Hydride Length Research Articles

Kinetics of crack growth in zirconium alloys (I): Temperature dependence of the crack growth rate

Delayed hydride cracking (DHC) tests were conducted on a cold-worked Zr–2.5Nb tube with hydrogen at different test temperatures ranging from 100 to 350 °C. Striation spacing corresponding to a critical hydride length increased with temperature, demonstrating that hydride cracking resistance is enhanced with temperature. Nonetheless, the crack growth rate (CGR) had a positive temperature dependence below 300 °C, showing that at temperatures below 300 °C, the CGR is governed by diffusion-controlled hydride growth. At higher temperatures above 300 °C, however, the CGR decreased rapidly, suggesting that the CGR is dictated not by the hydride growth rate but by the hydride cracking rate. This suggestion is evidenced by experiments where the threshold stress intensity factor for DHC or KIH increased sharply above 300 °C.

Effect of load ratio and hydrogen concentration on the crack growth rate in Zr–2.5Nb tubes

Crack growth rates (CGR's) were determined under sustained and cyclic loads using 17 mm compact tension and cantilever beam specimens taken from Zr–2.5Nb tubes charged to 6–100 ppm H. The cyclic load effect on the CGR was investigated at 250 °C where load ratios, R were varied from 0.13 to 1 with a constant K max. Under sustained loads, the CGR of the Zr–2.5Nb tube increased with supersaturation of hydrogen, Δ C and leveled off above 20–35 ppm H of the Δ C. Under cyclic loads with 1 cycle/min, the CGR at 250 °C decreased with decreasing R: 3.2 × 10 −8 m/s at R = 1 and 4.8 × 10 −9 m/s at R = 0.13. The striation spacing, corresponding to the critical hydride length, decreased with decreasing R, indicating easier cracking of the hydrides under cyclic loads. The decreased CGR under cyclic loads and its dependence on the Δ C are discussed using Kim's delayed hydride cracking model.

Threshold stress intensity factor, KIH for delayed hydride cracking of a Zr-2.5Nb tube with loading mode

Abstract The threshold stress intensity factors, KIH's, for delayed hydride cracking of a Zr-2.5Nb tube were determined using either load-increasing or decreasing modes over a temperature range of 160–280 °C with a step-wise load increase or decrease by 0 .5 MPa m , respectively. KIH's in the load-increasing mode were found to be higher than those in the load-decreasing mode. The striation spacing corresponding to the critical hydride length or lc showed a sharp drop between the 1st striation line to the 9th line and then leveled off to a constant value in the load-increasing mode. In the load-decreasing mode, it was rather constant from the 1st line to the 14th line due to a higher stress intensity factor KI with its gradual increase at a reduced KI closed to KIH. Supplementary tests demonstrated that a higher KIH in the load-increasing mode is due to the combined effects of a larger tip radius of the fatigue crack and creep working in the load-increasing mode. KIH had a negative temperature dependency in the load-increasing mode and it had no temperature dependency in the load-decreasing mode. To correlate KIH with twins, tensile tests were conducted on the Zr-2.5Nb tube and its textural changes during the tensile tests were investigated using an X-ray diffractometer. The number of twins increased over a temperature range of 150–300 °C and then decreased rapidly at over 300 °C with no twins at 350 °C. KIH of the Zr-2.5Nb tube with the loading modes was discussed in view of cracking of the hydrides by twining.

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.

Calculation of the delayed hydride cracking velocity vs. KI curve for Zr-2.5 Nb by critical hydride cluster length

In Zr-2.5 Nb alloy the delayed hydride cracking (DHC) velocity versus stress intensity factor KI relation exhibits a three stage curve. The first two stages of this curve have been numerically simulated by the authors in previous work, using the experimentally measured critical lengths of the hydride cluster for fracture and a numerical analysis of time-dependent hydride growth at the crack tip (D. Yan and R. L. Eadie, J. Mater. Sci.35 (2000) 5667; Idem., Scripta Mater. 43 (2000) 89). A modified experimental method was developed and this method allows hydride clusters formed under different KI to be separated so that the critical hydride length can be measured (Yan and Eadie, 2000). The numerical analysis was based on a simplified model, proposed by Shi and co-workers, that assumes a cylindrically symmetric stress distribution at the crack tip (S. Q. Shi, M. Liao and M. P. Puls, Modeling Simul. Mater. Sci. Eng.2 (1994) 1065; S. Q. Shi and M. P. Puls, J. Nucl. Mat.218 (1995) 30). In this work both the experimental work and the simulation of the DHC velocity versus KI curve are extended to include a different test temperature and the simulation results are compared with experimental measurements. This result is unique since both velocities and hydride cluster lengths have been determined in the same specimen over the range of KI right down to KIH. The two temperatures used 150 and 250°C cover the temperature range of most practical interest in CANDU pressure tubes. It was found that the simulated curves were in reasonably good agreement with the experimental measurements. The results also predicted the experimentally observed change in critical hydride length (striation size) with temperature.

Fracture strength of hydride precipitates in Zr–2.5Nb alloys

The hydride precipitate fracture strength as a function of precipitate size and temperature (23–250°C) in smooth tensile specimens of Zr–2.5Nb pressure tube material (nominal hydrogen content 100 ppm by weight) was studied using the acoustic emission technique. At room temperature, this strength is sensitive to hydride length when the average hydride length is short, and is insensitive to the hydride length when the average hydride length is longer than 25 μm. The hydride fracture strength decreases slightly with temperature, but a more rapid decrease in the yield strength offsets this decrease, resulting in a brittle-to-ductile transition at 120°C to 140°C in smooth tensile tests. The presence of hydrides causes a decrease in the ultimate tensile strength of the material at low temperatures, and has no effect at high temperatures for these smooth tensile specimens.

Hydride distribution around a blister in Zr–2.5Nb pressure tubes

Blisters were grown in Zr–2.5Nb pressure tube sections by a thermal gradient without applying external stress. The surrounding hydride distribution was analyzed. Hydride platelets were observed in the radial direction of the blister. The precipitation of these hydrides was found to be favored by low temperature of blister growth and slow cooling rate after blister formation. The misfit strain produced by hydride blister growth provides the stress necessary to promote radial precipitation. During the subsequent tensile test at 200°C (delayed hydride cracking test) the radial hydride length and thickness are increased. This increase is explained by a stress concentrator effect of the blister. When this effect vanishes, the increase of radial hydrides continues by an autocatalytic effect and stress concentrator effect of the hydride platelet. If a crack originated in the blister reaches the matrix it could propagate along a radial hydride previously precipitated.

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.

Modelling of time-dependent hydride growth at crack tips in zirconium alloys

The steady-state velocity model of delayed hydride cracking (DHC) in hydride-forming metals developed by Dutton and Puls has been extended to non-steady-state conditions. The development of a non-steady-state DHC model is important since it makes it possible to incorporate, for the first time, a realistic hydride fracture criterion as well as to determine time-dependent hydride growth at the crack tip. To accomplish this, a computer program, PDECHEB, has been used to simulate a moving-boundary problem at the tip of a growing hydride. Mathematical models that define the moving-boundary problem have been developed and tested. Preliminary results, assuming a constant critical hydride length, show that this program gives reasonable predictions on the hydride growth behaviour and parameters such as incubation time, maximum hydride length, and DHC velocity, as a function of stress intensity factor, yield stress, hydrogen concentration in solid solution, and temperature. Since, for simplicity, the theoretically expected dependence of the critical hydride length on the above parameters was not included in this study, very close agreement with experimental results is not expected. Nevertheless, comparison with limited experimental data shows qualitatively good agreement.

Effect of hydride precipitation on the elastoplastic stress field near a crack tip

Dissolved hydrogen in zirconium diffuses up the hydrostatic stress gradient and forms hydride platelets in the region of high stress. The hydride formation is accompanied by an expansion. The effect of hydride expansion on the elastoplastic stress, strain and displacement fields, is investigated in this paper by a finite-element discretization technique. It is shown that hydride formation causes an elastic unloading in the crack tip (reduction of the peak stress) and appearance of a peak stress at the front end of the hydride. Further unloading occurs along the hydride platelet, and depending on the hydride expansion, reversed plastic deformation may take place. Effects of the hydride length, its location with respect to the crack tip, and geometry of the front end extremity of the hydride, are also investigated.

Criteria of fracture initiation at hydrides in zirconium alloys II. Shallow notch

A general theoretical framework for DHC initiation, described in part I, is applied to the case of a shallow notch under tensile stress. A simple method of calculating the notch tip stress profile and the maximum normal stress σyymax that was developed previously is used to estimate the critical hydride length for DHC initiation. Comparison of the theoretical predictions of crack initiation with experimental data shows good agreement. It is suggested that a complete theoretical prediction of DHC initiation at blunt notches would require a combination of the proposed fracture criterion combined with the solution of a diffusion calculation.

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.

Modeling of Delayed Hydride Crack Initiation

This paper presents a solution to the one-dimensional time (transient condition) and temperature dependent diffusion problem adjacent to a crack-tip/flaw within the plastic zone region. The solution is used in addressing the problem of delayed hydride crack initiation in zirconium-2.5 wt. percent niobium. The mathematical solution predicts the critical hydride length at a given stress level and temperature for crack initiation.

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.

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.

The influence of hydride size and matrix strength on fracture initiation at hydrides in zirconium alloys

The effects of matrix strength (yield stress) on hydride fracture and alloy ductility have been studied as a function of stress state, hydride content, hydride size, and precipitation stress. Uniaxial and triaxial states of stress were investigated by using smooth and notched tensile specimens, respectively, containing 0.18 or 0.90 at. pct H, with the longest hydride platelet dimension varying from 5 to 400 μm. The majority of the hydrides in the specimens had their plate normals oriented parallel to the tensile axis direction. Crack initiation at hydrides was monitored using acoustic emission, finiteelement calculations were employed to determine the stresses and strains in the notched specimens, and metallographic and fractographic analyses were carried out to determine the state of fractured hydrides/voids near and on the fracture surface. These techniques showed that, up to a hydride platelet length of ∼50 to 100 μm and regardless of the stress state, a critical plastic strain, independent of matrix strength, controls the initiation of fracture in hydrides. The amount of plastic strain needed to fracture hydrides decreases as (a) the average hydride length increases and (b) the axiality of stress increases. The equivalent plastic strain to fracture small hydrides is ∼ 1 pct under a triaxial as opposed to ∼5 pct under a uniaxial state of stress. When the average hydride platelet lengths are longer than ∼50 to 100 μm, negligible plastic deformation is required to fracture hydrides. A critical applied stress then is the governing factor in all three materials, ranging from 750 to 850 MPa, depending on the stress state.

Some fractographic aspects of hydrogen-induced delayed cracking in Zr–2.5 wt% Nb alloys

The fractographic features after hydrogen-induced delayed cracking (HIDC) in Zr-2.5 wt% Nb pressure tube material have been studied as a function of stress intensity factor ( K), temperature and hydride dispersion. The important observations were of regularly spaced ductile striations parallel to the main crack front, and brittle cleavage markings between the striations. The striations were cusped due to dimple formation, and individual cleavage regions were separated by ductile ridges or shear cliffs. The size and morphology of the cleavage regions was consistent with the size and preferred orientation of hydrides near the crack tip. The inter-striation spacing increased exponentially with temperature, but within the range of study, was essentially independent of K. Neither hydride content nor dispersion had a significant effect on the fracture morphology. The results are consistent with a discontinuous mechanism of crack propagation involving the accumulation of hydride at the crack tip, followed by fracture through this embrittled region and subsequent crack arrest. The observations support recent theoretical models for HIDC which interpret the inter-striation spacing as a critical hydride length for crack advance.