PSI - Issue 5

Terekhina Alena et al. / Procedia Structural Integrity 5 (2017) 569–576 Terekhina Alena et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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a crack leading to failure or to a shortening of the assessed lifetime of structures. It is key to provide structural engineers with design methods suitable for evaluating the detrimental effect of notches on the overall strength of engineering components. Among the design formulations that account for this effect, the TCD (Taylor (1999, 2007), Susmel (2009)) is recognized as one of the most popular due to its simplicity and good results for a number of notch configurations. The central idea in the TCD is the definition of an effective stress, σ eff , based on the stress at a point located at a critical distance, L/2, from the stress concentrator (Point Method). Failure is expected to occur if σ eff exceeds a reference material strength, σ ref . This fundamental idea was first proposed by Peterson (1959), according to Peterson's assumption, the cracking behavior of notched components is not governed by the mechanical behavior of the material in the vicinity of the stress raisers being assessed, the Point Method postulates that the fatigue failure can be successfully prediction by using the stress state at a given distance from the assumed crack initiation point. Later, Novozhilov (1969) introduced a necessary and sufficient criterion for estimating the strength of an elastic body weakened by a crack in the form of the average stress limitation in the cohesive zone length d ahead of the crack tip. Studying the notch effect on the static strength of fiber composites, Whitney and Nuismer (1974) established the link between the critical distance and Linear Elastic Fracture Mechanics (LEFM), where the material's characteristic length can directly be determined through the LEFM fracture toughness and the material's ultimate tensile strength. The above-mentioned ideas were the basis of four formalized method of the TCD such as the Point, the Line, the Area, and the Volume Method (Taylor (2007)). These four methods use one characteristic material length parameter, so called critical distance L, to predict both brittle fracture and fatigue strength. It has also been proved that the TCD can be used to predict the static strength of notched brittle and quasi-brittle material [Cicero et al. (2012), Cicero et al. (2014), Susmel and Taylor (2008)) as well as of notched ductile metallic material subjected to uniaxial (Madrazo et al. (2012)) and multiaxial static loading (Susmel and Taylor (2010)). More recently, Yin et al. (2014, 2015) shown that Theory of Critical Distances is suitable for predicting the strength of notched metallic materials subjected to dynamic loading. According TCD various types of non-linearities can be accommodated into a framework that is entirely linear elastic. This work presents a design methodology suitable for estimating lifetime under conditions of static and dynamic tensile loading on cylindrical samples made of Grade 2. The methodology is based on the use of the Theory of Critical Distances (TCD) in the form of the so-called Point Method with use elasto-plastic analysis. Because the material behavior being, by nature, highly non-linear and cannot be described in the framework of the linear theory of elasticity it is assumed that elasto-plastic analysis will allow as to improve the accuracy of estimation of lifetime of notched components in comparison with use TCD based on the linearly elastic analysis. According to the theory of critical distances the static strength of notched engineering materials can be predicted using linear-elastic stress information in a critical region close to the notch tip. The central idea in the Point method of the TCD is the definition of an effective stress, σ eff , based on the stress at a point located at a critical distance, L/2, from the stress raiser (Figure 1). F ailure is expected to occur if σ eff exceeds the material plain inherent strength , σ 0 . The empirical relationship in terms of the Point Method to predict the fracture of laboratory samples with a complex geometry is represented by equation (1).   1 0 / 2, 0 eff r L         (1) where r ,  - polar coordinates, 1  - is the range of the maximum principal stress, L - material characteristic length. 2. Fundamentals of the Theory of Critical Distances 2.1. Critical distance approach for static loading