PSI - Issue 33

Francesco Freddi et al. / Procedia Structural Integrity 33 (2021) 371–384 Author name / Structural Integrity Procedia 00 (2019) 000–000

373

3

number of electrons involved in the cell reactions

n F

Faraday constant (96485.33 [s∙A / mol]) [C O/R ] concentration of the oxidized/reduced species [mol / mm 3 ] m stoichiometric coefficient of the oxidized species l stoichiometric coefficient of the reduced species b a/c Tafel slope coefficient for the anode/cathode reaction �� ��� current density of the oxidation / reduction semi-reaction [A/mm 2 ] E ���� electric potential of the oxidation / reduction semi-reaction [V] I Corr corrosion current density [A / mm 2 ] r rebar radius [mm] PA Fe iron atomic weight ρ Fe iron density [g/mm 3 ] γ iron to rust density ratio β iron to rust molar mass ratio u displacement field α damage field ε strain tensor G � fracture toughness [N/mm] ℓ internal length parameter [mm] λ first Lamè parameter μ second Lamè parameter � coercivity constant ℂ fourth order elasticity tensor 2. Carbonation induced corrosion cover cracking

The carbonation induced corrosion cover cracking phenomenon is a complex degradation mechanism which involves three main processes: concrete carbonation, corrosion of the steel rebar and cracking of the concrete cover. Let Ω ∈ ℝ � �� � ������ be a RC element with prescribed displacements on the boundary portion � . The state of the materials, concrete and rebar, is described by the displacement field u and a scalar continuous field α: Ω→[0, 1] which can be seen as the material damage variable. Value of α equal to 0 represent the sound material while value equal to 1 is assumed in the areas where cohesion is fully lost. Cracks within the body are therefore represented as a transition zone from the unbroken to fully broken material. The width of the transition area is governed by the internal length parameter ℓ. In addition, the concrete portion of the solid is subject to carbonation whereas the steel rebar undergoes corrosion mechanisms. A brief description is given below. 2.1. Carbonation Carbonation of concrete is a chemical process in which the carbon dioxide (CO 2 ) reacts with the calcium hydroxide (Ca(OH) 2 ) present in the cement paste producing calcium carbonates (CaCO 3 ). Carbon dioxide penetrates and diffuses in gas form though the concrete pores. In order to react with the calcium hydroxide, it dissolves within the water present in the pores changing from gaseous to liquid phase following the reaction H 2 O + CO 2 (g) → HCO 3 - (aq) + H + (aq) (1) HCO 3 - (aq) → CO 3 2 - (aq) + H + (aq) The calcium hydroxide present in the cement paste also dissolves within the pore water in concrete passing from the solid to liquid phase according to the reaction