PSI - Issue 65

A.S. Smirnov et al. / Procedia Structural Integrity 65 (2024) 255–262 A.S. Smirnov, A.V. Konovalov,V.S. Kanakin and I.A. Spirina/ Structural Integrity Procedia 00 (2024) 000–000

258

4

dt dR

   

2

 a R

 , if V a ,

r

r

5

6

   a

  

a V

1 1

 

7

      V  

V 

*

 , if V a ,



r

r

r

r

6

6

 V ,atV a , *

r

r

6

r t

dt dR

r     

dt,

at   

a , 4

0

1    r p n V V V , q a ln( a ).     9 8 1

Here, k is yield stress in the von Mises plasticity condition, q is the function describing the viscous properties of the material; ρ 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); ε r is the strain accumulated before the onset of dynamic recrystallization; R is the radius of a recrystallized grain, R ( t r ) = 0; t r is the time of the onset of dynamic recrystallization, defined by the condition ρ = a 4 ; a i ( i = 0,…,14) denotes the model parameters to be identified by the experimental data; V r is the volume portion in which dynamic recrystallization has occurred; V p is the volume portion containing dislocations blocked by dispersoids and impurity atoms; V n is the remaining volume portion of the alloy. At the initial time, i.e. before deformation, V n = 1, V r = 0, and V p = 0. The dots above the symbols indicate time derivatives. The system of equations (1) is a structural phenomenological 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, as well as softening resulting from dynamic recovery and recrystallization. The model (1) is identified under conditions of time-variable strain rate, this being fundamentally different from the identification of models written in the form of a function whose arguments are strain rate and strain. In order to satisfy the requirement of strain rate variability, the specimens are compressed according to the forms of loading (I– VI) shown in Figs. 2 and 3. It can be seen from these figures that the strain rate of the specimen varies nonmonotonically with time, i.e. there are sections of increasing and decreasing strain rate. Figures 2 and 3 show experimental flow stress curves (blue) obtained under forms of loading I–VI. It can be seen from these curves that the flow stress decreases despite the increasing strain rate. This is due to active alloy softening during plastic deformation. The model (1) for each test temperature is identified by minimizing the following function: 3. Model identification and result discussion

j  

j

z

N

j



i

i

j

z

n 1

n





 

i

1



J a , ,a 

min.



i

0

14

N

(2)

j

1



j