PSI - Issue 13

Sergiy Kotrechko / Procedia Structural Integrity 13 (2018) 11–21 Sergiy Kot echko/ Structural Integrity Procedia 00 (2018) 000–000

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Inability to use existing ideas about the mechanisms of radiation embrittlement to predict radiation life time is a serious shortcoming of the existing paradigm of life time prediction. In general, for today there is a gap between a sufficiently deep understanding of the physical nature of radiation embrittlement and purely empirical of methods RPV life time prediction. This contradiction can be solved within the framework of the LA to fracture, as this approach has been created to place prediction of structural integrity to the physical basis. However, both the conventional LA version and the proposed multi-scale version of LA are quite sophisticated for engineering calculations. In this regard, there is a need for a simplified (engineering) version of the LA. 3.1. Engineering version of Local approach The key problem of LA is to ascertain a connection between the value of stress of cleavage initiation within the local area ahead of a crack / notch, f σ , and the value of "applied" I K . This problem is caused by a substantially non-uniform distribution of stresses and strains inside the vicinity of macrocrack / notch. In conventional Beremin version of LA, Weibull stress W σ is used as a measure of local stress. This stress can be used as an integral characteristic for brittle strength of the region subjected to local yielding. Other approach to this problem was utilised by Kotrechko (2002) and developed by Kotrechko et al. (2007) and Kotrechko (2013). In this case, local fracture stress f σ is determined as the value of tensile stress 11 σ in the locus where probability of fracture initiation reaches it maximum value (Fig. 3). Such approach enables to compare directly the calculated magnitude f σ with experimental evidence determining by the value of tensile stresses at cleavage initiation site ahead of macro-crack tip and it permits to ascertain region where fracture initiates („process zone”) (Fig. 3). Earlier, Lin et al (1986) considered such approach.

As it is exhibited by Kotrechko (2013), the region of PZ may be much less than the whole area of local plastic yielding. In the multi-scale version of LA, the dimensions of "process zone" and the probability distribution of cleavage initiation within this zone (Fig. 3) are determined by computer simulation of the formation and instability of the crack nuclei for individual representative volumes (finite elements) into which the body with crack is “devided”. Unfortunately, this approach is rather complicated for engineering calculations. Introduction of the idea of the "characteristic" volume f V of «process zone» makes it possible to simplify this task significantly. Specific feature of the "characteristic" volume lies in the fact that within it the stress and plastic strains are uniformly distributed, however, the magnitude of cleavage stress f σ and the probability of its realisation are equal to the corresponding values in the real "process zone" (Fig. 3). It should be noted that the introduction of a "characteristic" size is a typical technique in describing plastic deformation and fracture in highly inhomogeneous fields of stresses and strains. In this case the expression for fracture probability in Weibull approximation is the following:

Fig. 3. Distribution of the local tensile stresses 11 σ , equivalent plastic strain e and local probability of cleavage initiation P in minimal cross-section ahead of a crack tip: f σ is the critical cleavage stress; f e is the value of equivalent strain at the locus of cleavage initiation; max P is the maximum probability of cleavage initiation (pre cracked Charpy specimen, 140 C  = − f T , RPV steel (15Cr2NiMoVA)).

   

   

   m

σ σ − σ f

  

th

= − − ρ exp 1

P

V

(3)

f

f

u

where ρ is the rate of crack nuclei formation within the volume unit; th σ is the threshold stress; m and u σ are the shape and scale parameters in