539.375 Within the framework of the model of plasticity bands, we consider an elastoplastic problem of fracture mechanics of the development of plasticity bands near the tips of a central crack in a disk. We assume that, in the plane stressed state, plastic strains in the vicinity of the crack tip are localized along three plasticity bands (L I , L 2 , and L~ ) one of which is located on the continuation of the crack and the other two make nonzero angles with the direction of the crack and that, under the conditions of plane deformation, plastic strains are localized along two plasticity bands (L I and ~ ). The band (~) is modeled by a line of discontinuity of normal and tangential displacements and the bands (L l and L 2) are modeled by lines of discontinuity of tangential displacements. The lengths and orientations of these lines are determined in the process of numerical solution of the problem by the method of singular integral equations. The values of the crack tip opening displacement are also determined.Disk specimens with notches or cracks are used in the investigation of the processes of initiation and development of cracks under static and cyclic loading [1][2][3][4]. The level of local strains near a concentrator characterized by the jump of normal displacements (opening displacement) at its tip 6 can be regarded as a parameter that controls these processes in elastoplastic materials. To find this parameter, it is necessary to solve the problem of determination of the strain-stress state of the disk taking into account elastoplastic strains near the tip of the concentrator. For this purpose, we use the model of plasticity bands (see, e.g., [5-1 1]) according to which the plasticity zone is localized along narrow bands lying on the continuations of the crack. As follows from the experimental data presented in [5][6][7], this model reflects the actual process of deformation in the first stage of the development of plastic strains in thin plates. However, in many cases (in particular, in disks with central cracks [6]), under loads of certain types, we observe the appearance of new bands inclined to the line of continuation of the crack. Neglecting these inclined bands, we get underestimated values of the displacement ~ [12].In the present work, within the framework of the model of plasticity bands, we solve the problem of elastoplastic equilibrium of a disk with central crack and study the influence of inclined plasticity bands on the crack tip opening displacement. Plane Stressed StateA thin disk of radius R containing a central crack L 1 of length 2/1 is related to a Cartesian coordinates xOy. The disk is subjected to tension by two concentrated forces F applied at points Zo = + ih (Fig. 1). The material of the disk is perfectly elastoplastic.In the disk subjected to tension, near the crack tips, we first observe the appearance of plastic bands directed along the continuation of the crack. Further, as the load increases, we observe the appearance of two additional bands at each tip making nonzero an...
In 1998, ten sessions of the seminar were held, where the following reports were presented: I. M. Andreiko (L'viv). Improvement of Strength and Cyclic Crack Resistance of Cold-Resistant HighStrength Cast Irons by Optimizing Their Structure. The author proposed a method for determination of the strain parameter that characterizes the resistance of structurally inhomogeneous materials, in particular high-strength cast irons, to nucleation and growth of fatigue macrocracks. As compared with the known force parameters, this parameter is more sensitive (by a factor of 1.5-2) to the influence of graphite inclusions. The resistance of highstrength cast irons of both the ferrite-pearlitic and pearlitic classes to brittle fracture essentially depends on the degree of sphericity of graphite. The regularities of low-temperature (down to -196~ fatigue fracture of cast irons are investigated, diagrams of their structural stren~h are plotted, and, on the basis of these diagrams, recommendations concerning the technology of production of high-strength and crack-resistant cast irons at normal and low service temperatures are developed. N. V. Gorbacheva (L'viv). Calculation of the Temperature and Stressed State of Friction Elements ofBrakes. On the basis of solutions of axially symmetric nonstationary heat problems of friction for a half space which is heated in a circular region of the surface by a friction heat flow, a method for determination of the temperature and stresses in the friction lining of a brake is proposed, The influence of roughness of the working surface of the lining, its convective cooling, and thermal properties on both the maximum temperature of the contour and the stress intensity is investigated. The method was tested by determining the mean temperature of the lining of a disk brake. I. Ya. Horbachevs'kyi (L'viv). Estimation of the Effect of Geometry and Locations of Thin Inclusions onthe Plane Stress-State of Materials. A model of strain of a thin elastic inclusion is proposed. On the basis of this model, the problem of determination of stresses in an elastic material with inclusions is reduced to a system of singular integro-differential equations of the Prandtl type for the unknown jumps of stresses and displacements on the surfaces of foreign elements. A closed solution of this system is deduced for an isolated oval tunnel-type defect with arbitrary rigidity. This enables one to obtain formulas describing the distribution of stresses in the vicinity of tips of the inclusion and inside it. Stresses in bodies with systems of interacting tunnel-type defects with arbitrary rigidity are investigated, and a method for the estimation of the concentration of residual stresses in an inhomogeneous body on plastic strain is proposed. Relevant analytic expressions for the cases of an isolated elliptic defect and periodic systems of coplanar and parallel defects are found. O. P. Datsyshyn (L'viv). Development of Theoretical Foundations of the Mechanics of Fatigue Fracture of Strained Solids in the Course of Their C...
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