Effects of hydride on crack propagation in zircaloy 4

Effects of Hydride on Crack Propagation in Zircaloy 4 Procedia Engineering 173 ( 2017 ) 1185 – 1190 Available online at www sciencedirect com 1877 7058 © 2017 The Authors Published by Elsevier Ltd Thi[.]

Procedia Engineering 173 ( 2017 ) 1185 – 1190

1877-7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of Implast 2016

doi: 10.1016/j.proeng.2016.12.105

ScienceDirect

11th International Symposium on Plasticity and Impact Mechanics, Implast 2016

Effects of hydride on crack propagation in zircaloy-4

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*, Manabendra Pathaka, R.N.Singhb

a Department of Mechanical Engineering, Indian Institute of Technology Patna, Patna 801 103, India

b Mechanical Metallurgy Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India

Abstract

Hydrogen diffuses in the zircaloy-4 fuel clad tube during its service and precipitates as brittle hydride phases beyond terminal solid solubility of precipitation Brittle hydride precipitates in the region of high stress like crack tips and assists crack propagation leading to failure of the cladding In order to elucidate the effects of hydride precipitated at the tip of the crack on crack propagation behaviour in zircaloy-4, the numerical simulation is performed on compact tension specimens using the extended finite element method (XFEM) in Abaqus 6.12 An attempt has been made to understand the effects of crack and hydride dimensions on crack propagation by evaluating stress intensity factor and J-integral for different length of crack and hydride Their values indicate that hydride assists the crack propagation, however, if the length of crack exceeds certain critical length, the effect of hydride precipitation on crack propagation is minimal The values of stress intensity factor and J-integral are also compared with the experimental values reported in the literature and found to be concordant

© 2016 The Authors Published by Elsevier Ltd

Peer-review under responsibility of the organizing committee of Implast 2016

Keywords: Hydride; Crack; Fracture; Zircaloy-4; XFEM

* Corresponding author Tel.: +91-612-3028019

E-mail address: mkkhan@iitp.ac.in

© 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of Implast 2016

1 Introduction

Zircaloy-4 is extensively used as a nuclear fuel cladding tube material It is preferred to other materials' cladding because of its strikingly low thermal neutron cross-section, apt thermal conductivity, dimensional stability and corrosion resistance in the harsh environment of a nuclear reactor core [1] The fuel cladding encases radioactive uranium fuel pellets undergoing fission and its outside surface is exposed to coolant water or heavy water to take away the heat generated for power generation [2,3] Zircaloy-4 fuel cladding tubes undergo waterside corrosion during service and hydrogen produced as a result of the corrosion diffuses into it Hydrogen remains in solid solution

up to terminal solid solubility and it precipitates as brittle hydride phase in the zircaloy-4 metal matrix beyond this limiting concentration (about 80 ppm at 300°C and about 200 ppm at 400°C) [4] Precipitation of brittle hydride phase affects the mechanical behaviour of cladding especially by causing embrittlement of its matrix Gross embrittlement induced by the hydride uniformly distributed in the matrix and localised embrittlement due to delayed hydride cracking or blister formation are the two widely acknowledged forms of hydride embrittlement of zircaloy-4 cladding [5] The cladding tubes failure by the delayed hydride cracking has been a potential concern for fuel integrity during a rapid power transient at high burnup as well as during dry storage of spent fuel cladding [6].The precipitation of hydrides at the higher stress zone like crack tips in group of platelets having their normal parallel to maximum tensile stress is a typical feature of delayed hydride cracking.Delayed hydride cracking involves the three consecutive processes: nucleation, growth, and cracking of hydrides at the tip of a notch or a crack Fracture of hydride at the crack-tip causes the propagation of a crack which leads to failure of fuel cladding [7]

Given the complexities in experimental investigation of delayed hydride cracking in zircaloy-4 fuel cladding, there are several attempts[6,8,9] made to analytically and numerically investigate the various phenomena related to

it Chao et al [6] studied the failure of Zr-2.5% Nb due to delayed hydride cracking with the help of finite element code of ANSYS used in conjunction with strain energy density theory Their work interpreted the effects of different hydride orientations, the amount of zirconium hydride, and various crack configurations on the crack growth during delayed hydride cracking Kubo and Kobayashi [8] also used ANSYS to investigate the effects of hydride precipitation on the stress distribution around the crack tip in zircaloy-2 claddings Hydride precipitation is found to significantly alter the stress distribution around the crack tip Tseng et al [9] employed finite element method to understand the effect of hydride on crack stability in zircaloy-4 fuel cladding The analyses were performed to investigate the effects of hydride dimensions, number of hydrides, the patterns of split in the hydride, and the presence of a circumferential hydride among radial hydrides on crack propagation Their study concluded that radial hydrides near the crack tip had a significant effect on crack propagation and the longer hydride platelet has more pronounced influence In all these studies only 2D model was considered and were only limited to stationary cracks 2D models cannot provide an exact evaluation of crack propagation behaviour since the stress state and hydrogen concentration are expected to be different for the surface and bulk At the surface area, plastic field around the crack tip is large under the plain stress sate, which would disperse the hydrogen and decrease the hydrogen concentration

at the crack tip [10] Moreover, conventional finite element method used in these analyses has high computational cost

In the present study, hydride-assisted 3D crack propagation is simulated in zircaloy-4 cladding using extended finite element method (XFEM) The effects of crack and hydride dimensions on crack propagation is presented in terms of fracture parameters like stress intensity factor and J-integral The simulated crack propagation behaviour is also compared with the experimental results and found to have quite similar in nature

2 Analysis methodology

2.1 Finite element model

Standard fatigue pre-cracked compact tension specimen of zircaloy-4 having dimensions in accordance with experimental specimens reported in the literature is taken as finite element model [11,12] These dimensions of the model also conforms ASTM E 1820-99 standard A pre-crack of length between 5.5–7.5 mm is inserted in the model A rectangular hydride having 1 mm width and length between 2–4 mm is considered at the tip of the crack,

as shown in Fig 1 (a) Individual material properties of zircaloy-4 and hydride given as input to model is given in Table 1 [13]

Table 1 Material properties used in the present study [13]

Zr

Elastic modulus 80.90 GPa

Hydride

Elastic modulus 65.44 GPa

2.2 Extended finite element method

The key in understanding the crack propagation is to capture the phenomenon occurring at the crack tip One classical and important approach in this area is the Linear Elastic Fracture Mechanics (LEFM) theory In this approach, the large stress effect at the crack tip is approximated as an ideal elastic crack with theoretically infinite stresses at the tip These stress fields are related to an engineering measure in the LEFM concept called the Stress Intensity Factor (SIF) XFEM is an extension of the conventional finite element method based on the concept of partition of unity i.e the sum of the shape functions must be unity Using the partition of unity concept, XFEM adds

a priori knowledge about the solution in the finite element space and makes it possible to model discontinuities and singularities independently of the mesh This makes it a very attractive method to simulate crack propagation since it

is not necessary to update the mesh to match the current geometry of the discontinuity and the crack can propagate

in a solution-dependent path LEFM theory based XFEM in Abaqus 6.12 is used in the present work Hexahedron sweep meshing with advancing front is used to mesh the FEM model The element size around the crack tip is kept small to generate high quality mesh in order to capture its propagation with higher accuracy One of the mesh model

is shown in Fig 1 (b) 3D stress element: An 8-node linear brick C3D8R element is selected with reduced

Fig 1 A crack with precipitated hydride at its tip in zircaloy-4 (a) schematic diagram; (b) meshed FEM

integration Concentrated force of 5000 N in opposite direction at the centers of specimen holding holes is applied as boundary conditions

3 Results and discussion

The stress intensity factor is used for the expression of the stress field at a crack tip and serve as a measure of the severity of the crack tip for different crack configurations They have a central role in crack assessment, where they can be related to critical levels of stresses resulting in crack growth and eventually fracture

The von Mises stresses are shown in Fig 2 for crack having in as-received zircaloy-4 and crack with precipitated hydride at its tip for a given load The stress generated is lesser in the absence of precipitated hydride implicating that the material has higher crack resistance Since, stress concentration at the crack tip is highly increased with crack tip hydride precipitation, it would have less value of critical stress intensity factor KIc than the model without hydride for any given length of existing crack and applied load, thus fracture toughness will decrease with precipitation of hydride [14] A number of experimental work has also reported the decrease in fracture toughness with hydride precipitation [11,12]

Fig 2 von Mises stresses in zircaloy-4 having (a) 5.5 mm crack; (b) 5.5 mm crack with 2 mm hydride precipitated at its tip

The stress intensity factor for different crack and hydride lengths has been plotted in Fig 3 (a) The value of KI for hydrided zircaloy-4 is about 50 Mpa√m and it conforms the values reported in the literature [15] The stress intensity decreases with the precipitation of brittle hydride phase at its tip, resulting in hydride-assisted crack propagation However, the effect of hydride is largely reduced with increase of crack length as it can be seen in the plot that the difference in stress intensity factors is getting reduced with increase in crack length In other words, the dimensions of hydride beyond a critical crack length is of no consequence Fig 3 (b) shows the variation in J-integrals for different crack and hydride lengths It is as expected and in accordance with stress intensity factors The maximum energy required is for as-received zircaloy-4 which means that crack will not propagate easily through this

Fig 3 Effects of crack and hydride dimensions (a) stress intensity factor (b) J-integral

Brittle hydride phase precipitates at crack tips given that these are high stress zones Hydride cracks and merges with the main crack in the matrix, thus assisting the crack propagation The same was confirmed in experimental results[16] and in present simulation An effort has been taken to qualitatively compare the crack propagation behaviour side by side in the Fig 4

Fig 4 Comparison of crack propagation behaviour with hydride at crack tip

4 Conclusions

Numerical investigation is performed on ASTM standard compact tension specimen using the extended finite element method (XFEM) in Abaqus 6.12 Influence of hydride precipitated at the tip of the crack on crack propagation behaviour in zircaloy-4 is simulated The effects of crack and hydride dimensions on crack propagation

is evaluated in terms of change in fracture parameters like stress intensity factor and J-integral for different length of pre-crack and hydride Their values indicate that hydride assists the crack propagation, however, if the length of crack exceeds certain critical length, the effect of hydride precipitation on crack propagation is minimal

Acknowledgement

We sincerely acknowledge the Board of Research in Nuclear Sciences (BRNS), Government of India No 36(2)/14/30/2014-BRNS/1665 for providing the financial support needed to carry out the present work

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