Effect of plastic bending on high temperature creep resistance of molybdenum single crystals
Graphical asbtract
Introduction
There is a constant need for metal pipes of a relatively small diameter (10–20 mm), which have increased strength when exposed to high temperatures and internal pressures. Such pipes are used for steam pipelines at thermal power plants, pipelines for fusible coolants at nuclear power plants, tubular elements of thermionic convertors (TIC)s, etc. [[1], [2], [3], [4], [5]].
This paper focuses exclusively on pure single crystals of such refractory metal as molybdenum. The reason is that any chemical inhomogeneity and interfaces (grain boundaries, interphase boundaries, etc.) contribute to the adsorption of radiation defects, that is crucial for nuclear applications and leads to degradation and destruction of material under the influence of pressure and elevated temperatures. Therefore, the possibilities of solid solution or dispersion strengthening are not applicable here.
Available literature data [6,7] indicate that in the process of high-temperature creep of molybdenum single crystals in the initial state a dislocation substructure forms with approximately the same total number of dislocations of different signs. As shown in [8,9], the strengthening efficiency correlates with the angle of the integral misorientation of substructure δ measured by X-ray diffraction as the maximum broadening of reciprocal lattice sites corresponding to the slip planes. Angle δ can be approximately represented by uniform bending of the crystal in the irradiated region, which corresponds to the accumulation of excess dislocations of the same sign (EDSS×) [[10], [11], [12]]. In [[13], [14], [15]], a distinct dependence of creep rate of metals and metallic solid solutions with FCC and BCC lattices on the angle δ was determined, where n = 2 and n = 4 at low and high applied stresses, respectively.
According to the dislocation mechanism of polygonization [16], an EDSS located in parallel slip planes is observed in a crystal after pure bending. Upon heating, partial annihilation of dislocations of opposite signs occurs. The remaining EDSS rearrange in the walls. The features of the dislocation structure formation upon bending and subsequent annealing of single crystals were studied in detail in [[17], [18], [19], [20]]. It was shown that this structure has a significant effect on the mechanical properties in general [21] and increases the creep resistance [22].
Therefore, one of the ways to provide increased strength of pipes is bending, which in many cases is included as a technological operation in their manufacturing. Nevertheless, up to now little attention has been paid to structural studies of the influence of bending deformation of metals on their behavior under high temperature creep conditions. This is especially true for molybdenum and tungsten single crystals which can be used for direct conversion of thermal energy into electricity in the TICs.
The data on creep of pure metals after substructure strengthening obtained in [23] suggest that plastic bending followed by stabilizing annealing is the most effective method of preliminary strengthening for subsequent exposure to high temperatures and stresses. In [24,25], optimal heating rates were found for obtaining the most stable, not recrystallized polygonized substructure in plastically bent Mo and W single crystals up to pre-melting temperatures. The creep of those strengthened substructures was investigated, and their effectiveness was shown. However, the tests were carried out on a 100-h basis, so they do not reflect the long-term behavior of single crystals strengthened by bending. There is no information in the literature about the features of the mechanism of creep of Mo and W single crystals and evolution of strengthened substructure after bending for long-term (1000 h and more) tests. This question is important for the development of small diameter pipes with enhanced strength at high temperatures and pressures (for TIC electrodes with decades-long lifetime).
The regularities found out in [26] for the formation of dislocation substructure during plastic bending of Mo and W single crystals made it possible to determine the optimal modes (temperatures and heating rates) to obtain a structure with the maximum strengthening effect. This allowed to fabricate mono-oriented (with the same crystallographic orientation at any point of the cylindrical surface) tubes with a diameter of 10 mm and a wall thickness of 0.8 mm by winding Mo and W single-crystal strips into a tubular spiral, followed by stabilizing annealing and electron beam welding of the spiral joints. Since the height and diameter of the rings which could be tested at the device described in [27] did not exceed 2 mm and 10 mm, respectively, it was impossible to carry out the transmission electron microscopic (TEM) studies on such objects. Therefore, in this work dumbbell-shaped specimens of conventional dimensions were prepared, and the dislocation substructure evolution during the creep in Mo single crystals after bending was studied in detail.
Section snippets
Experimental
A 20 mm thick bulk Mo single crystal (99.99% wt.) with 〈111〉 growth axis was selected for the studies. Four planes parallel to the growth axis were milled on the crystal: two {112} and two {110} planes (Fig. 1). Orientation control was carried out by X-ray diffraction at a DRON-3 M unit; the deviation of the true orientations of the planes from the indicated one did not exceed 4°. The width of the resulting plates was not less than 12 mm. Then crystal was plastically bent around a steel 130 mm
Сreep deformation
A comparison of the creep curve of a specimen cut from the tension zone (curve 1 in Fig. 2b) with the creep curves of Mo single crystals preliminarily strengthened by tension [20] shows that in the bent specimen the primary (unsteady) stage was 3–4 times shorter. But the most interesting is that the strain rate constantly decreased throughout the whole creep process (1700 h). Thus, for example, in a time range of 200–300 h the creep rate was 7·10−10 s−1, in the range of 1000–1200 h – 2.6·10−10 s
Discussion
In the case of creep of pure single crystals, it can be considered two-dimensional dislocation nets and dislocation loops. Within the framework of this model, the increase in density of dislocation loops is caused by action of the Bardeen-Herring sources [32]. Continuous multiplication of dislocation loops occurs due to climb of edge sessile dislocation fixed at both ends by screw dislocations. For this process, a high local concentration of vacancies is required near the edge dislocations.
Conclusions
1. During plastic bending Mo single crystal is divided onto a tension zone and a compression zone, which are separated by a neutral line. Mixed dislocations of two slip systems close to a screw orientation, numerous loops, and helicoids, as well as small angle subboundaries with an EDSS are formed in the compression zone. Similar structure is formed in the tension zone, but with one slip system of dislocations close to screw orientation.
2. Under plastic bending, intense accumulation of
Funding
This work was supported by the Science and Technology Center in Ukraine (STCU) [grant No. 50].
Data Availability
The raw/processed data required to reproduce these findings cannot be shared at this time due to legal and ethical reasons.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors express their deep gratitude to Professor E.V. Kozlov (Tomsk State University of Architecture and Building, former TEBI) for the help of TEM investigations of Fig. 5 of this article as part of the joint work of IMP and TEBI. This work was particularly carried out as a part of budget program of Institute for Metal Physics of National Academy of Science of Ukraine. The authors are grateful to the Scientific and Technological Center in Ukraine (STCU) for financial support of this work
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