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Influence of the Substrate Hardness on the Validity of Bückle's Rule
Author(s) -
Berg Gunnar,
Grau Peter
Publication year - 1993
Publication title -
crystal research and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0232-1300
DOI - 10.1002/crat.2170280722
Subject(s) - materials science , penetration (warfare) , indentation hardness , penetration depth , substrate (aquarium) , composite material , equivalence (formal languages) , optics , mathematics , physics , microstructure , pure mathematics , geology , oceanography , operations research
Generally the substrate hardness of a coated sample influences the measured compound hardness also for small penetration depths. But there exists the empirical rule (Bückle) that for small penetration depths this influence can be neglected. This should be right for values smaller than 1/10 of the film thickness with the limits 1/7 and 1/14. Bückle accentuates the equivalence of the rule for soft films on hard substrates and hard films on soft substrates, respectively. The possibility is shown that the compound hardness can be estimated from film and substrate hardness by an interpolation formula without any suggestions with respect of the depth dependence of the hardness of the two materials. By means of this formula one can show that the mentioned Bückle rule is not generally valid. Only for soft films on hard substrates one can estimate a noticeably Bückle region useful to measure the film hardness directly for penetration depths up to about 1/10 of the film thickness.