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some challenge in designing a reliable and predictive numerical model of hic is the sensitivity to the pressure field obtained from the atomistic modeling. for instance, the size and distribution of diffusion zones are strongly affected by the hydrogen pressure ( el-sayed et al., 1996 ; klibanov & klee, 2003 ). the direct computation of the hydrogen pressure is both complex and time-consuming, requiring adequate computational hardware. this was firstly solved by ni et al. (2013) through the implementation of a regional-cell pressure calculation, which is the approach followed in this review. it should be emphasized that the regional-cell pressure calculation in the fpz is not an alternative to the atomistic-scale pressure calculation. the fpz pressure is directly used by the code to calculate macroscopic strain rates for predicting slow crack growth using the hydrogen-enhanced scc (hesc) model ( mecking, 1990 ). to provide an overview of the approach, the scc model should be briefly recalled. the hesc model was introduced in the 1990s by mecking and subsequent studies by johnson (1993) on injection-induced stress corrosion cracking (iscc) in pipelines. it is based on the integration of fracture mechanics, which is well-known and understood in the oil and gas industry since decades, and thermodynamics to assess the coupling between fracture and crack tip.]( http://kip.uni-heidelberg.de/kip/l1.20/references/ref3.htm )
the open literature quotes for the steady-state condition as a result of advanced injection conditions ( >2000 kg/h) the formation of coherent hics for macroscopic crack lengths (allen et al., 1981 ; rajput et al., 1981 ; wolthuis & ellington, 1982 ; lindsay, 1992 ). typically, the crack growth rate increases with the square root of the load applied in the range from 2 to 10 % plastic strain. in all experiments under such conditions, only a small fraction of the crack tips was observed to be penetrated by micro cracks. on the other hand, cracks in the presence of hydrides are considered to grow at much higher rates ( gerberich et al., 1986 ; williams et al., 1986 ; huang & herberich, 1992 ; huang & herberich, 1994 ; gerberich, 2012 ).
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