A model of the electrochemical behaviour within a stress corrosion crack

A mathematical model of the electrochemical behaviour within a stress corrosion crack is proposed. Polarization field, crack geometry, surface condition inside the crack, electrochemical kinetics, solution properties and applied stress can be represented by the polarization potential and current, the electrochemical reactive equivalent resistance of the electrode, the change in electrolyte specific resistance and surface film equivalent resistance, respectively. The theoretical calculated results show that (i) when anodic polarization potential is applied, the change in the crack tip potential is small; (ii) when cathodic polarization potential is applied, the crack tip potential changes greatly with the applied potential; (iii) the longer the crack, the smaller the effect of the applied potential on the crack tip potential in both anodic polarization and cathodic polarization conditions. The calculated results are in good agreement with previous experimental results.Notation coordinate, from crack mouth (on the metal surface) to crack tip (cm) - y y = s_LL/(s₀ – s_L) + L – , function of (cm) - y₀ y₀ = s_LL/(s₀ – s_L) + L (cm) - V polarization potential (V) - galvanic potential of electrode (V) - ₁ galvanic potential of electrolyte (V) - t sample thickness (cm) - w sample width (cm) - S_L crack tip width (cm) - S_o crack mouth width (cm) - L crack length (cm) - s() crack width at position (cm) - _lo specific resistance of electrolyte, as a constant ( cm) - _s specific resistance of metal ( cm) - (, y) specific resistance of electrolyte, varies with potential and crack depth ( cm) - R_b (, y) electrochemical reactive equivalent resistance of electrode, varies with potential and crack depth () - R₁ electrolyte resistance () - R_s metal resistance () - r(, y) surface film equivalent resistance, varies with potential and crack depth () - r_o surface film equivalent resistance, as a constant () - I_o total polarization current (A) - I net polarization current from integrating 0 to in Fig. 2 (A) - polarization overpotential (V) - _a anodic polarization overpotential (V) - _c cathodic polarization overpotential (V) - Euler's constant