PSI - Issue 50

A.S. Smirnov et al. / Procedia Structural Integrity 50 (2023) 266–274 A.S. Smirnov, A.V. Konovalov,V.S. Kanakin and I.A. Spirina / Structural Integrity Procedia 00 (2022) 000 – 000

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The rheological behavior, the volume portion of dynamic recrystallization, and the strain – strain-rate conditions of deformation were interrelated by means of a structural hierarchical model of flow stress  (Smirnov et. al., 2015),

3

k 3  

q,

2

a

    a exp( a ) a , k a V (a a V ) , p n 11 10 0 12      

1

2

3

V

  V a a  

,

n

13

14

p

1



dt dR

          

2

 a R

 ,if V a ,

(1)

5

6

r

r

a

   

   

1 1

a V

 

7

V 

V 

*

 ,if V a ,



r

6

r

r

r

6

 V ,atV a , * 

6

r

r

r t

dt dR

r     

dt,

at   

a , 4

0

1    p r n V V V ,

q a ln( a ).     9 8 1 Here, k is yield stress due to the shear in the Mises plasticity condition, q is a function describing the viscous properties of the material;  is a quantity proportional to the dislocation density increment induced by plastic deformation;   is strain rate ( v / h   for the uniaxial stress state under compression); v is the speed of the testing machine grip; h is the current height of the specimen under deformation); r  is the strain accumulated before the onset of dynamic recrystallization; R is the radius of a recrystallized grain, 0  R(t ) r ; r t is the time of the onset of dynamic recrystallization, defined by the condition 4 a  ; i a ( i =0,…,14) denotes the model parameters to be identified by the experimental data; r V is the volume portion in which dynamic recrystallization has occurred; p V is the volume portion containing dislocations blocked by dispersoids and impurity atoms; n V is the remaining volume portion of the alloy. At the initial time, i.e. before deformation, 1  n V , 0  r V , 0  p V . The dots above the symbols indicate time derivatives. The system of equations (1) is a structural hierarchical rheological model describing, in the aggregate, the viscous and plastic properties of the medium, plastic hardening due to the dislocation density increment and blocking of free dislocations by dispersoids, and softening resulting from dynamic recovery and recrystallization. 3. Model identification and result discussion The model represented by Eq. (1) was identified at a time-variable strain rate. This is fundamentally different from the identification of models written as a function with the amount of strain and strain rate as its arguments. To meet these requirements, the specimens were compressed according to forms of loading I – III shown in Fig. 1. It can be seen from this figure that the strain rate does not change monotonically over time, i.e., there are zones of increasing and decreasing strain rates. Figure 2 shows experimental flow stress curves (blue) obtained for form of loading I – III. It can be seen from these curves that, despite the increasing strain rate, the flow stress decreases. It is