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

1014

5

Fig. 3. Shear stresses (a)  zy and (b)  xy in the substrate-coating interface.

To simplify the calculations, it is assumed that there are no residual stresses in the coating (i.e.,  res = 0). The normal stresses  x (  ) and  y (  ) of the coating in the x - and y -direction are calculated following the coordinate axis, which is given by Frank et al. (2009). It should be mentioned that a different designation of the direction of the axes is used in the research by Dolgov et al. (1995), Dolgov et al. (1996), and Dolgov et al. (1997) as well as Frank et al. (2009). In the following text, it will be assumed that a tensile load P is applied along the x -axis, and additional stresses are initiated in the coating in the direction of the y -axis, similar to the work of Frank et al. (2009). It is clearly seen that the results of the calculations according to the model of Frank et al. (2009) (  x (  = 0) = 1.835 GPa) and Dolgov et al. (1995), Dolgov et al. (1996) and Dolgov et al. (1997) (  x (  = x / l= 0;  = y/b= 0) = 1.864 GPa) do not differ significantly. The difference is less than 1%. For normal stresses σ y , the results are completely identical: according to the model of Frank et al. (2009) (  y (  = –0.5 = 0.5) = –0.632 GPa) and Dolgov et al. (1995), Dolgov et al. (1996) and Dolgov et al. (1997) ((  y (  = x / l= – 0.5 = 0.5;  = y/b= 0) = –0.632 GPa). In the calculations above, it is assumed that the elastic properties of the isotropic  -Ta and polyimide as substrate and coating materials are as follows E c = 186 GPa,  c =  s = 0.34 by DuPont (1976), while the strain  = 0.01 and the value of  is 0.1. The distribution of the normal stresses  x (  ) and  y (  ) in the coating, calculated by formulas (5) and (6), is shown in Fig. 4.

Fig. 4. Stresses σ x (  ) and σ y (  ) as a function of the reduced position  = x / l (where l – coating length)