PSI - Issue 40

Aleksandr Zalazinskiy et al. / Procedia Structural Integrity 40 (2022) 461–469 Aleksandr Zalazinskiy at al. / Structural Integrity Procedia 00 (2022) 000 – 000

466 6

* s m

  

   ,

 D L l



2

1

 

s

c

ctg

   4

p p ln

f

ln

    





(5)

f



3







s

where * s  is the effective value of the yield strength of the composite; m – the ratio of the yield strength of the matrix and fibers;  – extraction ( 2 2 D / d   );  – the angle of the matrix; L – the length of the workpiece; h – the gap between the surface of the workpiece and the container; c l – the length of the calibration belt; f – the coefficient of friction. s  – the yield strength of copper; f s m s     

To calculate the extrusion force, the formula was used

P D p 2 4  

.

(6)

The stress-strain state of material particles in the deformation focus was determined in a spherical coordinate system   , , r (Fig. 2). Material particles of the deformed part of the workpiece experience the following stress state (Zalazinskiy, 2000):

0

;

;

;   





r    

 

  

rr

s









 ;

1





r       2 3

2 1 2

T



(7)

rr



3

2

 2 1

  

    

.

k





rr

3



s

To assess the damage ω of the workpiece material, the phenomenological theory of metal destruction under large plastic deformations was used (Kolmogorov, 1970, Zalazinskiy, 2000)   f f tg ln     2 1 3   , (8) where f  is the angular coordinate of the current line of the material particle of the deformable material. Damage was calculated for the fiber experiencing the most intense deformation. At the same time,    f . To calculate the inhomogeneity of deformation along the section of the extruded bar, the formula was introduced

ln tg

 

3 1 2  



.

(9)

The results of mathematical modeling of the HMP process were used to perform a series of computational experiments. 4. Results of the computational experiment Nine computational experiments were performed to simulate and improve the HMP process of a bimetallic (Nb Ti)+Cu composite of a fibrous structure. The initial dimensions of the workpieces: diameter D = 20 mm, length L = 60 mm. Mathematical models represented by formulas (1) – (9) were used for the computational experiment. The