Transcript Title should be like this A P Robinson1, P L Lewin1, S Sutton2, S

The effect of sample thickness on the relative breakdown strength of epoxy systems
M
*
Reading ,
Z Xu, A S Vaughan and P L Lewin
University of Southampton, Southampton, UK
AC Electrical Breakdown Results
Since it is difficult to safely generate the very high voltages requird to give breakdown data
on final-geometry samples, especially without causing excessive damage to equipment,
smaller samples are often produced for testing to give an indication of the material’s
properties. In recent work, 100 mm thick samples were created to provide breakdown
strength data for a range of epoxy-based systems; the quantitative effect of scaling up from
the limited sample thickness to technologically realistic values needs to be considered.
Volume and area effects are intrinsic to Weibull analysis since they affect the probability of
a defect or impurity being in the breakdown path.
 For AC ramp breakdown testing a Phenix AC Dielectric Test Set, Type 600C was used with
a custom built test cell.
 The test cell used mushroom electrodes held horizontally covered in silicone oil to prevent
flashover. The electrodes were checked frequently for signs of pitting.
 12 breakdown sites were then chosen for each thickness material with the voltage at
breakdown recorded and processed using the Reliasoft Weibull 7++ software package.
Weibull Probability / %
This investigation aims to analyse the effect of sample dimensions on the experimental
breakdown strength of epoxy systems with varying sample thickness. Using a proven
sample production technique, thin epoxy films with thicknesses varying from 50 um up to
1 mm have been produced. These samples were then electrically tested using a
specialised electrical breakdown instrument and data processed using Weibull statistics.
This paper analyses the breakdown characteristics of the samples relative to their
thicknesses in order to (a) test the validity of the Weibull distribution and (b) to provide
estimates of the optimum sample dimensions for different material formulations.
Sample Production and Materials
99.9
99.0
95.0
99.9
99.0
95.0
70.0
70.0
50.0
50.0
Weibull Probability / %
Introduction
20.0
10.0
5.0
0.05 mm
0.07 mm
0.12 mm
0.19 mm
0.25 mm
0.3 mm
0.35 mm
0.5 mm
1.0 mm
1.0
0.1
 DER 332 epoxy resin cured with Jeffamine D-230 was chosen due to the large amount
of interest in such thermosetting materials of late.
20.0
10.0
5.0
1.0
0.1
0.0
0.0
 Samples were produced with a stoichiometric rate of 1000 resin to 344 hardener and
cured at 100 0C for 4 hours followed by gradual cooling for 10 hours.
10
20
30
40
40
breakdown voltages for all samples
breakdown voltages for all samples
Absolute Breakdown Voltage Vs Thickness
Relative Breakdown Voltage Vs Thickness
-1
35
Relative Breakdown Voltage / kVmm
Absolute Breakdown Voltage / kV
200
30
25
20
15
10
180
160
140
120
100
80
60
40
20
0
5
0
200
400
600
800
1000
1200
0
Table 1. Samples produced and Melinex spacers used
Sample
Thickness of
spacer / μm
50
70
120
190
250
A
B
C
D
E
Sample
Thickness of
spacer / μm
300
350
500
1000
F
G
H
I
200
400
600
800
1000
1200
Thickness of sample / m
Thickness of sample / m
1 mm thick sample
140 180
Figure 4. The Weibull plot for relative
40
Figure 2. Melinex spacers
80 100
Figure 3. The Weibull plot for absolute
 Sample thickness was varied using Melinex spacers obtained from DuPont to produce
the samples listed in Table 1. Example spacers are shown in Figure 2.
Figure 1. Pre-made mould produced
60
Relative Breakdown Voltage / kVmm-1
Absolute Breakdown Voltage / kV
 Samples were produced using a gravity fed pre-made mould technique established
previously, shown in Figure 1 with a 1 mm aluminium spacer and sample. A QZ13 release
agent was used to aid in removal of the polymer film from the mould.
0.05 mm
0.07 mm
0.12 mm
0.19 mm
0.25 mm
0.3 mm
0.35 mm
0.5 mm
1.0 mm
Figure 5. A plot of absolute breakdown voltage
Figure 6. A plot of relative breakdown
against thickness with a fitted exponential
voltage against thickness with a fitted
rise to maximum curve (α values)
exponential decay curve (α values)
 Observations
 Figure 3 shows that increasing the thickness of the samples increases the absolute
breakdown voltage, as expected.
 Figure 5 shows that this increase is not linear, and instead follows an exponential rise to
maximum.
 Figure 4 shows that the relative breakdown voltage drops with increasing thickness.
Weibull Analysis
 Figure 6 shows the decrease in relative breakdown voltage follows an exponential
decay.
 To analyse electrical breakdown data it is a standard that Weibull statistics are
employed. One, two or three parameter Weibull equations are often considered. The one
and three parameter equations are shown below in equation 1.
 C  t 
f t     
    
C 1
 t
exp  
 
C
   t    

f t    
    
 1
 t    
exp 

 


(1)
 The 1 parameter is often found to provide an unacceptable fit to data and the 3
parameter is considered by many to “over-paramaterise”, therefore a 2 parameter Weibull
equation is often preferred, shown in equation 2.
 x  x t 
Pf x   1  exp 

 


(2)
Here, Pf(x) is the cumulative probability of failure at time x, xt is a threshold time under
which no failures can occur, α represents the location parameter and β the shape
parameter.
 When assessing materials based upon data analysed using Weibull, it is often beneficial
to observe the α and β parameters, as these give an indication to the materials insulating
performance and uniformity respectively.
 For an ideal material one may expect the relative breakdown strength to be directly
proportional to the thickness of the material, so by doubling the thickness you would double
the breakdown strength however this is clearly not the case. These exponential trends could
therefore be due to the increased probability of the breakdown path meeting a defect within
the material, or that the ‘surface’ or ‘initiation’ of the material has more control over the
breakdown strength resulting in addition of further bulk material having little effect on the
overall behaviour.
Conclusions
 The breakdown strength dependence of a polymeric insulating material with respect to
sample thickness was investigated.
 The absolute breakdown strength of the epoxy increased with thickness, but fall below a
linear relationship, being well described by an exponential rise to maximum function.
 The relative breakdown voltage of the samples was seen to decrease in an exponential
decay, suggesting that addition of further material was proving less effective at increasing the
breakdown strength.
Contact details :
M Reading, [email protected]
University of Southampton, Highfield, Southampton, SO17 1BJ, UK