和基体厚度相比,涂层很薄,因此细观力学模型可把基体作为半无限弹性体。由于涂层和基体材料的膨胀系数及弹性系数不匹配,涂层材料中残余热应力的解析解为 E_c/(1-γ_c)·(α_s-α_c)△T。用有限元法校核,该应力和解析解吻合得好。通过对涂层产生裂纹驱动力和断裂韧性的讨论,提出了抗裂涂层厚度公式。 Compared to the substrate thickness, the coating is very thin, so the meso-mechanics model can treat the substrate as a semi-infinite elastomer. The analytical solution of the residual thermal stress in the coating material is E_c / (1-γ_c) · (α_s-α_c) ΔT due to the incompatible expansion coefficients and elastic coefficients of the coating and the substrate. Finite element method is used to verify that the stress agrees well with the analytical solution. Based on the discussion of crack driving force and fracture toughness of coatings, the formula of anti-crack coating thickness is proposed.