Solution of the problems of antiplane deformation for bodies with thin ribbonlike inclusions by the methods of integral
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SOLUTION OF THE PROBLEMS OF ANTIPLANE DEFORMATION FOR BODIES WITH THIN RIBBONLIKE INCLUSIONS BY THE METHODS OF INTEGRAL EQUATIONS. ІІ. ANALYSIS OF THE STRESS CONCENTRATION AND STRESS INTENSITY Ya. М. Pasternak1 and H. T. Sulym2
UDC 539.3
On the basis of pure physical reasoning, we deduce the relationship between the stresses acting at the tip of a defect and the coefficients of root singularity of the stress field, i.e., the generalized stress intensity factors. We propose approximate relations for the evaluation of the generalized stress intensity factors. The efficiency of the proposed approach is demonstrated by comparing the results of numerical analyses of specific problems performed by using the proposed and direct approaches. Keywords: thin ribbonlike inclusion, generalized stress intensity factors, stress concentration.
The end constants ! 0"3 and ! n"3 for a model of inclusion in the form of a line [1, 2] cannot sometimes be
compared with the forces distributed over the end faces of inclusions of actual geometric shapes because the notion of loading applied to the end face can be used only for inclusions with rectangular or trapezoidal profiles of the end faces. As a result of the replacement of an inclusion with closed surface (curve) which is, in addition, smooth (in particular, on the end face) by an open surface (line) with certain properties, we observe the appearance of the well-known [2] root singularity of the stress field and boundary functions !t j in the corresponding
solution of the problem near the edges of this surface (line). In this case, to compute the stress concentration, it is necessary to use the relationships between stresses and generalized stress intensity factors (SIF) taking into account the fact that the curvature of the end face of the defect is finite. The results of this sort were obtained, in particular, in [3] by the methods of series for inclusions with rounded tips whose shapes are similar to the shapes of pointed tips. To deduce relations of this sort, we use the developed model of thin inclusions.
Determination of the Stress Concentration at the End Faces of an Inclusion We now study the equilibrium of a part of the inclusion neighboring with its end face under the assumption that the end face of the inclusion is rounded (Fig. 1). The equation of static equilibrium of a fictitiously truncated part of the inclusion, with regard for the principle of conjugation and the conditions of perfect mechanical contact of the inclusion with the environment !t = " !t i , takes the form 1 2
Lutsk National Technical University, Lutsk, Ukraine; e-mail: [email protected] (corresponding author). Franko Lviv National University, Lviv, Ukraine.
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 48, No. 6, pp. 86–91, November–December, 2012. Original article submitted April 6, 2010. 788
1068-820X/13/4806–0788
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SOLUTION OF THE PROBLEMS OF ANTIPLANE DEFORMATION FOR B ODIES WITH THIN R IBBONLIKE INCLUSIONS
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Fig. 1. Schema
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