M.Gibson
28/2/06
Strain Investigations in Thin Membranes as used in
the ATLAS End-Cap Thermal Enclosure
Overview:Each end of the ATLAS End -Cap thermal enclosure is sealed with a thin (50 micron)
Copper-Kapton membrane. By necessity these are fitted at a nominal 20 deg C. Once
installed and working they will be at around -7 deg C a temperature variation of
approx 30 deg C. This temperature fluctuation will give rise to a shrinkage and
possible subsequent increase in strain. This document details the results of a simple
investigation into the effects and a correlation with the calculated date.
General.
The basic equipment is shown in picture 1. It consisted of a linear stage with a strain
gauge and two thermocouples fixed to the sample. The linear stage allowed the
distance between fixtures to be increased and the subsequent strain noted. By
enclosing the sample in a simple cardboard tube and blowing warm air in at one end
any variation in strain with temperature (as monitored by the thermocouples) could
also be monitored. The sample was constrained at one end by two bolts on a 5cm
pitch (which is similar to that on the full sized membrane); the other end was fixed in
the 4cm wide clip on the gauge head.
Picture 1
Thermocouple Calibration.
Each or the two thermocouples was calibrated by placing them in a container of
water along with a mercury thermometer and heating the liquid with a hot air blower.
Graph 1 shows the results
resistance in K ohms
thermocouple calibration
15
14.5
14
13.5
13
12.5
12
11.5
11
10.5
10
9.5
9
8.5
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
T1(K ohms)
T2 (K ohms)
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
temp in degs C
Graph 1
Strain vs. Displacement.
Graph 2 is a plot of strain vs. displacement. This was achieved by increasing the
distance between the gauge head and the fixed end by using the linear stage. The
linear part of the graph which begins at 10 Newtons, indicates that for a variation of
approximately 50 Newtons the extension was approximately 400 microns. (Previous
calculations had indicated that for a temperature variation of about 30 deg C there
would be approximately 300 microns of shrinkage giving rise to a radial load of 1200
Newtons/meter of circumference. (Equivalent to 60 Newtons/ 5 cm of circumference).
strain vs displacement for 50mm wide x 600 long sample of
50 micron thick copper Kapton
dsiplacement in microns
1600
1400
1200
1000
displacement
(microns)
800
600
400
200
0
0
50
100
150
strain in newtons
Graph 2
Strain vs. Temperature.
The foil was heated to approximately 40 deg C by blowing warm air through the tube
surrounding the sample. The low thermal mass of the sample compared to that of the
table and large aluminium stages and blocks meant that changes in temperature were
very swift. The linear stage was adjusted to give a loose fit to the copper Kapton and
the strain gauge zeroed. As the temperature fell the strain was noted.
strain (newtons) vs temp ( deg C)
temp (deg C)
50
40
30
t2
20
t1
10
0
0
0.5
1
strain (newtons)
Graph 3
1.5
2
Repeating this with a small quantity of pre-strain produced the data shown in graph 4.
Data was taken starting at 10 Newtons because in graph 2 it is linear from about 10
Newtons upwards. From this graph it can be seen that a change in temperature of 15
degrees produced a change in strain of about 15 Newtons. (Hence 40 deg C = 40
Newtons which is similar to that calculated)
temp vs strain with pre-strain
45
40
temp ( deg C)
35
30
25
t2
20
t1
15
10
5
0
0
5
10
15
20
25
30
35
strain (newtons)
Graph 4
Strain vs. Displacement with 3 folds
The middle of the sample was then creased 3 times to form a V in the sheet with the
separation between each fold being 6mm. The copper/Kapton cut to be 5cm wide at
that point. The Strain vs. displacement test was then repeated.
strain vs displacment with 3 folds
5000
4500
dsiplacement (microns)
4000
3500
3000
2500
disp
2000
1500
1000
500
0
0
5
10
strain (New tons)
Graph 5
15
20
Table 1 shows the approximate height of the ‘V’ as the displacement is increased. At
no time does one observe rates of change as large as 50 Newtons/400 microns as in
graph 2 while the crease exists.
Displacement (microns)
3000
4000
4600
Table 1
Vertical height of ‘V’
(mm)
2.0
1.0
0.0
Conclusions.
Without any stress relief (folds), the Kapton is quite stretchy for small loads – see
Graph 2. What this means in practice is that when a Membrane is placed, the small
deformations in the surface will easily be pulled out by small forces as the Membrane
is stretched gently to secure it. Once this has been done, the Kapton will appear quite
stiff, corresponding to the Young’s Modulus of the copper. The starting point for
deformations will be beyond the knee of the graph.
This means that the tendency to contract when cooled will induce significant stresses
in the Membrane.
At first glance, a similar behaviour might be expected for the Membrane with stressrelieving folds – see Graph 5. However, provided the Membrane is secured without
pulling out the folds, then there will be plenty of flexibility, allowing the Membrane
to shrink without inducing large stresses. The starting point for deformations can be
kept in the first part of the graph, before the knee, where there is plenty of freedom of
movement before the stiffness of the copper is apparent.