1
INOM
EXAMENSARBETE MASKINTEKNIK, AVANCERAD NIVÅ, 30 HP
STOCKHOLM SVERIGE 2020 ,
Utveckling och verifiering av metod för att bestämma
skjuvegenskaper hos Hybrixkärna
SANGHARSH BHUSTALIMATH
KTH
SKOLAN FÖR TEKNIKVETENSKAP
Development and verification of a method to determine the shear properties of Hybrix core
SANGHARSH BHUSTALIMATH
Master in Aerospace Engineering Date: June 12, 2020
Supervisor: Per Wennhage Examiner: Per Wennhage School of Engineering Sciences Host company: Lamera AB
Swedish title: Utveckling och verifiering av metod för att bestämma
skjuvegenskaper hos Hybrixkärna
iii
Abstract
This thesis helps develop a material model for a novel Fiber Core Sand- wich Sheet construction. A test method was used to determine the me- chanical properties of the sandwich material. Standard three point bend- ing tests coupled with digital image correlation was used. Results were extracted from the digital image data. These results supplemented the development and tuning of an FE model of the sandwich material. Con- clusions were drawn about the feasibility of the method in studying such a material.
Keywords: Fiber Core Sandwich Sheets, FCSS, Sandwich Construc-
tion, Digital Image Correlation, Three point bending test, Hybrix
iv
Sammanfattning
Denna avhandling genomfördes mot utvecklingen av en homogeniserad materialmodell för en ny sandwich-konstruktion med fiberkärna. En test- metod användes för att bestämma de mekaniska egenskaperna hos sand- wichmaterialet. Testmetoden involverade trepunkts i kombination med digital bildkorrelation. Resultaten extraherades från den digitala bildda- tan vid genomförande av trepunkts. Dessa resultat användes utvecklingen av en FE-modell av sandwichmaterialet. Slutsatser drogs om tillämplig- heten av metoden för att studera ett sådant material.
Nyckelord: Sandwichmaterial, fiberkärna, Digital bildkorrelation, Tre-
punkts, Hybrix
v
Acknowledgements
I would like to express my gratitude to professor Per Wennhage for guid- ing me, and supervising my thesis work. I would like to thank Lars Olovsson from Impetus AFEA AB, for his work concerning FE Simu- lations, that were a crucial part of this thesis. I am also grateful to Ramin Moshfegh & Bengt Nilsson from Lamera AB, for providing me the opportunity to perform this master thesis work. I would also like to thank Monica Norrby & Tomas Ekermann at the Lightweight Structures Laboratory for helping me with the experimental setup.
Sangharsh Bhustalimath,
Stockholm, 3 December 2018
Contents
1 Introduction 1
1.1 Background . . . . 1
1.2 Motivation . . . . 2
1.3 Problem statement . . . . 2
2 Review of Test Methods & Theory 3 2.1 Review of Test Methods . . . . 3
2.1.1 ASTM C273 - Test Method for Shear Properties of Sandwich Core Materials by Block Shear . . . . . 3
2.1.2 ASTM C393 - Test Method for Core Shear Prop- erties of Sandwich Constructions by Beam Flexure 4 2.1.3 Draw bending test . . . . 5
2.2 Conclusion of the review of test methods . . . . 6
2.3 Digital Image Correlation . . . . 7
2.4 Three point bending supplemented with DIC . . . . 8
2.5 Method Development Approach . . . . 9
3 Experiments 11 3.1 Materials . . . . 11
3.2 Apparatus . . . . 12
3.3 Procedure . . . . 13
3.3.1 Sandwich Beam Theory . . . . 16
3.3.2 DIC Extraction of Rotation . . . . 16
3.3.3 DIC Extraction of Displacement . . . . 18
4 Results 21 4.1 Observations . . . . 21
4.2 Summary . . . . 23
5 Conclusion and Future Work 29
vi
Chapter 1 Introduction
This thesis helps develop a method to determine the mechanical prop- erties of a special Fiber Core Sandwich Sheet. A series of experiments are done to qualify a test method and the mechanical properties are ex- tracted. These properties are used to fine-tune a material model that could be further used in performing numerical simulations.
1.1 Background
Hybrix (fig: 1.1) is a novel, lightweight replacement for sheet metals de- veloped by Lamera AB. It consists of an isotropic face sheet material with a stochastic polymeric fiber core, known popularly in the industry as Fiber Core Sandwich Sheets (FCSS). Sandwich theory is the design principle behind Hybrix, where a low density core is glued between two stiffer face sheets giving a composite three layer beam which has higher overall stiffness to weight ratio compared to that of it’s individual com- ponents.
Figure 1.1: Hybrix Construction (Src: www.lamera.se )
1
2 CHAPTER 1. INTRODUCTION
The material was developed as a lightweight replacement for sheet- metals in forming applications. Forming is a metal working process in which metal parts and objects are shaped using the principle of plastic deformation, without adding or removing material. Plastic deformation, in material science, is the deformation of object that is not undone upon removing an applied force.
As with any material in the engineering industry, Hybrix needs to have a material model that can be used to perform engineering simula- tions. The scope of this thesis is to formulate a test method and gather information to develop a model that captures the behavior of Hybrix material.
1.2 Motivation
There are no standard methods for testing a FCSS such as Hybrix. Also, it is difficult to observe deformation and damage in Hybrix due to the unique construction and the physical scale of the material. This the- sis suggests a simple test method to study the mechanical properties of Hybrix.
1.3 Problem statement
Engineering simulations of the Hybrix material require a numerical model.
During the forming process Hybrix is subjected to large deformations that
lead to a possible shear failure in its core. The thesis develops an experi-
mental testing method to capture its mechanical behaviour during large
deformations, and hence develop a model. The thesis also develops meth-
ods for the extraction of useful information from the data gathered from
the tests. Additionally, the thesis aids Impetus AFEA AB in developing
the numerical model.
Chapter 2
Review of Test Methods & The- ory
2.1 Review of Test Methods
In this work, the Hybrix face sheets are made of aluminum, and the core is made of polymeric fibers. As the core is relatively weaker than the face sheet material, it is likely that a core failure is observed when Hybrix is subjected to large deformations. Hence, emphasis was laid on the test methods that study the behaviour of the core.
The Industrial Standards applied to Continuous Fiber Reinforced Composite (CFRP) were studied. In particular, test methods related to sandwich composites.
2.1.1 ASTM C273 - Test Method for Shear Properties of Sandwich Core Materials by Block Shear
This method is used to determine the properties of core shear strength and core shear modulus of the core material used in sandwich composites.
A rectangular gauge section of core specimen is glued to steel plates that are loaded in tension or compression (fig: 2.1). This loading on the assembly results in an in-plane shear force on the core.
3
4 CHAPTER 2. REVIEW OF TEST METHODS & THEORY
Figure 2.1: ASTM C273 - Plate shear test
2.1.2 ASTM C393 - Test Method for Core Shear Prop- erties of Sandwich Constructions by Beam Flex- ure
ASTM C393 is a popular method used to evaluate the properties of core shear strength, core shear modulus and the bending stiffness in a sandwich composite. This method is popularly referred to as beam flexural test.
A rectangular sandwich beam specimen is loaded at one or more points while supported on two roller pins to achieve a bending normal moment (in the plane of the beam) in simply supported condition (fig:
2.2, 2.3).
The beam flexural test can be carried out in two different configura- tions as explained below.
Standard Configuration
The standard configuration refers to a three point loading configuration as shown in figure 2.2. This method is popularly known as the three point bending test.
The supports and loading bars are designed to facilitate free rotations
in the specimen at the loading and support points. Load is applied to the
CHAPTER 2. REVIEW OF TEST METHODS & THEORY 5
beam from the loading bar, mounted on a cross head, in a quasi-static manner while the load and the displacement are monitored.
Figure 2.2: ASTM C393 - Three point bending
Non-standard Configuration
The non-standard configuration refers to the four point loading config- uration as shown in figure 2.3. This method is popularly known as the four point bending test.
The specimen is supported at two points similar to the standard con- figuration, however the loading bars are designed to apply load at two different points along the beam. Load is applied in a quasi-static manner while the load and displacement are monitored.
2.1.3 Draw bending test
Draw bending tests are performed to understand the formability of sand- wich sheets. This method helps in evaluating the failure modes of the sandwich sheets.
The testing equipment consist of a die, a blank holder, and a punch.
A sandwich sheet is held between the blank holders and load is applied
in a quasi-static manner using the punch. The load and displacement
are monitored [1].
6 CHAPTER 2. REVIEW OF TEST METHODS & THEORY
Figure 2.3: ASTM C393 - Four point bending
Figure 2.4: Draw bending test
2.2 Conclusion of the review of test methods
ASTM C273 requires a separate core material in order to perform the test. With a porous-polymeric nature of the Hybrix core, it cannot be studied independent of its face sheets. This method is also sensitive to the bonding between the specimen and the steel plates, and the specimen surface preparation. Results are sensitive to the assembly alignment, loading eccentricities, and variation of the core thickness [2]. Due to these drawbacks, this method was not used.
Draw bending test method strongly reflects the use-case of Hybrix,
but it lacks a solid analytic foundation, such as the beam theory, in case
of the ASTM methods. This test method also requires special apparatus
to be successfully performed. There are elements in this method that are
difficult to measure, such as the frictional force between the punch and
CHAPTER 2. REVIEW OF TEST METHODS & THEORY 7
the specimen, and the contact surface, deeming this method difficult to perform and simulate. Hence, this method was not used.
In the four point bending test, the shear force is half of that observed in three point bending test, for a given displacement. The maximum achievable displacement of the specimen is less than that in the three point bending configuration. Hence, it is less likely to reflect the forming process. The distributed loading also causes it to be less susceptible to core damage. Hence, the standard configuration proves to be a better choice than the non-standard configuration for the testing of Hybrix.
The three point bending test method is simple when it comes to spec- imen construction, testing, and analysis as it involves one dimensional bending. In this method, the specimen is subjected to large deforma- tions similar to deformations observed in the forming process. Also, in this method, the failures occur due to stress concentrations and secondary stresses at the point of loading. The failure modes are influenced by the beam design, and they have been observed and studied for different beam designs [3]. For the aforementioned reasons, this method was chosen for testing Hybrix.
2.3 Digital Image Correlation
Digital Image Correlation (DIC) is a non-contact, optical method that employs tracking and image registration techniques for accurate 2D and 3D measurements of changes in images. DIC was used for the following reasons:
1. Allows for the measurement of full-field surface strain patterns 2. It is a non-contact optical method independent of sample geometry 3. Allows for the observation of deformations post-yielding of the spec-
imen material
The full-field surface strain and deformation data obtained from DIC can be used to observe local and global phenomena that can help in understanding the failure, and verify numerical simulations.
In order to perform DIC, a speckle pattern (fig: 2.5) is sprayed onto
the plane of deformation of the specimen. A camera setup is used to
capture time-series images of the speckle pattern as the specimen is being
deformed (fig: 2.6). The change in the speckle pattern in the time-series
8 CHAPTER 2. REVIEW OF TEST METHODS & THEORY
images is processed to obtain the full-field deformation using an image- processing software program [4].
Figure 2.5: Speckle pattern with white background and black spots (Src:
www.iopscience.iop.org)
2.4 Three point bending supplemented with DIC
Based on the above, a standard case of ASTM C393 (three point bending) supplemented with DIC was selected.
The simplicity of this method allows for an iterative execution while introducing necessary design changes to the method in each iteration.
Thus shifting the focus from execution to the method development and study of Hybrix core. This method can be supplemented by Digital Image Correlation to obtain full field displacement data that can be used to arrive at better conclusions. This facilitates the extraction of desired results for studying Hybrix.
The strong analytic background from beam theory can be used to improve the test method. The rationale for choosing three point bending over four point were based on beam theory:
1. Three point bending introduces a uniform shear force along the semi-span of the beam
2. The core is more susceptible to damage due to the concentrated load, at midspan, for a given displacement (fig: 2.7)
3. It produces large plastic deformations, and potentially failure modes,
that would be observed in Hybrix when subjected to forming loads
CHAPTER 2. REVIEW OF TEST METHODS & THEORY 9
Figure 2.6: DIC Setup (Src: www.researchgate.com)
2.5 Method Development Approach
An iterative approach was taken towards the development of the method.
A part of the method was performed at KTH Lightweight Structures
Laboratory. This consisted of the three point bending tests, processing of
data and extraction of the results. The method began with the execution
of three point bending tests, where the load displacement data and the
DIC data were collected. The collected data was then processed using
Matlab and DIC Instrument software to obtain the results. The extracted
results from the tests were then compared to the numerical simulation
results from Impetus AFEA AB. The model was fine-tuned to fit the test
data. The deviations of the model from the test were observed and these
observations were used to improve the test methods, and perform further
three point bending tests. This process was repeated until satisfactory
method and results were obtained. The specimens were investigated for
failures.
10 CHAPTER 2. REVIEW OF TEST METHODS & THEORY
Figure 2.7: Three point bending and four point bending configuration
comparison (Src: www.intechopen.com)
Chapter 3 Experiments
3.1 Materials
The specimens were prepared by Lamera AB with a patented procedure.
This procedure gave them a visual asymmetry at the bonding between two face sheets and the fibrous core. In order to differentiate between the two bonding surfaces, one of them has been referred to as the "glue-side".
All specimens were machined using water-jet tool, as per the dimen- sions in table 3.1. The obtained specimens were sanded using a P240 grit sandpaper to remove the burrs and unevenness on the edges. This was done so that there is a line contact between the pins and the specimen.
One of the edges was then sprayed with two coats of acrylic-based white spray paint, and speckled with a black spray paint. This, as discussed earlier in section 2.3, was the speckle pattern to be used with the DIC Instrumentation.
The nominal thickness measurements were made using vernier calipers.
Parameter Value
Face Sheet Material Aluminum
Length (L) 100 mm
Width (b) 20 mm
Face thickness (t
f) 0.5 mm Core thickness (t
c) 1.3 mm
Total thickness 2.3 +/- 0.03 mm Table 3.1: Specimen specification
11
12 CHAPTER 3. EXPERIMENTS
The core and face sheet thickness were obtained from Lamera AB, and were validated using the GOM software after scaling against a known length.
3.2 Apparatus
The apparatus consisted of the three point bending test rig (fig: 3.1), the Instron Universal Testing Machine (UTM, fig: 3.2), and the GOM DIC Instrumentation.
The three point bending test rig consisted of a loading pin, which was securely fastened to the moving cross-head on the Instron UTM. A milled steel block with V shaped grooves was used to harbor the support pins, and a central square groove in the block allowed for the movement of the deformed beam, as shown in figure 3.1. The V shaped grooves securely held the support pins in-place. The central groove allowed for large displacement of the punch [3]. The setup was designed to allow for the free rotation of the specimen at the loading and support points.
The support pins and loading punches of varying diameters were used to construct two different test setups.
A piece of graphing grid-line sheet, having a resolution of 1mm by 1mm, was pasted onto the steel block such that it lies into the imaging area of the DIC Camera setup. This graph was used for the scaling of the images captured using DIC Cameras.
Figure 3.1: Three point bending test rig
The Instron UTM consisted of a movable cross-head mounted with a
5kN load cell, a displacement sensor, and a rigid table below the cross
head. The Load transducer was positioned above the cross-head such
that the load from the loading pin and the displacement of the punch
is registered onto a software program running on a desktop computer.
CHAPTER 3. EXPERIMENTS 13
Figure 3.2: Instron model 5567
The process of loading, unloading, displacement and data recording was recorded into blocks of executables and saved as a method file onto the software program running the Instron machine.
The DIC Instrumentation consisted of a set of distance rings, a cal- ibration instrument, a set of two cameras mounted on an adjustable stand, and a desktop computer running GOM Correlate software (Src:
www.gom-correlate.com) for image acquisition and post-processing of the acquired data.
3.3 Procedure
The tests were performed at a room temperature of 23°C and a relative humidity of 50%.
A set of sample specimens were taken and their center along the length was measured and marked using a measuring scale. This was done so that the specimen is placed as symmetric as possible on the support pins such that the loading pin/punch lies exactly at the center of the specimen.
Twenty test specimens were tested on two different three point bending
14 CHAPTER 3. EXPERIMENTS
Parameter Value
Punch/Loading pin displacement - max 5mm
Punch/Loading pin displacement speed 0.5mm/min
DIC Measuring method & distance ring 2D with 10mm distance ring
DIC measuring distance 250mm
5DIC measuring frequency 1/3Hz & 1/2Hz Table 3.2: Summary of test parameters
Figure 3.3: Three point bending test setups used in the experiments rig setups (fig: 3.3). The span length is the distance between the centers of the two support pins. The span length, the size of the loading pin and the support pins varied between the two setups. In Setup I, the supporting pins’ diameter were 6mm each, the loading pin diameter was 10mm, and the span length was 20mm. In Setup II, the supporting pins’
diameter were the same as in Setup I, but the loading pin diameter and the span length were varied to 6.05mm and 17.5mm, respectively (fig:
3.3).
The tests began in Setup I configuration. A sample specimen was
placed on the two support pins. The cross-head was displaced to come in
contact with the specimen. A punch displacement speed of 0.5mm/min
was used to achieve quasi-static state [3]. The dynamic strain effects were
difficult to capture using DIC, hence quasi-static displacement speed was
opted. Initially the maximum punch displacement was set to 3mm, but
on observing that there was minimum damage to the core, it was decided
that a punch displacement of 5mm was to be used to achieve sufficiently
large displacement.
CHAPTER 3. EXPERIMENTS 15
Specimen
3PB# Setup Changes Introduced
1 - 4 Trial Runs
5, 6 I Flipped to glue-side down configuration
7, 8 Lubricated
9 Corrupt data file
10 - 13 Sampling frequency increased to 1/2Hz 14 - 20 II New span length and
punch diameter
Table 3.3: Design changes introduced to method
The DIC equipment allowed for two different measurement methods, namely, 3D imaging and 2D imaging. The 3D imaging allowed for the measurement of through-plane displacements. Here through-plane refers to the displacements along the z axis according to the co-ordinate system in figure 3.6. The 2D imaging neglected the through-plane displacements.
3D imaging was initially attempted, but 2D imaging was opted eventually because: it was time consuming to calibrate the fairly busy equipment;
and the margin of error for having 2D over 3D imaging was said to be of the order of 0.01mm according to GOM (Src: www.gom-correlate.com).
It was decided that a rectangular window of 100mm height and 20mm
width would be captured by the DIC camera. This will be referred to as
the measuring area (fig: 3.6). A speckled sample specimen was placed in
the three point bending rig as discussed earlier. A distance ring was used
to reduce the distance between the measuring area and the DIC camera
lens. The cameras were placed at a particular distance from the specimen
using a measuring scale, the distance was fine tuned using adjustment
rings on the stand. The illumination lights provided on the support stand
were positioned to enhance the imaging. A sample image was captured
and a quality check was run on the DIC software. Image sampling rate
is the number of images captured every second. Two different image
sampling rates of 1/3Hz and 1/2Hz were used in these experiments.
16 CHAPTER 3. EXPERIMENTS
Figure 3.4: Shear deformation of a beam with thick faces (Src: Analysis and Design of Structural Sandwich Panels [5])
3.3.1 Sandwich Beam Theory
According to section 2.6 in Analysis and Design of Structural Sandwich Panels [5], for a simply supported beam with central point load having antiplane core and thick faces: the local bending stiffness of the faces cannot be ignored as in the case of the thin face sandwich beams. Since the faces are thick and significantly more rigid than the core, the shear deformation of a beam with thick faces is as shown in figure 3.4. The core shear strain is represented by γ. This thesis extracts the strain data using DIC which is then used to fine tune the numerical simulations carried out by Impetus AFEA AB. The extraction is as described in section 3.3.2.
3.3.2 DIC Extraction of Rotation
The time-series displacement images were captured in the image acqui- sition and processing software GOM Correlate. The graphing sheet was used to scale the images to match the real world dimensions of the spec- imen by selecting two points on the graph and adding their length in SI units. The origin of the co-ordinate system used for all the geometric computations was the intersection of the load line from the punch and the mid-plane of the core. The horizontal axis to the right of the punch as seen in figure 3.6 was considered to be +x axis and the vertical axis above the mid-plane of the specimen was considered to be the +y axis.
A surface component was created to include the face sheet areas visi-
ble in the captured images. A surface component includes an area whose
displacement is completely traceable using the speckles in the time-series
images captured. It is seen as the green area in the figure 3.6. A sur-
CHAPTER 3. EXPERIMENTS 17
face component consists of several well resolved facet points. A facet point is a stochastic pattern structure that can be traced throughout the time-series images to gather the displacement information.
Figure 3.5: Illustration of rotational displacement
Seven sections were selected along the length of the beam. They were selected to be equidistant and symmetric, so that the information captured on these sections could be plotted to easily compare with the FE/numerical simulations and the other specimens’ results for verifica- tion. The sections were 2mm apart from each other.
The thickness of the face sheet was known from the data obtained from Lamera AB. Using this data, the facet points close to the midpoint of the face sheet could be located. These facet points are represented by A and B for the top face sheet, and C for the bottom face sheet in figure 3.5.
A geometric angle
6BAC could now be constructed using the three facet points. Since A, B and C are located on the relatively stiff face sheet, they are nearly fixed throughout the test. The displacement of these points relative to each other, during the bending test, allows for the extraction of strain data for the core. This is given by the difference in
6BAC’ and
6
BAC, represented by ∆θ. This angle was extracted using the angle tool
in GOM Correlate at a displacement of 2mm, 4mm and 5mm (fig: 3.10)
at the seven sections. The displacements of 2mm and 5mm were selected
because the displacement of 2mm happens to be within the elastic limit
and 5mm was the maximum displacement of the punch when the beam
is subjected to three point bending. 4mm was also selected because a
18 CHAPTER 3. EXPERIMENTS
slight rotation of the pins was seen, at this displacement, in some of the tests. The shear strain values obtained from the geometric angles were extracted in an excel file and plotted using Matlab.
Figure 3.6: Construction in GOM Correlate for rotations
3.3.3 DIC Extraction of Displacement
Facet point I and J were created at the midpoint of the top and bottom face sheet at each of the seven cross sections similar to points A and C in the previous section. A geometric line IJ could then be constructed. The displacements ∆x and ∆y could now be computed along the x and y axes, respectively, using the line IJ’ post deformation as shown in figure 3.8.
The displacement associated with shear deformation and the compression
of the core was obtained using the two facet points and the extensometer
tool in GOM Correlate. The displacements were extracted at 2mm, 4mm
and 5mm of punch displacement and plotted using Matlab.
CHAPTER 3. EXPERIMENTS 19
Figure 3.7: Rotational angles at maximum punch displacement
Figure 3.8: Illustration of displacement
20 CHAPTER 3. EXPERIMENTS
Figure 3.9: Construction in GOM Correlate for rotational displacements
Figure 3.10: Local displacements at maximum punch displacement
Chapter 4 Results
4.1 Observations
The visual asymmetry at the bonding between the two face sheets and the fibrous core of Hybrix was investigated (sec: 3.1). It was suspected that this asymmetry could result in face material wrinkling or local failures of the face sheet. It was observed that the bonding between one of the face sheet surfaces and the core appeared to contain more glue than the bonding between the other face sheet surface and the core. In order to differentiate between the two bonding surfaces, the surface of the specimen that appeared to contain more glue has been referred to as glue side. Tests were conducted in two different positions of the specimen. In one case, referred to as glue side up, the glue side face was positioned upwards such that the punch applies the load on this surface. In the second case the glue side face was positioned downwards and this was referred to as glue side down position. The load displacement data of the specimen in the two different orientations was investigated. Since, there was no difference in the load-displacement data (fig: 4.1), the asymmetry due to these orientations was ruled out.
Due to the longer span length and punch diameter in Setup I, at large displacement of 5mm, there was a slight rolling of the pins. This was sus- pected to be caused by friction. Specimen were tested by applying a layer of PTFE spray lubricant on the face sheets, but the load-displacement plots did not show any significant differences (fig: 4.2). On consulting with Impetus AFEA AB, it was observed that there was asymmetry in the results extracted from Setup I due to small offset in the V grooves of the steel block. This made it difficult to match the results of the numeri-
21
22 CHAPTER 4. RESULTS
Figure 4.1: Load-displacement plot comparing the loading of specimen with the glue side down and glue side up positions (load values are nor- malized)
cal simulations. It was also observed that the radius of curvature in Setup I, with a punch diameter of 10mm, was too high to introduce any shear failure. Due to these problems with Setup I, it was decided to reduce the span length and the punch diameter to try to induce shear failure in the material specimen. The span length was changed to 17.5mm and the punch diameter to 6.05mm in Setup II using a different three point bending rig.
The punch displacement speed was set to 0.5mm/min and the image acquisition frequency was set at 1/3Hz giving us a resolution of 0.025mm in the images captured in Setup I. This means that between any two consecutive pictures, captured by the DIC Camera, the specimen was displaced by 0.025mm. The frequency was increased to 1/2Hz to give a resolution of 0.0167mm in Setup II. All the post-processing results were compiled for specimen numbered from 14 up to 20 using Setup II (table:
3.3).
In order to understand the extracted results and compare it with the
model developed by Impetus AFEA AB, the rotations and displacements
for specimen 14 and 16, were plotted against each other. The strain
CHAPTER 4. RESULTS 23
Figure 4.2: Load-displacement plot comparing lubricated specimen with the non-lubricated specimen (load values are normalized)
obtained in the three point bending tests was higher than the strain obtained in FE Simulations. For example, for a punch displacement of 5mm in the three point bending tests, the average strain (rotation angle γ) was obtained to be about 28° at a section 2.5mm from the punch center (fig: 4.5). The shear strain at the same point in the FE Simulation was found to be 20°.
Asymmetry was observed in the displacements along the +x and -x axes as seen in figures 4.6, 4.7, and 4.8.
There was significant compression effect observed at large displace- ments, especially below the loading line as observed in figures 4.10 and 4.11.
4.2 Summary
The core of the material model created by Impetus AFEA AB was more rigid compared to the results obtained from the three point bending tests.
The model was corrected using the strain values obtained through the
tests.
24 CHAPTER 4. RESULTS
Figure 4.3: Rotation angle γ along the beam length (x axis), at 2mm punch displacement
Figure 4.4: Rotation angle γ along the beam length (x axis), at 4mm
punch displacement
CHAPTER 4. RESULTS 25
Figure 4.5: Rotation angle γ along the beam length (x axis), at 5mm punch displacement - max displacement
Figure 4.6: Displacement ∆x along the beam length (x axis), at 2mm
punch displacement
26 CHAPTER 4. RESULTS
Figure 4.7: Displacement ∆x along the beam length (x axis), at 4mm punch displacement
Figure 4.8: Displacement ∆x along the beam length (x axis), at 5mm
punch displacement
CHAPTER 4. RESULTS 27
Figure 4.9: Displacement ∆y plotted against the beam length (x axis), at 2mm punch displacement
Figure 4.10: Displacement ∆y plotted against the beam length (x axis),
at 4mm punch displacement
28 CHAPTER 4. RESULTS
Figure 4.11: Displacement ∆y plotted against the beam length (x axis), at 5mm punch displacement
There was significant asymmetry in the displacements between spec- imens 14 and 16. This could be attributed to the accuracy of the test setup and the asymmetry in the material.
The difference in displacement ∆x is larger than displacement ∆y for specimens 14 and 16 as seen in figures 4.6 to 4.11. This difference increases with the increase in the punch displacement. This supports the idea that the specimen is likely to fail in shear when subjected to larger displacements.
The specimens were sanded to remove the paint from the speckle pattern and carefully observed to see some form of core shear failure.
The bending rig setup parameters according to Setup II could not induce
shear failure but proved to be significantly better than the parameters in
Setup I. The method needs to be refined to observe shear failure without
inducing other modes of failure.
Chapter 5
Conclusion and Future Work
Several practical challenges were addressed in performing the tests. These include the spraying of the specimens to obtain a uniform speckle pattern, calibration and setup of the DIC Imaging Instrumentation, the friction and the movement of the pins, the symmetry of the three point bending rig setup, to name a few. Certain problems such as the friction and the movement of the pins, the speckle pattern, the calibration and setup of DIC Imaging Instruments were successfully addressed, but the problems of the asymmetry of the setup and the material could not be addressed due to time constraints of the thesis.
The stiffness and the deformation data obtained from the tests was used to fine-tune the FE model developed by Impetus AFEA AB. The fine-tuned model results significantly matched the results from the sub- sequent three point bending tests.
Failure was observed, but it was difficult to attribute it as a core shear failure. Because of the fibrous nature of the Hybrix core it was difficult to pin point the location of core shear failure.
A collapse mechanism mapping diagram such as the one plotted by B.
P. Russel and V.S. Deshpande [6] could be obtained from the numerical methods. Basically, a number of collapse mechanisms could be predicted using the FE model with the specimen design variables parametrized.
These collapse mechanisms could then be verified through experiments.
This could give us more insight into the design factors that influence core shear failure.
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