PSI - Issue 13

N.S. Selyutina et al. / Procedia Structural Integrity 13 (2018) 700–704 Author name / StructuralIntegrity Procedia 00 (2018) 000 – 000

701

2

(Selyutina and Petrov (2018)). These theoretically calculated 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 (Fig.1). 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 (2015)).

Fig. 1. Prediction of stress-strain curves of aluminum alloy 2519 A (Liu et al. (2014)) for strain rates 0.001 s -1 (3,4 lines) and 5542 s -1 (1,2 lines): the experimental data are shown by lines with symbols (rhombus – 0.001 s -1 , triangles – 5542 s -1 ) and the calculation results on the basis of modified Johnson-Cook model (Liu et al. (2014)) and of the relaxation model of plasticity (Selyutina et al. (2016), Petrov and Borodin (2015)).

2. Relaxation model of plasticity

Let us consider behaviour of yield strength at the initial instant of plastic deformation within the structural temporal approach based on the incubation time concept (Gruzdkov and Petrov (1999), Gruzdkov et al. (2002), Gruzdkov et al. (2009)):



    

   

s ( )

t

t Int

ds

 ( ) 1

.

( ) 1,  t Int p where

(1)



p





t





y

Here, Σ(t) is a function describing the time dependence of stress,  is the incubation time, σ y is the static yield stress, α is a coefficient of amplitude sensitivity of the material. Note that the onset of macroscopic yield t * is determined from the condition of equality (1). The introduced time parameter  , independent of the specific features of deformation and sample geometry, makes it possible to predict the behaviour of the yield strength of material under static and dynamic loads (Gruzdkov and Petrov (1999)). It was shown by Selyutina et al. (2016) that the incubation time can be related to different physical mechanism of plastic deformation. One can use an elastic approximation of stress ( ) ( ) t E t    and consider the case of equality in the criterion (1) in order to define the macroscopic time of the plastic flow beginning t * ; here E is the Young’s modulus. We propose a primary version of the relaxation model in the present paper for the case of a linear increase of strain ( ) ( ) t tH t     together with time starting from the zero time moment 0  t . Let us introduce a dimensionless relaxation function 0 ( ) 1   t  , defined as follows