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Explicit phase diagram for a one‐dimensional blister model
Author(s) -
Chmaycem G.,
Jazar M.,
Monneau R.
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201500226
Subject(s) - blisters , phase diagram , residual stress , materials science , lift (data mining) , elasticity (physics) , buckle , mechanics , thermal expansion , substrate (aquarium) , composite material , delamination (geology) , diagram , residual , phase (matter) , mathematics , physics , computer science , algorithm , geology , statistics , quantum mechanics , paleontology , oceanography , tectonics , subduction , data mining
We consider a thin film bonded to a substrate. The film acquires a residual stress upon cooling due to the mismatch of the thermal expansion coefficients between the film and the substrate. The film tends to lift off the substrate once this residual stress is compressive and large enough. In this work, this phenomenon is described by a simplified one‐dimensional variational model. We minimize an energy and study its global minimizers. This problem depends on three parameters: the length of the film, its elasticity and the temperature. Our main result consists of describing a phase diagram, that depends on those parameters, in order to identify three types of global minimizers: a blister, a fully delaminated blister and a trivial solution (without any delamination). Moreover, we prove various qualitative results describing the shape of the blisters and allowing us to identify the smallest blister that may appear.