**3. Experimental study of stress-strain states**

Computational and experimental studies of the deformation fields of a structure make it possible to determine the relationship between the levels of stress-strain fields in hazardous zones of the structure which are inaccessible for direct experimental research, and in areas which are accessible for the purpose of continuous observation. The determination of these functional dependencies forms the experimental and theoretical basis for monitoring the operational performance of the installations.

The main stages of research into the stresses to which the critical elements of power installations are exposed include:

• an analysis of the initial data on -magnetic fields, ponderomotive loads and boundary conditions which is necessary for research using models, full-scale elements and mathematical calculations;


Below are some of the main results of the research on the T-15 installations.

The T-15 installation is designed to create and study plasma with parameters that are close to the thermonuclear level and are sufficient for a reliable transition to the plasma state. One of the main technical features of the T-15 installation is the use of superconducting toroidal field coil (STFC).

Each coil unit contains coils of a superconducting current-carrying components, enclosed in a rigid steel case. The coil is a transversally isotropic ring made of a complex composite material consisting of a niobium-tin superconductor in a copper matrix, insulating materials and channels for a coolant (helium).

The T-15 unit contains 24 STFC units located around the central support cylinder along the torus-shaped vacuum chamber. A structural diagram of the SCTF unit is shown in **Figure 6**.

It has been established that as a result of the interaction of the STFC currents with the toroidal and poloidal magnetic fields in the STFC units, two types of volumetric ponderomotive loads arise:


For the purposes of the operation of the T-15 unit, provision is made for nominal and forced modes with and without disruption by plasma current. The values of the loads acting on one unit are shown in **Table 1**.

The maximum strain of a superconductor in any mode may not exceed 0.2%, since the current-carrying capacity of superconducting systems (SCS) drops sharply at strains of more than 0.5%.

Due to the symmetry of structure and loads, all STFC units are subject to the same conditions. Therefore the calculation and experimental study of their *Theoretical and Experimental Analysis of Structural Properties of Load-Bearing Components… DOI: http://dx.doi.org/10.5772/intechopen.94531*

#### **Figure 6.**

*Structural diagram of the STFC unit.*


#### **Table 1.**

*Loads acting on the unit.*

stress-strain state (SSS) is carried out taking into account the corresponding symmetry and support cylinder conditions.

To study the effects Q (τ) of stresses σ τ( ) and strains e(τ) associated with the action of magnetic and thermal fields, foil strain gauges with sensitive elements made of constantan and wire (wire diameter 30 μm) and high-temperature tensoresistors made of a nickel-molybdenum and iron-chromoaluminum alloy were used. The tensoresistors were installed on samples consisting of three materials, simulating the main structural materials of the tokamak: stainless steel, copper alloy and a composite material. As a result of the first series of experiments, it was found that in magnetic fields of 1–3 T the response of the output signals from the strain gauges was 20x10–6, with standard deviations of about S = 1.5 × 10–6,.

To develop tensoresistors with optimal characteristics at cryogenic temperatures, nickel-molybdenum tensoresistor alloys with a low electrical resistance coefficient in the temperature range of -269 to = 200 С (4–300 *K*) were created. Under

appropriate heat treatment modes (**Figure 7**) these alloys have a high residual electrical resistance *K*t at ultralow temperatures down to 0.5 × 10−6 *K*−1.

**Figure 8** shows the layout of the primary converters and the results of the study of stresses during cool-down and the injection of current into the system consisting of two experimental STFC units located side by side and not aligned. With the units arranged in this way, the interaction of their fields creates a load that approximately corresponds to the load on the units in the operating mode. It has been established by measurement that at a cooling rate of up to 3 K/h, the maximum stresses arise at temperatures up to 60 K and do not exceed the yield stress σy. With a further decrease in temperature, the level of the stresses decreases, and

#### **Figure 7.**

*Temperature correlation between electrical resistance after quenching and various stabilizing annealing modes (1 - quenching, 2 - quenching and annealing for 30 minutes at a temperature of 470°C, 3 - annealing for 2 hours, 4 - annealing for 5 hours).*

#### **Figure 8.**

*Arrangement of tensoresistors on the strain gauge model of the case of the STFC unit in the T-15 installation (the figures refer to the - numbers of the tensoresistors located along the diameter, across and at an angle of 45°).*

*Theoretical and Experimental Analysis of Structural Properties of Load-Bearing Components… DOI: http://dx.doi.org/10.5772/intechopen.94531*

**Figure 9.**

*Temperature and stresses in the housing of the STFC unit during cool-down.*

the temperature field becomes more uniform. The measurement of displacements of the SCS relative to the body during the initiation of the current revealed shifts of up to 15 mm, which could lead to the delamination of the SCS from the walls of the body. On the basis of these measurements, measures were taken to increase the stiffness of the sealing of the coils in the body of the standard STFC units to ensure their operational fitness.

The results of the temperature *t*(τ) and stress measurements *σ*(τ) during cooling are shown in **Figure 9**. The layout of the resistance thermometers, RT, and tensoresistors, T, is shown under the curves.

The numbers of the curves correspond to the numbers of resistance thermometers RT.

Measurement of the changes in stresses when current - from 0 to 15 kA - was introduced into the superconducting systems showed that in the support cylinder the stress reached 110 MPa, and 40 MPa when the discharge chamber was heated.

## **4. Calculations and physical modeling**

The initial computational study of the stress-strain state of the STFC unit as a result of the action of toroidal forces in a complete setting provides a solution to the spatial problem. By using equivalent elasticity modules and taking into account the nature of the load, this problem can restated more simply, in two dimensions. The nature of the SSS in radial sections of the STFC, which are remote from the support column, can be investigated in an axisymmetric setting. The SCS coil housed in the steel power case of the STFC is anisotropic in the circumferential and radial directions. These problems can be solved using the finite element method.

At the initial design stage, calculations were carried out in order to select the best design option. Then, for the selected design option, a study of the stress-strain state of the STFC unit was carried out in relation to the refined design schemes using the finite element method and physical modeling, which allows specific features of the design to be taken more fully into account.

The influence of the following factors was studied:


The superconducting toroidal field coil (STFC) has a strong anisotropy in respect of its mechanical and thermophysical properties. On the planes adjacent to the strips separating the half-shells, contact friction arises during each pulse, which in cryogenic conditions is undesirable from the point of view of heat release and insulation integrity. The ponderomotive forces which compressing the STFC in the radial direction and stretching it in the circumferential direction during each pulse cause gaps to appear between it and the body bandaging it. The significant lack of uniformity in the mechanical and thermophysical properties of the SCS causes a significant lack of uniformity in the stresses to which it is subject, which can lead to appearance of plastic deformations and accumulation of residual stresses in the SCS.

The modeling of strains and stresses in the SCS was carried out using polarization and optical methods.

The calculations of the SSS of the STFC unit, taking into account all the above factors, are shown in **Figure 10**.

In order to ensure that the electrical insulation is reliable, the contact interaction at the node where the support column is connected with a pin to the metal-polymer coils of the STFC (see **Figure 6**) needs to be calculated and assessed. The stress state of the node is almost flat and skew-symmetric. The initial contact takes place near the corner point (**Figure 11a**). At this point of contact, the stresses are very high, which may lead to destruction of the polymer coating. The simplest stress-limiting change in a contact surface is the - rounding of a sharp edge. However, the stress distribution remains significantly uneven (**Figure 11c**), with a sharp increase in stresses near the rounded edge at point A. Analysis of similar options for the contact interaction between a rigid punch and an elastic layer shows that a more favorable pressure distribution takes place when the punch is convex in shape, in which case the curve on the diagram is close to parabolic, with zero pressures at the boundary of the contact area (**Figure 11c**).

The determination of the SSS of the STFC unit resulting from the action of poloidal forces, *Q ,*- is a complex spatial problem involving the mechanics of a

#### **Figure 10.**

*Circumferential stresses in the unit body when it is supported by the column along the AB line; solid lines (-) − values reached by experiment; dotted lines (--) − calculated values.*

*Theoretical and Experimental Analysis of Structural Properties of Load-Bearing Components… DOI: http://dx.doi.org/10.5772/intechopen.94531*

#### **Figure 11.**

*Distributions of contact pressures on a metal-polymer pin with various hole shapes and a split support column with a sharp (a) and rounded (b) edge and (c) with a displacement of the point of initial contact A.*

#### **Figure 12.**

*Distributions of bending and torque moments and shearing forces arising in the forced mode when the plasma current is disrupted.*

deformable solid body. This task was solved using a pivotal approach. To determine the SSS, the rod theory is used: this theory takes into account the potential energy of bending, torsion and antiplane shear deformations. A rod is viewed as an elastic

curve with bending, torsional and shear stiffness. Since the stiffness of an SCS coil with such indicated deformations is low, compared to the stiffness of the unit body, the former can be ignored, thus increasing the design safety margin. The calculation is performed using the force method. The calculation results for the forced mode, in the form of distributions of bending and torque moments and shearing forces, with a disruption of the plasma current when these loads are at a maximum, are shown in **Figure 12**.
