Institute of Fundamental Technological Research

In the present paper, the question of the mechanism of discontinuous plastic flow (DPF) occurring at extremely low temperatures (in the proximity of absolute zero), is for the first time raised in the context of kinematically controlled combined loads (independent control of displacement and rotation) and non-proportional loading paths. In order to identify the multiaxial stress state during DPF, a unique set-up for testing tubular samples under kinematically controlled traction and torsion in liquid helium (4.2 K) has been developed. The results of tests performed on grade 304 stainless steel thin-walled tubular samples subjected to combined loads (traction and torsion) in the proximity of absolute zero are for the first time reported. These novel results confirm the assumptions accepted when building the multiaxial constitutive model of discontinuous plastic flow, namely, the production of lattice barriers, the pile-ups of dislocations and the criterion of their collective failure, as well as the assumption that the serrations may be recorded by force and torque transducers independently. Thus, the numerically implemented model allows to reproduce the observed serrations, and to redistribute them between the loading directions.

plasticity, discontinuous plastic flow, cryogenic temperatures, combined loads, non-proportional loading paths

Modern superconducting intermetallic materials (e.g. NbTi, Nb3Sn) are used to build conductors composed of a matrix and the superconductor strands. One of the most popular materials for matrix is copper, because of its excellent physical and mechanical properties at extremely low temperatures. Ductile OFE copper stabilizes, on one hand, the mechanical response of brittle superconductor strands and, on the other hand, takes over the electrical charge in case of quench (resistive transition). Thus, the composite structure of modern conductors used to build the coils of superconducting magnets is fully justified. Such a composite structure results in common deformation of the matrix and the strands when winding the coils and during the operation, when the coils are subjected to the prestress and to the Lorentz forces at extremely low temperatures (liquid or superfluid helium). When the loads are large enough, the copper-superconductor strands composite is subjected to inelastic deformation, including moderately large plastic strains. It is known, that copper and superconductor strands exhibit the so-called discontinuous plastic flow (DPF) at extremely low temperatures, that results in abrupt drops of stress against strain of different amplitude and frequency. In order to describe correctly the behaviour of composite superconductors at extremely low temperatures, a constitutive model of DPF has been developed and applied to both components: matrix and strands. The results of numerical analysis are compared with the experiments, carried out in dedicated cryostat containing liquid helium and the relevant instruments.

superconductor, plastic deformation, cryogenic temperatures, constitutive model

A popular class of materials massively used at cryogenic temperatures comprises the stainless steels of different grades, such as 304, 304L, 316, 316Ti, 316L, 316LN etc. Such materials are metastable at extremely low temperatures, and usually undergo plastic strain induced phase transformation. In addition, these materials applied in the proximity of absolute zero exhibit the so-called discontinuous (intermittent, serrated) plastic flow (DPF). It consists in frequent, abrupt drops of stress against strain, characterized by increasing amplitude of the stress oscillations. Strong coupling between both phenomena: DPF and phase transformation is observed. Recent experiments performed by means of stainless steel samples tested in liquid helium (4.2 K) clearly indicate strong strain localization during DPF, in the form of shear bands propagating along the sample. However, as soon as the phase transformation process takes place, the motion of shear bands is hindered by formation of secondary phase. A physically based constitutive model developed in the present paper reflects coupling between the discontinuous plastic flow and the plastic strain induced phase transformation in the temperature range 0–T1. The model involves nonlinear mixed hardening, that occurs during the 2nd stage of each serration (stress–strain oscillation). The hardening is based on two mechanisms: interaction of dislocations with the inclusions of secondary phase, evolution of tangent stiffness operator due to changing proportions between the primary and the secondary phases. Nonlinear hardening strongly increases the stress level during each serration, which affects production of the internal lattice barriers, and the amount of the accumulated plastic strain. This, in turn, affects intensity of the phase transformation (full coupling). The constitutive model and its numerical version allow to reproduce the observed serrations, which is crucial for its application in the design of components operating at extremely low temperatures.

multiscale constitutive model, discontinuous plastic flow, strain induced phase transformation, cryogenic temperatures

Evolution of micro-damage in the course of discontinuous plastic flow (DPF, serrated yielding) at extremely low temperatures is investigated. DPF is observed in many metals and alloys loaded in cryogenic conditions, within the temperature range specific of a given material and starting practically at absolute zero. The appearance of DPF is similar to dynamic strain ageing, however, its origin is attributed to the mechanism of local catastrophic failure of lattice barriers under the stress fields related to edge dislocation pile-ups. Failure of barriers, occurring in weakly excited lattice, leads to dynamic and massive motion of released dislocations. The phenomenon is accompanied by step-wise increase of the strain rate and drastic drop of stress during each serration. DPF has strong thermodynamic background consisting in the fact, that the plastic power dissipated in the course of serrations is partially converted to heat, which results in a local jump of temperature. It results from the so-called thermodynamic instability associated with vanishing specific heat when the temperature tends to absolute zero. The evolution of micro-damage affects loading and unloading moduli during each serration. This, in turn, results in gradual evolution of the amount of plastic slip accompanying each serration. The physically based constitutive model describes damage affected serrated yielding at the temperatures close to absolute zero. The model accounts for the thermodynamic background, including phonon mechanism of heat transport. Experimental identification of parameters of the constitutive model has been carried out based on a number of loading/unloading traction tests. A comparison between the experimental and the numerical results is presented and discussed.

Multiscale constitutive model, Discontinuous plastic flow, Microstructures radiation induced damage, Cryogenic temperatures

The phenomenon of strain localization in the course of discontinuous plastic flow (DPF) at extremely low temperatures is investigated. DPF is observed mainly in fcc metals and alloys strained in cryogenic conditions, practically down to absolute zero. These materials undergo at low temperatures a process similar to dynamic strain ageing, manifested by the so called serrated yielding (DPF). DPF is attributed to the mechanism of local catastrophic failure of lattice barriers (including Lomer–Cottrell locks), under the stress fields related to the accumulating edge dislocations. Failure of LC locks leads to massive motion of released dislocations, accompanied by step-wise increase of the strain rate (macroscopic slip) and drastic drop of stress. Recent experiments indicate strong strain localization in the form of shear bands propagating along the sample. The plastic power dissipated in the shear band is partially converted to heat, which results in a local drastic increase of temperature promoted by the so-called thermodynamic instability (nearly adiabatic process). The Dirac-like temperature function is measured by two thermometers located in the gage length of the sample. Spatio-temporal correlation indicates smooth shear band propagation, as long as the process of phase transformation remains on hold. A physically based multiaxial constitutive model presented in the paper describes both DPF and strain localization, accompanied by temperature distribution represented by Green-like solution of heat diffusion equation. The model accounts for the thermodynamic background, including phonon mechanism of heat transport, accompanied by specific heat vanishing with the temperature approaching absolute zero. Experimental identification of parameters of the constitutive model is carried out. A projection of the model to the range where the phase transformation takes place is discussed.

Multiscale constitutive model, Discontinuous plastic flow, Cryogenic temperatures, Strain localization

FCC metals and alloys are massively used in cryogenic applications down to the temperature of absolute zero, because of suitable physical and mechanical properties including high level ductility. Many of these materials undergo at low temperatures a process similar to dynamic strain ageing, reflected by the so-called discontinuous plastic flow (DPF, serrated yielding). The physically based multiaxial constitutive model presented in the paper constitutes a generalization of the previous uniaxial model that proved efficient in describing the plastic flow instabilities occurring at extremely low temperatures. The model takes into account thermodynamic background, including the phonon mechanism of heat transport and thermodynamic instability caused by specific heat vanishing with the temperature approaching absolute zero. The DPF is described by the mechanism of local catastrophic failure of lattice barriers (for instance Lomer-Cottrell locks) under the stress fields related to the accumulating edge dislocations. The failure of LC locks leads to massive motion of released dislocations accompanied by step-wise increase of the strain rate (macroscopic slip). In the present paper the plastic flow discontinuity associated with the proportional loading paths is studied. Identification of parameters of the constitutive model is based on the experimental data collected during several campaigns of tensile tests carried out on copper and stainless steel samples immersed in liquid helium (4.2 K).

Multiscale constitutive model, Discontinuous plastic flow, Cryogenic temperatures, Multiaxial loads

We present a new design study of the neutrino Super Beam based on the Superconducting Proton Linac at CERN. This beam is aimed at megaton mass physics, a large water Cherenkov detector, proposed for the Laboratoire Souterrain de Modane in France, with a baseline of 130 km. The aim of this proposed facility is to study CP violation in the neutrino sector. In the study reported here, we have developed the conceptual design of the neutrino beam, especially the target and the magnetic focusing device. Indeed, this beam presents several unprecedented challenges, related to the high primary proton beam power (4 MW), the high repetition rate (50 Hz), and the low kinetic energy of the protons (4.5 GeV). The design is completed by a study of all the main components of the system, starting from the transport system to guide the beam to the target up to the beam dump. This is the first complete study of a neutrino beam based on a pebble-bed target capable of standing the large heat deposition of MW class proton beams

The EUROnu project has studied three possible options for future, high intensity neutrino oscillation facilities in Europe. The first is a Super Beam, in which the neutrinos come from the decay of pions created by bombarding targets with a 4 MW proton beam from the CERN High Power Superconducting Proton Linac. The far detector for this facility is the 500 kt MEMPHYS water Cherenkov, located in the Fréjus tunnel. The second facility is the Neutrino Factory, in which the neutrinos come from the decay of μ+ and μ− beams in a storage ring. The far detector in this case is a 100 kt magnetized iron neutrino detector at a baseline of 2000 km. The third option is a Beta Beam, in which the neutrinos come from the decay of beta emitting isotopes, in particular He6 and Ne18, also stored in a ring. The far detector is also the MEMPHYS detector in the Fréjus tunnel. EUROnu has undertaken conceptual designs of these facilities and studied the performance of the detectors. Based on this, it has determined the physics reach of each facility, in particular for the measurement of CP violation in the lepton sector, and estimated the cost of construction. These have demonstrated that the best facility to build is the Neutrino Factory. However, if a powerful proton driver is constructed for another purpose or if the MEMPHYS detector is built for astroparticle physics, the Super Beam also becomes very attractive