Author’s reply to “Review of the thermodynamic basis for models of delayed hydride cracking rate in zirconium alloys, M.P. Puls in J. Nucl. Mater. 393 (2009) 350–367”

The aim of this work is a reply to Puls’s paper entitled “Review of the thermodynamic basis for models of delayed hydride cracking (DHC) rate in zirconium alloys in J. Nucl. Mater. 393 (2009) 350–367” claiming that the thermodynamic basis of Dutton and Puls’s model termed the first version of the old models is valid when compared to Kim’s new model. The critical defect of the first version old model is to assume that the bulk hydrides are the source of diffusible hydrogen and the stress would decrease the crack tip concentration in solution even without hydride precipitation, creating the difference in hydrogen concentration or ΔC between the crack tip and the bulk. The latter assumption leads to predict DHC even at high temperature above 300 °C without a thermal cycle, demonstrating that the first version old model is unrealistic. The second version old DHC model assumes that the stress gradient is driving hydrogen to the crack tip, increasing the crack tip concentration over the bulk concentration, which is faulty because it violates the thermodynamic principle that tensile stresses lower the chemical potential of hydrogen or the hydrogen solubility. Despite the old models’ claim that the driving force for DHC is the stress gradient, their analytical equations indicate that the crack growth rate (CGR) is governed by the ΔC, demonstrating that the driving force for the DHC is the ΔC, not the stress gradient.