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Analytical Modeling of Fracture of Materials with Environment Assisted Delaminations

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We consider delamination crack growth controlled by gas diffusion into the crack. If the gas is accumulated inside the delamination, after some incubation period, the crack starts growing under the pressure of the accumulated gas. An important example is given by hydrogen induced delamination. Hydrogen absorbed by a metal is typically dissolved in the proton form within the lattice. Some of the protons reach the surface of pre-existing or freshly created cracks or delaminations where they recombine with electrons and form molecular hydrogen in the crack cavity. Since the molecular form of hydrogen is thermodynamically more stable, this process leads to accumulation of hydrogen gas inside the delamination crack. Under the excessive hydrogen pressure fracture often takes place even in the absence of any additional external loading. It is known, that the fracture toughness KIc in most cases cannot be assumed crack velocity independent in conditions of hydrogen embrittlement, however described by some kinetic functions KIc(v). As numerically shown in the author's earlier work for the internal crack growth, the crack velocity first increases in accordance with the kinetic function until reaching some value of vs and remains at the same level afterwards. Since, as has been obtained by the author in a previous paper, kinetic equations for internal and delamination cracks are essentially identical, the same conclusion can be derived for the latter. In this paper the stability and asymptotic approach to the constant velocity of delamination growth is proved analytically. If vs is known, the corresponding value of fracture toughness, Ks, is obtained by substituting vs into the kinetic function KIc(v) resulting in Ks=KIc(vs).

Affiliations: 1: Mathematics Department, Spelman College, Atlanta, Georgia 30314, USA


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