the experimental assessment of thermal strains in porous ......modelling of porous shells the...

Modelling of Porous shells The experimental assessment of

thermal strains in porous shells

João André da Silva Petiz

Thermo-elastic characterization of triax-honeycomb core samples

Supervisors at FEUP: Prof. Mário Vaz,

Supervisor at INEGI: Eng. Pedro Portela, Dr. Jaime Monteiro

Faculdade de Engenharia da Universidade do Porto

Master in Mechanical Engineering

September 2008

Modelling of porous shells

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Abstract

The industrial design of lightweight components has been a constant challenge for designers working with optimization methods in structures in the last decades. To achieve an optimal design it is necessary to fully characterize the external forces acting in the component. Such forces involve static or dynamic disturbances eventually combined with thermal actions. FEM software is a design tool in predicting the structure and material response to stressing. In order to save up computation time, specific application finite elements have been developed for the FE programmers.

In this project it is carried out an experimental analysis of the thermo-elastic behavior of 3 samples having different composition, to validate the finite elements developed and used.


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Acknowledgements

The author would like to thank the Laboratory of Optics and Experimental Mechanics (LOME) at the Faculty of Engineering of Oporto University (FEUP), an institution that provided the equipment and know-how on the experimental techniques. Also special thanks to Dr. Bern Jakobsen for having kindly offered an INVAR plate test specimen for the research.


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List of abbreviations

CFRP Carbon fiber reinforced polymer CFRS Carbon fiber reinforced silicon CTE Coeficient of thermal expansion ESA European space agency ESPI Electronic speckle patterns interferometry FE Finite element FEM Finite element method FEUP Faculty of engineering of Oporto university HPS High Performance Space Structure Systems, GmbH INEGI Institute of mechanical engineering and industrial managment IR Infrared radiation LLB Institute of lightweight Structures

Aerospace Department Technical University of Munich

LOME Laboratory of optics and experimental mechanics TAHARA Technical Assessment of High

Accuracy Large Space Borne Reflector Antenna TUM Technical University of Munich UV Ultra violet


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Index

1 Introduction ........................................................................................................................................ 13

1.1 Partners .............................................................................................................................................. 13

1.2 Main goals .......................................................................................................................................... 14

1.3 Difficulties ........................................................................................................................................... 15

2 State of the art ................................................................................................................................... 17

3 Experimental techniques ................................................................................................................... 29

3.1 Electronic Speckle Pattern Interferometry (ESPI) .............................................................................. 29

3.2 Termography ...................................................................................................................................... 32

4 Thermo-Elastic Test .......................................................................................................................... 37

4.1 Requirements ..................................................................................................................................... 37

4.2 Preliminary tests ................................................................................................................................. 38

4.3 Sample description ............................................................................................................................. 40

4.4 Test setup .......................................................................................................................................... 43

4.5 Equipment .......................................................................................................................................... 49

5 Results .............................................................................................................................................. 51

5.1 Heating characterization..................................................................................................................... 51

5.2 Thermo-elastic results ........................................................................................................................ 59

6 Conclusions ....................................................................................................................................... 67

6.1 Future works ...................................................................................................................................... 69

7 References ........................................................................................................................................ 71

8 Appendicles ....................................................................................................................................... 73


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Figure index

FIGURE 1 SMART DESIGN STRUCTURE (A) AND MANUFACTURED MODEL ............................................................. 18

FIGURE 2 ASTRIUM DESIGN CONCEPT (A) TRANSPORTATION POSITION (B) OPERATING POSITION .................... 19

FIGURE 3 ASTRIUM MANUFACTURED MODEL (A) CLOSED (B) OPERATING SITUATION ......................................... 19

FIGURE 4 SSBR ANTENNAS ASSEMBLED TO THE SUPPORT ARM ............................................................................ 20

FIGURE 5 SSBR DESIGN MODEL (A) GEOMETRY (B) STIFFENER PRINCIPLE ........................................................... 20

FIGURE 6 FTR REFLECTOR, REVOLUTE JOINTS ....................................................................................................... 21

FIGURE 7 FRT REFLECTOR, STIFFENERS LOCATIONS ............................................................................................. 21

FIGURE 8 TESTED SPECIMENS PRODUCED BY LLB ................................................................................................. 24

FIGURE 9 (A) SPECIMEN ASSEMBLAGE AT THE DILATOMETER (B) TESTED SAMPLES AND CALIBRATION RODS ....... 24

FIGURE 10 THERMAL DEFORMATION GRAPHS AND CTE FOR STANDARD SPECIMENS [1] ...................................... 25

FIGURE 11 THERMAL STRAIN VS TEMPERATURE FOR 0-DIRECTION AND 90-DIRECTION ........................................ 26

FIGURE 12 THERMAL DISTORTION TESTS – SETUP, SAMPLE GEOMETRY AND MEASURING GRID ........................... 27

FIGURE 13 CONSTRUCTIVE AND DESTRUCTIVE WAVE INTERFERENCE ...................................................................................... 29

FIGURE 14 TYPICAL FUNCTIONING OF AN ESPI SYSTEM ......................................................................................... 30

FIGURE 15 DYNAMIC DISPLACEMENT MEASURING WITH ESPI ................................................................................ 31

FIGURE 16 INFLUENCE OF THE WAVELENGTH AND TEMPERATURE IN THE SPECIFIC SPECTRAL EMISSIVITY [5] ..... 33

FIGURE 17 COMPARISON OF THE EMISSIVITY AS A FUNCTION OF THE WAVELENGTH BETWEEN (A) NON-METALLIC

AND (B) METALLIC MATERIALS ...................................................................................................................... 34

FIGURE 19 APLICATION OF TERMOGRAPHIC METHODS IN DIFFERENT SITUATIONS ................................................. 35

FIGURE 18 VARIATION OF THE SPECTRAL TRANSMISSIVITY OF THE AIR WITH THE RADIATION WAVELENGTH ........ 35

FIGURE 20 CHOSEN BOUNDARY CONDITIONS TO BE TESTED .................................................................................. 37

FIGURE 21 ESPI CAPTURED PICTURES (A)(B) AND POSTPROCESSOR (C)(D) – FRONT THERMAL LOAD ................ 38

FIGURE 22 TESTED SAMPLES, PROJECT DESIGNATION AND CORRESPONDING USED NAME .................................. 40

FIGURE 23 LAY-UP AND ENGINEERING PROPERTIES OF THE SAMPLE1 (ESACOMP® 3.1) ..................................... 40

FIGURE 24 PLY GEOMETRY AND MANUFACTURING STRUCTURE ............................................................................. 42

FIGURE 25 HONEYCOMB STRUCTURE (LEFT) AND GLOBAL DIMENSIONS (RIGHT) ................................................... 42

FIGURE 26 DESIGN FRAME FOR “4 EDGE FIX” CONDITIONS ..................................................................................... 43

FIGURE 27 ELEMENT SOLID45................................................................................................................................ 44

FIGURE 28 MESHING OF USED SUPPORT MODEL ..................................................................................................... 45

FIGURE 29 DISPLACEMENTS ALONG X (RIGHT) AND Y (LEFT) DIRECTIONS .............................................................. 45

FIGURE 30 X, Y AND Z SUPERIMPOSED DISPLACEMENTS ........................................................................................ 45

FIGURE 31 SETUP CHARACTERISTICS ON THE OUT-OF PLANE MEASUREMENTS ..................................................... 46

FIGURE 32 CLAMPED SAMPLE (A) AND NUMBERING OF SAMPLING POINTS (B) ........................................................................ 47

FIGURE 33 SETUP CHARACTERISTICS ON THE LATERAL MEASUREMENTS .............................................................. 47

FIGURE 34 CLAMPED SAMPLE (A) AND MEASURING POINTS NUMBERING (B) .......................................................... 48

FIGURE 35 GENERAL VIEW OF THE LATERAL MEASUREMENTS ................................................................................ 48

FIGURE 36 CHOSEN POINTS FOR CHARACTERIZING THE TEMPERATURE DISTRIBUTION ON THE PLATE ................. 51

FIGURE 37 HEAT/COOL AT THE POSH_SAMPLE1 ................................................................................................... 52

FIGURE 38 – PICTURES TAKEN WITH THE THERMOGRAPHIC CAMERA DURING THE HEATING STAGE (POSH_SAMPLE1) .................... 53

FIGURE 39 HEATING PATTERN AT THE POSH_SAMPLE2 ........................................................................................ 54

FIGURE 40 - PICTURES TAKEN WITH THE THERMOGRAPHIC CAMERA DURING THE HEATING STAGE (POSH_SAMPLE2)..................... 55

FIGURE 41 HEATING PATTERN AT THE POSH_SAMPLE3 ........................................................................................ 56


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FIGURE 42 - PICTURES TAKEN WITH THE THERMOGRAPHIC CAMERA DURING THE HEATING STAGE (POSH_SAMPLE3)..................... 57

FIGURE 43 FOLLOWED MEASUREMENTS .................................................................................................................. 59

FIGURE 44 HYSTERETIC EFFECT .............................................................................................................................. 60

FIGURE 45 LINEAR AND QUADRATIC TENDENCY LINE ............................................................................................... 60

FIGURE 46 MEASUREMENTS ON POINT 6 AND 7 ...................................................................................................... 61

FIGURE 47 DISPLACEMENT RECOVERY TO NEGATIVE VALUES ................................................................................ 62

FIGURE 48 HYSTERETIC EFFECT WITH FINAL GAP ................................................................................................... 63

FIGURE 49 HYSTERETIC EFFECT WITHOUT FINAL GAP ............................................................................................. 63

FIGURE 50 X-DIRECTION DIMENSIONLESS DISPLACEMENT (ON POINT6) ................................................................. 64

FIGURE 51 Z-DIRECTION CTE MEASURED IN DIFFERENT POINTS ............................................................................ 64

FIGURE 52 Z-DIRECTION CTE MEASURED IN DIFFERENT POINTS (ZOOM) ............................................................... 65


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1 Introduction The project “Modelling of porous shells” is an ESA project having as main objective the

development of new structures, materials and auxiliary modelling tools in the design of

lightweight satellite antennas. This project is being developed by 6 companies or institutes

in 3 different countries: Portugal, Sweden and Germany.

The developed work is linked to this ESA TRP project under development at INEGI, under

subcontract to HPS-GmbH.

The integration as a FEUP master research project was proposed by engineer Pedro

Portela representing INEGI. This report doesn’t make a theoretical and analytical analysis.

It describes especially the setup development and presents the obtained experimental

results. On the chapter 2 a quick presentation of the work developed before September

2007 is presented to contextualize the reader. From the chapter 3 inwards the report is

organized chronologically:

• Study of the experimental techniques;

• Preliminary tests to fully understand the sample behaviour;

• Setup design attending to the equipment limitations and availability;

• Experimental test programme, analysis of results and discussion.

1.1 Partners


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1.2 Main goals

According to the text of the technical proposal NO. A027-06,

“The objective of this study is to further develop ultra-light shell configurations using

porous material with a parallel improvement of respective modelling tools.”

This goal achievement it’s a consequence of the previously named partner’s cooperation

defined during the consortium constitution. Part of the INEGI contribution for this project is

based on the experience with optical measurements techniques. The work here presented

is part of the test programme defined in the project for the materials characterization.

Essential procedures:

• Prepare the ESPI setup for measurement of CFRP sandwich samples;

• Perform preliminary thermo-elastic distortion measurements on CFRP sandwich

samples;

• Design of a test rig allowing the heating of the test samples by IR radiation;

• Perform thermo-elastic measurements of the triax-honeycomb core samples in

different boundary conditions;

• Determine, by analysis of results, the equivalent CTE in the three main directions.


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1.3 Difficulties

During this project several difficulties were noticed, either technical or organizational.

A delayed choice of the supervisor and the lack of work meetings resulted, sometimes, on unfocused work. Also the unspecific requirements leaded to measurements that weren’t relevant to the needs of the project. The scarce information about the simulations previously done left us without a specific starting point.

The major difficulties during the measurements are due to the lack of equipment. On the project brief was asked to determine the CTE of the sample with noncontact methods (specifically ESPI and thermography) and applying radiation as the only heating mechanism. During the preliminary tests we realized that those methods are very difficult to apply on continuous measurements especially if the experiment evolution is fast. We tried to make discrete measurements with a step of 5 ºC but the time needed to take and process each picture is not compatible with the experiment speed.

To apply only radiation on the sample we must isolate the heat transfer mode and minimize the conduction between the support and the sample and principally the convection. To minimize the convection, we should have a vacuum chamber were we could set all the equipment. At CEMUP (Centre of Materials of the University of Porto) we found an intermediate solution (a vacuum chamber were we could mount the sample with a glass window to measure through) but it was too small for these samples and the glass could affect the measurement accuracy.

Finally, the high sensitivity of the sample to thermal loads turns these deviations influence also very high. With this equipment, the achievement of accured results was impossible.


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2 State of the art

As it was discussed in the introduction, the project “Modelling of porous shells” is

being developed by several entities for the last two years. It’s a very recent project, were

the first iteration of modelling and testing is still being done. As in every new development

areas, the main difficulty is the lack of background on modelling and testing this type of

materials and structures. The structures studied on this report can play both functions:

reflective membrane and structural support. Other solutions were previously appointed.

According to the TAHARA report developed by the Lehrstuhl für Leichtbau (LLB) at the

Technische Universität München (TUM) - Institute of lightweight Structures, Aerospace

Department,– four large deployable reflectors (LDR) were designed and analyzed. For

each design solution the operation principle and the summarized results of the thermo-

elastic tests will now be presented. At the end of the present report some thermo-elastic

tests performed on some membrane materials will be described. The composite normally

used in these structures are triax CFRS and CFRP woven materials which structure is

similar to the ply structure of the samples tested in this work.

SMART prototype

The SMART prototype consists of six rafters attached to a central hub. Between the radial

ribs a system of auxiliary ribs is supporting the reflecting surface. The main radial rib

consists of two components. The stiffener is a radially deployable telescopic rod. The

profiled membrane is attached to the central unit and to the end of the pantograph and is

stretched as the pantograph deploys.


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(a) (b)

figure 1 SMART design structure (a) and manufactured model

The final stiffness and geometric accuracy is defined by the pantograph and the

membrane. The value of the CTE (coefficient of thermal expansion) of the used material

defines the overall dimensional stability of the reflector. However, the membrane material

must fulfil the following requirements:

• compatibility of the material to the space environment;

• low outgassing;

• UV resistant ;

• withstand wide range of temperature (between –150°C and +200°C);

• transparency to a large band of electromagnetic radiation.

According to these requirements the selected materials were carbon as reinforcement and

silicone elastomer S 690 from Wacker as a matrix material.

ASTRIUM prototype

The ASTRIUM solution consists on a CFRP thin shell central dish which is glued over its

outer rim to the Central Support Structure and a hollow CFRP ring providing the end stops

for the deploying panels as well as the interfaces for the panel deployment axes. It has 30

individual deploying panels that are independent from each other. There is a small gap in

between the adjacent panels.


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figure 2 ASTRIUM design concept (a) transportation position (b) operating position

figure 3 ASTRIUM manufactured model (a) closed (b) operating situation

The assumed low thermo-elastic deformation properties becomes, from a low overall CTE,

around 0.5e-6/ºC, having a good matching between shell and rib with the same CTEs, the

assumption that no thickness gradient is considered (very thin lamina) and that the thermal

conductivity between shell and rib is sufficient high.


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figure 4 SSBR antennas assembled to the support arm

SSBR - Stiffened Spring-Back Reflector

The SSBR solution has a collapsible stiffener along the rim of the reflector surface. Two

pairs of circumferential slits are introduced in the connection between the dish and the

stiffener. While the stiffener, during folding, significantly increases the overall stiffness of

the dish in the deployed configuration, the slits in the stiffener allow the stiffener to buckle

elastically resulting in a reflector that can still be folded elastically. The subtended angles

by the slits are the crucial design parameter; if the slits are shorter the deployed SSBR is

stiffer but the peak stress during folding is higher; if the slits are longer the peak stress is

smaller but the deployed SSBR is less stiff.

(a) (b)

figure 5 SSBR design model (a) geometry (b) stiffener principle


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Foldable Tips Reflector (FTR)

Foldable tips reflector consists of three separate sandwich panels reinforced by stiff

sandwich ribs on the back convex surface. The two side panels are attached to the central

one by means of revolute joints, which allowed them to fold towards the rear of the central

panel. The skins of the sandwich panels consist of four layers of CFRP with (0/90/90/0)

and a total thickness of 0.4 mm. The core is made of aluminium honeycomb with 6 mm

thick.

figure 6 FTR reflector, revolute joints

figure 7 FRT reflector, stiffeners locations

The four solutions here presented are normally used in the structure of antennas for

satellites and spacecrafts. The following tables make a comparison of the thermo-elastic

behaviour between the presented structures. The considered temperature gradient was

100K in the x-direction. The influence of the thermal load on geometry was studied by

analysing the following parameters:

F: focal length of the best fit surface


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α : 1st rotation about the x-axis transforming (x,y,z) into (x’,y’,z’)

β : 2nd rotation about the y’-axis transforming (x’,y’,z’) into (x”,y”,z”)

k o : translation of the vertex along z” direction.

SMART

ASTRIUM

SSBR

Foldable Tips Reflector

As can be seen, the SMART and the SSBR antennas experienced the smallest focal

length distortion. The SMART and the ASTRIUM antennas have a greater out-of-plane

deformation. These behaviours depend on the structure solution and on the thermal

characteristics of materials used in its construction.


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A thermo-mechanical characterization of two new reflecting materials (triax CFRS and triax

CFRP) performed by LLB will now be presented. For this work more attention on the

testing procedure will be considered. In the first case, LLB used two types of reinforcement

(triax and 0/90º fabrics of carbon T300 fibres) with a S 690 from Wacker silicon matrix.

Note that these are the chosen materials for the membrane of the SMART antenna.

To fully characterize TWF CFRS material the following samples were manufactured:

• 9 layers laminate with the similar fibre orientations in each ply. Specimens cut from

this laminate were used for tensile and CTE tests - figure 8(a);

• single layer laminates with different thickness and produced with different

manufacturing techniques - figure 8(a);

• single layer laminates for CTE measurement using the rolled tube shape for the

specimens - figure 8(b);

• Single layer Triax CFRS RF specimens of size 0.5x0.5m two different specimens

were manufactured - figure 8(c);

• RF specimens for WG measurements, 20x40mm and 12.5x25mm - figure 8(d);

(a)

(b)

(c)

(d)


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figure 8 Tested specimens produced by LLB

The test was made using a dilatometer WSK TMA 500 with a temperature range from -200

to +500 ºC. Different materials with metallic or zerodur zero expansion were also tested to

perform the proper alignment of the dilatometer sensor rod.

(a)

(b)

figure 9 (a) specimen assemblage at the dilatometer (b) tested samples and calibration rods


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From these tests the following graphic were obtained:

figure 10 Thermal deformation graphs and CTE for standard specimens [1]

The graphical analysis allows some obvious conclusions:

• CTE of the CFRS is nonlinear in the temperatures ranging from -150 to 200ºC;

• Three characteristics behaviours are identified:

o Bellow -110ºC (~Tg of silicone)

The first range measurements showed stable results (in order of 10*10-

6/K). Since all specimens are relatively stiff in that temperature range

silicone influence on the resulting CTE is significant. Specimens with

higher silicone volume showed also higher CTE;

o From -110 to 100

This range is characterized with almost no influence of silicone, resulting

CTE is always negative and close to fibres CTE (in the order of -0.7*10-

6/K);


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o From 100 to 200.

At approximately 100ºC the deformation temperature curve slightly

change its direction, therefore the next range is defined above 100 up to

200ºC. CTE in this range is law with some negative and some positive

values. Average CTE is about 0.24*10-6/K.

The same test was performed with Kevlar rolls between -150 and 140 ºC. The graphics

that can be seen in figure 11shows that in this case a linear behaviour is observed.

figure 11 Thermal strain vs temperature for 0-direction and 90-direction[1]

Finally, a thermal distortion test was made with a planar lamina that was manufactured for

this proposes. Thermal distortions of one-ply triaxial woven material were measured using

the photogrammetry software Photomodeler Pro 5.2.2. A thermocouple was placed in the

chamber near the specimen and an invar bar was used as a reference. The figure 12

shows the specimen dimensions and location of the target points used to evaluate its

geometry change.


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figure 12 Thermal distortion tests – setup, sample geometry and measuring grid

In these tests an anisotropic behaviour was observed. The thermal displacement in the 0º

directions is almost twice the thermal displacement in the 90º direction.

It is concluded that relatively significant thermal distortions occur in these specimens,

which are more severe in the narrower specimens, due to their uneven distribution of resin

through the thickness. With these previous measurements can be concluded that the

global behaviour of the final structures is influenced by the thermo-mechanic

characteristics of the each of the materials used in the fabrication of its components.


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3 Experimental techniques

Once the objective of this work is not to study the measuring techniques but to

characterize the given samples, in this chapter only a brief presentation of each

technique is presented. The working characteristics will be listed as well as the specific

equipment used.

3.1 Principles of Electronic Speckle Pattern Interferom etry (ESPI)

Interferometry is a technique based on the interference of two or more wave fronts to

detect differences between them. For that coherent wave fronts are superimposed

generating a energy redistribution due to

interferometric phenomena. Points where two

waves with the same frequency that have the

same phase will add to each other

(constructive), on the other hand two waves with

opposite phase will subtract (destructive). To

generate coherent wave fronts the original wave

front coming from a coherent source (LASER) is

split into two (or more) coherent parts, which

travel different paths. The parts are then

combined to create the interference. When the paths differ by an even number of half-

wavelengths, the superposed waves are in phase and interfere constructively,

increasing the amplitude of the output wave. When they differ by an odd number of

half-wavelengths, the combined waves are 180° out o f phase and interfere

destructively, decreasing the amplitude of the output (figure 13). Thus anything that

changes the phase of one of the waves by only 180° shifts the interference from a

maximum to a minimum. This makes interferometers sensitive measuring instruments

for anything that changes the phase of a wave front, such as path length or refractive

index.

figure 13 constructive and destructive wave interference


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figure 14 Typical functioning of an ESPI system

On the figure 14 is shown a schematic presentation of typical ESPI system. The laser

energy is divided on a beam splitter, part is directly used as the reference, and the

remaining is projected on the measuring surface. The interference occurs on the target

of a video camera being the obtained signal processed by specific software. In some

compact set-ups the laser light can be drove to the image system or the measuring

surface by an optical fibre.

The available system at the LOME (Laboratory of Optics and Experimental Mechanics)

has most of the reference beam bath inside an optical fibre.

The interferometric techniques have several advantages when compared with classical

measurement methods. They are a non destructive method, is contactless which

reduces significantly the influence on the measured samples, it has a high sensitivity

(half the laser wavelength), it doesn’t requires an expensive surface preparation and

allows field measurements, an area instead of a point.

The ESPI system can be used for measuring static or dynamic displacements.

Because of its high sensitivity it is necessary to use minimize any external perturbation

during the tests. This can be performed by using vibration isolated tables and very

stable environmental conditions. For example, a person breading near the equipment

can cause significant deviations on the results.


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(a) (b)

figure 15 Dynamic displacement measuring with ESPI

(a) General view of the test object

(b) Modal shape of an eigenmode of a guitar soundboard

visualized in real time

Using ESPI the results of each measuring are obtained as digital images on a

computer memory. These images are normally processed to extract the phase

distribution of the interferometry patterns which corresponds to the

displacement field or to the distribution of the vibration amplitude. The data

obtained allows the measurements of displacements or amplitudes with a

resolution that can goes well down to 0,01 mm.


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3.2 Termography

Any body of a temperature above absolute zero (-273.15 °C) emits electromagnetic

radiation. This principle is the ground of the thermography. Infrared thermography is a

technique that uses an imaging system to measure the electromagnetic energy emitted

from a surface in the IR radiation band. This kind of energy is also known as thermal

radiation. By determining object radiation intensity its temperature can thereby be

determined in a non-contact way.

The bodies occurring in real life show very diverse radiation properties. Therefore, it

has proved worthwhile to initially consider the simplified laws of a model body of ideal

radiation properties to be then applied to actually occurring objects. This model body is

known in radiation physics as the “black body”. A black body is a body capable of

absorb all the received radiation.

The spectral spread of radiation emitted by a black body is described by Planck’s

radiation law [5]:

Were,

λ – Wavelength;

Mλ – Emitted radiation by a body on the wavelength λ;

C1 – Radiation constant;

C2 – Radiation constant;

T – Temperature of the black body (ºK);

The figure 16 is a representation of the Planck’s law. This representation shows that

the spectral composition varies with the object temperature. For instance, bodies of a

temperature of beyond 500 °C, also emit radiation i n the visible range. Furthermore, it


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must be noted that, at each wavelength, radiation intensity increases with temperature

rising.

figure 16 Influence of the wavelength and temperature in the specific spectral emissivity [5]

Planck’s radiation law represents the principal correlation regarding non-contact

temperature measuring. However, it is not directly applicable in this form to many

practical calculations. Different correlations can be derived from it. One of those is

called the Stefan Boltzmann’s law, which states that the total energy radiated per unit

surface area of a black body in unit time (known variously as the black-body irradiance)

is directly proportional to the fourth power of the black body's absolute temperature [5]:

Where,

M – Emitted radiation by a black body;

σ – Steffan-Boltzmann constant;

T – Temperature of the black body (ºK);

K – Absolute temperature of the black body

Real surfaces then are not perfect blackbodies, but emit only a percentage of the

radiation of a blackbody. The fraction that they emit is the measure of their emissivity.

The emissivity value ranges from 0 (when the body reflects all the radiation) up to 1 for

black bodies.

The emissivity of real objects to be measured may show more or less strong

dependence on wavelength. The following parameters may also be of some influence:


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• Material composition;

• Oxide film on the surface;

• Surface roughness;

• Angle of the incidence vector radiation to the surface normal;

• Temperature;

• Polarisation degree.

Several non-metallic materials show high and relatively constant emissivity, regardless

of its surface structure figure 17 (a). In contrast, metals generally have low emissivity

that greatly depends on the surface properties and dropping when wavelength

increases figure 17(b).

(a) (b)

figure 17 Comparison of the emissivity as a function of the wavelength between (a) non-metallic and (b) metallic materials[5]

As a reference value, the carbon fibre (reinforcement used on the studied samples) has

a emissivity of 0,53 however no values for CFRP were found.

From Planck equation one can also see that the wavelength associated with the

maximum spectral emissivity of a blackbody decreases as the temperature increases.

This wavelength is given by differentiating Planck equation with respect to the

wavelength and setting the result to zero. The result is known as Wien’s displacement

law [5]:


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For the temperature range to be measured [20,170] ºC, the maximum wavelengths fall

within the range 7–11 µm which is in the range of long wave infrared.

Once infrared thermography is a non-contact procedure, the radiation needs to travel

over a certain distance between the object to be measured and the measuring device

which may affect the measured result. In this case, the medium is likely to be air

The level of transmissivity of

air is strongly dependent on

wavelength. Ranges of high

attenuation alternate with

ranges of high transmittance,

called "atmospheric

windows". While

transmittance in the range [8,

14[ µm, i.e., the long-wave

atmospheric window, maintains

to be equally high over longer distances, measurable attenuation caused by the

atmosphere already occurs in the range [3,5[ µm, i.e., the short-wave atmospheric

window, at measuring distances of ten meters (figure 18).

To conclude, using a termographic camera one should pay attention to: material being

examined and its surface characteristics; environmental medium; temperature

measuring range; distance to the measuring object; angle to the surface normal.

(a) (b) (c)

figure 19 Aplication of termographic methods in different situations

figure 18 Variation of the spectral transmissivity of the air with the radiation wavelength


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This technique has a large application field supporting areas such quality control of

electronic components (figure 19 (c)), motors, cooling towers; construction, windows

(figure 19 (b)), doors, pipes; preventive maintenance in industrial equipment ; medical

applications as breast cancer (figure 19 (a)) or blood circulation.

The main advantages of thermography are:

• A visual picture is obtained so temperatures can be compared over a large

area;

• It is real time capable of capturing moving targets evolution;

• Able to find deteriorating components prior to failure;

• Measurement in areas inaccessible or hazardous for other methods;

• It is a non-destructive test method.

The limitations and disadvantages of thermography are:

• Quality cameras are expensive and are easily damaged;

• Images can be difficult to interpret accurately even with experience;

• Accurate temperature measurements are very hard to make because of the

emissivity’s variation;

• Most cameras have ±2% or worse accuracy, less accurate than contact

methods;

• Ability to only measure surface areas.


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4 Thermo-Elastic Test

4.1 Requirements

The following requirements were set by HPS and were respected when it was possible:

• The test should be made with different boundary conditions;

The free-free condition is not applicable to ESPI techniques because of rigid body movements. Therefore, the chosen boundary conditions were cantilever (1), fixed back ply by two sides (2) and fixed both plies by four sides (3). This last hypothesis requires the production of a proper frame.

figure 20 Chosen boundary conditions to be tested

• Temperature range between 20ºC and 170º C, never less than 120ºC;

The heathen should be made by radiation and the temperature should be measured with non-contact equipment like a thermographic camera.

• The tests should be performed in high-vacuum, i.e., P=10-5 Pa mbar.

This requirement wasn’t respected due to the inexistence of a vacuum camera with the necessary characteristics.

(1) - CASE1 (2) – CASE2 (3) – CASE3

Side radiation


38

4.2 Preliminary tests

Preliminary ESPI tests were performed to analyze if the samples have a typical or

atypical behaviour. A high precision was not necessary in this case so. The three

samples have a similar behaviour. The figure 21 presents the observed image of the

POSH_sample1 in the “CASE2” boundary conditions.

(a) (b)

X 1.27

20.81 40.35

59.89 79.42 98.96

Y

95.99 77.53

59.08 40.63

22.17 3.72

Z

-1.67 -1.04 -0.41 0.22 0.85 1.49

Deformation [µm]

X 1.27

20.81 40.35

59.89 79.42

98.96 Y

95.99

77.53

59.08

40.63

22.17

3.72

Z

-0.29 0.05 0.38 0.71 1.04 1.37

Deformation [µm]

(c) (d)

figure 21 ESPI captured pictures (a)(b) and postprocessor (c) (d) – front thermal load

This results show that this samples don’t have a typical global deformation. Each cell

behaves almost has a single hexagonal clamped plate. Part of the cells out-of-plane

displacement occurs in the positive direction and part on the negative direction. This

might be an effect caused by the residual manufacturing stresses. The non uniform cell

deformation is caused by manufacturing defects such as matrix resin or adhesive local

concentration. During the cooling could be seen with the thermographic camera that


39

some parts took more time to cool down. On these parts it’s easily seen a higher resin

volume fraction.

During the tests, a problem was detected. For temperature loads higher than 5ºC, the

ESPI system is not applicable because the displacements exceed the measuring range

of this system.

To solve this problem we tried to make a 5ºC step by step test. The problem of doing

this is that there is a gap between the first step data acquisition and the reset for the

next step. It’s impossible to guarantee that the end of the first step corresponds to the

beginning of the second which invalidates the cumulative results of this approach.

From now on, the test will be performed using a vibrometer. The vibrometer is a laser

with an internal ESPI system. It permits to measure higher displacements but only

permits a point-by-point measuring.


40

4.3 Sample description

All the experimental work was based in three different triax-honeycomb samples (one

specimen for each structure) provided by HPS-GmbH. Each specimen has a specific

project code. To simplify this report they will be known as sample 1, 2 and 3.

STAN-MAT SW1_CTE_3D_6 SW1_CTE_3D_a

POSH_sample1 POSH_sample2 POSH_sample3

figure 22 Tested samples, project designation and corresponding used name

The sample1 is constituted by two plies with four carbon fibre twill layers connected to

a carbon fibre honeycomb by an adhesive (0/45/45/0/adh./honeyc./adh./0/45/45/0).

Due to aluminium deposition it has a high light reflection. The engineering constants of

each layer are known (appendicle A). The figure 23 presents the lay-up and the global

properties of the sample1 calculated with the software ESAcomp® 3.1.

figure 23 Lay-up and engineering properties of the sample1 (ESAcomp® 3.1)


41

For the POSh_sample1, as we have the mechanical properties of each part it’s

possible to make a sensibility analysis. This analysis permits to understand the impact

of the deviation of layer properties in the global sandwich properties. For instance, if

the Young modulus of the ply in the fibre direction has a 1% error (due to the

manufacturing process or fibre properties deviation) the sandwich thermal expansion

coefficient in the same direction might suffer a variation of 1,15 %.

Table 1 – Sensibility of the sample global characteristics to the variation of each layer

characteristics

Table 2 – Sensibility of the sample global characteristics to the variation of plies angle

E_x 0,83 %/degree E^f_x 0,84 %/degree alpha_x 0,00 %/degree

E_y 0,83 %/degree E^f_y 0,84 %/degree alpha_y 0,00 %/degree

G_xy 1,22 %/degree G^f_xy 1,23 %/degree

nu_xy 1,58 %/degree nu^f_xy 1,59 %/degree

nu_yx 1,58 %/degree nu^f_yx 1,59 %/degree

The analysis of these tables shows us that the great influence that the ply properties

have in the global properties. Therefore, it is important to assure a small error in the

fibre and ply production and a good accuracy in the ply assembly angle. The sandwich

properties that are more sensible to the specified production and manufacturing errors

are the thermal expansion coefficient and the Poisson’s ratio.

Adhesive core ply alpha_1 alpha_2 E_1 E_2 alpha_1 alpha_2 E_1 E_2 alpha_1 alpha_2 E_1 E_2 E_x - - 0.04 0.04 - - 0.01 0.01 - - 0,81 0,80 %/% E_y - - 0.04 0.04 - - 0.01 0.01 - - 0,81 0,80 %/% G_xy - - 0.04 0.04 - - 0,00 0,00 - - 0,81 0,80 %/% nu_xy - - 0,00 0,00 - - 0.01 0.01 - - 0,81 0,80 %/% nu_yx - - 0,00 0,00 - - 0.01 0.01 - - 0,81 0,80 %/% alpha_x 1,11 1,11 1,12 1,12 0.01 0.02 0.02 0.04 2,07 2,08 1,15 1,15 %/% alpha_y 1,11 1,11 1,12 1,12 0.01 0.02 0.02 0.04 2,07 2,08 1,15 1,15 %/%


42

The POSH_sample2 and POSH_sample3 have no visible difference. Both are

constituted by a carbon fibre honeycomb, adhesive and two plies. Instead of laminas,

the plies are the triaxially woven described on figure 24. The global, layer or fibre

properties are not known.

figure 24 Ply geometry and manufacturing structure

The honeycomb is obtained by “gluing” several conformed parts has shown on figure

25. For the tests is defined a local axis system where x-axis is defined by the direction

of the honeycomb discontinuity and the y-axis is defined by the honeycomb continuity.

The honeycomb cell is a hexagon with 8 mm (smaller side length).

The samples have the dimension 80x80x10 mm. The neighbouring sides are not

perfectly perpendicular due to manufacturing and cutting deviation.

figure 25 Honeycomb structure (left) and global dimensions (right)

8


43

4.4 Test setup

According to the problem requirements the test should be performed with three

boundary conditions. The correct implementation of the boundary conditions is always

a problematic issue. The easiest boundary condition to simulate is the “full free edges”

condition. For this measurements techniques that’s not possible. In truth, it’s impossible

to create a perfect fixation. The material which the support is made undergoes from

elastic and thermo-elastic phenomena transferring undesirable loads into the samples.

In practice we try to minimize this effect. The support should have a smaller CTE than

the testing samples and must be stiff enough to support the sample expansion. The

TAHARA report concludes that the single layer triax CFRS (similar to POSH_sample2

and 3 plies) has a CTE around 10e-6 (1/ºC). In a sandwich structure we can expect this

value to be minor. The ESAcomp simulation of the POSH_sample1 indicates a CTE

around 3x10e-7 (1/ºC). Any regular steel has a CTE around 10e-5. The solution is to

use a special low thermal expansion alloy commercially known as Invar. The Invar is a

Nickel-Molybdenum alloy used for composites forming tools. The considered properties

of the material are presented in the product data sheet (appendicle B). At 20ºC its CTE

is virtually zero. At 100ºC it’s between 0,6 and 1,4x10e-6 (1/ºC). Based on this material

a frame was design. The frame must have a very low global CTE and must be flexible

enough to accept small dimensional differences between the samples.

figure 26 Design frame for “4 edge fix” conditions

101,5 mm

13 8,5


44

The frame consists of four Invar pieces joined by normal design screws(figure 26). A

measurement window is defined by a 76 mm side square. Two adjustable slides permit

the necessary flexibility. The adjustment is made by the C3 steel screws which

expansion compensates the main piece expansion. The relation between materials and

dimensions result on a frame which linear thermal expansion coefficient is around 1e-

8/K:

Example:

∆W = 101,5 mm x 1e-6(1/ºC). -8,5mm x 10e-5(1/ºC).- 13 x 1e-6(1/ºC).= 3,5e-6 mm/ºC

∂W = ∆W / WL = 3,5e-6 (mm/ºC)/ 76 (mm) = 4,6e-8 (1/ºC)

Where,

∆W – measurement window side length

∂W – deviation of the window side length per ºC

To confirm this simple calculation a simulation of the using the software ANSYS was

done.

The used element was SOLID45 of the ANSYS library described on figure 27.

figure 27 element SOLID45

SOLID45 is used for the 3-D modelling of solid structures. The element is defined by

eight nodes having three degrees of freedom at each node: translations in the nodal x,

y, and z directions. The element has plasticity, creep, swelling, stress stiffening, large

deflection, and large strain capabilities.


45

The supporting rig was simply fixed over the bottom, left side and rear face. The

reference temperature used was 25ºC and we applied 100ºC on the front surface. The

mesh it composed by tetrahedical elements of 3,8 mm side length.

figure 28 Meshing of used support model

figure 29 Displacements along x (right) and y (left) directions

figure 30 x, y and z superimposed displacements

X z

y


46

On the figure 30 we can see that there’s no big deformation of the frame shape. The

average linear stretch of the window is 0,45e-5 mm which is on order lower than the

previously calculated.

Finally a lid closes the sample constraining the out-of plane peripheral displacements.

Unfortunately the Invar plates didn’t arrive at time for this report. Future works may use

it.

The figure 26 is a representation of the setup for the out-of-plane measurements. The

figure 32 shows how the samples were fastened and the measured points. Every point

are located in the centre of a cell, were the displacements are bigger. The temperature

was measured in the point 5 (centre of the plate). The samples and the heating devices

were placed in a pneumatic isolating table. The vibrometer sensor head and the data

acquirers were placed outside the table. Every contact interface was placed outside the

table to minimize external perturbations.

figure 31 Setup characteristics on the out-of plane measurements


47

(a) (b)

figure 32 Clamped sample (a) and numbering of sampling points (b)

The measurement points are located in the lateral surfaces of the cells. The

temperature was measured in the point 5 (centre of the plate). The samples and the

heating devices were placed in a pneumatic isolating table. The vibrometer sensor

head and the data acquirers were placed outside the table. Every contact interface was

placed outside the table to minimize external perturbations. A great handicap in the

lateral measurements was the unavailability of the SPIDER. We had to register the

data manually with all the errors that are associated. That fact of the results analysis be

based on a tendency line minimizes these errors.

figure 33 Setup characteristics on the lateral measurements

x y 1

2 3

4

5


48

(a) (b)

figure 34 Clamped sample (a) and measuring points numbering (b)

figure 35 General view of the lateral measurements

On every point is glued an aluminium tape. This is necessary to guarantee a perfect

reflection of the laser. The points 9, 10 and 11 couldn’t be measured on the

POSH_sample3. The lack of a surface perpendicular to the laser leads to invalid

results.

These setups are equal for the three samples. The axis system is coherent with the

defined axis system in sub-chapter “sample characterization”.

x

z

6

7

8

y

x

9

10

11


49

4.5 Equipment

Per

turb

atio

n is

olat

or

• One Newport pneumatic isolation table

TYPE XL-A

ES

PI s

yste

m

• One Laser

COHERENT Verdi V2 – A5203

Max cw laser at 532 nm

• Optical equipment:

Optics, mirrors, optical fibres and one camera

Vib

rom

eter

pac

k

• One vibrometer sensor head

Polytec OFV 303


50

Vib

rom

eter

pac

k

• One vibrometer controller

Polytec OFV 3001

Hea

ting

devi

ce

• Two portable halogen lamps - 500W each

Tem

pera

ture

mea

sure

men

t dev

ices

• One thermographic camera

FLIR SYSTEMS ThermaCAM PM 575

• One thermocouple plus one multimeter

Dat

a ac

quis

ition

• Two data acquires plus one desktop

“Spider 8-30”


51

5 Results

5.1 Heating characterization

To apply a uniform radiation, the radiation source should be, theoretically, infinitively

far. Two problems must be solved. The first one, it’s impossible to place the radiation

source “so far”. We could place the source at a couple of meters but we would need a

very high power source which we don’t have and that would heat the whole room. The

compromise solution (described on the sub-chapter “setup”) leads to a non-uniform

surface temperature.

Making use of a thermographic camera and thermocouples the heating cycle was

characterized. During the heating the different samples were photographed and the

temperature was registered in specified points (figure 36) by a thermocouple. For each

point one experiment was made. That’s why the different points cool down at different

moments. As we don’t know the material emissivity, the camera was previously

calibrated by the comparison with a thermocouple.

figure 36 Chosen points for characterizing the temperature distribution on the plate


52

The POSH_sample1 has a very well distributed heating. In the figure 37 we can see

that despite of a little difference on the heating velocity, every point achieves the same

temperature, around 150ºC. We can see that the point 5 (centre of the plate) is the one

which temperature increases faster. In the range [25, 100[ ºC the temperature

increases ta an average velocity of 2.2ºC/ second.

POSH_sampl1

0

20

40

60

80

100

120

140

160

1 27 53 79 105 131 157 183 209 235 261 287 313 339 365

time (s)

Tem

p (ºC) P1

P2

P3

P4

P5

figure 37 Heat/cool at the POSH_sample1

The following pictures were taken during the heating characterization tests. The first

picture at 25ºC (room temperature) was shoot before the test. As we can see, as the

temperature raises the heat concentrate on the centre and top-centre of the plate. This

effect happens due to free convection phenomena. We can also see that for higher

temperatures, the temperature distribution is worst, as expected. The difference

between the higher and the lowest temperatures doesn’t exceed the 10ºC

corroborating the thermocouples measurements.

Tref = 25ºC T=45ºC


53

T=50ºC T=75ºC

T=93ºC T=115ºC

figure 38 – Pictures taken with the thermographic camera during the heating stage (POSH_sample1)

The POSH_sample2 presents a more irregular behaviour. The maximum temperature

varies between 140ºC and 170ºC representing a very significant difference on the heat

distribution. The temperature rising velocity is nearly the same as in the

POSH_sample1. The irregular curves might be explained by higher perturbation

caused by the convective effect. The more irregular and “drilled” surface provokes a

more turbulent air flux. There is, also, mass transfer with the inside of the cells.


54

POSH_sample2

0

20

40

60

80

100

120

140

160

180

1 20 39 58 77 96 115 134 153 172 191 210 229 248 267 286 305 324

time (s)

Tem

p (ºC)

TP1

TP2

TP3

TP4

TP5

TPA

TPB

TPC

TPD

figure 39 Heating pattern at the POSH_sample2

On the thermographic analysis we can see again the tendency to have the higher

temperatures on the central (due to the high radius concentration) and upper part (due

to the convection effects) of the plate. Higher temperature differences greater than

10ºC are visible from 75ºC. The carbon fibre is more conductive than the epoxy matrix

what leads to a heat concentration at the cell vertices were, due to manufacturing

issues, the matrix volume fraction is higher. It is also the place were the relation

surface/volume is greater. The last picture shows an almost uniform temperature

distribution. When the heating takes longer the material as enough time to flow the heat

through the whole plate.



55

T=45ºC T=75ºC

T=98ºC T=150ºC

figure 40 - Pictures taken with the thermographic camera during the heating stage (POSH_sample2)

The POSH_sample3 has a similar behaviour to the POSH_sample2. The temperature

difference at in steady state is around 40ºC.


56

Posh_sample3

0

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

180.000

200.000

0 100 200 300 400 500 600

Time (s)

Tem

p (º

C)

P1PAP2PBP3PCP4PDP5

figure 41 Heating pattern at the POSH_sample3

We can notice, by the thermographic picture at 110ºC, that on this sample

manufacturing the resin is not perfectly distributed. On the centre of the plate the cells

joints are too big, indicating resin excess, and on the left side of the plate, there are at

least three cells which centre lacks resin.



57

T=60ºC T=80ºC

T=110ºC T=150ºC

figure 42 - Pictures taken with the thermographic camera during the heating stage (POSH_sample3)

Because of the difficulty to acquire and correlate the termographic camera data with

the point-by-point displacement data, we have chosen to measure the temperature in

the centre of the plate, using it has reference, knowing the presented behaviours are

repetitive. The graphic on the next page is a resume of this analisys.


58

POSH_sample3

0

20

40

60

80

100

120

140

160

180

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113time (s)

tem

pera

ture

(ºC

)

P5151ºC

130ºC

99ºC

73ºC

50ºC

33ºC


59

5.2 Thermo-elastic results

In this subchapter we will present some characteristic results that reveal the samples

behaviour. We will also present the summarized tables as final results. The complete is

presented on the appendicle C. The calculation of the CTE in each direction is based

on the samples characteristic dimensions on the same direction.

For each plate ,11 measuring points were chosen. In the POSH_sample1 5 points were

tested, in the POSH_sample2 11 points were tested and in the POSH_sample3 8

points were tested. For each point an average of four tests was made guarantying at

least three coherent measurements on each point. The preliminary results are not

considered.

POSH_Sample1

The figure 43 represents three consecutive measurements at point 5. Here we can see

a situation that repeated itself several times in all samples without an explained motive.

When the sample cools down, the displacement recovers to negative values, always

around -1,5x10e-6 m (pink line bellow zero).

figure 43 followed measurements

The same effect is seen on the figure 44. Here the displacement recovery happens in a

hysteretic way. This, obviously, represents energy loss that might be associated to

some accommodation of the support during the process.

P5

0

20

40

60

80

100

120

140

160

1 132 263 394 525 656 787 918 104911801311144215731704

time (s)

tem

p (º

C)

-5

0

5

10

15

20

25

disp

l. (x

10-

6 m

)

Série1

Série2


60

figure 44 Hysteretic effect

This process leads to different CTEs on the heating and cooling. For this work we will

consider just the curve corresponding to the heating. On the figure 45 is represented a

linear and a quadratic trend line. The difference is not significant however the quadratic

line fits better. For the CTE calculation we derivate the quadratic line and calculate the

tangent line near the medium point of the temperature range (75ºC was chosen). This

approach is used just on the out-of-plane measurements.

figure 45 linear and quadratic tendency line

P1_a

-0,0015

-0,001

-0,0005

0

0,0005

0,001

0,0015

0,002

0,0025

0,003

0,0035

0,004

0 20 40 60 80 100 120 140 160

temp (ºC)

strain ( / )

P1_cy = -8E-08x2 + 5E-05x - 0,001y = 3E-05x - 0,0004

-0,0005

0

0,0005

0,001

0,0015

0,002

0,0025

0,003

0,0035

0,004

0,0045

0,005

0 20 40 60 80 100 120 140 160

temp (ºC)

stra

in ( /

)


61

Applying the method for all point we get the following table:

Table 3 – z-direction CTE

P1 P2 P3 P4 P5 a 3,00E-05 6,40E-07 1,05E-05 1,10E-05 1,20E-05 b 3,50E-05 6,25E-07 1,10E-05 1,10E-05 1,30E-05 c 3,80E-05 7,10E-07 1,00E-05 1,10E-05 1,25E-05 d 3,80E-05 6,40E-07 8,00E-06 1,10E-05 -

average 3,53E-05 6,54E-07 9,88E-06 1,10E-05 1,25E-05 desv pad 3,77E-06 3,82E-08 1,31E-06 0,00E+00 5,00E-07

POSH_Sample2

The same analysis is made for the sample2. As expected, the biggest CTE is

presented in the z-direction. Important is also the fact that the point 5 (centre of the

plate) has the smallest displacements. This reinforces the acknowledge behaviour in

the preliminary analysis, i.e., the plate doesn’t behave has a whole.

Table 4 - z direction CTE

P1 P2 P3 P4 P5 a 2,00E-05 3,25E-05 3,95E-05 3,65E-05 2,80E-05 b 3,50E-05 3,70E-05 3,25E-05 3,65E-05 2,95E-05 c 3,80E-05 3,25E-05 2,95E-05 3,80E-05 2,95E-05 d 3,80E-05 2,80E-05 3,80E-05 3,10E-05

average 3,28E-05 3,25E-05 3,38E-05 3,73E-05 2,95E-05

desv pad 8,62E-06 3,67E-06 5,13E-06 8,66E-07 1,22E-06

figure 46 Measurements on point 6 and 7

P6y = 5E-06x - 1E-04

0,00E+00

5,00E-05

1,00E-04

1,50E-04

2,00E-04

2,50E-04

3,00E-04

3,50E-04

4,00E-04

20 30 40 50 60 70

Temp ( ºC )

Ensaio 1

Ensaio 2

Ensaio 3

delta med

Linear (delta med)

P7y = 4E-06x - 0,0001

-5,00E-05

0,00E+00

5,00E-05

1,00E-04

1,50E-04

2,00E-04

2,00E+01 3,00E+01 4,00E+01 5,00E+01 6,00E+01 7,00E+01

Temp ( ºC )

Ensaio 1

Ensaio 2

Ensaio 3

delta med


62

The measurements on the lateral directions were made based on the temperature instead of the time. For the same temperature we got several displacement data. Than we are able to calculate a normal average curve from where we calculated the respective CTE.

The results are shown on the Table 5.

Table 5 - x and y directions CTEs

x-direction

P6 P7 P8 average 5,00E-06 4,00E-06 4,00E-06 4,33E-06

y-

direction P9 P10 P11 3,00E-06 4,00E-06 4,00E-06 3,67E-06

Comparing the CTE on the lateral directions, the x-direction has the greater CTE. The

x-direction is perpendicular to the honeycomb fibers which mean that the main

responsible for the expansion is the matrix. This result is in agreement to the moisture

theory for laminates.

POSH_sample3

On the sample3, as we see again the recovering to negative values. A new issue is

related to the figure 47 and figure 48. The hysteretic effect happens in both situations

but now the graphic 15 the sample recovers to the beginning point.

P1_f

0

50

100

150

200

1 29 57 85 113141169197225253281309337

time (s)

Tem

p (º

C)

-200

0200

400600

800

disp

l. (1

0^-6

m)

Série1

Série2

figure 47 Displacement recovery to negative values

-78e-6 m


63

P1_f

-0,02

0

0,02

0,04

0,06

0 50 100 150 200

temp (ºC)st

rain

( /

)

figure 48 Hysteretic effect with final gap

P1_e

-0,02

0

0,02

0,04

0,06

0,08

0,1

0 50 100 150 200

temp (ºC)

stra

in (

/ )

figure 49 Hysteretic effect without final gap

The table 6 represents the summarized results for the z-direction CTE of the

POSH_sample3.

Table 6 – z-direction CTE

P1 P2 P3 P4 P5 a 7,50E-04 2,80E-05 2,65E-05 2,25E-05 2,50E-05 b 7,00E-04 2,40E-05 2,40E-05 2,25E-05 2,50E-05 c 7,50E-04 2,40E-05 2,40E-05 2,40E-05 2,65E-05 d 7,50E-04 2,55E-05 2,40E-05 2,70E-05 2,65E-05 e 6,65E-04 2,70E-05 2,70E-05 2,55E-05 2,80E-05 f 4,50E-04 1,95E-05

average 6,78E-04 2,57E-05 2,51E-05 2,43E-05 2,51E-05

desv pad 1,17E-04 1,79E-06 1,52E-06 1,96E-06 2,96E-06


64

P6y = 4E-06x - 9E-05

0

0,00005

0,0001

0,00015

0,0002

0,00025

0,0003

0,00035

0,0004

20 40 60 80 100 120

Temp ( ºC)

Ensaio 2

Ensaio 3

Ensaio 4

delta med

figure 50 x-direction dimensionless displacement (on point6)

On the figure 50 and table 7 it’s possible to see a good group of measurements. The different measurements on each point and the results on the different points are very similar indicating invariance on the test perform.

Table 7 – x-direction CTE

x-direction P6 P7 P8 average 4,00E-06 5,00E-06 5,00E-06 4,67E-06

figure 51 z-direction CTE measured in different points

sample comparison

0

0,0001

0,0002

0,00030,0004

0,00050,0006

0,0007

0,0008

P1 P2 P3 P4 P5

CTE ( 1

/ºC

)

sample1

sample2

sample3


65

figure 52 z-direction CTE measured in different points (zoom)

The figure 51 and figure 52 show the comparison between the different samples. The POSH_sample1 is the more stabile, followed by the POSH_sample3. We can also ask if the sample3 is well manufactured near the point 1 or if it wasn’t properly fasten in that corner.

sample comparison

00,000005

0,000010,000015

0,000020,0000250,00003

0,0000350,00004

0,0000450,00005

P1 P2 P3 P4 P5

CTE ( 1

/ºC

)sample1

sample2

sample3


67

6 Conclusions

During this work, the achievement of valid results became very difficult. The high

sensity of the samples and the extreme conditions of its application asks for special

laboratory conditions which were not used. The difficulties felt during this project

revealed some incoherence between what was asked to do and what was really

possible to do.

Although, is now presented the possible technical conclusions of this measurements.

• In the out of plane measurements, the observed displacements are

consequence of each alveolus expansion; the global expansion of the sample is

insignificant;

• On the 3 principal directions the structure CTE is greater than the linear CTE of

the fiber;

• Hysteresis was observed between heating and cooling however we cannot

distinguish if it represents the behavior of the sample or of the frame;

• The sample show manufacturing non-uniformity; the concentration of resin in

some points leads to particular hot zones; it is seen specially during cooling;

• The displacement curves shape depend of the heating velocity;


68


69

6.1 Future works

The immediate task to be performed is testing the samples in the “four-edge fix”

boundary condition. As soon as the equipment is available, some tests in high vacuum

should also be performed.

To measure the in-plane displacements an image correlation technique might be used.

The technique is simple requiring a current photographic camera. The main issue to be

taken care is an image analyser algorithm which is already developed at LOME. A 3D

ESPI system could also be used however it is not available at FEUP or INEGI.

Future approaches might include the time dependence of the thermo-elastic behaviour.

For instance, using an oven and determining the thermal strains for different heating

velocities we could correlate these results with the thermal conductivity and conclude

about the thermal inertia mechanisms.

On the other hand, a fatigue run-test could benefit the understanding of cumulative

strain and stresses (if it exists) during the heating-cooling cycles in spatial conditions.

To characterize the dynamic behaviour of these materials/structures vibro-acoustics

tests are also being prepared. As a suggestion this might be performed at different

temperatures due to the visco-elastic matrix nature.

All the tests, thermo-elastic and dynamic, will be repeated on an antenna specimen in

some control points to be compared to the FEM results worked by HPS.


70


71

7 References

[1] L. Datashvili, M. Lang, N. Nathrath, Ch. Zauner, H. Baier, O.Soykasap, L.T. Tan, A.

Kueh, S. Pellegrino D. Fasold, Final Technical Report -TAHARA, Ref.: LLB-FR-09/05/05-02D-02, Munich, May 2005

[2] HPS Gmbh, Modelling of porous shells – volume II technical proposal,

Braunschweig/Munich, June 2006 [3] T. Ernst , M. Lang , M. Lori , C. Schöppinger , J. Santiago Prowald, HIGHLY

STABLE Q/V BAND REFLECTOR MATERIAL TRADE-OFF AND THERMO-ELASTIC ANALYSIS;

[4] T. Ernst(1), S. Linke(2), M. Lori(3), Prof. D. Fasold(4), W. Haefker(5), E. H.

Nösekabel(6), J. Santiago Prowald(,HIGHLY STABLE Q/V BAND REFLECTOR DEMONSTRATOR MANUFACTURING AND TESTING;

[5] L. A. Ferreira, Laboratory of lubrication and vibration - script, FEUP

[6] M. Moura, A. Morais, A. Magalhães, Materiais compósitos – materiais, fabrico e comportamento mecânico, Publindústria, Porto, 2005

[7] www.tyssenkruppvdm.de

[8] Ansys 11 – Student edition

[9] ESAcomp® 3.1


73

8 Appendicles


a

Appendicle A – POSH_sample1 mechanical properties


a

This appendicle contains the given engineering properties of each layer of the POSH_sampl1.

NO. ANGLE THK MAT EX EY

--- ----- -------- --- -------- --------

1 0.0 0.970E-01 7 0.182E+06 0.182E+06

2 45.0 0.970E-01 7 0.182E+06 0.182E+06

3 45.0 0.970E-01 7 0.182E+06 0.182E+06

4 0.0 0.970E-01 7 0.182E+06 0.182E+06

5 0.0 0.137 200 0.296E+04 0.00

6 0.0 12.7 111 20.0 20.0

7 0.0 0.117 200 0.296E+04 0.00

8 0.0 0.970E-01 7 0.182E+06 0.182E+06

9 45.0 0.970E-01 7 0.182E+06 0.182E+06

10 45.0 0.970E-01 7 0.182E+06 0.182E+06

21 0.0 0.970E-01 7 0.182E+06 0.182E+06

-------------------------------------

SUM OF THK 13.7


b

BONDING RESIN & FILM ADHESIVE t=0.127 MAT_ID=200

Modulus of elasticity X-Direction [MPa] 2964.4

Thermal expansion coefficient X-Direction [1/K] 5.04E-05

Major Poisson's ratio XY-Plane [ - ] 0.3

Density [t/mm³] 1.19E-09

Specific Heat [(t*mm²/s²)/(K*t)] 1400000000

Thermal conductivity X-Direction [W/(K m)] 1.0

Thermal conductivity Y-Direction [W/(K m)] 1.0

Thermal conductivity Z-Direction [W/(K m)] 1.0

Limit Stress in Tension X-Direction [MPa] 5.00

Limit Stress in Compression X-Direction [MPa] -5.00

Limit Stress in Tension Y-Direction [MPa] 5.00

Limit Stress in Compression Y-Direction [MPa] -5.00

Limit Stress in Tension Z-Direction [MPa] 5.00

Limit Stress in Compression Z-Direction [MPa] -5.00

Limit Stress in Shear XY-Plane [MPa] 5.00

Limit Stress in Shear YZ-Plane [MPa] 5.00

Limit Stress in Shear XZ-Plane [MPa] 5.00


c

Ultracore Carbon Honeycomb UCF-126-3/8-2.0 MAT_ID=111

Modulus of elasticity X-Direction [MPa] 20

Modulus of elasticity Y-Direction [MPa] 20

Modulus of elasticity Z-Direction [MPa] 117

Thermal expansion coefficient X-Direction [1/K] 2.00E-07

Thermal expansion coefficient Y-Direction [1/K] 5.00E-07

Thermal expansion coefficient Z-Direction [1/K] 4.00E-06

Shear modulus XY-Plane [MPa] 10

Shear modulus YZ-Plane [MPa] 276

Shear modulus XZ-Plane [MPa] 165







Limit Stress in Tension X-Direction [MPa] 1.10

Limit Stress in Compression X-Direction [MPa] -1.00

Limit Stress in Tension Y-Direction [MPa] 1.00

Limit Stress in Compression Y-Direction [MPa] -1.00

Limit Stress in Tension Z-Direction [MPa] 1.19

Limit Stress in Compression Z-Direction [MPa] -1.19

Limit Stress in Shear XY-Plane [MPa] 1.04

Limit Stress in Shear YZ-Plane [MPa] 1.04

Limit Stress in Shear XZ-Plane [MPa] 0.59


d

PF-YSH70A-100/LTM123 (40%RW); Vf=58%; t=0.097mm MAT_ID=7

Modulus of elasticity X-Direction [Pa] 181619000000

Modulus of elasticity Y-Direction [Pa] 181619000000

Modulus of elasticity Z-Direction [Pa] 7200000000

Thermal expansion coefficient X-Direction [1/K] -7.10E-07

Thermal expansion coefficient Y-Direction [1/K] -7.10E-07

Thermal expansion coefficient Z-Direction [1/K] 4.03E-05


Major Poisson's ratio YZ-Plane [ - ] 0.28

Major Poisson's ratio XZ-Plane [ - ] 0.28

Shear modulus XY-Plane [Pa] 3140000000

Shear modulus YZ-Plane [Pa] 1133000000

Shear modulus XZ-Plane [Pa] 1133000000






Limit Stress in Tension X-Direction [Pa] 597000000

Limit Stress in Compression X-Direction [Pa] -176000000

Limit Stress in Tension Y-Direction [Pa] 487000000

Limit Stress in Compression Y-Direction [Pa] -176000000

Limit Stress in Tension Z-Direction [Pa] 1000000000

Limit Stress in Compression Z-Direction [Pa] -1000000000

Limit Stress in Shear XY-Plane [Pa] 44000000

Limit Stress in Shear YZ-Plane [Pa] 57000000

Limit Stress in Shear XZ-Plane [Pa] 57000000


a

Appendicle B – INVAR Pernifer®36


b

Appendicle C – results list


a

POSH_sample1

Point Temp. & displ. Vs time Strain vs temp

1

P1_a

0

20

40

60

80

100

120

140

160

1 29 57 85 113 141 169197225253 281309337

t ime ( s)

-20

-10

0

10

20

30

40

50

Temp (ºC)

displ. (µm)

P1_b

020406080

100120140160

1 19 37 55 73 91 10 127 145 16 181 19 217 23 25 271

t ime (s)

-10

0

10

20

30

40

50

60

Temp (ºC)

displ. (µm)

P1_c

0

20

40

60

80

100

120

140

160

1 24 47 70 93 116 139 162 185208 231254277

t ime ( s)

-10

0

10

20

30

40

50

60

70

Temp (ºC)

displ. (µm)

P1_d

0

50

100

150

200

1 31 61 91 121151181211241271301

time (s)

Tem

p (º

C)

-20

0

20

40

60

80

disp

l. (1

0-̂6

m)

Temp (ºC)

displ. (µm)

P1_a

y = -2E-07x2 + 6E-05x - 0,0012

-0,00050

0,00050,001

0,00150,002

0,00250,003

0,00350,004

0 50 100 150 200

temp (ºC)

displ. (µm)

Polinómio (displ. (µm))

P1_b

y = -1E-07x2 + 5E-05x - 0,0011

-0,001

0

0,001

0,002

0,003

0,004

0,005

0 50 100 150 200

temp (ºC)

displ. (µm)


P1_c

y = -8E-08x2 + 5E-05x - 0,001

-0,001

0

0,001

0,002

0,003

0,004

0,005

0 50 100 150 200

temp (ºC)

displ. (µm)


P1_d

y = -8E-08x2 + 5E-05x - 0,001

-0,001

0

0,001

0,002

0,003

0,004

0,005

0 50 100 150 200

temp (ºC)

displ. (µm)



b


2

P2_a

0

50

100

150

200

1 20 39 58 77 96 115134153172191210229248267286305324343

t ime (s)

-50

51015

2025

Temp (ºC)

displ. (µm)

P2_b

0

50

100

150

200

1 20 39 58 77 96 115 134153172191210 22 24 26

t ime (s)

-5

0

5

10

15

20

25

Temp (ºC)

displ. (µm)

P2_c

0

50

100

150

200

1 17 33 49 65 81 97 113 129 145161 177 193 209 225241 257 273

t ime (s)

-5

0

5

10

15

20

25

Temp (ºC)

displ. (µm)

P2_d

0

50

100

150

200

1 16 31 46 61 76 91 106 121 136 151 166 181 196 211 226 241 256 271 286 301 316

t i me (s)

-5

0

5

10

15

20

25

Temp (ºC)

displ. (µm)

P2_a

y = -4E-10x2 + 7E-07x - 2E-05

-0,00002

0

0,00002

0,00004

0,00006

0,00008

0 20 40 60 80 100 120 140 160

temp (ºC)

stra

in ( /

)

P2_b

y = -5E-10x2 + 7E-07x - 2E-05

-0,00002

0

0,00002

0,00004

0,00006

0,00008

0,0001

0 20 40 60 80 100 120 140 160

temp (ºC)

stra

in ( /

)

P2_c

y = -6E-10x2 + 8E-07x - 3E-05

-0,00002

0

0,00002

0,00004

0,00006

0,00008

0,0001

0 20 40 60 80 100 120 140 160

temp (ºC)

stra

in ( /

)

P2_d

y = -4E-10x2 + 7E-07x - 2E-05

-0,00002

0

0,00002

0,00004

0,00006

0,00008

0 20 40 60 80 100 120 140 160

temp (ºC)

stra

in ( /

)


c


3

P3_a

0

20

40

60

80

100

120

140

160

1 27 53 79 105 131 157 183209235 261287 313339

t ime ( s)

-5

0

5

10

15

20

Temp (ºC)

displ. (µm)

P3_b

020406080

100120140160

1 15 29 43 57 71 85 99 113 127 141 155 169

t ime (s)

0

5

10

15

20

25

Temp (ºC)

displ. (µm)

P3_c

02040

6080

100120

140160

1 20 39 58 77 96 115 134 153 172 191 210

t ime (s)

-5

0

5

10

15

20

25

Temp (ºC)

displ. (µm)

P3_d

0

50

100

150

200

1 38 75 112149186223260297

time (s)

Tem

p (º

C)

-5

0

5

10

15

20

disp

l. (1

0̂-6

m)

Temp (ºC)

displ. (µm)

P3_a

y = 1E-08x2 + 9E-06x - 0,0002

-0,0005

0

0,0005

0,001

0,0015

0 50 100 150 200

temp (ºC)

stra

in ( /

)

P3_b

y = 2E-08x2 + 8E-06x - 0,0002

-0,0005

0

0,0005

0,001

0,0015

0,002

0 20 40 60 80 100 120 140 160

temp (ºC)

stra

in ( /

)

P3_c

y = 6E-08x2 + 1E-06x - 7E-05

-0,0005

0

0,0005

0,001

0,0015

0,002

0 50 100 150 200

temp (ºC)

stra

in ( /

)

P3_d

y = 4E-08x2 + 2E-06x - 0,0001

-0,0005

0

0,0005

0,001

0,0015

0 50 100 150 200

temp (ºC)

stra

in ( /

)


d


4

P4_a

02040

6080

100120

140160

1 35 69 103 137 171 205 23 273 307 341

t ime (s)

-5

0

5

10

15

20

25

Temp (ºC)

displ. (µm)

P4_b

020406080

100120140160

1 23 45 67 89 111 13 155 177 19 22 24 26

t ime (s)

-5

0

5

10

15

20

25

Temp (ºC)

displ. (µm)

P4_c

0

50

100

150

200

1 70 139208277346415484

time (s)

Tem

p (º

C)

0

5

10

15

20

25

disp

l. (1

0̂-6

m)

Temp (ºC)

displ. (µm)

P4_d

0

50

100

150

200

1 21 41 61 81 101121141

time (s)

Tem

p (º

C)

05

101520

2530

disp

l. (1

0̂-6

m)

Temp (ºC)

displ. (µm)

P4_a

y = 4E-08x2 + 5E-06x - 0,0001

-0,0005

0

0,0005

0,001

0,0015

0,002

0 50 100 150 200

temp (ºC)

P4_b

y = 2E-08x2 + 8E-06x - 0,0002

-0,0005

0

0,0005

0,001

0,0015

0,002

0 50 100 150 200

temp (ºC)

P4_c

y = 4E-08x2 + 5E-06x + 6E-05

0

0,0005

0,001

0,0015

0,002

0 50 100 150 200

temp (ºC)

P4_d

y = 4E-08x2 + 5E-06x + 0,0002

0

0,0005

0,001

0,0015

0,002

0 50 100 150 200

temp (ºC)


e


5

P5_a

02040

6080

100120

140160

1 35 69 103 137 171 205 23 273 307 341

t ime (s)

-5

0

5

10

15

20

25

Temp (ºC)

displ. (µm)

P5_b

020406080

100120140160

1 71 141 211 281 351 421491 561 631 701

t ime (s)

-5

0

5

10

15

20

25

Temp (ºC)

displ. (µm)

P5_c

0

20

40

60

80

100

120

140

160

1 40 79 118 157 196 235 274 313 352 391

time (s)

-5

0

5

10

15

20

25

Temp (�

the experimental assessment of thermal strains in porous ......modelling of porous shells the...

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