Compensation Systems for Low Temperature Applications

Large scale cryogenic systems applied in modern fusion reactors (Claudet and Aymar 1990), superconducting particle accelerators (Lebrun 1999b; Van-Sciver 1998) or coolant transfer lines (Lebrun 1999a) as well as small scale refrigerators and cryo-coolers generate significant progress in multiple domains related either to material sciences or to structural behaviour. When designing large scale cryogenic systems the engineers quickly realise that it is impossible to build a continuous “cold mass” since the material — by its physical nature — exhibits the thermal contraction and the thermo-mechanical strain fields, developed locally in the constraint structure might damage the object. Thus, any large cryogenic system has to be subdivided into the “cold segments”, each of them constructed separately and all of them assembled together in the destination place. A typical example can be found in the domain of particle accelerators where a continuity of the magnetic field is strongly postulated by the accelerator physics. On the other hand, the real structure has to be discontinuous, since the magnets are limited in length (for technological reasons) and separated by the so-called interconnections (Fig. 1.1). A similar problem appears in the cryogenic transfer lines, that convey liquid nitrogen or helium, where the maximum length of segments is often a function of the technological process of their manufacture and assembly. A typical liquid and gaseous helium transfer line containing several headers, located next to a superconducting accelerator, is shown in Fig. 1.2.

The processes occurring in metals at very low temperatures are strictly related to their physical and mechanical properties, to the type of lattice and its imperfections as well as to the mechanisms of heat transport. The basic mechanism of inelastic deformations remains the same and is based on the motion of dislocations. However, as the Peierls-Nabarro potential increases at low temperature, the dislocations are less mobile. Thus, the same load applied at the temperatures close to 0 K will produce much less inelastic deformation than at room temperature. Nevertheless, when approaching the absolute zero several parameters like the thermal conductivity and the thermal contraction coefficient or state functions like the specific heat at constant volume and the entropy also tend to zero. This phenomenon yields a thermodynamic instability at very low temperatures and has a fundamental importance for the existence and triggering of special mechanisms of inelastic deformation like the shear bands. When analysing the response of thin-walled structures at low temperatures all these phenomena have to be taken into account.

The most often used stainless steel grades for cryogenic applications are the AISI grades 304, 304L, 316, 316L and 316LN. Sometimes the grades 316Ti and 321 were used for low temperature service, however the recent studies show their rather limited applicability. An important feature of the above mentioned stainless steel grades is the presence of large amount of chromium reaching some 16 ÷ 20% as well as reduced amount of carbon of around 0.030.08% (specially limited in the grades denoted L). Also, all these grades are characterised by the presence of significant amount of nickel (8 ÷ 14%), which stabilises the austenitic matrix at cryogenic temperatures. A controlled addition of nitrogen (N) improves the yield point and the tensile strength when compared to the traditional grades. The other important elements in the chemical composition of stainless steels are: Si (around 1%), Mn (around 2%), Mo (up to 3%), S (around 0.03%) and P (around 0.05%). In the grades 316Ti, 321 titanium is present to the upper limit of 0.7%. Composition of typical grades of wrought stainless steel for low temperature use is shown in Table 3.1 (as quoted in the ASTM and ASME specifications, cf. INGO Databook, 1974).

As long as the stress-strain curve is smooth (mechanism of plastic deformation based on the movement of dislocations) and below the critical strain rate the low temperature plasticity can be modelled in a classical rate independent way. For the stainless steel, that shows high ductility at cryogenic temperatures, the normality law expressed via the associated flow rule is good enough. Above the critical strain rate both the hardening modulus and the ultimate strength depend strongly on the strain rate, therefore a rate dependent plasticity shall rather be applied. A survey of different plastic and visco-plastic models, potentially applicable at cryogenic temperatures is given below.

As already mentioned in the previous chapters, the Fe-Cr-Ni stainless steels are commonly used to manufacture components of superconducting magnets and cryogenic transfer lines since they retain their ductility at low temperatures and are paramagnetic. The nitrogen strengthened stainless steels of series 300 belong to the group of metastable austenitic alloys. Under certain conditions the steels undergo martensitic transformation at cryogenic temperatures that lead to a considerable evolution of material properties and to a ferromagnetic behaviour. The martensitic transformations are induced mainly by plastic strain fields and amplified by high magnetic fields. Spontaneous transformations due to the cooling process — identified with respect to some alloys — are not observed in the most often used grades 304L, 304LN, 316L, 316LN. The stainless steels of series 300 show at room temperature a classical γ-phase of face centred cubic austenite (FCC). This phase may transform either to α′ phase of body centred tetragonal ferrite (BCT) or to a hexagonal ε phase. The most often occurring γ — α′ transformation leads to formation of martensite sites dispersed in the surrounding austenite matrix. In the course of the strain induced transformation the martensite platelets modify the FCC lattice leading to local distortions. The amount of the martensite depends on the chemical composition, temperature, stress state, plastic strains and exposure to magnetic field. It is well known that the solutes like Ni, Mn and N considerably stabilise the γ-phase. For instance the strain induced martensitic content in the grades 304LN, 316LN at low temperatures is much lower than in the grades 304L, 316L for the same level of plastic strain (Morris et al. 1992).

The main mechanism of instability of the bellows expansion joints consists in the so-called column buckling. The pressurised bellows behaves like a flexible Euler’s column and the mode of buckling corresponds to the column mode. Such a response can be modelled by using a slender pressurised thin-walled tube (Haringx 1952). This equivalent tube subjected to inner pressure and supported at the extremities buckles again like a column subjected to axial stress (Fig. 6.1).

The corrugated bellows work often in extremely severe service conditions comprising temperature variations between ambient and operational level, high internal pressure, large cyclic axial offset and different types of misalignment offsets. This implies development and evolution of plastic strain fields in these components subjected to thermo-mechanical loads at low temperatures. The evolution of plastic strain fields is usually accompanied by two phenomena: ductile damage and strain induced martensitic transformation (already discussed in the previous chapters). Cryogenic temperatures catalyse the process of opening of micro-cracks and micro-voids shifting simultaneously deformations towards the elastic domain (considerable increase of yield strength). Nevertheless, the behaviour of corrugated bellows, highly optimised with respect to their size and stiffness, is affected by the low cycle fatigue phenomena.

The modern high energy physics needs very sophisticated and complex tools in order to explore the world of elementary particles constituting the matter. One of the most important aims over the past 30 years was confirmation of the so-called Standard Model which assumes that the fundamental constituents of matter form three families of quarks and leptons. The relevant scientific tools are called accelerators, storage rings and colliders and their main function is to produce, accelerate, store and collide the beams of particles in order to search for the new elementary events, announcing the potential discoveries, and to provide more statistics for the already known reactions. Generally speaking the beam-beam high energy colliders equipped with the appropriate detectors form a basic tool of high energy physics. Till now the colliders were usually built in the form of rings since the required energy per beam was obtained by smooth accelerating of particles during many turns around the ring. The beams were accelerated by means of the so-called accelerating cavities, kept on their trajectory by using the bending dipole magnets, were focalised and defocalised by means of the quadrupole magnets. The main accent was laid on the technology of the bending dipole magnets with the superconductivity as the recent achievement. The present chapter gives a brief overview of the variety of different technologies needed to construct a modern circular accelerator, that means: superconductivity, helium cryogenics, ultra-high vacuum, materials and structures (compensation systems).