A quantum-mechanically informed continuum model of hydrogen embrittlement
We present a model of hydrogen embrittlement based upon: (i) a cohesive law dependent on impurity coverage that is calculated from first principles; (ii) a stress-assisted diffusion equation with appropriate boundary conditions accounting for the environment; (iii) a static continuum analysis of crack growth including plasticity; and (iv) the Langmuir relation determining the impurity coverage from its bulk concentration. We consider the effect of the following parameters: yield strength, stress intensity factor, hydrogen concentration in the environment, and temperature. The calculations reproduce the following experimental trends: (i) time to initiation and its dependence on yield strength and stress intensity factor; (ii) finite crack jump at initiation; (iii) intermittent crack growth; (iv) stages I and II of crack growth and their dependence on yield strength; (v) the effect of the environmental impurity concentration on the threshold stress intensity factor; and (vi) the effect of temperature on stage II crack velocity in the low-temperature range. In addition, the theoretically and experimentally observed intermittent cracking may be understood as being due to a time lag in the diffusion of hydrogen towards the cohesive zone, since a buildup of hydrogen is necessary in order for the crack to advance. The predictions of the model are in good quantitative agreement with available measurements, suggesting that hydrogen-induced degradation of cohesion is a likely mechanism for hydrogen-assisted cracking.
© 2004 Elsevier. Received 17 August 2003, Revised 4 February 2004, Accepted 13 February 2004, Available online 13 April 2004. E.A.C. and M.O. are grateful to the US Department of Defense for support provided through Brown University's MURI Center for the "Design and Testing of Materials by Computation: A Multi-Scale Approach." E.A.C. also acknowledges the Army Research Office for partial support. M.O. acknowledges the Office of Naval Research for partial support provided under grant N00014-96-1-0068.