Temperature and constraint effects on hydride fracture in zirconium alloys

https://doi.org/10.1016/S0013-7944(99)00107-1Get rights and content

Abstract

The fracture of hydrides in zirconium alloys is under consideration. According to the present boundary value problem, a hydride platelet lies ahead of a semi-infinite crack, along the crack plane. The surrounding material is elastic–plastic zirconium alloy. The platelet is either continuous or split into two parts, connected by a ductile matrix ligament. At distances from the crack tip, which are large compared to the hydride and the plastic zone size, the KT field is applied and mode I, plane strain and contained yielding conditions prevail. Hydride platelet failure initiation and growth is simulated by using a de-cohesion crack growth model and the stress intensity factor, which causes fracture, is estimated at various temperatures as well as under various constraint conditions. Comparison of the calculated temperature effect on toughness with the experimental one is satisfactory. Fracture toughness decreases with T-stress. This effect is attributed to the interaction of the KT field with hydride expansion, during precipitation. The reduction becomes more important at elevated temperatures and moderates the benefits on fracture toughness, caused by temperature increase. In addition to the detailed finite element results, analytical estimates on fracture toughness are presented, based on a cohesive zone model.

Introduction

Zirconium alloys show a combination of good mechanical properties and low neutron-absorption behavior. For these reasons zirconium alloys are used for the construction of nuclear reactor components (e.g. fuel cladding and fuel channels in light water reactors). However, reduction of the fracture toughness of these components is possible, caused by hydrogen embrittlement (e.g. [1], [2]).

In light water reactors, hydrogen is generated by oxidation during service (Zr+2H2O→ZrO2+2H2). Subsequently hydrogen diffuses in the metal under the influence of concentration, temperature and stress gradients and it is contained in solid solution up to a limiting concentration, which is called the terminal solid solubility. When hydrogen concentration exceeds the terminal solid solubility, zirconium hydrides precipitate in composite platelets, made of thin layers of zirconium alloy matrix and stoichiometric (i.e. pure) hydride; see, for example, Fig. 3 in [1] or Fig. 30 in [2]. The hydrides are brittle phases and reduce ductility of the material and fracture toughness [1], [2], [3]. Therefore, the redistribution of hydrogen and the formation of hydrides in zirconium alloys has been given considerable attention (e.g. [2], [4], [5]).

Hydrides may precipitate during reactor operation, in which case the variation of structure loading and its effect on hydride and zirconium alloy fracture is of interest. Hydride precipitation is also possible during reactor shutdown. Indeed, decrease in temperature during shutdown leads to decrease in hydrogen solubility limit and consequently to increase in hydride precipitation. Under these conditions, hydrogen induced delayed cracking, a sub-critical crack growth phenomenon, becomes important. This phenomenon allows crack propagation to proceed in a discontinuous fashion; a complete crack growth cycle includes hydride formation at the existing crack tip, hydride fracture and crack arrest in the ductile zirconium alloy matrix.

The objective of the present study is the estimation of the effect of hydrides on zirconium alloy toughness at different temperatures as well as under different constraint conditions. Information on hydride properties and structure are incorporated into the de-cohesion model (e.g. [6], [7], [8]), used for simulating crack growth in hydrides, as well as into the geometry of the boundary value problem.

Analytical models on the effect of hydrides on zirconium alloy toughness have been presented [9], [10]. These models consider stationary defects, under small scale yielding, and provide fracture toughness estimates, based on K-field [11] as well as on existing elastic solutions for the residual stresses, which develop during hydride formation [12], [13]. In the present study, the transient problem of hydride fracture initiation and propagation is considered by using a finite strain elastic–plastic numerical model. The combined effect of constraint and temperature on fracture toughness is also estimated. Analytical fracture toughness estimates for small scale yielding conditions are also discussed, in an effort to present a simple tool for engineering applications. The analytical estimates were derived by a cohesive zone approach, which was initially presented in the pioneering works of Dugdale [14] and Barenblatt [15]. The cohesive stress distribution considered in this model is approximated by a function, which has the features derived by the finite element calculations. The analysis does not require matrix yielding under the influence of the crack tip field and it is valid for a wide temperature range. Applications of cohesive zone model on hydride fracture have also been given in [16], [17], based on matrix yielding.

The numerical and analytical toughness estimates are found to be in good agreement with existing experimental results on stress intensity factor threshold values for hydride induced cracking.

The results of the effect of constraint are surprising, since negative T-stresses are associated with decrease in apparent fracture toughness. This behavior is attributed to the interaction of T-stress with hydride expansion.

The structure of the paper is the following. In Section 2, the boundary value problem is described. Material constitutive relations are presented in Section 3. The de-cohesion model used for crack growth simulation is described in Section 4. The numerical results are discussed in Section 5 and the analytical fracture toughness estimates in Section 6. Finally, concluding remarks are given in Section 7. The finite element implementation of material’s constitutive relations as well as of the de-cohesion model can be found in Appendix A. A discussion for the effect of cohesive traction distribution on toughness estimates, derived by the analytical approach, is given in Appendix B.

Section snippets

Boundary value problem

The hydride platelets, which precipitate in zirconium alloys, are composite sandwich structures, made of zirconium alloy and δ-hydride layers, interrupted by thin zirconium-based matrix ligaments. The boundary value problem has been designed in a way that takes into account the effect of the above-mentioned hydride platelet structure on the threshold stress intensity factor for hydride induced cracking.

In the discussions, which follow in the present and subsequent sections, the terms hydride

Material constitutive relations

In the present analysis, viscous effects are not studied. However, elastic–viscoplastic constitutive relations are derived by expanding a previously developed elastic–viscoplastic model [27] as well as by considering future applications where time-dependent material deformation could be taken into account together with other time-dependent processes, such as hydrogen diffusion. A detailed study could also be performed by considering crystal plasticity. In this case, plastic rate of deformation

De-cohesion model

Crack growth within the hydride platelet is simulated by de-cohesion model. Consider a crack propagating in a solid. Ahead of the crack tip, there is a zone, where fracture processes operate. The thickness of that zone is of the order of the characteristic length, associated with the failure mechanism. In the de-cohesion model, a slice, as thick as the fracture process zone, is taken off the material, along the crack path. This slice is the de-cohesion layer. The cohesive traction is applied

Discussion of finite element results

The expansion of the hydride, which is associated with its formation, leads to the development of residual compressive stresses in the hydride. Therefore, the hydride fails when the remote loading produces near-tip stresses, normal to the crack plane, which overcome the strength of the hydride, σmax, as well as the above-mentioned residual stresses. Consequently, hydride expansion, leads to the increase in fracture toughness. In other words, one may say that during hydride expansion, the

An analytical cohesive zone model for hydride fracture

The purpose of the present section is the development of an analytical model for the prediction of hydrided zirconium alloy toughness under small scale yielding, which could be used as a simple tool for engineering applications. The development is based on cohesive zone approach and characteristic features of cohesive traction distribution found by the detailed finite element study.

Let us consider an infinite elastic body containing a crack of length 2a under mode I loading (Fig. 9). The crack

Concluding remarks

In the present paper, we have shown that both finite element analysis, based on a finite strain elastic–plastic theory and the de-cohesion model for crack growth, and an analytical method, based on elasticity theory and cohesive zone approach of Dugdale and Barenblatt, offer reasonable estimates of fracture toughness of Zr-alloys in the temperature range of 350–550 K. Note that information derived by finite element analysis were used to develop the analytical model. At higher temperatures, the

Acknowledgements

A. G. Varias acknowledges the support of ABB Atom AB under the contract 4500023569. We thank Anette Medin for graphic assistance.

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