Summary of the Structural Analysis and Design of the NOvA Detector

March 17, 2006

Ang Lee (FNAL)

Victor Guarino (ANL)

Jim Grudzinski (ANL)

1.  **Introduction**

The NOvA detector is a unique structure that is constructed completely
from alternating layers of vertical and horizontal PVC extrusions that
are connected together only by an adhesive between layers. The current
design envisions 31 planes of PVC extrusions (a block) being assembled
and adhered together in the horizontal position on block raiser and then
rotated into the vertical position.

Critical to the success of this design is the strength of the PVC and
the adhesive joint between extrusions. The PVC must not only act as the
main structural element of the detector but it also is required to
provide a high level of reflectivity so that there is sufficient light
output from the detector. As a result the reflectivity requirement on
the PVC a commercial PVC mixture that is commonly available most likely
will not work for the experiment. Therefore, the structural analysis on
the detector has progressed without a complete knowledge of the type of
PVC that would be used. Certain assumptions have been used on the
acceptable level of stress that would minimize creep affects and the
modulus of elasticity that should be used over the life of the
experiment.

The adhesive that is used between layers is also critical to the
structural integrity of the structure. The adhesive will have to be
applied over large surfaces so ES&H concerns have dominated the criteria
for selecting the adhesive to date. The adhesive must have a work life
of approximately 20 minutes to allow extrusions to be placed during
assembly, but cure rather quickly so that sufficient strength in a 24
hour period so that the block can be rotated into the vertical position.

Throughout the analysis a safety factor of 5 on the maximum stress and
buckling has been the goal of the design. It is felt that a safety
factor of 5 is needed in a unique structure such as NOvA that is
constructed completely from PVC extrusions bonded together.

This paper will summarize the work that has been done on the PVC
material properties, adhesive between the extrusions, and structural
analysis of the PVC extrusions and assembled NOvA structure.

This paper will be divided into the following sections.

-   PVC material properties

-   Adhesive

-   Analysis of individual PVC extrusions

-   Detailed Description of FEA model of Assembled Planes

-   Methods for modeling adhesive joints

-   Buckling analysis of assembled PVC planes

-   Stress/deflection analysis of assembled PVC planes.

-   Adhesive Stresses

-   Conclusions/recommendations.

2.  **PVC Material Properties**

2.1 Baseline PVC Material

The PVC extrusions form the main structural element of the NOvA
detector. As discussed above the PVC material must meet not only
mechanical requirements for strength, creep, impact strength, but also
requirements for reflectivity. Research on reflectivity currently
indicates that relatively high concentrations of TiO~2~, (\>15%) are
needed. This amount greatly exceeds that used in commonly available PVC
pipe resins or other commonly used building materials. Similarly we have
to restrict certain common additives such as acrylic impact modifiers
and UV absorbers which absorb light in the spectrum we are concerned
with (blue). One consequence of developing a unique PVC mixture is that
mechanical properties, particularly creep, are not well known. This is
in contrast with a standard PVC pipe compounds which are developed to an
industry standard with known minimum properties.

The current baseline PVC mixture is the so called PET B mixture. This
mixture is shown in table 1 (listed both as total percentage and the
plastic industry standard representation of parts per hundred, phr ).
Various polymer additives are added to the base PVC polymer to alter
mechanical properties as well improve the processing. The PET-B compound
was arrived at in an attempt to make an extrudable PVC containing 15%
TiO2 with minimal other additives. based on existing data, it has shown
the highest reflectivity of various trails. R+D is continuing for the
PVC composition to confirm and further improve the mechanical and
reflectivity properties.

  ----------------------- ----------------------- -----------------------
  PVC Resin               100 phr                 78.6%

  TiO2 uncoated Rutile,   18 phr                  14.9%
  size \<0.2 micron                               

  Internal and External   1 phr                   3.9%
  Lubricants                                      

  Organo-Tin Stabilizers  2.3 phr                 1.8%
  ----------------------- ----------------------- -----------------------

**Table 1. Composition of PET-B PVC compound.**

2.2 Mechanical properties

As the structural analysis must progress in parallel to the PVC R&D
effort, the material specifications is iteration between required
minimum and achievable properties. Table 2 lists the current desired
minimum mechanical properties. These have been arrived at by combination
of considering values used in the PVC pipe industry, the particular
measured values of the PET-B material, and the results of FEA analysis
of the structure. Similarly, a maximum tensile design stress of 1000 psi
was based on PVC pipe industry references. Each of these values has
different levels of significance to the design. Similarly the
uncertainty of the current measured values as well as the application of
these values in design varies for each. The current state of each of
these properties is discussed individually below.

  ----------------------- ----------------------- -----------------------
  Material Property       Value                   Test Method

  Modulus of Elasticity   450,000 psi             ASTM D638

  0.2 % Offset Yield      4000 psi                ASTM D638

  Ultimate tensile Stress 5500 psi                ASTM D638

  Notched Izod Impact     1 ft-lb/in              ASTM D256
  Test                                            

  Creep Modulus           360,000 psi after 20    ASTM D2990
                          years                   
  ----------------------- ----------------------- -----------------------

**Table 2. Desired minimum mechanical properties for the NOVA PVC
compound.**

2.2.1 Modulus of Elasticity (E)

While the value of E drives the deformation and stress distributions of
the structure, the more significant concern is the effect on buckling
stability. The safety factor of buckling as discussed below is not
excessive. A reduction in the stiffness would further reduce this value.
The analysis is linear and uses a value of 360,000 psi. The PET-B
material has been measured at 470,000 psi. It is important to say two
things about this value. The first is that this is the instantaneous E
measured in a short time tensile test. As will be discussed in section
2.2.2, PVC is viscoelastic which implies the E is a funtion of time.
Secondly, PVC does not have a well defined elastic yield point. Figure 1
shows a representative plot from 10 PET-B tensile test samples. The
value of E is the slope of the stress/strain curve where the curve
remains linear. Again noting that the design stresses are limited to
1000psi, it is important to note that this linear region persists up to
2000 psi.

![](media/image1.wmf){width="5.997222222222222in"
height="3.5722222222222224in"}

**Figure 1. Representative stress strain diagram for PET-B tensile
specimen.**

2.2.2 Creep Modulus

As mentioned above, PVC is viscoelastic which implies that the material
will flow over time. This can manifest itself as stress relaxation in
constant strain or creep under constant load. We are more concerned with
creep since we are in a constant load situation. The deformation over
time lends itself to an apparent creep modulus where it can be thought
of as a reduced stiffness over time.

There are three possible problems related to creep. 1. The material
initial loaded and stable deforms until it ruptures (creep rupture). 2.
Creep initiates crazing. 3. The deflections lead to an instability such
as buckling (reduced effective stiffness).

All of these problems are functions of stress. This is the driving force
behind a relatively low design stress (1000 psi ) as compared to the
yield stress such as 4500 psi. Similarly, as mentioned above, the value
of E used in the FEA has been 360,000 psi which is considerably lower
than the measured values. This value is used a lower bound to see the
effect of a reduction of the initial modulus in time. This leads to the
current requirement that the E after 20 years is greater or equal to
360,000 psi.

The creep modulus is not yet measured for PET-B and it is not clear that
the value of 360,000psi is achievable. Tests are under way to measure
this. The difficulty of course is in predicting a value 20 years from
now based on short term tests. The standard procedure for extrapolating
such information is by exploiting the time-temperature relation ships
for PVC. We are currently planning and performing accelerated creep and
stress relaxation tests at various temperatures in an attempt to
determine this value. At the same time we have long term creep tests in
progress that will be used as a validation of the predictions. see
figure 2. Similar tests were run for 1.5 years on Extrutech PVC samples
and the results are descirbed in NOvA note 49. We are also considering
employing expert consultants in this area to assist in the development
of the test and interpretation of the data.

![](media/image2.wmf){width="4.4944444444444445in"
height="4.127083333333333in"}

**Figure 2. Long term creep apparatus.**

![](media/image3.jpeg){width="5.4375in" height="3.209722222222222in"}

![](media/image4.jpeg){width="5.402777777777778in"
height="2.4305555555555554in"}

**Figure 3. Apparatus for accelerated stress relaxation test at elevated
temperature.**

2.2.3 Ultimate and Yield stresses

These values are normally important in designs such as from steel where
the safety factor is based on these values. For plastic design as
mentioned above, creep dominates the design stress. The yield stress and
ultimate become less meaningful. Referring to figure 1, the 0.2 % offset
yield point is shown. This method is used since a well defined yield
point does not exist for PVC.

2.2.4 Impact strength

Polymers can behave in a brittle manner depending on the strain rate and
temperature. The NOvA detector does is not exposed to see dynamic,
impact, or alternating loads by design. Impact loads are possible from
accidental contact such as tool dropping. There is no guidance from
industry for an impact design criteria and at this point we have not
determined one. Aside from impact, the impact strength tells you
something about the fracture characteristics. In a qualitative sense, we
desire a material that behaves in a ductile manner and has sufficient
fracture toughness.

There are several ways of measuring impact toughness the most common
being Izod impact test and drop weight tests. These are simple and quick
but only allow relative comparisons. Fracture mechanic tests are
available that measure true material properties but these are expensive.

We have included the Izod impact value in table 2 that matches that
defined fro PVC pipe. PVC\'s can take on a value of 1-15 ft-lb/in and so
this value is relatively low. We are investigating getting fracture
mechanics type tests done on PET-B to help quantify the fracture
toughness. the desire is to then relate this to an Izod impact or
similar test value to allow comparison between compounds as well as QC
measurement.

2.3 Resistance to Liquid Sinctillator

The PVC structure will also be exposed to the liquid scintillator. It is
essential that the liquid does not degrade the mechanical properties.
Historical tests for the MINOS collaboration that looked to see
degradation of liquid scintillator housed in PVC found no evidence. This
is a good indication that PVC is not attacked by the liquid
scintillator. Nonetheless we are performing tests to confirm this.
Preliminary tests of samples exposed between 1 and 30 days to the liquid
scintillator reveal no significant material loss. This test has
systematic difficulties and so in itself is not conclusive. Similarly,
PET-B specimens are currently soaking in liquid scintillator with the
plan to perform mechanical tests at various time periods. In particular,
impact and tensile properties will be investigated. There is also plans
to duplicate the accelerated creep tests while exposed to liquid to see
if differences are observed.

3.  **Adhesive Strength**

The selection of an adhesive has been dominated by concern about vapor
and volatiles as large plane of PVC extrusions 53ft square are bonded
together. As a result of these concerns epoxies have been focused on as
the adhesive of choice, however, recent concerns about the bond strength
of epoxies has led recently to a re-examination of solvent adhseives.

Several adhesives are being considered for the NoVA structure and
standard ASTM tests (shear/peel/cleavage) have been performed in order
to understand their relative strengths. The initial tests were conducted
using specially fabricated fixtures for insuring a consistent glue line
thickness and consistency between test samples. The fixtures are shown
in the figures below.

![](media/image5.jpeg){width="4.317361111111111in"
height="5.756944444444445in"}

**Cleavage Sample in Test Fixture**

![](media/image6.jpeg){width="4.374305555555556in"
height="3.2805555555555554in"}

**Cleavage Test Sample in Fixture for Gluing**

![](media/image7.jpeg){width="5.983333333333333in" height="4.4875in"}

**Double Shear Test Samples in Gluing Fixture**

![](media/image8.jpeg){width="5.992361111111111in" height="3.2in"}

**Dimensions of Double Shear Test Specimen**

The cleavage and peel test specimen are mainly used for a relative
comparison between adhesives. The double shear test though can be
directly related to the strength of the bond joint. The initial
specimens were fabricated using ¼" thick material and the dimensions
shown in the Figure above. The results are shown in the chart below:

![](media/image9.wmf){width="5.125in" height="2.8541666666666665in"}

The R designation indicates adhesives that had the mating surfaces
roughened using a 60 grit emery paper.

Two adhesives have achieve the shear strength that is needed. The first
is 3M 2216 epoxy with the surface roughed up. There is considerable
experience with this epoxy within the collaboration because this is the
same epoxy that was used during Minos to glue modules (\~8m x 1m)
together. The ES&H concerns of this epoxy are well understood and it is
believed that it is possible to provide the needed ventilation. 3M 2216
is currently the baseline adhesive for the detector. In addition, Devcon
Plastic welder has significantly higher shear strength and ductility
than 2216, however, there are many concerns about the volatiles that are
emitted by this adhesive. The Devcon product is used in industry to bond
large surfaces together and the collaboration is currently investigating
the ways in which industrial manufacturers have alleviated the ES&H
hazards of this product.

Once concern with using 2216 and any other epoxy is that they display
significant brittleness. Several test specimens were destroyed after
being dropped and the epoxy bond shattering.

4.  **Analysis of Individual PVC extrusions**

The structural analysis of the NOvA structure began with an examination
of individual PVC extrusions. The pressure at the bottom of the vertical
extrusions is 19psi due to the 53ft head of the liquid scintillator. The
horizontal extrusions are not subjected to this pressure because they
are supported individually by adjacent vertical extrusions and there is
no accumulation of weight from the extrusions above.

The geometry of the extrusions and cells has been optimized to minimize
the stress within extrusion to approximately 600psi when subjected to
the maximum 19psi hydrostatic pressure. The 600 psi stress was chosen
based on initial understanding of the PVC creep as described above.
Figure 4 shows the basic geometry of the extrusion. The current baseline
geometry for the extrusion is to have a 3mm thick outer wall and a 2mm
thick inner web for the horizontal modules and a 4.5mm thick outer wall
and 3.0mm thick inner web for the vertical extrusions. The difference is
wall thickness between vertical and horizontal extrusions is done to
minimize adhesive stresses as described below. The scallops shown are
needed in order to reduce the stress concentrations in the corner of the
cell. Figure 5 below shows the stress distribution within the PVC
extrusion under the 19psi internal pressure and Figure 6 shows the
expected deflection.

![](media/image10.jpeg){width="5.992361111111111in" height="3.2in"}

**Figure 4**

**Geometry of Horizontal Extrusion**

![](media/image11.png){width="4.581944444444445in"
height="3.591666666666667in"}

**Fig 5**

**Stress of Vertical extrusion subjected to 19 psi for wall
thickness=3/2 mm**

![](media/image12.png){width="4.800694444444445in"
height="3.7756944444444445in"}

**Fig 6**

**Deflection of Vertical extrusion subjected to 19 psi for wall
thickness=3/2 mm**

For details of the analysis see Nova Note 0079.

5.  **Modeling & Calculation Details of Adhesive Joints**

Optimizing the geometry of the PVC extrusion to withstand the 19psi
hydrostatic pressure within the detector is a fairly straightforward
analysis. However, once these extrusions are bonded together to form a
monolithic structure the challenge of the structural analysis is
significantly magnified. The buckling/stress/deflection analyses of the
assembled detector that are described in the sections below depend on
how the adhesive bond is modeled.

The analysis an adhesive bonded joint is considered to be one of the
most challenging tasks. The difficulty is not only on the complex stress
state within the adhesive but also due to the complicated geometry being
modeled as well as the limitation of computational capacity. Several
methods including the average stress method, the maximum stress method
and fracture mechanics method has been discussed in great details in
reference (1). For the case of a nominal thickness of the adhesive in
the PVC structure being around 10 mils (0.25 mm), to model it with 3-D
element combined with a large scintillator structure will result in a
FEA model of formidable size.

As an alternative, two widely used approaches are considered in this
study. One is to extract the nodal force by assuming the interface
between the vertical and horizontal plane will move together with a
connected node \_\_ merged node. The second approach is to model the
adhesive layer as three spring elements as suggested by Tahmasebi ^(2)^
and Zhu & Keyward ^(3)^ : Two springs are accounted for the in-plane
shear stiffness of adhesive and one is for the normal stiffness of
adhesive. This can be accomplished by using a spring element (#14) in
ANSYS.

The nodal force, in both methods is extracted and divided by its element
area to calculate the average shear and normal stress around that
location. Finally, by using a Mohr's circle, a maximum shear stress
(principle shear stress) can be obtained as

$$\tau_{\text{max}} = \sqrt{(\frac{\sigma_{\text{normal}}}{2})^{2} + \tau^{2}}$$

and compared with the average stress data taken from a test coupon with
the same geometry and material. It is a similar approach as that
described by in reference 1.

As described in detail in Reference 1, the stresses that develop in an
adhesive joint is dependent upon the geometry of the joint itself.
Standard ASTM tests of double shear peel strength, and cleavage can only
provide information on the comparative strength of different adhesive.
Physical tests that most closely mimic the actual adhesive joint in
service can provide the best correlation with structural analysis and
estimate expected performance. Therefore, in order to correlate the
stresses determined in the structural analysis to the actual strength of
the various adhesives being considered a double shear test was performed
using 3mm thick PVC and an adhesive area of 0.776" square which mimics
the area modeled in the FEA model.

6.  **Detailed description of FEA model of Assembled Planes**

Several finite element models have been developed to understand the PVC
structure. An initial FEA model was a simple 2-D model to calculate the
stress due to 19 psi hydrostatic pressure for the vertical extrusion as
shown in section 4 above. Subsequently, a more complex model has been
developed to understand the structure as whole assembly in terms of the
stress and its stability. The structure has 15 x 15 m cross section with
1674 layers PVC extrusion as described above. The vertical and
horizontal extrusions are alternated by 90 degree. For such geometry,
the best approach is to use the shell element (STIF 63 in ANSYS) to
efficiently model the structure. It has similar characteristic of the
beam element. To reduce the size of the problem and to accommodate the
computer limitations as well as the computational time, only a "slice of
the structure" in the mid of the structure is modeled with a symmetry
boundary condition imposed on the both side to reflect other portion of
the structure. The mesh size of shell element is around 0.5"\~0.7" for
the structure with its full height being \~600". The model is
approximately 260,000 nodes (6 degree of freedom_DOF per node) with
total 1.5 million DOF for a 31 planes block without counting the spring
elements used for the adhesive layers. The boundary condition is
considered to be a free for the top and fixed for the bottom as a worst
case. The hydrostatic load of 19 psi is applied linearly along the
vertical extrusion and zero pressure for the horizontal extrusion. The
density of PVC has been modified to reflect the weight of the liquid.
This baseline model as well as its boundary condition has been modified
many times to study the structure implications under the different
scenarios as described more details in the references.

![](media/image13.png){width="5.623611111111111in"
height="4.090277777777778in"}

![](media/image14.png){width="5.125694444444444in"
height="3.877083333333333in"}

**Fig 7 A FEA model with the shell element**

7.  **Buckling Analysis of Assembled PVC extrusions**

A buckling analysis was done on the 31 plane block for four different
conditions: the block empty and unguided at the top; the block empty and
guided at the top; the block filled and unguided at the top; the block
filled and guided at the top.

**Buckling SF for a 31 planes**

+-------------+-------------+-------------+-------------+-------------+
| Case        | Filled      | Unfilled    | Filled      | Unfilled    |
|             |             |             |             |             |
|             | Top free    | Top free    | Top guided  | Top guided  |
|             |             |             |             |             |
|             | bottom      | Bottom      | Bottom      | Bottom      |
|             | fixed       | fixed       | fixed       | fixed       |
+-------------+-------------+-------------+-------------+-------------+
| SF          | 5           | 20          | 6.17        | 24.6        |
+-------------+-------------+-------------+-------------+-------------+

![](media/image15.png){width="4.873611111111111in"
height="3.6180555555555554in"}

Figure 3a - Top free and bottom fixed \_\_unfilled

![](media/image16.png){width="4.344444444444444in"
height="3.5104166666666665in"}

Figure 3b - Top guided and bottom fixed \_\_ filled

![](media/image17.png){width="5.001388888888889in"
height="3.915277777777778in"}

Figure 3c - Top guided and bottom fixed \_\_ unfilled

![](media/image18.png){width="4.000694444444444in" height="3.15625in"}

**Fig 3d - Buckling SF for 31 block with 4.5mm/3mm for vertical
extrusion only**

8.  **Stress/Deflection Analysis of Assembled PVC Extrusions.**

The stresses and deflections of the planes once they are assembled
together were examined. A series of analysis were done over the last
year which showed that as the number of planes increased the swelling at
the bottom of the detector, due to the internal pressure, increased
which in turn increased the stresses in the PVC. In order to keep the
stresses to within a range that it was felt was acceptable for creep the
number of planes within a block was restricted to 31. The stresses in
the PVC could be further reduced by reducing the number of planes within
a block, however, below 31 planes the buckling stability falls below the
target safety factor of 5.

The figures below show the stresses and deflections within a 31 plane
block

![](media/image19.png){width="5.185416666666667in"
height="3.892361111111111in"}

**Fig 10 Deflection along the beam direction (4.5mm/3mm for vertical
only)**

![](media/image20.png){width="5.252083333333333in"
height="3.4291666666666667in"}

**Fig 11 Stress near the bottom (4.5mm/3mm for vertical only)**

9.  **Adhesive Stresses**

The adhesive stresses were also examined in order to understand the
strength requirement for the adhesive. The initial analysis examined 32
planes filled with scintillator. Figures 12 and 13 below show the
distribution of the adhesive stresses from the bottom to the top of the
detector and Figure 14 shows the location of the shear stresses in the
FEA model. The maximum adhesive shear stresses occur at the bottom of
the detector and are approximately 165psi but then taper off to
approximately 140psi throughout the remainder of the plane.

![](media/image21.wmf){width="6.247916666666667in"
height="4.770833333333333in"}

**Fig 12 Adhesive stress for several conditions**

![](media/image22.wmf){width="5.998611111111111in"
height="4.000694444444444in"}

**Fig 13 Shear stress at different interface for 31 planes block with**

**(4.5 mm/3mm for vertical only)**

![](media/image23.png){width="4.163194444444445in" height="4.375in"}

**Figure 14**

**Location of Shear Stresses shown in Figure 12-13**

An examination of the adhesive stresses has shown that there are three
components contributing to them. The first component is very small and
is due to the weight of the horizontal extrusions being transferred to
the horizontal extrusions. The second component is due to the stress
from the PVC deformation due to swelling. The third component is due to
the differential strain between the vertical and horizontal extrusions
from the weight of the extrusions and scintillator.

Since the maximum adhesive stresses occur at the bottom of the detector
an analysis was performed to simulate failure of the adhesive on the
bottom two horizontal extrusions. In the case where the bottom two
horizontal extrusions have no adhesion to the vertical extrusions the
buckling safety factor drops to approximately 1.5 from 5.1 when there is
a full bond. If only the very bottom horizontal extrusion is not bonded
the buckling safety factor drops to 4.0. The PVC stresses increase
slightly too approximately 900psi and the adhesive stresses throughout
the detector remain virtually unchanged. See DocDB-400 for additional
details.

10. **Recommendations/Conclusions**

The following conclusions and recommendations have been drawn from the
work that has been done so far.

PVC Stress

The final PVC composition must be selected and extensive testing done in
order to determine the creep modulus that can be used in buckling
calculations and to determine an acceptable level of stress for the
design. The PVC stress in the loading conditions examined so far is no
greater than 700 psi which was the target of the design based on an
initial survey of the literature on PVC. However, further testing is
needed to show that this is adequate and if creep will be a long term
problem for the experiment.

Adhesive Stresses and Bonding

The current calculations show average adhesive stresses at the bottom of
the detector in the range of 125-165psi. To achieve a safety factor of
5.0 adhesive bond strength of approximately 750psi is needed. So far
testing has shown found only one adhesive that meets this criterion, 3M
2216. The required strength was achieved using 3M 2216 by roughing up
the surface of the PVC. Also, all of the calculations to date have been
based on 100% adhesive coverage of the PVC surface and further
calculations and testing is needed to understand the maximum stresses
that occur if less than 100% coverage is achieved. Finally, the 3M epoxy
has shown problems with brittleness, test samples that were
inadvertently dropped broke on impact. It is unclear what the
brittleness of the epoxy will mean for the long term strength of the
detector but this must be evaluated. A more promising adhesive has been
found, Devcon Plastic Welder, but this adhesive poses a number of ES&H
risks that need to be addressed in the near future in order to determine
whether it is practical to use.

**Reference:**

1)  Engineered Materials Handbook -- Adhesives and Sealants Volume 3,
    ASM International

2)  F Tahmsebi, PhD, "Finite Element Modeling of an Adhesive in a Bonded
    joint", FEMCI, NASA Goddard Space Flight Center, July,1999

3)  Y Zhu & K Kedward, " Method of Analysis and Failure Predictions for
    Adhesively Bonded Joints of Uniform and Variable Bond line
    thickness", DOT/FAA/AR-05/12, Final Report, May, 2005