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A. Wagner, D. Holec, M. Todt, P.H. Mayrhofer, M. Bartosik:
"An analytical study on the role of misfit dislocations in fracture toughness enhancement of superlattice coatings";
Vortrag: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Vienna; 18.02.2019 - 22.02.2019.

Coherently grown multilayer coatings with a periodicity length in the nanometer range exhibit a superlattice (SL) effect in mechanical properties like hardness and fracture toughness. A strong dependency of this enhancement on the bi-layer period has been shown in [1, 2]. The superlattice effect in hardness is well described by the model after Chu and Barnett [3] based on dislocation glide across and within the layers. However, the fracture toughness enhancement derived from experiments showing brittle fracture must be a consequence of a bilayer-perioddependent mechanism active in the absence of plastic deformations. One of these mechanisms might be the residual stress state after the manufacturing process, which will be discussed in this study.
We can distinguish between extrinsic residual stresses due to a mismatch of the coefficients of thermal expansion and intrinsic stresses originating from the film growth process. A major part of the latter originates from the epitaxial growth of the coating and a lattice mismatch of its constituents leading to coherency stresses. Up to a critical thickness of the layers this mismatch
is accommodated by elastic strain, thereafter misfit dislocations form [4, 5].
The analytical model developed within this study is based on the Euler-Bernoulli beam theory applied to an inhomogeneous beam in conjunction with an overall energy balance. Considering the energy necessary for a dislocation to form and the strain energy of the substrate-coating system, a certain dislocation density can be calculated for each layer depending on its thickness. Modelling a layer-by-layer growth including misfit dislocations, the residual stress state of superlattice systems is predicted as a function of the bilayer period.
Finally, the analytically estimated residual stresses are used to predict the apparent fracture toughness and its dependence on the bilayer period of respective SL architectures, considering the intrinsic fracture toughness of the phases and the spatial variation of elastic properties.

[1] U. Helmersson, S. Todorova, S.A. Barnett, J.-E. Sundgren, L.C. Markert, J.E. Greene, J. Appl. Phys. 62 (1987) 481.
[2] R. Hahn, M. Bartosik, R. Soler, C. Kirchlechner, G. Dehm, P.H. Mayrhofer, Scr. Mater. 124 (2016) 67
[3] X. Chu, S.A. Barnett, J. Appl. Phys. 77 (1995) 4403.
[4] L.B. Freund, S. Suresh, Thin Film Materials: Stress, Defect Formation, and Surface Evolution, Cambridge University Press, Cambridge, 2003.
[5] D. Holec, P.M.F.J. Costa, M.J. Kappers, C.J. Humphreys, J. Crystal Growth 303 (2007) 314

Projektleitung Paul Heinz Mayrhofer:
Hard coating materials