Transient hydrogen diffusion and hydride formation coupled with material deformation are studied in Zr-2.5Nb alloys used in the pressure tubes of CANDU nuclear generating stations. The energetics of the hydride formation is revisited and the terminal solid solubility of hydrogen in solution is defined on the basis of the total elastoplastic work done on the system by the forming hydride and the external loads. Probabilistic precipitation of hydride is modeled in the neighborhood of a crack tip under mode I plane strain loading and a uniform initial hydrogen concentration below the stress free terminal solid solubility. Finite element analysis is used to monitor the local distribution and time evolution of hydrogen concentration, hydride volume fraction, stress, and strain as the externally applied loads increase. The mechanistic effects of the solute hydrogen and hydride formation on the stresses at the crack tip are analyzed and their consequence on the fracture toughness resistance of the material is determined.

The finite element method was used to solve the coupled elastic–plastic boundary value problem and transient hydrogen diffusion initial boundary value problem. Solutions were obtained at room temperature and under plane strain deformation in the neighborhood of a blunting crack tip under small scale yielding conditions and in the neighborhood of a rounded notch in a 4-point bend specimen. A discussion of the finite element results in conjunction with different mechanisms of hydrogen embrittlement is presented. If a critical amount of hydrogen is required for hydrogen induced crack initiation, the present results predict locations of crack initiation sites at steel bend specimens which are in agreement with experimental observations on the occurrence of the first microcracking event.

The finite element method is used to solve the coupled large strain elastoplasticity boundary value problem and transient hydrogen diffusion initial boundary value problem. As an example, solutions are obtained in the neighborhood of a rounded notch in a 4-point bend specimen of alloy X-750 at two temperatures under plane strain deformation conditions. The model accounts for the dilatational strain caused by the presence of hydrogen in the lattice and the hydrostatic stress induced drift of hydrogen. The hydrogen population profiles in both normal interstitial lattice sites (NILS) and trapping sites are calculated and conditions for the predominance of the total amount of hydrogen by either of the populations are studied. The competition between hydrostatic stress and plastic strain in the enhancement of local hydrogen concentrations is investigated. The effect of different types of traps on the relative level of trapped hydrogen as a portion of the total hydrogen is examined. The numerical analysis in conjunction with current experimental evidence suggests a specifically designed line of experiments that will isolate the parameters crucial to hydrogen induced material degradation in X-750.

In a previous work (Lufrano et al., 1996), the authors investigated stress driven diffusion of hydrogen in a hydride forming system whose constitutive response was modeled as linearly elastic. In the present work the more realistic constitutive assumption of a purely elastic hydride that is accommodated elastoplastically by the surrounding matrix is used. Due to the nonlinearity in the material deformation, the classical description and calculation of the accommodation energy of formation and the interaction energy associated with an external stress using Eshelbys methodology are no longer valid. The elastoplastic deformation of the matrix due to the volume dilatation induced by the hydride, and the interaction of this deformation with externally applied stresses, are studied. The energetics of the hydride formation is revisited and the terminal solid solubility of hydrogen in solution is defined on the basis of the total elastoplastic work done on the system by the forming hydride and the external loads. Hydrogen diffusion and hydride formation coupled with the elastoplastic deformation of the material are modeled at a blunting crack tip in the case of the niobium–hydrogen system. Nonlinear finite element analysis is used to monitor the local distribution and time evolution of hydrogen concentration, hydride volume fraction, stress, and strain as the externally applied loads increase. A Griffith fracture criterion allows the calculation of a critical hydride size, in the neighborhood of the crack tip, at which cracking of the hydride particle by the local stresses is energetically favorable. Using this criterion for fracture initiation, one can predict the reduced fracture resistance of hydride forming systems quantitatively and investigate the fracture toughness dependence of the material on initial concentration and loading rate.

The finite element method was used to solve the coupled elastic–plastic boundary value problem and transient hydrogen diffusion initial boundary value problem. Solutions were obtained at room temperature and under plane strain deformation in the neighborhood of a blunting crack tip under small scale yielding conditions and in the neighborhood of a rounded notch in a four-point bend specimen. The hydrogen population profiles in both normal interstitial lattice sites (NILS) and trapping sites were calculated and conditions for the predominance of the total amount of hydrogen by either of the populations were studied. A discussion of the finite element results in conjunction with different mechanisms of hydrogen embrittlement is presented. If a critical amount of hydrogen is required for hydrogen induced crack initiation, the present results predict locations of crack initiation sites at steel bend specimens which are in agreement with experimental observations on the occurrence of the first microcracking event.

Transient hydrogen diffusion and elastically accommodated hydride formation coupled with material elastic deformation are studied in a hydride forming system. The constitutive behavior of the material is modeled as isotropically linear elastic and account is taken of the effect of the dilatational strain induced by the solute hydrogen and formed hydride. The concept of terminal solid solubility of hydrogen as affected by stress is described and the mode of hydrogen diffusion through the two-phase material (matrix + hydride) is discussed. Probabilistic precipitation of hydride is modeled in the neighborhood of a stationary sharp crack tip under mode I plane strain loading, fixed hydrogen concentration on the crack surfaces and the outer boundary, and a uniform initial hydrogen concentration below the stress-free terminal solid solubility. A full transient finite element analysis allows for numerical monitoring of the development and expansion of the hydride zone. Information about the shape, size and density of the hydride in the hydride zone is obtained. The mechanistic effects of the solute hydrogen and hydride formation on the stress intensity at the crack tip are analyzed and their consequence on the fracture toughness resistance of the material is discussed.

Finite element analysis is used to study the effect of mobile interstitial hydrogen on the deformation of metals and alloys in the case when hydrogen is in equilibrium with local stresses. The effect is studied by calculating the hydrogen atmosphere around a stationary crack tip in a linearly elastic isotropic material loaded in mode I plane strain conditions. Stresses, strains and equilibrium hydrogen concentrations are determined through an iterative finite element analysis while accounting for stress relaxation due to hydrogen induced local volume and elastic modulus changes. Numerical calculations reveal a zone immediately ahead of the crack tip in which the lattice is saturated with hydrogen. The dimensionless size of the saturation zone is found to be independent of the applied loads. The stiffness derivative method is used to calculate the hydrogen induced changes in the stress intensity factor. Calculations show that the presence of mobile interstitial hydrogen produces crack tip shielding when hydrogen induced changes in the elastic moduli are considered. The implications of the elastic analysis of the interaction between hydrogen in equilibrium with local stresses near a crack tip on the fracture resistance of materials are discussed. Then results are examined in conjunction with the elastic-plastic deformation at the tip.