Nuclear Engineering and Design 77 (1984) 87-95 87 North-Holland, Amsterdam THE EFFECT OF ANISOTROPY ON THE BALLOONING OF ZIRCALOY CLADDING J.R. MATFHEWS Theoretical Physics Division, AERE Harwell, Oxon. 0 X l l ORA, United Kingdom Received 22 April 1983 The effect of creep anisotropy on the ballooning of Zircaloy LWR fuel rod cladding tubes is investigated. A perturbation method for calculating the effect of temperature inhomogenitiesis developed further. The results are compared with a simple method that is not restricted to small deviations from axisymmetry. The perturbation method is shown to have only limited applicability to the Zircaloy ballooning problem. The other method which assumes that the cladding tubes retain a circular cross-section provides a more useful technique for fuel rod behaviour analysis. Studies of the bending of cladding tubes and the effect of restraint on deformation and failure are presented. Apart from cladding tube bending the effects of creep anisotropy on clad deformation and failure are not large. 1. Introduction The possibility of ballooning deformation of Zircaloy cladding tubes is an important feature in the assessment of water reactor fuel rods during loss of coolant acci- dents [1]. The a-phase of Zircaloy is usually associated with a strong anisotropy in creep behaviour, amongst other properties. The anisotropy arises from the hexago- nal crystal structure of the material and is manifested because of the texture induced by tube drawing. This may be enhanced by annealing at the limit of the a-phase temperature range and almost completely eliminated by annealing in the fl-phase region [2]. Dur- ing isotropic creep, cladding tubes, which may be idea- lised as closed ended cylindrical pressure vessels, will suffer no significant length changes as they increase in diameter. The type of anisotropy exhibited by Zircaloy tubes, however, produces a substantial shortening of the tube which is typically in the range of 20 to 40% of the diametral strain. This axial contraction also means that any temperature variation around the tubes will pro- duce a tendency to bend, with the curvature concave towards the hot side. During laboratory tests or in the actual conditions relevant to a PWR LOCA accident this bending of fuel rods can be important. It will alter the relative position of the fuel cladding to heater elements, fuel pellets or other fuel rods, producing complicating feed-back ef- fects. This is likely to influence the observed diametral strain to failure and the degree to which flow channels are blocked at the time of failure. The bending may also produce substantial forces on spacer grids. Tlais paper develops further a perturbation treatment of ballooning in an anisotropic creeping cylinder [3]. It is shown that such an approach has limited applicability to the present problem because of the high local strains commonly observed in Zircaloy. The technique is useful as it allows a simple understanding of the processes involved. In order to calculate the effect of anisotropy on ballooning at large strains a simple approximation is presented that rests on the observation that the cross- section of the fuel rods remains circular during the ballooning process. This is used to study the effects of various types of restraint on ballooning. 2. Anisotropy and axisymmetric deformation We will restrict ourselves to the deformation of Zircaloy in the a-phase. In LOCA conditions the stresses are low enough to ignore instantaneous plastic deforma- tion and the strains exhibited by the cladding are large so primary creep may be neglected. The secondary creep of a-Zircaloy is represented to a good approximation by: = B(T)o" =A exp(-Q/T)o ~, (1) where A, Q and n are structural parameters, T and o are the absolute temperature and applied stress respectively. To cope with anisotropic response under a multiaxial 0029-5493/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)