This paper deals with the passage from discrete to continuous in modeling the static elastic properties, in the setting of anti-planar linear elasticity, of vertical screw dislocations in a cylindrical crystal. We study, in the framework of Γ-convergence, the asymptotic behavior of the elastic stored energy induced by dislocations as the atomic scale ε tends to zero, in the regime of dilute dis...

We deal with a class of reaction-diffusion equations, in space dimension d > 1, perturbed by a Gaussian noise ∂wδ/∂t which is white in time and colored in space. We assume that the noise has a small correlation radius δ, so that it converges to the white noise ∂w/∂t, as δ ↓ 0. By using arguments of Γ-convergence, we prove that, under suitable assumptions, the quasi-potential Vδ converges to the...

We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Γ-convergence. We also analyze the continuum problem for a rectangular bar under tensile boundary conditions and find that depending on the boundary loading the minimizers are either ho...

We prove the stability of a large class of unilateral minimality properties which arise naturally in the theory of crack propagation proposed by Francfort and Marigo in [22]. Then we give an application to the quasistatic evolution of cracks in composite materials.

We give results for the Γ-limit of a scaled elastic energy of a film as the thickness h > 0 converges to zero. The elastic energy density models materials with multiple phases or variants and is thus non-convex. The model includes an interfacial energy that allows sharp interfaces between the phases and variants and is proportional to the total variation of the deformation gradient.

Platinum-diffused γ+γ' coatings (~20 at.% Al, ~22 at.% Pt) were synthesized on René 142 and René N5 Ni-based superalloys by electroplating the substrates with ~7 μm of Pt, followed by an annealing treatment in vacuum at 1175°C. In order to study the compositional and microstructural evolution of these coatings at elevated temperatures, interdiffusion experiments were carried out on coated speci...

In order to investigate the mechanical properties of developed wrought γ'-hardened Ni-based superalloy, LESS alloy (Low Eta Sigma Superalloy), and understand deformation behavior, tensile tests were carried out from room temperature 800oC in comparison with IN 740H alloy. Like other superalloys, found be dependent on temperature. As rose between 700oC, ultimate strength (UTS) decreased slightly...

Abstract Nickel-base superalloys are extensively used in the production of gas turbine hot-section components as they offer exceptional creep strength and superior fatigue resistance at high temperatures. Such improved properties due to presence precipitate-strengthening phases such Ni3Ti or Ni3Al (γ′ phases) normally face-centered cubic (FCC) structure solidified nickel. Although this second p...