13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- The analysis of the HAF process presents a serious difficulty: the experimental determination of the value of hydrogen concentration C( x,t) at certain point, x, for a given time t. This difficulty becomes particularly important in the analysis of HAF process for critical conditions, Ccr = C( cr x ,t cr). To solve this objection is essential (i) to find the HAF focus by means of metallographic techniques of the fractured specimens analysis [9,11,12], and (ii) to determine the local values of the variables governing the diffusion process, i.e., hydrogen concentration C, the hydrostatic stresses σi and equivalent plastic strains Piε (i = 1,2,3). The mechanical variables representing the stress-strain state in the hydrogen diffusion model can be obtained by numerical simulation revealing the evolution of stress-strain state in the notched specimen during CERT test. Unfortunately, nowadays an advanced numerical simulation code of general use that solves the problem stated in this paper is not available: the analysis of transient hydrogen diffusion assisted by stresses considering a 2D approach. To overcome this difficulty, the hydrogen concentration at any place and time of the transient diffusion assisted by stress state can be obtained by means of an ad hoc numerical code based on the finite element method (FEM) developed by the authors [13]. With the help of this tool the analysis of the time evolution of hydrogen concentration can be developed in the notched samples considered in this study during the CERT tests performed under different extension rates. The numerical simulations were carried out taking into account both approaches of the hydrogen diffusion assisted by stress state: one-dimensional (1D) and two-dimensional (2D). The differences between both simulations reveal a loss of directionality of hydrogen diffusion into metal. 2. Problem Statement The numerical modelling of this problem raises a huge complexity due to the following fact: the hydrogen diffusion equation must consider the stress field generated by the remote load applied during CERT test. In general terms hydrogen diffusion in metals obeys a Fick type diffusion law including an additional term to account the effect of the stress state, which is time dependent, i.e. transient for the analyzed cases. Thereby, the stress-assisted diffusion flux of hydrogen is: ∇σ + ∇ = C RT V D C D H J , (2) where D is the diffusion coefficient, VH the molar partial volume of hydrogen in metal, R the ideal gases constant and T the absolute temperature. The role of stress in hydrogen diffusion is commonly associated with one of the stress tensor invariants: the hydrostatic stress (or mean normal stress) σ. The relevance of stress in hydrogen transport by diffusion and HAF is well known from previous references [14-16], and, according to Eq. (2) is established that hydrogen diffuses not only to the points of minimum hydrogen concentration C (driven by the gradient of concentration), but also to the sites of maximum hydrostatic stress σ (driven by the gradient of stresses) [17]. So, the hydrogen diffusion process assisted by stress in non-homogeneous stress fields can be expressed as follows [8]: ∇ − ∇ ∇σ− ∇ σ = ∂ ∂ 2 H H 2 C RT V C RT V D C t C . (3) i.e., a parabolic-type partial differential equation given in terms of hydrogen concentration C and hydrostatic stress s as the relevant variables of the process od hydrogen transport.
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