Plastic Strain Induced Damage Evolution and Martensitic Transformation in Ductile Materials at Cryogenic Temperatures

The Fe-Cr-Ni stainless steels are well known for their ductile behaviour at cryogenic temperatures. This implies development and evolution of plastic strain fields in the stainless steel components subjected to thermo-mechanical loads at low temperatures. The evolution of plastic strain fields is usually associated with two phenomena: ductile damage and strain induced martensitic transformation. Ductile damage is described by the kinetic law of damage evolution. Here, the assumption of isotropic distribution of damage (microcracks and microvoids) in the Representative Volume Element (RVE) is made. Formation of the plastic strain induced martensite (irreversible process) leads to the presence of quasi-rigid inclusions of martensite in the austenitic matrix. The amount of martensite platelets in the RVE depends on the intensity of the plastic strain fields and on the temperature. The evolution of the volume fraction of martensite is governed by a kinetic law based on the accumulated plastic strain. Both of these irreversible phenomena, associated with the dissipation of plastic power, are included into the constitutive model of stainless steels at cryogenic temperatures. The model is tested on the thin-walled corrugated shells (known as bellows expansion joints) used in the interconnections of the Large Hadron Collider, the new proton storage ring being constructed at present at CERN

Design of the CLIC Quadrupole Vacuum Chambers

The Compact Linear Collider, under study, requires vacuum chambers with a very small aperture, of the order of 8 mm in diameter, and with a length up to around 2 m for the main beam quadrupoles. To keep the very tight geometrical tolerances on the quadrupoles, no bake out is allowed. The main issue is to reach UHV conditions (typically 10-9 mbar static pressure) in a system where the vacuum performance is driven by water outgassing. For this application, a thinwalled stainless steel vacuum chamber with two ante chambers equipped with NEG strips, is proposed. The mechanical design, especially the stability analysis, is shown. The key technologies of the prototype fabrication are given. Vacuum tests are carried out on the prototypes. The test set-up as well as the pumping system conditions are presented

Influence of Micro-Damage on Reliability of Cryogenic Bellows in the LHC Interconnections

To achieve maximum beam energy in the LHC the accumulated length of the interconnections between LHC main magnets has been limited to around 3% of the total magnetic length in the Arcs and Dispersion Suppressors. Such a low ratio leads to a very compact design of components located in the LHC interconnections. This implies development and evolution of high intensity plastic strain fields in the stainless steel expansion bellows subjected to thermo-mechanical loads at low temperatures. These components have been optimised to ensure high reliability standards required for the LHC. Nevertheless, initial damage can occur and lead to a premature fatigue failure. For structures in which plasticity is not confined to the crack tip region, standard failure mechanics, based classically on the stress intensity factor or the strain energy density release rate, can not be used. In the present paper, a constitutive model taking into account plastic strain induced g->a' phase transformation and orthotropic ductile damage is presented. This local approach is used to predict the impact of initial imperfections on the fatigue life of thin-walled LHC bellows expansion joints

Testing Alternative Theories of the Property Price-Trading Volume Correlation

This article examines the correlation between the real housing price and trading volume. Contrary to the predictions of standard rational expectation models, a robust positive correlation between the two variables is identified. While no clear lead-lag relationship is found in the raw data, which is more consistent with the downpayment effect model, the medium-run component of the trading volume tends to lead (and Granger cause) the corresponding component of the property price, which is more consistent with the search theoretic model. An explanation for this difference in behavior is suggested and several future research directions are provided.

Installation and Quality Assurance of the Interconnections between Cryo-assemblies of the LHC Long Straight Sections

The interconnections between the cryomagnets and cryogenic utilities in the LHC long Straight Sections constitute the last machine installation activity. They are ensuring continuity of the beam and insulation vacuum systems, cryogenic fluid and electrical circuits and thermal insulation. The assembly is carried out in a constraining tunnel environment with restricted space. Therefore, the assembly sequence has to be well defined and specific tests have to be performed during the interconnection work to secure the reliability of the system and thus to ensure the global accelerator availability. The LHC has 8 long straight insertion zones composed of special cryomagnets involving specific interconnection procedures and QA plans. The aim of this paper is to present the installation and quality assurance procedures implemented for the LHC LSS interconnections. Technologies such as manual and automatic welding and resistive soldering will be described as well as the different quality controls, such as visual and radiographic inspection of welds, electrical checks and leak testing. An evaluation and statistical analysis of the results of the interconnection work will be presented

Copper Heat Exchanger for the External Auxiliary Bus-Bars Routing Line in the LHC Insertion Regions

The corrector magnets and the main quadrupoles of the LHC dispersion suppressors are powered by a special superconducting line (called auxiliary bus-bars line N), external to the cold mass and housed in a 50 mm diameter stainless steel tube fixed to the cold mass. As the line is periodically connected to the cold mass, the same gaseous and liquid helium cools both the magnets and the line. The final sub-cooling process (from around 4.5 K down to 1.9 K) consists in the phase transformation from liquid to superfluid helium. Heat is extracted from the line through the magnets via their point of junction. In dispersion suppressor zones, approximately 40 m long, the sub-cooling of the line is slightly delayed with respect to the magnets. This might have an impact on the readiness of the accelerator for operation. In order to accelerate the process, a special heat exchanger has been designed. It is located in the middle of the dispersion suppressor portion of the line. Its main function consists in providing a local point of heat extraction, creating two additional lambda fronts that propagate in opposite directions towards the extremities of the line. Both the numerical model and the sub-cooling analysis are presented in the paper for different configurations of the line. The design, manufacturing and integration aspects of the heat exchanger are described

Primitive Words, Free Factors and Measure Preservation

Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more generally, subgroups of F_k which are free factors. The first criterion is graph-theoretic and uses Stallings core graphs: given subgroups of finite rank H \le J \le F_k we present a simple procedure to determine whether H is a free factor of J. This yields, in particular, a procedure to determine whether a given element in F_k is primitive. Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from the direct product of k copies of G to G), where G is an arbitrary finite group. We call w measure preserving if given uniform measure on G x G x ... x G, w induces uniform measure on G (for every finite G). This is the second criterion we investigate: it is not hard to see that primitivity implies measure preservation and it was conjectured that the two properties are equivalent. Our combinatorial approach to primitivity allows us to make progress on this problem and in particular prove the conjecture for k=2. It was asked whether the primitive elements of F_k form a closed set in the profinite topology of free groups. Our results provide a positive answer for F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I: A New Algorithm", and "On Primitive Words II: Measure Preservation". 42 pages, 14 figures. Some parts of the paper reorganized towards publication in the Israel J. of Mat

Photostimulated desorption performance of the future circular hadron collider beam screen

Synchrotron radiation (SR) originated at superconducting bending magnets is known to be at the origin of several beam detrimental effects related to vacuum instabilities. One of the major challenges in the design of the vacuum beam pipes of high-energy hadron colliders is the SR coping strategy. In the case of the future circular hadron collider (FCC-hh), a Cu-coated beam screen (BS) operating in the range of 40–60 K has been designed with the aim of protecting the superconducting magnet cold bores from direct synchrotron irradiation. In order to experimentally study the FCC-hh BS vacuum and cryogenic performance, two sample prototypes were manufactured and installed in the beam screen test-bench experiment (BESTEX) at the Karlsruhe Research Accelerator (KARA) at the Karlsruhe Institute of Technology (KIT). The emitted SR has a critical energy of 6.2 keV, very similar to the 4.6 keV of FCC-hh. Irradiation at both room (RT) and cryogenic (77 K) temperatures showed a significant reduction of the molecular photostimulated desorption yields (η) of the FCC-hh beam screen compared to those of Cu samples. A first approximation of η and its evolution with the photon dose accumulated on the FCC-hh BS prototype at 77 K allows to estimate that a machine conditioning period of ∼1.2 months would be needed to reduce the photostimulated molecular density at the necessary levels to ensure a 100 h beam lifetime at nominal FCC-hh operation