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In this work, we consider the diffusion-controlled axisymmetric fracture in an
infinite space, and half-space. An important example of diffusion-controlled
fracture growth is given by hydrogen induced cracking. In metals, hydrogen is
typically dissolved in the proton form. When protons reach the crack surface,
they recombine with electrons and form molecular hydrogen in the crack cavity.
Then, the fracture can propagate even in the absence of any external loading, that
is, only under the excessive pressure of gas hydrogen accumulated inside the
crack.