M.P. Puls

ELASTIC AND PLASTIC ACCOMMODATION EFFECTS ON METAL-HYDRIDE SOLUBILITY

Abstract A model is presented that is capable of accounting for the hysteresis observed in the measured terminal solid solubilities (TSS) of metal hydride systems. Two distinct TSS are identified: 1. (i) a TSS determined on cool-down governed by hydride nucleation and the elastic accommodation energy arising from the hydride-matrix misfit; 2. (ii) a TSS determined on heat-up and dominated by plastic accommodation effects. The energy associated with the plastic accommodation effects is expected to be much smaller than that due to elastic accommodation. The heat-up TSS is therefore expected to be a good approximation to the “equilibrium”, or stress-free, TSS. It follows that the hysteresis between the activation energies of the heat-up and cool-down TSS is approximately equal to the elastic accommodation energy. The predictions of the model are tested with reference to TSS data derived from measurements on the V, Nb, Zr and Ti-H systems and are found to be in reasonable agreement with the data. Possible effects that the hysteresis of the TSS may have on the hydrogen-induced delayed cracking mechanism are discussed.

The terminal solid solubility of hydrogen and deuterium in Zr-2.5Nb alloys

Abstract The terminal solid solubility (TSS) of hydrogen or deuterium is an important parameter in Zr alloys that are used in the nuclear industry. If this solubility is exceeded, it can make the alloys susceptible to delayed hydride cracking. Accurate expressions for the TSS are necessary for modelling delayed hydride cracking as well as deuterium ingress into pressure tubes and blister formation in pressure tubes in contact with their calandria tubes. Measurements of the changes in the dynamic elastic modulus have been used to establish expressions for the TSS as a function of temperature and to study the hysteresis between hydride dissolution and precipitation. It is shown that the hysteresis is particularly sensitive to the thermal history of the sample (such as the prior maximum temperature, hold time at maximum temperature and cooling rate). As a result, the precipitation TSS (TSSP) has a range of values bounded by the solubility equations designated TSSP1 and TSSP2. These are obtained, respectively, by cooling from an upper- and a lower-bound maximum temperature. The TSSD equation obtained in this study is very close to previously determined expressions, but the TSSP equations differ significantly from earlier results.

Effects of crack tip stress states and hydride-matrix interaction stresses on delayed hydride cracking

A model of slow crack propagation based on the delayed hydride cracking (DHC) mechanism in hydride-forming alloys has been critically examined and evaluated to take account of recent experimental and theoretical advances in the understanding of hydride fracture and terminal solid solubility (TSS). The model predicts that the DHC velocity is a sensitive function of the hydrogen concentration induced in the bulk of the material as a result of the direction of approach to test temperature. For test temperatures approached from below, factors such as the hydridematrix accommodation energies, the stress state at the crack tip, and the value of the yield stress have a strong effect on the DHC arrest temperature in the technologically interesting temperature range of 400 to 600 K. A fracture criterion is explored based on the need to achieve a critical hydride length in the plastic zone at the crack tip. A necessary condition for DHC is that the crack tip hydride must grow to this critical length. An approximate estimate is made for the steady-state growth limit of the crack tip hydride as a function of the direction of approach to temperature and the crack tip stress state. For temperatures approached from below, growth of the crack tip hydride is limited to just outside the plastic zone boundary at low temperature, gradually receding toward and inside the plastic zone boundary with increasing temperature. At lowKI values, this limits the crack tip hydride lengths to below their critical values for fracture. This could be one condition forKIH. For test temperatures approaches from above, the growth limit is significantly increased, and the sensitivities to the above parameters become less evident.

Criteria for fracture initiation at hydrides in zirconium alloys. I: Sharp crack tip

Abstract A theoretical framework for the initiation of delayed hydride cracking (DHC) in zirconium is proposed for two different types of initiating sites, i.e., a sharp crack tip (considered in this part) and a shallow notch (considered in part II). In the present part I, an expression for KIH is derived which shows that KIH depends on the size and shape of the hydride precipitated at the crack tip, the yield stress and elastic moduli of the material and the fracture stress of the hydride. If the hydride at the crack tip extends in length at constant thickness, then KIH increases as the square root of the hydride thickness. Thus a microstructure favouring the formation of thicker hydrides at the crack tip would result in an increased KIH. KIH increases slightly with temperature up to a temperature at which there is a more rapid increase. The temperature at which there is a more rapid increase in KIH will increase as the yield stress increases. The model also predicts that an increase in yield stress due to irradiation will cause an overall slight decrease in KIH compared to unirradiated material. There is good agreement between the overall predictions of the theory and experimental results. It is suggested that more careful evaluations of some key parameters are required to improve on the theoretical estimates.

The effects of misfit and external stresses on terminal solid solubility in hydride-forming metals

Abstract General expressions are derived for the solubility of hydrogen in equilibrium with internally and externally stressed hydrides. These expressions are applied to some data for the terminal solid solubility (TSS) of hydrogen in zirconium and its alloys to estimate (a) the amount of hydride-matrix misfit strain energy lost to plastic deformation and (b) the amount of undercooling below the constrained TSS needed to initiate hydride nucleation. It is found that about 50% of the total, theoretically estimated misfit strain energy is converted to plasttic deformation energy. This estimate varied little amongst the various TSS data. Undercooling values, on the other hand, showed considerable variation, ranging from about 0 K to 40 K. The analysis implies that the hydrides likely retain some coherency with the matrix and that the undercooling required to overcome the barrier to nucleation contributes, in some cases, significantly to the total shift between the TSS data measured on heating and on cooling.

Hydrogen concentration limit and critical temperatures for delayed hydride cracking in zirconium alloys

Abstract An experimental study was carried out to determine the hydrogen concentration limit as a function of temperature at which delayed hydride cracking (DHC) commences in Zr-2.5 Nb pressure tube material. For a given hydrogen content of the specimen, two critical temperatures were observed in this work — a DHC initiation temperature, T c at which DHC would initiate when approaching the test temperature from above the solvus (or terminal solid solubility) for hydride dissolution (TSSD) and a DHC arrest temperature, T h , obtained by heating the same specimen from T c after DHC had started. Both of T c and T h are close to, but below, temperatures defined by TSSD for the specific hydrogen content of the specimen. A theoretical analysis was carried out to quantitatively derive the hydrogen concentration limit and these critical temperatures. The theoretical por T c depends sensitivity on the particular solvus or terminal solid solubility curve for hydride precipitation (TSSP) used, since there is a wide range of values for TSSP depending on the thermal-mechanical history of the material. It is also suggested that T h is governed by the TSSP for hydride growth, in contrast to T c , which is governed by the TSSP for hydride nucleation. A model for a previously observed critical temperature ( T A ) is also proposed. T A is a DHC arrest temperature, obtained by approaching the test temperature from a lower temperature. The model suggests that T A is controlled by the energy difference between TSSD, TSSP and the hydrostatic stress at the crack tip.

On the consequences of hydrogen supersaturation effects in Zr alloys to hydrogen ingress and delayed hydride cracking

Abstract Previous experimental and theoretical studies of hydrogen charging in Zr alloys are critically reviewed. A previously developed model of the hysteresis in the terminal solid solubility (TSS) of hydride-forming metals is extended to derive an expression for the solubility limit during cooldown in the presence of hydrides and applied to rationalize the extant results on hydrogen charging. The various TSS values and the hysteresis between them is governed by the elastic and plastic components of the elastic-plastic hydride/matrix accommodation energy. These energies vary significantly with temperature as a result of their dependence on the yield stress. In thin samples coated with a hydride layer, the ability of the interior of the sample (under thermal cycling) to increase its hydrogen content above that expected from a simple equilibration with the external layer is explained in terms of this model for TSS hysteresis and the difference in TSS levels between interior and exterior hydrides. The same model can be used to explain the high interior hydrogen levels attainable under isothermal or temperature-cycling hydrogen-ingress conditions. Previous models of hydrogen ingress can account for the observed results if modified to include the TSS hysteresis effects. The model of TSS hysteresis is used to provide an explanation for the effect of direction of approach to test temperature on delayed hydride crack velocity.

Fracture initiation at hydrides in zirconium

The effect of hydride size and stress state on fracture initiation at hydrides in a reactor grade Zr material has been studied. Uniaxial and triaxial states of stress were imposed by using smooth and notched tensile specimens, respectively. Crack initiation at hydrides was monitored using acoustic emission (AE). The specimens contained, nominally, either 0.18 or 0.90 at. pct hydrogen. Plate-or needle-shaped hydrides having different lengths were produced by varying the cooling rate to room temperature from the hydrogenation temperature. Initial orientation of the plate normals of the hydrides with respect to the tensile axis was mainly random. After deformation, the hydrides near the fracture surface were all oriented with their plate normals perpendicular to the tensile axis direction. Regardless of the hydride size, fracture at hydrides commenced at stress levels just above the proportional limit under uniaxial deformation. Average plastic strain values at initiation were ~0.2 pct. Slightly lower values of plastic strain were needed to initiate fracture at hydrides under triaxial loading. Fracture of the hydrides was always through-thickness and specimen fracture ductile. This is in contrast to previous results on hydride fracture obtained using the pressure tube alloys. In these materials, the fracture of hydrides with their plate normal oriented parallel to the tensile axis became less ductile as the hydride length increased.

Finite element calculations of the accommodation energy of a misfitting precipitate in an elastic-plastic matrix

The elastic-plastic accommodation energy generated by the formation of a plate-shaped inclusion in an effectively infinite solid is calculated using two-dimensional (2-D) and three-dimensional (3-D) finite element techniques. A typical example of the occurrence of such an inclusion, modeled in detail in this article, is the formation of a zirconium hydride platelet in a zirconium alloy. To verify the finite element models, initial calculations were based on a linear elastic model of the inclusion and the surrounding matrix material, plus elastic-plastic solutions of an isotropically misfitting spherical inclusion expanding within an elastic/perfectly plastic, infinite solid. Good agreement with the corresponding exact analytical results was found. The finite element analysis was used to determine the accommodation energy of isotropically and anisotropically misfitting oblate spheroids contained in an elastic/perfectly plastic medium. Calculations were carried out for oblate spheroids with aspect ratios (semiminor to semimajor axes) of 0.75, 0.5, 0.25, and 0.1. In contrast to the elastic result, the elastic-plastic accommodation energy values increased with decreasing aspect ratio. This result is due to an increase in the hydrostatic component of the stress in the matrix and a consequent loss in ability to decrease the misfit stresses by plastic deformation. Three-dimensional analyses of cuboidal inclusions expanding into infinite elastic and elastic/plastic solids were also performed. The results depended on mesh density, but reasonable values could be obtained at moderate mesh densities.

Delayed hydride cracking in zirconium alloys in a temperature gradient

Abstract Past theoretical models of delayed hydride cracking in zirconium alloys have assumed a uniform temperature distribution in the material. However, in real components, a temperature gradient may be set up, for example, when a through-wall crack leaks hot, pressurized fluid. Since hydrogen is thermodynamically inclined to diffuse to cold regions, its diffusion to the flaw tip in a thermal gradient will be affected. We have modified the steady-state model of delayed hydride cracking to take account of such a temperature gradient. The new model predicts an increase in the crack velocity in a positive temperature gradient (crack-tip cooler than surroundings) and a reduction in a negative temperature gradient. The model also predicts a shift in the temperature at which cracking ceases if the temperature is attained by heating; this critical temperature increasing in a positive gradient and decreasing in a negative gradient. Experiments have confirmed the trends predicted by the modified model of DHC.