Błażej T. Skoczeń

Combined Model of Strain-Induced Phase Transformation and Orthotropic Damage in Ductile Materials at Cryogenic Temperatures

Ductile materials (like stainless steel or copper) show at cryogenic temperatures three principal phenomena: serrated yielding (discontinuous in terms of dσ/dε), plastic strain-induced phase transformations and evolution of ductile damage. The present paper deals exclusively with the two latter cases. Thus, it is assumed that the plastic flow is perfectly smooth. Both in the case of damage evolution and for the 0 phase transformation, the principal mechanism is related to the formation of plastic strain fields. In the constitutive modeling of both phenomena, a crucial role is played by the accumulated plastic strain, expressed by the Odqvist parameter p. Following the general trends, both in the literature concerning the phase transformation and the ductile damage, it is assumed that the rate of transformation and the rate of damage are proportional to the accumulated plastic strain rate. The 0 phase transformation converts the initially homogenous material to a two-phase heterogeneous ”composite”. The kinetics of phase transformation is described by the relevant linearized law of evolution of the volume fraction of 0 martensite in the austenitic matrix [Garion, C. and Skoczen, B. (2002a). The evolution of orthotropic damage is characterized by the fact that the principal directions of damage are generally not colinear with the principal directions of stress. The damage rate tensor depends linearly on the strain energy density release rate tensor (conjugate force) and on the material properties tensor C, that reflects the orthotropy level. The relevant kinetic law of damage evolution and the combined constitutive model, including phase transformation, are developed in the present paper. The model is particularly suitable to describe the evolution of highly localized damage fields in thin-walled shells, subjected at cryogenic temperatures to the loads far beyond the yield point. It has been applied to the prediction of the response of the bellows expansion joints (corrugated thin-walled shells) designed for the inter-connections of the Large Hadron Collider at CERN.

The interconnections of the LHC cryomagnets

The main components of the LHC, the next world-class facility in high-energy physics, are the twin-aperture high-field superconducting cryomagnets to be installed in the existing 26.7-km long tunnel. After installation and alignment, the cryomagnets have to be interconnected. The interconnections must ensure the continuity of several functions: vacuum enclosures, beam pipe image currents (RF contacts), cryogenic circuits, electrical power supply, and thermal insulation. In the machine, about 1700 interconnections between cryomagnets are necessary. The interconnections constitute a unique system that is nearly entirely assembled in the tunnel. For each of them, various operations must be done: TIG welding of cryogenic channels (=50 000 welds), induction soldering of main superconducting cables (=10 000 joints), ultrasonic welding of auxiliary superconducting cables (=20 000 welds), mechanical assembly of various elements, and installation of the multi-layer insulation (=200 000 m/sup 2/). Defective junctions could be very difficult and expensive to detect and repair. Reproducible and reliable processes must be implemented together with a strict quality control. The interconnection activities are optimized taking into account several constraints: limited space availability, tight installation schedule, high level of quality, high reliability and economical aspects. In this paper, the functions to be fulfilled by the interconnections and the various technologies selected are presented. Quality control at different levels (component/ interconnect, subsystem, system) is also described. The interconnection assembly sequences are summarized. Finally, the validation of the interconnection procedures is presented, based in particular on the LHC prototype cell assembly (STRING2).

Constitutive Modeling of Dissipative Phenomena in Austenitic Metastable Steels at Cryogenic Temperatures

In the present paper the constitutive model of dissipative material at cryogenic temperature is presented. Three coupled dissipative phenomena: plastic flow, plastic strain induced phase transformation and evolution of damage are considered using a thermodynamically consistent framework. The theory relies on notion of local state, and involves one state potential for the writing of the state laws, and dissipation potential for the description of the irreversible part of the model. The kinetic laws for state variables are derived from the generalized normality rule applied to the plastic potential, while the consistency multiplier is obtained from the consistency condition applied to the yield function. The model is applied for simulation of two distinct dissipative phenomena taking place in FCC metals and alloys at low temperatures: plastic strain induced transformation from the parent austenitic phase to the secondary martensitic phase, and evolution of micro-damage.

Damage evolution in a stainless steel bar undergoing phase transformation under torsion at cryogenic temperatures

Phase transformation driven by plastic strains is commonly observed in austenitic stainless steels. In the present paper, this phenomenon is addressed in connection with damage evolution. A three-dimensional constitutive model has been derived, and scalar variables for damage and the volume fraction of the transformed phase were used. The model was solved using Abaqus UMAT user defined procedure, as well as by means of simplified one-dimensional approach for a twisted circular bar. Large experimental campaign of tests was performed, including martensite content measurements within the cross-section and on the surface of the bar during monotonic and cyclic loading. Based on the residual angle of twist, damage variable was calculated. The global response of torque versus the angle of twist was measured as well. Comparison between the experimental results and the results obtained from the simplified one-dimensional approach and from the full three-dimensional approach are presented. It turns out that one-dimensional formulation agrees quite well with full three-dimensional model. Thus, much simpler approach can effectively be used. Moreover, experimental results agree well in terms of the martensite content evolution and relation: torque versus the angle of twist. Damage evolution is correctly predicted in terms of the maximum values. Lastly, the evolution of damage during cyclic torsion is discussed, as the experimental results indicate rather surprising effect of unloading modulus recovery after each reversion of twist direction.

Strain Induced Martensitic Transformation at Low Temperatures

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 e 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).

Thermodynamics of Processes Occurring in Metals at Low Temperatures

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.

Properties of Austenitic Stainless Steels at Cryogenic Temperatures

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).

Applications: Accelerators for High Energy Physics and Cryogenics Transfer Lines

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).

Stability of Corrugated Axisymmetric Shells (Bellows)

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).

Material and Fatigue Induced Structural Instabilities of Corrugated Bellows at Low Temperatures

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.