Hydride Cracking In Zirconium Alloys Research Articles

Multi-physics modeling of delayed hydride cracking in zirconium alloys

Delayed hydride cracking (DHC) threatens the safety and integrity of Zircaloy components. The typical feature of DHC is presented as the intermittent fracture with the striations on the fracture surface. To reproduce the multi-field coupling process and reflect the essential features of DHC, an improved cohesive model is developed considering the hydride embrittlement and irradiation effects, based on which a multi-field coupling computation scheme is proposed. The model is validated by comparing the predictions of DHC velocity and striation spacing with some experimental results. A comprehensive study of multi-field coupling DHC behavior is performed The evolution and interplay of the mechanical and chemical fields are obtained together with the effect of temperature. The results indicate that: (1) the stress concentration around the crack tip is an important factor to drive the process of multi-field coupling DHC; (2) the subsequent incubation periods are much shorter than the first incubation period, because the formed hydrides during the previous cracking provide an effective source of hydrogen for a new process of cracking. This work lays a foundation for the future research on DHC.

The first step for delayed hydride cracking in zirconium alloys

Two models for delayed hydride cracking (DHC) in zirconium alloys are distinguished by their first step: – The loading of a crack induces hydride precipitation. The hydride is postulated to create a hydrogen concentration gradient, where the bulk concentration is greater than that at the crack tip. This concentration gradient is taken as the driving force for diffusion of hydrogen to the crack tip, and subsequent hydride growth. This model is called the precipitate first model (PFM). – The tensile stress at the crack tip induces a gradient in chemical potential that promotes the diffusion of hydrogen to the crack tip. Hydrides form if the hydrogen concentration reaches the solubility limit for hydride precipitation. The mechanism is postulated to create a hydrogen concentration gradient, where the bulk concentration is lower than that at the crack tip. The gradient in chemical potential is taken as the driving force for diffusion of hydrogen to the crack tip, and subsequent hydride growth. This model is called the diffusion first model (DFM). The second model, DFM, is developed. This model is shown to describe the main features of the experimental observations of DHC, without invoking new phenomena, such as reduction in the solubility limit for precipitation of hydride, as required by the PFM.

Comment on ‘A combined SIF and temperature model of delayed hydride cracking in zirconium materials’, by A.A. Shmakov et al.

Given the experimental facts related to delayed hydride cracking in zirconium alloys and the DHC models proposed so far, critical comments on “A combined SIF and temperature model of delayed hydride cracking in zirconium materials” by A.A. Shmakov were made, demonstrating that the authors’ DHC model is irrational.

Review of the initiation and arrest temperatures for delayed hydride cracking in zirconium alloys

Based on Kim's delayed hydride cracking (DHC) model, this study reanalyzes the critical temperatures for DHC initiation and arrest in zirconium alloys that had previously been investigated with Puls DHC model. In an unratcheting thermal cycle where DHC crack tip hydrides were dissolved fully at the peak temperature, the DHC initiation was suppressed, which required a supercooling or ΔT from the terminal solid solubility for dissolution (TSSD) temperatures. At a hydrogen concentration as 7 ppm H, the DHC initiation temperatures coincided with the TSSD, which is in conflict with Puls' DHC model. In a ratcheting thermal cycle, where the hydrides precipitated at the DHC crack tip were not fully dissolved, the DHC initiation was enhanced, so as to require a lesser ΔT, compared to that of the unratcheting thermal cycle. Therefore, the DHC initiation temperatures are concluded to depend upon at what temperatures the hydrides can nucleate in the zirconium matrix with the supersaturated hydrogen concentration. The DHC arrest temperatures were governed by the critical supersaturated hydrogen concentration or ΔC regardless of the thermal cycle treatment, providing further supportive evidence that Kim's DHC model is feasible.

Diffusion Model of Delayed Hydride Cracking in Zirconium Alloys

We develop a method for the evaluation of the rate of delayed hydride cracking in zirconium alloys. The model is based on the stationary solution of the phenomenological diffusion equation and the detailed analysis of the distribution of hydrostatic stresses in the plane of a sharp tensile crack. The rate of delayed hydride cracking in reactor tubes made of Zr-2.5% Nb alloy is found both theoretically and experimentally. It is shown that the theoretical results are in good agreement with the experimental data.

Critical length and thickness of hydride plates with delayed hydride cracking in zirconium alloys

A method for calculating the critical length and thickness of hydrides with delayed cracking in commercial zirconium alloys is developed. The critical characteristics of hydride precipitates are estimated for pipes made of the alloy Zr-2.5%Nb. It is shown that the theoretical results agree with the experimental data.

A theoretical study of the kinetics of hydride cracking in zirconium alloys

A diffusion model is suggested for computing the rate of delayed hydride cracking (DHC) in nonirradiated zirconium-base alloys. The rates of DHC in claddings of fuel elements of VVER and RBMK reactors and in pressure pipes of CANDU reactors are predicted.

Delayed hydride cracking in zirconium alloys in a temperature gradient

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.

Embrittlement and the Bistable Crystal Structure of Zirconium Hydride

The stability of the $\ensuremath{\epsilon}$ phase of zirconium hydride is studied using the pseudopotential plane wave method. The fluorite structure is mechanically unstable with respect to a tetragonal distortion. However, the minimum corresponding to $c>a$ is almost degenerate in energy with that for $c<a$. The distortion explains the uniaxial misfit strain responsible for delayed hydride cracking in zirconium alloys.

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

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.

Dependence of the threshold stress intensity factor on hydrogen concentration during delayed hydride cracking in zirconium alloys

The theoretical work on the criterion for fracture initiation at hydrides at sharp crack tips in zirconium alloys is extended to include the effect of hydrogen concentration in solid solution on the threshold stress intensity factor, K IH. The analysis shows that the crack-tip hydride can only grow to a certain maximum length which depends on hydrogen concentration in solution and the stress intensity factor. Analytical and numerical solutions of the critical hydride length for fracture show that it increases as temperature increases and as the stress intensity factor decreases. These results are used to develop the relationship between the hydrogen concentration in solution and K IH. This shows that K IH increases as the hydrogen concentration in solution decreases. The variation of the crack-tip critical hydride length with temperature, yield strength and applied K I is also derived and the results compared with striation spacing data obtained from fracture surfaces.

Categorization of delayed hydride cracking in zirconium alloys in terms of cumulative and non-cumulative fracture modes

Cottrell categorized [2] fracture modes into two types: non-cumulative and cumulative. The former in its extreme form, is typified by the behaviour of a sharp slit in a fully ductile solid opening up under plane strain tension as shown somewhat ideally in Fig. 1; the behaviour is represented by the injection of edge dislocations into the material from the tip along slip lines at about 45 ° to the tensile loading. The plastic notch widens as it deepens and each dislocation of Burgers vector b, injected into a slip line from the tip, contributes an increment b/¢2 to both the width and depth of the notch. The plastic zones spread much mere readily than the notch across the section, and we therefore have a "non-cumulative" situation in which each increment of growth of the plastic notch requires the injection of more dislocations into the slip lines, and these push the existing dislocations further across the section. The plastic zone increases in size and soon spans the whole load-bearing cross-section, so becoming general yield. We therefore have a stable situation provided the applied stress is below general yield levels. With the extreme form of non-cumulative fracture shown in Fig. 1, the crack growth resistance is high (the slope of the J~ curve is very high) and is manifested by a crack tip opening angle (CTOA) of 908.

Initiation of delayed hydride cracking in zirconium-2.5 wt% niobium

Delayed hydride cracking in zirconium alloys is caused by the repeated precipitation and cracking of brittle hydrides. The growth kinetic of the hydrides have been measured to evaluate the critical hydride length for crack initiation. Hydride growth leading to crack initiation follows an approximate (time) 1 3 law on the average; crack propagation proceeds in a stepwise fashion. The critical length of hydride for crack initiation increases with stress and temperature. The fracture criterion for crack initiation predicts the critical hydride length at a give stress level and temperature. The fracture initiation mechanism of the hydride confirms the temperature effects for heating and cooling cycles under services loads.

Modelling Delayed Hydride Cracking in Zirconium Alloys

The most recent theory of delayed hydride cracking in zirconium alloys, herein called herein Dutton-Puls theory, is reviewed. The theory is examined in relation to recent experimental results pertaining to the partial molar volume of hydrogen in zirconium, the size of the crack tip hydrides and the effect of temperature changes on the cracking rate. The straition markings on the fracture surface are considered. An alternate theory of striation formation originally proposed for titanium alloys and involving a semi-cohesive zone at the crack tip is recommended.Arguments are presented from the literature that the hydride transformation is martensitic in nature and that the hydride constraint energy W t inc should be modified. Suggestions for further work in the areas of the precipitation hysteresis and with regard to the effect of hydride precipitation on crack tip stresses are made.

Modelling Delayed Hydride Cracking in Zirconium Alloys

Modelling Delayed Hydride Cracking in Zirconium Alloys

The precipitation of γ-hydride plates in zirconium

On slow cooling high purity zirconium containing 40 ppm hydrogen, γ-hydride (ZrH) precipitates as acicular plates. This paper considers the possibility that such plates form by a displacive or shear transformation. The habit planes and orientation relationships of hydrides have been determined and related to possible dislocation mechanisms for the transformation. It is shown that habit planes close to {10–17} Zr are predicted for hydrides having a [l1̄0] γ ∥[12̄10] Zr, (111̄) γ~ ∥(0001) Zr orientation relationship. Hydrides with {10-10} habit planes have a [11̄0] γ or [101̄] γ ∥[12̄10] Zr and [001] γ or [010] γ ∥[0001] Zr orientation relationship. In this case, the observed habit plane can only be invariant if the pure lattice strain is succeeded by a pure shear shape change. Experimentally, internal twinning in the plates and dislocation arrays at the interface are observed and it is suggested that these accomplish the required shape change. In the final section of the paper, these results are related to the problem of hydride reorientation and hydride cracking in zirconium alloys.