PSI - Issue 13

A. Vedernikova et al. / Procedia Structural Integrity 13 (2018) 1165–1170 Author name / Structural Integrity Procedia 00 (2018) 000–000

1166

2

from the notch tip. Neuber (1958) proposed to calculate an effective stress to estimate the high-cycle fatigue strength of notched components by averaging the linear-elastic stress over a line emanating from the assumed crack initiation point. After, 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, 2008). The TCD makes use of a characteristic material depended length to post-process the linear-elastic stress fields in the vicinity of the assumed crack initiation locations (Susmel, 2008). The employed length scale parameter depends on the specific microstructural features of the material under investigation. However, the physical meaning of the effective length parameter is still issue of fracture mechanics. This work is devoted to the development of one possible explanation of the nature of the critical distance theory on the base of statistical model of the evolution of defects proposed Naimark (2009). 2. Application of the TCD to the static strength assessment of the notched titanium alloy Grade 2 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 (Susmel, 2010). Failure 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 specimens 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. The critical distance takes the following form: 2

0       

1 Ic L K  

(2)

where Ic K is the plane strain fracture toughness and 0  is the material inherent strength.

b)

a)

Fig. 1. (a) Geometry of the investigated specimens; (b) Determination of the critical distances value.

The most accurate and simple way to determine critical distance and inherent material strength is to test samples containing two different geometrical features (sharp and blunt notch), the coordinates of the point at which the two linear elastic stress-distance curves in the incipient failure condition intersect each other directly gives the values of both L and σ 0 (Taylor, 2008). According to this procedure, using linear-elastic stress fields for a sample with a V shaped stress concentrator and for a plane sample (geometry of the specimen is presented in figure 1a) a critical distance value for the case of quasi-static tensile (strain rate 0.0078 1/s) notched specimens from titanium alloy Grade2