Within the framework of the classical theory of elasticity and the Leonov-Rusynko theory of macrostresses, we study the beginning of brittle fracture of a microinhomogeneous body with a slot-like defect of arbitrary size and sharpness. We determine the influence of the parameter p of material inhomogeneity, the linear size 2a of the defect, and the radius of curvature rt of the tip of the defect on the stress concentration and the characteristics of fracture of the material under tension. The effect of micro-and macrodefects whose configuration varies from cracks (ri --0) to cylindrical holes (r~ ---a), on the strength of materials is investigated from a common position.Microinhomogeneities randomly distributed in a body substantially disturb local stresses. Therefore, in some materials (e.g., gray cast iron and concrete), artificially made notches of certain sizes weakly or even do not affect strength. Therefore, in investigating the strength of bodies, it is necessary to take into account, along with the geometry of macrodefects, the actual structure of the material (microdefects and microinhomogeneities). It is known that fracture of specimens with stress concentrators, even ones made of rather brittle materials, occurs under loads much higher than those predicted by the formula %--r a where Op and Ou are the ultimate strengths of specimens with and without stress concentrators, respectively, and r a is the theoretical stress concentration factor [1]. For this reason, in engineering calculations, one usually employs the expressionwhere k a is the effective stress concentration factor, which is determined experimentally for various concentrators and materials and can be found in handbooks [2][3][4][5]. Deviation of the value of k, from the theoretical value is mainly caused by structural microinhomogeneities of the material and microplastic strains [3,4,[6][7][8]. , having developed a theory of macrostresses, substantially extended the framework of the theory of brittle fracture of microinhomogeneous materials.
Theory of MacrostressesThis theory is based on a model of a microinhomogeneous but macrohomogeneous body. A body is called macrohomogeneous if the mechanical properties of all elementary volumes V 0 of certain size arbitrarily cut out from the body are identical. A sphere of radius p (which is taken as a structural parameter of the material) is chosen as the elementary volume.The stress-strain state of the body is characterized by a macroelongation em of diameter 2p and macrostresses calculated according to Hooke's law s m = 2G~ m + ~'ec, where G is the shear modulus, ~ is the Lam6 constant, Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv.