PSI - Issue 40

Vladlen Nazarov et al. / Procedia Structural Integrity 40 (2022) 341–347 Vladlen Nazarov / Structural Integrity Procedia 00 (2022) 000 – 000

344

4

Large displacements

r u bu r b r     2 2 2 b

(7)

u

At u b b  small displacements





r u            2 1 1 2 1 2 2 2 2 2 r r r bu r r u b b b    

   

   

2

1

r bu 2

r bu

2

small

b

b

(8)

u bu 2

u

r  

 

r

b

b

2

r

The relation between the radial strains and porosity

    r r

(9)

 

Radial displacements in pores material

r

a a dR u u u u         r r

(10)

a

Hypothesis for porosity, which is determined through the proportion between differential and integral characteristics

sec

  

sec 

 

(11)



Relative change of integral mean radius

b

b a 1

u

sec

r dr

 

(12)



 

r

a

Porosity (final formula)

 b a

r sec  

u

r

(13)

dR



 b a

u

R

r

The text below shows an example of calculating Cauchy strains and porosity and in more detail the output of the final formula can be found in Nazarov (2014a) and Nazarov (2016). 3. Solution example The evolution of the porosity leads has an effect on strains (Fig. 2). Calculations of strains and porosity have been obtained for 24.27 mm  a , 33 mm  b , 3.75 mm   a u , 3 mm  b u and 0.05 sec   .