Modelling of the hydrogen distribution at a crack tip

Abstract

A model has been developed to predict the distribution of hydrogen atoms at a crack tip with the unique feature of incorporation of generalised boundary conditions which account realistically for the electrochemistry-diffusion interface. The use of boundary conditions involving expressions for the flux allows identification of the conditions for diffusion and surface reaction control of hydrogen transport. For ferritic steels, which have a relatively large diffusivity compared with face centred cubic alloys, the model predicts that hydrogen transport is controlled by the kinetics of cathodic generation of hydrogen atoms. The crack-tip concentration is approximately an order of magnitude less than that predicted assuming the conventional constant concentration boundary conditions derived from diffusion controlled transport. The results imply that crack growth rates will be limited by the kinetics of surface reactions and that predictive models of crack growth rates and thresholds for cracking based on diffusion control should be reassessed. The use of generalised boundary conditions also enables the calculation of the time evolution of the hydrogen distribution in initially precharged metals. It is shown that the crack tip and crack walls act as sinks for hydrogen atoms in these circumstances, depleting the hydrogen atoms in the crack-tip region. The loss of hydrogen through the crack tip in precharged samples may affect the location of hydrogen cracking and is an additional factor to be considerred in comparing internal and external hydrogen embrittlement. It also raises questions concerning the meaning of tests on cadmium plated samples because of the loss of hydrogen through the crack tip once the coating has been fractured due to dynamic straining or crack advance.