PSI - Issue 28

Vedernikova Alena et al. / Procedia Structural Integrity 28 (2020) 1160–1166 Author name / Structural Integrity Procedia 00 (2019) 000–000

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2

According to TCD, failure is expected to occur if effective stress calculated either at a certain distance from the notch tip, averaged either at the some distance or at area, exceeds the inherent material strength. In earlier works it has been shown that when estimating strength of notched components under dynamic loading by directly postprocessing the elastoplastic stress fields acting on the material in the notch tip the critical distance is a material parameter (Terekhina et al. (2017)). This fact led to the suggestion that critical distance is a parameter determined by the features of the fracture process. The purpose of this work is to study the physical basis of the parameters of theory of critical distances based on investigation physical processes taking place at a micro/mesoscopic level near the notch tip. The description for the evolution of ensemble of defects near the stress concentrator performed on the basis of the original statistical model of mesoscopic defect in solids developed at ICMM UB RAS (Naimark et al. (2004)). 2. Critical distance concept for dynamic loading case The TCD postulates that the notched component being designed does not fail as long as the following condition is assured (Taylor, 2007): where eff  is the effective stress calculated according to the one of methods of TCD (point method, line method, area method), 0  is the inherent material strength. For some materials 0  is seen to be equal to the material ultimate tensile strength UTS  , as far as for other materials 0  is determined phenomenological by testing of specimens with different notch sharpness (Susmel et al. (2010)). Critical distance concept for dynamic loading case based on the hypothesis that since both the dynamic failure stress f  and dynamic fracture toughness Id K vary as applied strain rate   increases, in the same way the also the inherent material strength 0  depends on the strain rate, and hence the value of the critical distance L : eff 0    , (1)

  

    

b

f

a



    

0

  

0

0



    

b

f

a



0

f

   

f

f



(2)



f

 

 

1 K 1  



 

       

      L

Id K f



N M , 

L f

Id



 

 

K

0          0 0 a b

Id

where   is the strain rate; f a , f b ,  ,  , 0 a , 0 b , M , N are the material constants. For titanium alloy Grade 2 it was shown that if strength of notched components under dynamic loading estimate by directly postprocessing the elastoplastic stress fields acting on the material in the notch tip the critical distance is a material parameter (Terekhina et al. (2017)), while with linear-elastic analysis the critical distance is a function of the strain rate (Fig. 1).

Fig. 1. Dependence of the critical distance value to the strain rate for Grade 2 specimens.