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Highlights: [•] We develop multiaxial constitutive model of discontinuous plastic flow at very low temperatures. [•] The constitutive model takes into account the thermodynamic instability near-0K. [•] The model is physically based and contains multi-scale approach (micro-meso-macro). [•] The thermo-mechanical coupling is taken into account (fluctuations of temperature). [•] The behavior of yield surface and conditions of violation of Drucker’s postulate are explained. [ABSTRACT FROM AUTHOR]

Abstract: FCC metals and alloys are frequently used in cryogenic applications, nearly down to the temperature of absolute zero, because of their excellent physical and mechanical properties including ductility. Some of these materials, often characterized by the low stacking fault energy (LSFE), undergo at low temperatures three distinct phenomena: dynamic strain ageing (DSA), plastic strain induced transformation from the parent phase (γ) to the secondary phase (α′) and evolution of micro-damage. The constitutive model presented in the paper is focused on the discontinuous plastic flow (serrated yielding) and takes into account the relevant thermodynamic background. The discontinuous plastic flow reflecting the DSA effect is described by the mechanism of local catastrophic failure of Lomer–Cottrell (LC) locks under the stress fields related to the accumulating edge dislocations (below the transition temperature from the screw dislocations to the edge dislocations mode T 1). The failure of LC locks leads to massive motion of released dislocations accompanied by the step-wise increase of the strain rate. The response of stress is defined in terms of four stages within each serration cycle. In the fourth stage, the strain rate sensitivity model with temperature playing the role of relaxation parameter is applied. Identification of parameters of the constitutive model is based on the experimental data collected during a campaign of tensile tests carried out on copper and stainless steel samples immersed in liquid helium (4.5K), by means of a unique equipment developed at CERN. [ABSTRACT FROM AUTHOR]

Modern superconducting intermetallic materials (e.g. NbTi, Nb 3 Sn) 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. [ABSTRACT FROM AUTHOR]

Highlights • The paper deals with model of discontinuous plastic flow (DPF) coupled with strain induced fcc–bcc phase transformation. • The tensile test results indicate rather strong strain localization in the form of shear bands propagating. • The intersections of shear bands can be very effective plastic strain induced nucleation sites of the martensitic embryos. • The evolution of martensitic phase in the austenite affects the strain hardening modulus. • The numerical model allows to reproduce the observed serrations during DPF coupled with the phase transformation. Abstract 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–T 1. 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• The model of multiaxial discontinuous plastic flow in the context of kinematically controlled combined loads and non-proportional loading paths is proposed together with the algorithm of numerical integration of physical relations. • The unique set-up for testing tubular samples under kinematically controlled traction and torsion in liquid helium (4.2 K) is presented. • The experimental results (304ss) confirm the redistribution of serration between the loading directions. • The torsion activates all the cross-sections in terms of the plastic flow, and this implies local softening in the axial direction, before the hardening can restart. 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. [Display omitted] [ABSTRACT FROM AUTHOR]