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

1016

7

1) The model allows the mismatch of the Poisson’s ratios of the substrate and coating to be taken into account. 2) The singular effect near the free surface of the coating for the shear stresses in the substrate-coating interface is not taken into account. 3) In the case of thick coatings with high stiffness, bending stresses must be considered. However, the porcelain coatings have an elastic modulus lower than the elastic modulus of a metal alloy; therefore, this effect can be ignored. 4. Conclusions The analytical model, presented in the research, allows normal stresses in the coating and shear stresses in the substrate- coating interface to be evaluated. The mismatch of the Poisson’s ratios of the substrate and coating are taken into account. In the present paper, the developed model was approved using an example of porcelain coatings on a dental Co Cr alloy. The results about the normal stresses, determined by the developed model, are in good agreement with the model of Frank S. et al. The shear stresses in the substrate-coating interface can cause the delamination of the coating. It was proven that additional normal stresses, perpendicular to the action of the external tensile load, are initiated in the coating. They should not be neglected as a reason for the coating fracture. Experimental investigations of the failure mechanisms in porcelain coatings on a Co-Cr dental alloy during tensile tests will be carried out in the future.

Appendix A.

(

)

2

;

2 3 d d H G h G h c s + = = ;

; d 5 =(1 –  c  s )  ; d 5

* =( 

c –  s ) 

(A1)

1  −

(

(

)

) 2

c

1 4 d E H G h G h c s c +  =

d

=

4

2

E

c

k n =  n/l ;

(A2) (A3)

 n =  n/b

s 1 = k n

1 + d 2 ; s 2 = k n

3 + d 4 ; p 1 =  n

1 + d 2 ; p 2 =  n

3 + d 4 ; r n =( s 2/ s 1 )

– 0,5 ; q

n =( p 2/ p 1 )

2  d

2  d

2  d

2  d

– 0,5

n =2 m +1 in which m =0, 1, 2, …

References Agrawal, D.C., Raj, R., 1989. Measurement of the ultimate shear strength of a metal-ceramic interface. Acta Metallurgica 37, 1265 – 1270. Agrawal, D.C., Raj, R., 1990. Ultimate shear strengths of copper-silica and nickel-silica interfaces. Materials Science and Engineering: A 26, 125 – 131. Al Jabbari, Y.S., Koutsoukis, T., Barmpagadaki, X., Zinelis, S., 2014. Metallurgical and Interfacial Characterization of PFM Co – Cr Dental Alloys Fabricated via Casting, Milling or Selective Laser Melting. Dental Materials 30, e79 – e88. Andersons, J., Tarasovs, S., Leterrier, Y., 2009. Evaluation of Thin Film Adhesion to a Compliant Substrate by the Analysis of Progressive Buckling in the Fragmentation Test. Thin Solid Films 517, 2007 – 2011. Choudhury, P., Agrawal, D.C., 2011. Sol-gel Derived Hydroxyapatite Coatings on Titanium Substrates. Surface and Coatings Technology 206, 360 – 365. Cordill, M.J., Taylor, A., 2015. Thickness Effect on the Fracture and Delamination of Titanium Films. Thin Solid Films 589, 209 – 214. Cox, H.L., 1952. The Elasticity and Strength of Papers and Other Fibrous Materials. British Journal of Applied Physics. 3, 72 – 79. Dikova T., Dolgov, N, Dzhendov, Dzh., Simov, M., 2017. Adhesion Strength Evaluation of Ceramic Coatings on Cast and Selective Laser Melted Co-Cr Dental Alloys Using Tensile Specimens. Materials Science. Non-Equilibrium Phase Transformations 3, 49 – 52. Dikova, T. 2018 Bending Fracture of Co-Cr Dental Bridges, Produced by Additive Technologies: Experimental Investigation. Procedia Structural Integrity 13, 461 – 68. Dikova, T., Vasilev, T., Dolgov, N., 2019. Failure of Ceramic Coatings on Cast and Selective Laser Melted Co-Cr Dental Alloys under Tensile Test: Experiment and Finite Element Analysis. Engineering Failure Analysis 105, 1045 – 1054. Dolgov, N.A., Lyashenko, B.A., Rushitskij, Ya.Ya., Veremchuk, V.S., Terletskij, V.A., Kovalenko, A.P., 1995. Effect of Difference in Elasticity Characteristics of the Base and Coat on the Stress-Strained State of Composite. Communication 1. On the Estimation of Coat Tensile Stresses. Problemy Prochnosti 9, 37 – 43. Dolgov, N.A., Lyashenko, B.A., Rushitskij, Ya.Ya., Veremchuk, V.S., Terletskij, V.A., Kovalenko, A.P., 1996. Effect of Elasticity Characteristic Differences of Base and Coats on Stressed State of Composite. Communication 2. Distribution of Tensile Stresses Over Coats. Problemy Prochnosti 5, 63 – 67.