PSI - Issue 28

Nikolay Dolgov et al. / Procedia Structural Integrity 28 (2020) 1010–1017 Nikolay Dolgov & Tsanka Dikova / Structural Integrity Procedia 00 (2019) 000 – 000

1013

4

The distributions of the shear stresses  zу ( x , z ) and  xу ( x , z ) in the coating-substrate interface are determined using formulas by Dolgov et al. (1996) and Dolgov et al. (1997):

(3)

  

  

  

  

1

ch r b ch r b x n ( / 2) ( ( / 2 −

))

n ( ) 8  

ch r b ch r b x n ( / 2) ( ( / 2 −

))

  

  

s d

−

 

( , ) 4

cos

l x z h =

k z n



+

5

2 max

zy

1,3,5...

n

=

2

n

n

(4)

   

   

1   

  



( ( / 2

))

n ( ) 8  

( ( / 2

))

  

  

d

ch q l

z

ch q l

z

−

−

−

 

( , ) 4

cos

b x z h =

x



n 

+

5

2 max

n

n

xy

( / 2)

( / 2)

p

ch q l

ch q l

1,3,5...

n

=

2

n

n

The values of the elastic characteristics, used in the calculations, are obtained experimentally or given in the literature. The elastic modulus of the Co-Cr dental alloy Co 212-f ASTM F75 (213 GPa), produced by selective laser melting, and the porcelain coating (72 GPa) are previously determined in tensile tests of flat specimens by Dikova et al. (2017). The same tensile test is used for measuring the Poisson's ratio of the alloy (0.32), as longitudinal and transverse strains are measured using strain gages by Dolgov et al. (2016). The Poisson's ratio of the porcelain, used in the calculations, is 0.2 by Suansuwan and Swain (2001). The calculations are performed for the substrate strain equal to 0.1%. The thickness of the substrate – 2 H is 2 mm, the width of the substrate and coatings – b is 6 mm, while the coating thickness – h is 1.5 mm, and the coating length – l is 35 mm. 2. Results obtained The distribution of the normal and shear stresses in accordance with equations (1) – (4) are shown in Fig. 2 and Fig. 3. In order to make a comparison, the normal stresses are also calculated by the method of Frank et al. (2009) using formulas (5) and (6): ( )   1 ( , ) 1 1 ( ) 2          f E res c s c c x   − − + − = (5)

  

 

1     E c − = 2

(6)

( 1 1 





 ( , )



)   



( )

( , )

1      f  − 

f

 c

− −

− +

 

y

c s

s

res

c

c

where  ,  are dimensionless parameters, f (  ,  ) is dimensionless function given by Frank et al. (2009).

Fig. 2. Normal stresses (a) σ z and (b) σ x in the coating (the scale of x -axes and z -axes is shown conditionally).