Zirconium alloys are used in the
nuclear industry as fuel rod cladding due to zirconium's high strength and low neutron absorption cross-section. It can be subject to high
strain rate loading conditions during forming and in the case of a
reactor accident. In this context, the relationship between strain rate-dependent mechanical properties, crystallographic texture and deformation modes, such as
slip and
deformation twinning. and 𝝎 is the rotation axis calculated in the present work, orthogonal to both the slip plane normal and slip direction. The crystal direction of the rotation axis vectors is labelled on the IPF colour key.
Zirconium has a
hexagonal close-packed crystal structure (HCP) at room temperature, where 〈𝑎〉
prismatic slip has the lowest
critical resolved shear stress. 〈𝑎〉 slip is
orthogonal to the
unit cell 〈𝑐〉 axis and, therefore, cannot accommodate deformation along〈𝑐〉. To make up the five independent slip modes and allow arbitrary deformation in a polycrystal, secondary deformation systems such as twinning along
pyramidal planes and 〈𝑐 + 𝑎〉slip on either 1st order or 2nd order pyramidal planes play an important role in Zr polycrystal deformation. Therefore, the relative activity of deformation slip and twinning modes as a function of texture and strain rate is critical in understanding deformation behaviour.
Anisotropic deformation during processing affects the texture of the final Zr part; understanding the relative predominance of deformation twinning and slip is important for texture control in processing and predicting likely failure modes in-service. The known deformation systems in Zr are shown in Figure 1. The preferred room temperature slip system with the lowest critical resolved shear stress (CRSS) in dilute Zr alloys is 〈𝑎〉 prismatic slip. The CRSS of 〈𝑎〉prismatic slip increases with interstitial content, notably oxygen, carbon and nitrogen, and decreases with increasing temperature. 〈𝑎〉
basal slip in high purity single crystal Zr deformed at a low strain rate of 10−4 s−1 was only seen at temperatures above 550 °C. At room temperature, basal slip is seen to occur in small amounts as a secondary slip system to 〈𝑎〉 prismatic slip, and is promoted during high strain rate loading. In-room temperature deformation studies of Zr, 〈𝑎〉 basal slip is sometimes ignored However, single crystal room temperature microcantilever tests in commercial purity Zr show that 〈𝑎〉 basal slip has only 1.3 times higher CRSS than 〈𝑎〉 prismatic slip, which would imply significant activation in polycrystal deformation given a favourable stress state. 1st order 〈𝑐 + 𝑎〉 pyramidal slip has a 3.5 times higher CRSS than 〈𝑎〉 prismatic slip. Jensen and Backofen observed localised shear bands with 〈𝑐 + 𝑎〉 dislocations on {112̅ 4} planes during 〈𝑐〉 axis loading, which led to ductile fracture at room temperature, but this is not the slip plane as 〈𝑐 + 𝑎〉 vectors do not lie in {112̅ 4} planes.
Deformation twinning crystallographic planes
Deformation twinning produces a coordinated
shear transformation in a crystalline material. Twin types can be classed as either contraction (C1, C2) or extension (T1, T2) twins, which accommodate strain either to contract or extend the <𝑐> axis of the
hexagonal close-packed (HCP) unit cell. Twinning is crystallographically defined by its twin plane 𝑲𝟏, the mirror plane in the twin and parent material, and 𝜼𝟏, which is the twinning shear direction. Deformation twins in Zr are generally lenticular in shape, lengthening in the 𝜼𝟏 direction and thickening along the 𝑲𝟏 plane normal. The twin plane, shear direction, and shear plane form the basis vectors of an orthogonal set. The axis-angle misorientation relationship between the parent and twin is a rotation of angle 𝜉 about the shear plane's normal direction 𝑷. More generally, twinning can be described as a 180° rotation about an axis (𝜼𝟏 or 𝑲𝟏 normal direction), or a mirror reflection in a plane (𝑲𝟏 or 𝜼𝟏 normal plane). The predominant twin type in zirconium is 𝑲𝟏 = {101̅2} 𝜼𝟏 = (T1) twinning, and for this {101̅2} twin, there is no distinction between the four transformations, as they are equivalent. and is activated in preference to basal slip during deformation at 550 °C. According to Hayes et al.,
zirconium behaves like class II metals. This means that at low temperatures and low stresses, it has a stress component (n) of ~1. This is the Harper-Dorn creep, dominated by
grain boundary diffusion. As stress increases, the stress exponent increases to ~6, which would be in the power-law creep, dominated by dislocations. Above stresses 2×10−3, power-law breakdown is reached. An important application of zirconium alloys is as
cladding for nuclear reactors. Therefore, the creep effects of irradiation are significant. Many researchers have reported lower values of creep in irradiated zircaloy alloys- meaning that irradiation increases creep resistance.
Influence of loading conditions on deformation modes Kaschner and Gray observe that
yield stress increases with increasing strain rate in the range of 0.001 s−1 and 3500 s−1, and that the strain rate sensitivity in the yield stress is higher when uniaxially compressing along texture components with predominantly prismatic planes than basal planes. They conclude that the rate sensitivity of the flow stress is consistent with Peierls forces inhibiting dislocation motion in low-symmetry metals during slip-dominated deformation. This is valid in the early stages of room temperature deformation, which in Zr is usually slip-dominated. Samples compressed along
texture components with predominantly prismatic planes yield at lower
stresses than texture components with predominantly basal planes, studied twinning as a function of grain orientation within a sample. They calculated a global Schmid factor using the macroscopic applied stress direction. They found the resolved shear stress on any grain without considering local intergranular interactions, which may alter the stress state. They found that although the majority of twins occur in grains favourably oriented for twinning according to the global Schmid factor, around 30% of grains which were unfavourably oriented for twinning still contained twins. Likewise, the twins present were not always of the highest global Schmid factor variant, with only 60% twinning on the highest Schmid factor variant. This can be attributed to a strong dependence on the local stress conditions in grains or grain boundaries, which is difficult to measure experimentally, particularly at high strain rates. Knezevic
et al. ==Applications==