PSI - Issue 6

N.S. Selyutina et al. / Procedia Structural Integrity 6 (2017) 77–82 Author name / StructuralIntegrity Procedia 00 (2017) 000 – 000

78

2

models, formulated in the last two decades, show that applied in numerous engineering software tools empirical models do not have versatility when used in the field of high-speed loading of materials. Let us consider two modified Johnson-Cook models at room temperature, described:  a rate dependence of yield strain rate by Couque et al. (2006):

   

   

   k





  

   

  





  p 





n

A B

1 ln  C

D

,



 

(1)

y



1 





0

 a stress-strain dependence by Liu et al. (2014):     . 1 ln 0 2 2 1                  C A F F p p y

   

   

(2)

 Cowper-Symonds formula (Cowper and Symonds (1957)):

   

   

q

1 /



  



1      A

,



(3)

y

P

Here, A, B, C, n are the constant parameters of the Johnson-Cook model; ε p is the equivalent plastic strain;   is the plastic strain rate; 1 0 1s     (Johnson and Cook (1985)); 1 1 1000 s     (Couque et al. (2006)); D and k are the constants of the modified model of Couque et al. (2006): (at D=0 and k=0 Eq. (1) has the form of the classical Johnson-Cook law); F 1 and F 2 are the constants of the modified model of Liu et al. (2014); P and q are the constants of Cowper-Symonds formula. The structural-temporal approach for determining the yield strength on the basis of the introduction of a characteristic time of the stress relaxation proved oneself to be an alternative method for describing temporal effects in the high-speed deformation of metals, as shown by Gruzdkov and Petrov (1999). This method was applied in those strain rate ranges in which the classical Johnson-Cook empirical formula and its modifications does not work (see Fig.1, Fig.2). These theoretically obtained parameters gave a satisfactory correspondence of the structural temporal plasticity model with experiment (Gruzdkov et al. (2002), Petrov and Borodin (2015)). On the other hand Gruzdkov and Petrov (1999) compared numerical models with the structural-temporal approach only at the initial moment of the plastic flow of metals. In this paper, it is expected to continue constructing analytical relationships to the entire deformation curve and to figure out connections between parameters of empirical models and those of the relaxation model of plasticity (Selyutina et al. (2016), Petrov and Borodin (2017)).