Modelling of Porous shells
The experimental assessment ofthermal 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
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.
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.
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
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
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 4SSBR ANTENNAS ASSEMBLED TO THE SUPPORT ARM ... 20
FIGURE 5SSBR DESIGN MODEL (A) GEOMETRY (B) STIFFENER PRINCIPLE ... 20
FIGURE 6FTR REFLECTOR, REVOLUTE JOINTS ... 21
FIGURE 7FRT REFLECTOR, STIFFENERS LOCATIONS ... 21
FIGURE 8TESTED SPECIMENS PRODUCED BY LLB ... 24
FIGURE 9(A) SPECIMEN ASSEMBLAGE AT THE DILATOMETER (B) TESTED SAMPLES AND CALIBRATION RODS ... 24
FIGURE 10THERMAL DEFORMATION GRAPHS AND CTE FOR STANDARD SPECIMENS [1] ... 25
FIGURE 11THERMAL STRAIN VS TEMPERATURE FOR 0-DIRECTION AND 90-DIRECTION ... 26
FIGURE 12THERMAL DISTORTION TESTS – SETUP, SAMPLE GEOMETRY AND MEASURING GRID ... 27
FIGURE 13 CONSTRUCTIVE AND DESTRUCTIVE WAVE INTERFERENCE ... 29
FIGURE 14TYPICAL FUNCTIONING OF AN ESPI SYSTEM ... 30
FIGURE 15DYNAMIC DISPLACEMENT MEASURING WITH ESPI ... 31
FIGURE 16INFLUENCE OF THE WAVELENGTH AND TEMPERATURE IN THE SPECIFIC SPECTRAL EMISSIVITY [5] ... 33
FIGURE 17COMPARISON OF THE EMISSIVITY AS A FUNCTION OF THE WAVELENGTH BETWEEN (A) NON-METALLIC AND (B) METALLIC MATERIALS ... 34
FIGURE 19APLICATION OF TERMOGRAPHIC METHODS IN DIFFERENT SITUATIONS ... 35
FIGURE 18VARIATION OF THE SPECTRAL TRANSMISSIVITY OF THE AIR WITH THE RADIATION WAVELENGTH ... 35
FIGURE 20CHOSEN BOUNDARY CONDITIONS TO BE TESTED ... 37
FIGURE 21ESPI CAPTURED PICTURES (A)(B) AND POSTPROCESSOR (C)(D) – FRONT THERMAL LOAD ... 38
FIGURE 22 TESTED SAMPLES, PROJECT DESIGNATION AND CORRESPONDING USED NAME ... 40
FIGURE 23LAY-UP AND ENGINEERING PROPERTIES OF THE SAMPLE1 (ESACOMP® 3.1) ... 40
FIGURE 24PLY GEOMETRY AND MANUFACTURING STRUCTURE ... 42
FIGURE 25HONEYCOMB STRUCTURE (LEFT) AND GLOBAL DIMENSIONS (RIGHT) ... 42
FIGURE 26DESIGN FRAME FOR “4 EDGE FIX” CONDITIONS ... 43
FIGURE 27ELEMENT SOLID45... 44
FIGURE 28MESHING OF USED SUPPORT MODEL ... 45
FIGURE 29DISPLACEMENTS ALONG X (RIGHT) AND Y (LEFT) DIRECTIONS ... 45
FIGURE 30 X, Y AND Z SUPERIMPOSED DISPLACEMENTS ... 45
FIGURE 31SETUP CHARACTERISTICS ON THE OUT-OF PLANE MEASUREMENTS ... 46
FIGURE 32CLAMPED SAMPLE (A) AND NUMBERING OF SAMPLING POINTS (B) ... 47
FIGURE 33SETUP CHARACTERISTICS ON THE LATERAL MEASUREMENTS ... 47
FIGURE 34CLAMPED SAMPLE (A) AND MEASURING POINTS NUMBERING (B) ... 48
FIGURE 35GENERAL VIEW OF THE LATERAL MEASUREMENTS ... 48
FIGURE 36CHOSEN POINTS FOR CHARACTERIZING THE TEMPERATURE DISTRIBUTION ON THE PLATE ... 51
FIGURE 37HEAT/COOL AT THE POSH_SAMPLE1 ... 52
FIGURE 38–PICTURES TAKEN WITH THE THERMOGRAPHIC CAMERA DURING THE HEATING STAGE (POSH_SAMPLE1) ... 53
FIGURE 42-PICTURES TAKEN WITH THE THERMOGRAPHIC CAMERA DURING THE HEATING STAGE (POSH_SAMPLE3)... 57
FIGURE 43FOLLOWED MEASUREMENTS ... 59
FIGURE 44HYSTERETIC EFFECT ... 60
FIGURE 45LINEAR AND QUADRATIC TENDENCY LINE ... 60
FIGURE 46MEASUREMENTS ON POINT 6 AND 7 ... 61
FIGURE 47DISPLACEMENT RECOVERY TO NEGATIVE VALUES ... 62
FIGURE 48HYSTERETIC EFFECT WITH FINAL GAP ... 63
FIGURE 49HYSTERETIC EFFECT WITHOUT FINAL GAP ... 63
FIGURE 50X-DIRECTION DIMENSIONLESS DISPLACEMENT (ON POINT6) ... 64
FIGURE 51Z-DIRECTION CTE MEASURED IN DIFFERENT POINTS ... 64
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.
1.2 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;
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.
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-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.
(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.
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.
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.
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:
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
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)
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)
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);
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.
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.
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 Interferometry (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
figure 14 Typical functioning of an ESPI system
On the figure 14is 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
(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.
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;
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.
• 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) non-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
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
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;
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
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
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.
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
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 %/%
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.
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
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
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
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 32shows 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.
(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
(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 x z 6 7 8 y x 9 10 11
4.5 Equipment P e rt u rb a ti o n i s o la to r
• One Newport pneumatic isolation table
TYPE XL-A E S P I s y s te m • One Laser
COHERENT Verdi V2 – A5203
Max cw laser at 532 nm
• Optical equipment:
Optics, mirrors, optical fibres and one camera V ib ro m e te r p a c k
• One vibrometer sensor head
V ib ro m e te r p a c k
• One vibrometer controller
Polytec OFV 3001 H e a ti n g d e v ic e
• Two portable halogen lamps - 500W
each T e m p e ra tu re m e a s u re m e n t d e v ic e s
• One thermographic camera
FLIR SYSTEMS ThermaCAM PM 575
• One thermocouple plus one multimeter
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.
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) T e m 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.
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.
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) T e m 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.
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.
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) T e m p ( ºC ) P1 PA P2 PB P3 PC P4 PD P5figure 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.
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.
POSH_sample3
40
60
80
100
120
140
160
180
te m p e ra tu re ( ºC )P5
151ºC 130ºC 99ºC 73ºC 50ºC5.2 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 10491180 1311144215731704 time (s) te m p ( ºC ) -5 0 5 10 15 20 25 d is p l. ( x 1 0 -6 m ) Série1 Série2
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.
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) s tr a in ( / ) P1_c y = -8E-08x2 + 5E-05x - 0,001 y = 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) s tr a in ( / )
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
P6 y = 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)
P7 y = 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
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 T e m p ( ºC ) -200 0 200 400 600 800 d is p l. ( 1 0 ^ -6 m ) Série1 Série2 -78e-6 m
P1_f -0,02 0 0,02 0,04 0,06 0 50 100 150 200 temp (ºC) s tr a in ( / )
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) s tr a 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
P6 y = 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
sample comparison 0 0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007 0,0008 P1 P2 P3 P4 P5 C T E ( 1 /º C ) sample1 sample2 sample3
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 0 0,000005 0,00001 0,000015 0,00002 0,000025 0,00003 0,000035 0,00004 0,000045 0,00005 P1 P2 P3 P4 P5 C T E ( 1 /º C ) sample1 sample2 sample3
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;
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.
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
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 ---
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
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
Major Poisson's ratio XY-Plane [ - ] 0.3
Density [t/mm³] 3.20E-11
Specific Heat [(t*mm²/s²)/(K*t)] 15000000
Thermal conductivity X-Direction [W/(K m)] 0.1000
Thermal conductivity Y-Direction [W/(K m)] 0.1000
Thermal conductivity Z-Direction [W/(K m)] 0.1000
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
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 XY-Plane [ - ] 0.03
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
Density [t/mm³] 1.510E-09
Specific Heat [(t*mm²/s²)/(K*t)] 710000000
Thermal conductivity X-Direction [W/(K m)] 75.0
Thermal conductivity Y-Direction [W/(K m)] 75.0
Thermal conductivity Z-Direction [W/(K m)] 1.1
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
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 i me ( s) -20 -10 0 10 20 30 40 50 Temp (ºC) displ. (µm) P1_b 0 20 40 60 80 100 120 140 160 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 2447 70 93 116 139 162 185208 231254277 t i me ( 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) T e m p ( ºC ) -20 0 20 40 60 80 d is p l. ( 1 0 ^ -6 m ) Temp (ºC) displ. (µm) P1_a y = -2E-07x2 + 6E-05x - 0,0012 -0,0005 0 0,0005 0,001 0,0015 0,002 0,0025 0,003 0,0035 0,004 0 50 100 150 200 t emp ( 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 t emp ( ºC) displ. (µm) Polinómio (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) Polinómio (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 t emp ( ºC) displ. (µm) Polinómio (displ. (µm))
