Modeling stress and temperature history effects on the initiation
of hydride cracks at blunt flaws in Zr-2.5%Nb pressure tubes
Lars O. Jernkvist, Ali R. Massih
Quantum Technologies AB, Uppsala, Sweden, Malmö University, Malmö, Sweden.
Objective
To develop an integrated computational model for stress- and temperature-directed hydrogen transport, metal-hydride phase transformation and hydride induced emrittlement, crack initiation and crack
propagation in zirconium alloys. The model utilizes continuum mechanics in a three-dimensional finite element setting and is intended for macro-scale engineering analyses of components with arbitrary geometry and thermal-mechanical operating history.
Background
Hydrogen absorption by zirconium and other group 4 or 5 transition metals may lead to precipitation of a binary metal hydride phase, MHx, where x ranges from about 1.5 to 2.0. Since the hydride phase is
very brittle, the hydride precipitation may significantly degrade the material’s strength and ductility.
a) Precipitates of zirconium -hydride at a stressed notch in Zr-2.5%Nb CANDU pressure tube material [1].
b) Zirconium-hydrogen binary phase diagram. The yellow region is of practical interest for hydride induced embrittlement.
Predicting hydride induced failures in zirconium alloys is complicated, since the precipitation of hydrides depends on the space-time variation of stress and temperature in the material. Several phenomena have to be considered and modeled simultaneously:
Hydrogen diffusion, driven by gradients in stress, temperature and hydrogen concentration Metal-hydride phase transformation, i.e. precipitation and dissolution of hydrides
Stress-directed orientation of the platelet-shaped hydride precipitates, which induces a strong anisotropy for the expansion and strength of hydrided material
Expansion of the material, caused by interstitial hydrogen atoms as well as hydride precipitates, and resulting in internal (misfit) stresses
Cracking and fracture of the hydrided material
In the work presented here, submodels for these phenomena have been merged into a comprehensive computational model, intended for engineering applications [2].
Modeling approach
The multi-field partial differential equations (PDEs) for the aforementioned phenomena are solved in a 3D finite element (FE) setting, in which the solutions for hydrogen transport and mechanical equilibrium are separated. A continuum description is used for the
hydrided material, meaning that hydride precipitates are ”smeared”. The platelet- shaped -hydrides are represented by two local state variables: the hydride volume fraction and the hydride mean orientation.
These internal variables are key parameters in the calculation of local strength, toughness and expansion of the hydrided material. Their space-time variation is calculated from the space-time variation of temperature and stress through point-kinetics
models for metal-hydride phase transformation and stress-directed orientation of hydride precipitates.
Fracture of the hydrided material is explicitly modeled by use of interface elements and a cohesive zone fracture model in the FE implementation. The cohesive strength,
c, and fracture energy, G, of the material are calculated
from the local concentration and orientation of hydrides
through correlations based on mechanical tests (see below).
Application: History effects on crack initiation
The model has been validated and calibrated against data from separate effect tests, e.g. tests on
stress- and temperature-directed hydrogen diffusion, stress-directed orientation of hydride precipitates, and various types of fracture tests on hydrided zirconium alloys. Below is an example, in which the
model is used to simulate a series of tests on crack initiation in notched three-point bend specimens, sampled from unirradiated Zr-2.5%Nb CANDU pressure tubes with 45 wppm hydrogen [1].
The tests aimed at investigating the effects of preceding history of stress and temperature on the stress needed for crack initiation at the notch. The samples were first subjected to ratcheting thermal cycles (peak temperature insufficient to dissolve all hydride phase) while held at constant and moderate load. This resulted in local accu-mulation of hydrides at the notch, due to stress-directed hydrogen diffusion. The samples were then loaded at room temperature until acoustic emissions indicated hydride fracture. This crack initiation stress (bending stress at the tube inner surface at time of hydride fracture) was
para-metrically studied with respect to the number of preceding thermal cycles and the constant stress level at which the notch-tip hydrides were formed during thermal cycling.
a-b) Three-point bend specimen and 2D FE mesh thereof. c) Load and temperature history for a test with 3 thermal cycles under a constant bending stress of 190 MPa.
d-e) Calculated notch-tip distributions after 10 thermal cycles with a constant bending stress of 190 MPa.
f) Calculated crack initiation stress versus number of
thermal cycles and bending stress during thermal cycling. Measured data from [1] included for comparison.
g) Calculated evolution of local hydrogen concentration and hydrostatic stress, 10 µm ahead of the notch tip.
Conclusions
A computational model, intended for engineering analyses of hydride induced embrittlement and fracture of zirconium alloys, has been developed and validated against experiments.
The model solves the governing multi-field PDEs for mechanical equilibrium together with
temperature- and stress-directed hydrogen diffusion in a 3D FE setting. Point-kinetics models are used for metal-hydride phase transformation and stress-directed orientation of hydrides, while a cohesive zone fracture model caters for initiation and propagation of cracks.
The presented application of the model to crack initiation tests on hydrogen-charged Zr-2.5%Nb
pressure tube material confirms the observed effect of ”thermal ratcheting” on lowering the threshold stress for hydride induced crack initiation. The effect is caused by local accumulation of brittle
hydride precipitates at stress concentrations, in cases where the peak temperature of the thermal cycle is insufficient to dissolve all hydride phase.
The model reproduces the crack initiation tests with fair accuracy.
Differences are caused mainly by imprecise correlations for the material’s fracture properties. The presented results underline the importance of thermal-mechanical operating history
to the embrittlement and fracture of zirconium alloy components exposed to hydrogen.
References
[1] J. Cui et al., 2009.
Journal of Pressure Vessel Technology, Vol. 131, Paper ID 041406.
[2] L.O. Jernkvist, A.R. Massih, 2013.
Computational Materials Science, (Articles to appear in forthcoming issues).
[3] T. Asada et al., 1991.
American Society for Testing and Materials, ASTM STP-1132, pp. 99-118.
a) Correlation for the fracture energy of dilute Zr alloys, plotted with respect to hydride volume fraction and hydride orientation. b) Results of fracture toughness tests on hydrided
Zr-2.5wt%Nb materials with slightly different orientation of the hydrides [3].
a) b) a) b) MS &T 2013, Oct. 27 -31, 2013. Montreal , Q C, C anada. a) b) c) d) Volume fraction hydride phase f) g) e) Fraction radial hydride precipitates
