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I have been reading the book The Mechanics and Reliability of Films, Multilayers and Coatings (https://doi.org/10.1017/9781316443606) on chapter 4.2 and got stuck in chapter 4.2 and 4.3. Suppose that I have a bulk material with a thin coating, and both of them have no residual stress at room temperature. The material is then subjected to a cold shock on the coating side such that the coating wants to shrink, but have its movement constrained by the bulk material (which hasn't felt the temperature change). In this scenario, please correct me if I'm wrong, I think that the stress in the material will go from being in tension (starting on the coating layer), gradually goes to 0, and goes to be in compression (ending on the bulk). My question is on how I can convert the stress state of the material to the resultant P (force) and M (moment) expressed on Figure 4.3: Figure 4.3 on the book

I'm mostly concerned on the signs of P and M in the mode mix determination equation, equation 4.12: Equation 4.12: mode mix determination

Thank you in advance for the help, I'm just started to learn about coating delamination so this material is new to me.

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  • $\begingroup$ Isn't there expression for the stress depending on depth in the book? $\endgroup$ Aug 22, 2023 at 16:45

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