Morphological instabilities of a stressed pore channel

Colin, Jérôme; Grilhé, J.; Junqua, N.

doi:10.1016/s1359-6454(97)00068-2

Cited by 20 publications

(12 citation statements)

References 11 publications

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“…The morphological instability of such microscopic channels has been observed in practice [13]: such voids have been artificially introduced in titanium ion-implanted sapphire substrates, and were seen to 'heal' during hightemperature annealing. The results presented here are related to earlier work by Colin et al [5] in which the axisymmetric perturbations of a pore channel were studied. They analyzed the surface evolution of a cylindrical pore, when the surrounding solid is subjected to constant uniaxial stress and the perturbations are axisymmetric.…”

Section: Introductionsupporting

confidence: 78%

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Morphological instability of pores and tubules

Kirill¹,

Davis²,

Miksis³

et al. 2002

Interfaces Free Bound.

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We present a linear stability analysis of a uniaxially stressed, hollow cylindrical tubule, where the mass transport mechanism is surface diffusion driven by surface curvature-and elastic-energy. We find that there are always two distinct eigenmodes for any choice of wavenumbers, applied stress, and geometry. We also find that applied stress has a destabilizing effect, increasing the range of unstable wavenumbers. For any choice of applied stress and geometry, the most dangerous mode is axisymmetric, and can be either sinuous or varicose depending on choices of geometry and applied stress. The case of a cylindrical pore in a stressed infinite solid emerges as a limiting case.

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Section: Introductionsupporting

confidence: 78%

“…This model has been extended to more complicated situations, for example rods and spheres [12], lines on substrates [10], and films [15,17,18]. Work has also been done on extending this model to include diffusion driven by elastic-strain energy [2,5,6,16].…”

Section: Introductionmentioning

confidence: 99%

Morphological instability of pores and tubules

Kirill¹,

Davis²,

Miksis³

et al. 2002

Interfaces Free Bound.

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“…(2) Formation of Dislocation Loops by Cross Slip Similar loops were reported for sapphire 23,24 deformed by compression at high temperatures (@12001C). It was modeled on the basis of the Rayleigh instability, 28,29 describing the morphological change of solid rods or pore channels. However, conservative climb in sapphire involving pipe diffusion 23,24 is unlikely to occur at room temperature.…”

Section: Discussionmentioning

confidence: 99%

Deformation Microstructure in (001) Single Crystal Strontium Titanate by Vickers Indentation

Yang

2009

Journal of the American Ceramic Society

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Recent interests on the plastic deformation of strontium titanate (SrTiO3) are derived from its unusual ductile‐to‐brittle‐to‐ductile transition (DBDT). The transition is divided into three regimes (A, B, and C) corresponding to the temperature range of 113–1053 K (−160° to 780°C), 1053 to ∼1503 K (780° to ∼1230°C), and ∼1503–1873 K (∼1230° to 1600°C), discovered by Sigle and colleagues in the MPI‐Stuttgart. We report the dislocation substructures in (001) single crystal SrTiO3 deformed by Vickers indentation at room temperature, studied by scanning and transmission electron microscopy. Dislocation dipoles of screw and edge character are observed and confirmed by inside–outside contrast using ±g‐vector by weak‐beam dark field imaging. They are formed by edge trapping, jog dragging, and cross slip pinching‐off. Similar to dipole breaking off in deformed sapphire (α‐Al2O3) at 1200°C and γ‐TiAl intermetallic at room temperature, the dipoles pinch off at one end, and emit a string of loops at trail. Two sets of slip systems {110}〈〉 and {100}〈011〉 are activated under both 100 g and 1 kg load. The suggestion is that plastic deformation has reached the stage II work hardening, which is characterized by multiplication of dislocations through cross slip, interactions between dislocations, and operating of multiple slip systems.

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“…For example, the study of the axi-symmetrical rods evolution by surface diffusion under longitudinal stress has given rise to an extensive literature. Introducing axial and radial sinusoidal fluctuations onto the surface of the cylinder, the conditions of its stability have been characterized (Suo and Wang, 1994;Colin et al, 1997;Wang and Suo, 1997). The case of non-axi-symmetric instability has been also recently investigated (Kirill et al, 1999;Kirill et al, 2002).…”

Section: Introductionmentioning

confidence: 99%

Morphological instability of two stressed spherical shells

Colin

2007

International Journal of Solids and Structures

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The morphological stability of the external free surface of a composite structure made of two shells stressed through the interface has been investigated when mass rearrangement along the surface is controlled by surface diffusion. Due to epitaxy or thermal change, an eigenstrain located in the inner shell is considered. The resulting stress and strain tensors have been first calculated assuming that the interface between the two initially spherical shells is coherent. The roughness appearing by surface diffusion on the external surface of the structure has been then developed on a basis of complete spherical harmonics and the linear stability of the surface has been investigated with respect to each harmonic Y m l ðh; uÞ. The growth rate of the lth order harmonic has been determined and the influence of the geometric and physical parameters such as the radius of the interface, the radii of the free surfaces, the intrinsic deformation or the surface energy has been characterized. The case of a spherical solid embedded in a finite-size matrix has been also discussed.

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Morphological instabilities of a stressed pore channel

Cited by 20 publications

References 11 publications

Morphological instability of pores and tubules

Morphological instability of pores and tubules

Deformation Microstructure in (001) Single Crystal Strontium Titanate by Vickers Indentation

Morphological instability of two stressed spherical shells

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