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13-001208-HMF-01

TO: Distribution

FROM: H.M. Fan

DATE: December 8, 2000

SUBJECT: Stress Analysis of Loss of Coolant on Cool down of TF Coil
Inner Leg

A finite element stress analysis was performed to investigate the
insulation shear stresses due to loss of coolant in one of the TF turn
in the center stack. The loss of coolant will causes higher temperature
in the TF turn during the cool down period and will induce shear
stresses in the insulation.

The analysis was performed by using ANSYS 3-D model that consists of the
top half of the full inner leg. The model was formed by solid element
SOLID45. The temperatures are assumed to be 20 C for turns with cooling
and 40 C for the turn without cooling. A plot of temperature
distribution is shown in Fig.1

![](media/image2.jpeg){width="5.798611111111111in"
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Figure 1 Temperature distribution on the TF coil leg

Vertical displacement constraints were applied at the lower end of the
model. Three additional horizontal constraints were placed at the inner
turns in the lower end to prevent the rigid body movement of the model.
The isotropic material properties were used for the copper and
insulation as follows:

Copper Insulation

Modulus of elasticity (Pa) 117.0E+9 12.4E+9

Coef. Of thermal expansion (m/m/C) 17.6E-6 10.8E-6

Poisson\'s ratio 0.30 0.33

The ANSYS results for the shear stresses in the insulation are
summarized in Figs. 2-4. The unit of stress is in Pa. The cylindrical
coordinate system was used in which x, y, and z representing three
orthogonal axes in the radial, circumferential, and vertical directions,
respectively.

For Sxy in Fig. 2, the high stresses occur at the outer vertical edges
where the maximum distortions were found in the horizontal cross
section. The maximum shear stress in the radial direction (Sxy) is 12.4
MPa (1.80 ksi), which occurs about 0.04 m from the upper edge. The shear
stress is relatively uniform along the height and slightly smaller at
the top end due to an abrupt change of stiffness. The maximum shear
value matches closely with the previous results using model containing
two adjacent turns and 2-D plane stain element.

![](media/image3.jpeg){width="5.798611111111111in"
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Figure 2 Radial shear stress in TF insulation

The maximum shear stresses for Syz is 11.3 MPa (1.64 ksi) as shown in
Fig. 3. The peak stress occurs on the upper edges where the maximum
distortions due to the difference of vertical thermal expansion were
found. The shear stress become smaller as it is away from the upper edge
and becomes null in a very short distance. The maximum shear value Syz
is slightly smaller than the maximum radial shear value Sxy as shown in
Fig. 2.

The maximum shear stresses for Sxz is 8.33 MPa (1.21 ksi) as shown in
Fig.4,. The peak stress was found in the insulation between inner and
outer TF coil turns due to the deformation differential of the inner TF
turn and outer TF turn . As shear stress Syz, the shear stress also
become smaller as it is away from the upper edge. The hot TF turn
produces some bending moments along the longitudinal axis of the coil
bundle, therefore, the maximum shear stress value of Sxz is smaller than
the maximum shear stress value of Syz.

![](media/image4.jpeg){width="5.798611111111111in"
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Figure 3 Vertical shear stress Syz in TF insulation

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Figure 4 Vertical shear stress Sxz in TF insulation

A plot of Tresca stress, which is defined as twice the maximum shear
stress and is equal to the largest algebraic difference between any two
of the three principal stresses, is given in Fig. 5. The peak Tresca
stress is 28.6 MPa (4.15 ksi) which gives the peak shear stress of 2.07
ksi in any direction. Noted that the Tresca stress is in general not
parallel to the surface of the insulation. However, it provides the
information where the maximum shear stress may occur on the surface of
insulation.

To search for the maximum shear stress on the insulation surface, the
vector sum of the two combined shear stresses must be calculated. It is
expected that it may take place on the top edge where the maximum Tresca
stress and the maximum Syz are discovered. Another possible location is
at the nodal point of peak radial shear stress Sxy . The calculations of
maximum combined stresses yield:

Node location Sxy Syz Ssum

(ksi) (ksi) (ksi)

13485 max. Syz 1.195 1.637 2.026

13260 max. Sxy 1.798 0.459 1.855

![](media/image6.jpeg){width="5.798611111111111in"
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Figure 5 Tresca stress in TF insulation

The allowable shear stress in insulation varies with the normal stress
on the shear surface. The test results show the compression improve the
maximum shear value. To consider the effects of the normal stress, Fig.
6 gives the stress plot of the circumferential stress Sy in the
insulation. These stresses represent the normal stresses on the
insulation between the adjacent TF turns in the same radial locations.

The high tensile stresses with a peak stress value of 13.189 MPa (1.913
ksi) are limited to a very local area near the top corner. The tensile
stress for nodal point next to the top corner point on the outer edge
(0.02m below the top corner) is 5.998 MPa (0.870 ksi). The average
tensile stress becomes 1.391 ksi. Away from the upper edge zone, the
normal stresses on the radial insulation experience nearly uniform
stress pattern with a tensile stress of 8.08 MPa (1.17 ksi) at the outer
edge and a compressive stress of -6.40 MPa (-0.928 ksi) at the inner
edge. This stress behavior is due to the restraint effects of the inner
TF coils during the thermal expansion of the hot TF coil. The restraints
in the circumferential direction produce the bending moments on the
sidewalls of the hot TF turn.

![](media/image7.jpeg){width="5.798611111111111in"
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Figure 6 Tensile and compressive stresses in the circumferential
direction

Distribution:

P Heitzenroeder

M. Williams

C. Neumeyer

M. Ono

A. Brooks