PSI - Issue 28

S.V. Suknev et al. / Procedia Structural Integrity 28 (2020) 903–909 Author name / Structural Integrity Procedia 00 (2019) 000–000

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1. The point method. In this approach, an elastic stress analysis is conducted and failure is assumed to occur if the stress is equal to ultimate strength at a certain distance from the notch. 2. The line method is similar to the point method except the stress is determined by averaging along a line starting at the notch-root. 3. The imaginary crack method is a fracture mechanics approach. A crack is imagined to exist at the root of the notch: failure is predicted to occur when this crack reaches the critical stress-intensity factor c K . 4. Finite fracture mechanics (FFM). In this approach the condition for failure is derived using an energy balance similar to that of LEFM, but assuming a finite amount of crack extension d : 2 0 2 1 c d K dl K d   . Recently, there have been a large number of works (Negru et al. 2015, Li et al. 2016, Fuentes et al. 2017, Vargiu et al. 2017, Vedernikova et al. 2019, Justo et al. 2020, etc.) devoted to the development of the TCD and its application for estimating the strength of materials and structural members with notches. In quasi-brittle materials, such as geomaterials (concrete, gypsum, and rocks), composites, ceramics, cast iron, and graphite, the formation of a prefracture zone is usually associated with local damage in the material as a result of microcracking or the growth of microvoids. The damage zone or the fracture process zone (as it is often called) not only precedes the crack initiation, but also accompanies it during the propagation process, surrounding the crack tip. At the same time, stress redistribution within the material length 0 d is mostly caused by microstructural discontinuity inherent to the real solid rather than material damage and inelastic deformations related to it. Therefore, the field of application of nonlocal criteria is limited by brittle or quasi-brittle fracture with a small process zone d when its size is not very different from 0 d , i.e., with fulfillment of a condition const 0   d d . In this case, the inelastic (plastic) properties of the material are weakly manifested. At the same time, if the material has sufficiently pronounced plastic properties, the formation of inelastic deformations increases the fracture process zone and violates a condition const  d . The paper considers the possibility of extending the field of application of the TCD-based criteria to quasi-brittle fracture with a developed process zone 0 d d  when the stress redistribution in it is determined not only by the microstructural discontinuity of the material, but also by its plastic properties. 2. Size of the fracture process zone Below, quasi-brittle fracture is understood as a sudden propagation of a crack (also characteristic of brittle fracture), accompanied by the formation of a process zone that size exceeds the size of structural components of the material. The size of the fracture process zone d is not compared with the crack length, as is customary in fracture mechanics, but with the material length 0 d . We talk about brittle fracture if 0 d d  and ductile fracture if 0 d d  . The size of 0 d is, in fact, the size of a representative volume of material, i.e., the minimum volume in which the averaged stresses can be calculated according to the theory of elasticity. Therefore, the redistribution of stresses within the material length 0 d is not related with the plastic (in the macroscopic sense) deformation of the material. The plastic properties of the material begin to appear when 0 d d  , and the larger d with respect to 0 d , the more they manifest themselves. Taking this into account, we represent d in the following form: e d d L    0 . (1) Here e L is the size of the stress concentration zone,  is the dimensionless parameter that characterizes the plasticity of the material. For brittle materials, 0   ; for ductile materials, 1   . In the case where  ~ 1, the material is characterized by moderate plastic properties. For geometrically similar notches (stress raisers), the size e L is proportional to the notch size (under constant boundary conditions). With ductile fracture, the critical stress does not depend on the notch size, so the size of the process zone is proportional to the notch size and, accordingly, to the size e L . On the contrary, with brittle fracture, the size of the process zone does not depend on the notch size and is determined by the microstructure of the material.