Abstract
The roughness of the free surface of a non-hydrostatically stressed solid has been expanded in Fourier series and the influence of the first three harmonics of this development has been investigated by means of a static variational calculation of the elastic and surface energies. The deformation of the bumps and grooves of the roughness has been determined and the optimal shape of the free surface has been characterized.
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References
P. Bossis, Doctoral Thesis, Institut National Polytechnique de Grenoble (1999).
R.J. Asaro and W.A. Tiller, Interface morphology development during stress corrosion cracking: part I. Via surface diffusion. Metallurgical Transactions 3 (1972) 1789–1796.
M.A. Grinfeld, Instability of the separation boundary between a non-hydrostatically stressed elastic body and a melt. Soviet. Phys. Dokl. 31 (1986) 831–834.
D.J. Srolovitz, On the stability of surfaces of stressed solids. Acta Metall. 37 (1991) 621–625.
J. Grilhé, Study of roughness formation induced by homogeneous stress at the free surfaces of solids. Acta Metall. 41 (1993) 909–913.
B.J. Spencer, P.W. Voorhees and S.H. Davis, Morphological instability in epitaxially strained dislocation-free solid films. Phys. Rev. Lett. 67 (1991) 3696–3699.
C. Chiu and H. Gao, Stress singularities along a cycloid rough surface. Internat. J. Solids Structures 30 (1993) 2983–3012.
P. Nozières, Amplitude expansion for the Grinfeld instability due to uniaxial stress at a solid surface. J. Phys. I 3 (1993) 681–686.
P. Nozières, Lectures at the Beg Rohu Summer School in “Solids far from equilibrium”, C. Godrèche (ed.). Cambridge Univ. Press, Cambridge (1991).
K. Kassner and C. Mishba, Non-linear evolution of a uniaxially stressed solid: A route to fracture. Europhys. Lett. 28 (1994) 245–250.
W.H. Yang and D.J. Srolovitz, Cracklike surface instabilities in stressed solids. Phys. Rev. Lett. 71 (1993) 1593–1596.
B.J. Spencer and D.L. Meiron, Nonlinear evolution of the stress driven morphological instability in a two-dimensional semi-infinite solid. Acta Metall. 42 (1994) 3629–3641.
F. Jonsdottir and B. Freund, Instability of a biaxially stressed thin film on a substrate due to material diffusion over its free surface. J. Mech. Phys. Solids 41 (1993) 1245–1264.
F. Jonsdottir, Computation of equilibrium surface fluctuations in strained epitaxial films due to interface misfit dislocations. Modelling Simul. Mater. 3 (1995) 503–520.
L.B. Freund, Evolution of waviness on the surface of a strained elastic solid due to stress-driven diffusion. Internat. J. Solids Structures 32 (1995) 911–923.
H. Gao and W.D. Nix, Surface roughening of heteroepitaxial thin films. Annual Rev. Materials Sci. 29 (1999) 173–209.
J. Müller and M. Grant, Model of surface instabilities induced by stress. Phys. Rev. Lett. 82 (1999) 1736–1739.
J. Grilhé, Surface instabilities and dislocation formation at the free surfaces of stressed solids. Europhys. Lett. 23 (1993) 141–146.
S. Timoshenko and J.N. Goodier, Theory of Elasticity. McGraw-Hill, New York (1951).
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Mathematics Subject Classifications (2000)
82B24, 73C05, 73C02, 73V25, 73B30, 73S10.
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Colin, J., Grilhé, J. Nonlinear Effects of the Stress Driven Rearrangement Instability of Solid Free Surfaces. J Elasticity 77, 177–185 (2004). https://doi.org/10.1007/s10659-005-4650-2
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DOI: https://doi.org/10.1007/s10659-005-4650-2