PSI - Issue 33

O.B. Naimark et al. / Procedia Structural Integrity 33 (2021) 1115–1122

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2 Naimark O.B. et al / Structural Integrity Procedia 00 (2021) 000–000 important elements of machines and structures. The results of the last decade in the field of experimental studies of static and cyclic crack resistance, numerical modeling indicate a significant effect of the size of cracks and cuts, the geometry of samples, their loading patterns and thicknesses on the characteristics of crack resistance and stress strain state in the vicinity of the crack tip. It is promising to create a model that allows transforming the crack resistance of a standard sample with a crack into the crack resistance of a structural element with a crack or notch by introducing an additional criterion parameter into the model that reflects the stress-strain state in a small vicinity of the crack tip. Models and criteria of the so-called two-parameter fracture mechanics are based on the laws of deformation and fracture in the fracture process zone at the tip of a crack-like defect, taking into account the nonsingular components ( T- stresses) of the stress field at the crack front. This makes it possible to form criterion equations for describing the generalized crack resistance diagram. Models and criteria of two-parameter fracture mechanics are effective in de termining the trajectory of crack propagation and strength calculations in the presence of cracks and notches and were discussed by Matvienko (2020). The process of damage-failure transition can be divided into several stages ac cording to the degree of its locality. Damage appears at the first stages of material deformation and fracture is asso - ciated with development of cracks. In the first stages of failure the microcracks arise and the damage localization leads to crack formation. Material damage processes are concentrated at the front of a crack in the so-called process zone providing the crack propagation. The understanding of physics and mechanics of damage-failure transition makes it possible to create models and formulates the criteria for the initiation of microcracks and small cracks. Fracture mechanics models and criteria do not explicitly take into account fracture micromechanisms and are based on fracture mechanics approaches. Theory of elasticity and plasticity make it possible to solve parametric problems of functional relationship between critical external stresses (forces) and the crack size as the fracture criteria. The formulation of fracture criteria can be based both on local approaches associated with the analysis of the critical state of local regions at the crack tip, and on global approaches involving the analysis of the critical state of sample or construction. The main problems of crack mechanics include the definition of the limiting state of a construction with a crack, the determination of the trajectory of crack and laws of its propagation. Thus, fracture mechanics makes it possible to answer the question of the strength of structures and machines in the presence of cracks. The conditions for deformation of a solid at the crack tip determine the use of the corresponding parameters and criteria of fracture mechanics. The fundamentals of fracture mechanics are associated with seminal works of G. Irwin, who proposed the force criterion in the form of reaching its limiting value by the stress intensity at the crack tip. The stress intensity factor reflects the peculiarity of stress field (intermediate self-similar solution) at the crack tip in asymptotic formulas and its critical value is associated with the property of crack resistance of the material, which is called fracture toughness. It was shown by Williams (1957) that a criterion characterizing the material state at the crack tip can be associated with the non-singular expansion term of the Irwin solution (in the modern interpretation of the T -stress). Studies show that to expand the applicability of classical fracture mechanics in the model and fracture criteria, it is necessary to introduce additional parameters that more fully characterize the stress-strain state and reflect the so-called "local constraint of deformations", indirectly reflecting the state and damage of the material in the vicinity of the crack tip. The representation of the stress field at the crack tip in the form of singular and nonsingular components reads:

,

(1)

where is the Kronecker symbol. The third term, which is proportional to the value of the coefficient A3, in some cases can also make an appreciable contribution to the resulting stress field (1). Stresses reflect the degree of constraint of deformations ahead of the crack front, act in the plane of the crack in the direction of its possible propagation and can be either tensile or compressive, depending on the type of stress state and material damage. The effect of constraining deformations along the crack front is due to the action in its direction of - stresses, which is largely reflected in the crack resistance of the specimen due to a change in its thickness. The concepts of the two parameter fracture mechanics, which takes into account in the analysis of the stress-strain state not only the singular is the stress intensity factor of normal stress mode; is angular function;