PSI - Issue 59

4

Ivan Shatskyi et al. / Procedia Structural Integrity 59 (2024) 407–412 Shatskyi et al. / Structural Integrity Procedia 00 (0000) 000 – 000

410

2 dx d u 2

( )

( )

D y y 

E y

E y

P

| | x





y

C

( , ) y х

( )(

)   C

(cos

| |), sin 

(0,

),

x y y

e

x

x y

H





y 





y

y

c

x

2

2

4

y 

1

( ) y

1

( ) y









H y

H y

P

| | x



y 

( ) x y k u x y y  (, )

(cos

sin

| |) x

,

(0, ) y H  ,

e

x













y

y

y

y

2

where H H h c   is a total thickness of composite coating.

3.2. Critical equilibrium

The strength of each of the layers is estimated by the von Mises criterion. Thus, the strength condition for a plane deformed composite layered coating will be:

2

2

2 y

2

( ) (1 ( ) y y

( ))( y

) (1 2() 2 ()) y y

[ ]( ) y      .



  

   

   



eq

x

x y

Here eq  is a von Mises equivalent stress, [ ]  is the allowable stresses for composite coating materials ( n Y / [ ]    , where Y  is a yield strength, and n is a safety factor). Y  is also piecewise stable function:

    

     , 1 1 1 m i m i i

    Y

   

,

 h h m N , 1,

y





, Y m

i

( ) y

.





Y

,

( , )

 y H H



c

The results obtained make it possible to determine the value of the allowable load, which depends on the mechanical and geometric characteristics of the layered coating. 3.3. Example Next, we give an example of assessing the stress and limit state of a three-layer composition under a local load. Let we consider the composite coating Cr/Ni/Cu containing the outer chromium, intermediate nickel, and inner copper layers. In this case 2  N , and we study the bending of the Cr/Ni-plate resting on the Cu-foundation. The initial data for calculating the equivalent stresses eq  and the safety factor Y eq n   /  are given in the table 1, and the results of the calculations are shown in Figs. 2 – 4.

Table 1. Mechanical properties of coating layers.

Material

Characteristics of layers

Cr ( m =1)

Ni ( m =2)

Cu

E , GPa

280

210

110

0.21

0.3

0.35



h , µm

10

25

35

Y  , MPa

270

430

210