Effect of plastic shearing on damage and texture on Zircaloy-4 cladding tubes: experimental and numerical study
Introduction
Zircaloy 4 (Zy4) is a zirconium alloy used for fuel cladding tubes in pressurised water nuclear reactors. As these tubes require a high quality level they are manufactured by cold pilgering (Mannesman 25 VMR). The tube is repeatedly rolled over a mandrel by two grooved dies. The grooved cross-section is basically a half circle which diameter evolves in an orthoradial direction with a parabolic law (between the initial and final tube diameters) [1]. The dies rotate around their axis while they move along the rolling axis (Fig. 1). A pinion-rack gearing system imposes synchronism. After each back and forth movement (stroke) of the dies, the raw tube is advanced by about 1 mm and turned by approximately 50°.
The plastic deformation and the subsequent texture formation that occur during cold pilgering of copper or Zy4 tubes, have been extensively studied [2], [3], [4], [5], [6]. However, experimental and theoretical works take into account a plastic strain tensor that is purely diagonal. This can be explained by the fact that the diagonal components can be obtained directly from dimensional measurements of the tube thickness and diameter before and after rolling. In fact, as we show in the present study, the strain path is much more complicated and the shear component in the rolling-radial direction is not negligible. Measurements of this shear strain were performed and the influence of pilgering parameters was studied with the help of experimental design techniques. The obtained values were then used as an input into a damage model. For that, the strain path undergone by a volume element of metal was described by the combined use of our measurements and a two-dimensional finite element method. The calculated damage was then compared with the defect rate found experimentally for various rolling conditions.
The cold pilgering texture of zirconium alloys is well known [6], [7]. Generally, studies were performed in cold-rolled sheets or rods with characteristic symmetrical basal {00.2} pole figures (PF). For Zy4 tubes, the {00.2} PFs show a twin-mode distribution of intensities in the RD–TD plane (RD: radial and TD: tangential sample directions) but an asymmetrical distribution of pole densities in RD–AD plane (AD: axial direction). This behaviour can be correlated to cold pilgering and to the shear strain produced in tubes.
Various attempts to explain the texture with micromodelling of deformation mechanisms have been performed [3], [4], [5], [6], [8], [9], [10]. For instance, Lebensohn and Tomé [3], [4] have proposed a self-consistent viscoplastic (VPSC) model, however the simulated PF did not fit accurately the experimental ones. In this work, we propose two improvements to reach a better agreement: a variation of the active strain systems during pilgering and a strain rate taking into account the shear component in the macroscopic plastic strain tensor.
Section snippets
Strain measurements
To observe the strain path in a copper tube during cold pilgering, Sheurer et al. [11] screwed pieces of rods in the thickness of the tube. We used this technique to analyse the last rolling pass of Zy4 cladding tubes [12]. The thickness of a raw tube (before cold-pilgering) was 1.8 mm and small cylinders of 0.4 mm diameter were inserted.
Several experiments have been performed:
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Rolling of raw parts containing 120 inserts aligned along the axis of the tube on four lines at 90°. The rolling was
Presentation of the geometrical elements calculation
We observed the evolution of a material element, in the bottom of the groove, from the beginning of the reduction zone to the end of this zone. The calculation of the strain increments Δεrr,Δεθθ and Δεzz proceeds from the tools geometry and the process kinematics. For the ith stroke of roll, the theoretical position of a particle is defined by the (i−1)th position and the product of the feeding by the elongation (that is to say, the ratio between the initial section and the local one).
We made
Crystalline texture simulation
In order to analyse the different active deformation modes present in each grain, strain texture simulation was performed from a VPSC model [3], [4]. Each grain is treated as an inhomogeneity embedded in the homogeneous effective medium represented by the polycrystal, with the condition that the average of stress and strain rate over all the grains must be consistent with the equivalent macroscopic magnitudes.
The VPSC model combined with a volume fraction transfer (VFT) scheme, developed by
Conclusion
Measurements of the shear strain of Zy4 tubes during cold pilgering have been performed with inserts. An experiment design showed that it mainly depends on the friction difference between internal and external contacts with the tools. A damage model derived from Lathan and Cockroft was propos4 take into account this shear strain. It gives good correlation with experimental damage measurements and with tool profile changes.
A VPSC model allowed one to show that the prismatic mode is the most
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