2a) can be reduced to two auxiliary problems: the problem of bending of a defect-free specimen by the force P (Fig. 2b) and the problem of constant shear load by forces τ acting upon the lips of the edge crack in the cantilever beam specimen (Fig. 2c). In this case, the force τ (Fig. 2c) is determined for a beam without cracks (Fig. 2b) on the basis of the distribution of tangential stresses in a beam with constant cross section by the Zhuravs’kyi formula and the law of parity for tangential stresses as follows:
τ = τ max ,
(1)
where τ max is the maximum tangential stress acting in the plane y = 0 . In a given cross section, under the
conditions of plane bending of the beam (Fig. 1), this quantity is given by the formula:
τ max = 1 2
P f0 ( α, ε, θ 0 , θ ) . t0 H
(2)
Karpenko Physicomechanical Institute, Ukrainian National Academy of Sciences, Lviv, Ukraine. Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 50, No. 2, pp. 50–53, March–April, 2014. Original article submitted September 20, 2013. 212
1068-820X/14/5002–0212
© 2014
Springer Science+Business Media New York
DETERMINATION OF THE STRESS INTENSITY F
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