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Assessment on the methods to determine the fibre misalignment angle
The above presented methods to determine the fibre misalignment angles are characterised by the fact that they involve complex techniques that are specified on low volume areas requiring a lot of experimental technical resources, as well as accessible image analysis software.
In the scope of this study, Yurgartis’s method was chosen to determine the in- and outof plane fibre misalignment angles, because it was immediately applicable, the required equipment (sectioning and polishing machines, optical microscope, analysing software) was available, and effort and benefit fitted in the time schedule of the present research work. In the scope of this study, a protocol containing five steps to determine the fibre misalignment angles was established. These steps will be presented in Sec. 3.3.1 to Sec. 3.3.5. The present study describes hence an original study on the fibre misalignment angle determination of seven material series consisting of different IM carbon fibres and epoxy resins, frequently used in the nautical sector, using Yurgartis’s method. Specimens are sectioned along the thickness and width to determine the in- and out-of-plane fibre misalignment angles from at least 1000 ellipses. A further distinction is made on the investigated zones. In- and out-of-plane fibre misalignment angles are determined on the mould and sealant sides in order to investigate the impact of the fabrication process. Further, a discussion on the choice of the fibre diameter, which is necessary to determine the fibre misalignment angles, will be made in Sec. 3.2.3. Lastly, the creation of cartographies showing the spatial fibre angle distribution completes the study on the fibre misalignment determination of the seven series and provides information on how the in- and out-of-plane fibre misalignment angles are applicable in the analytical solutions of Budiansky & Fleck [1993] and Grandidier et al. [2012].
Presentation of the material for fibre misalignment angle determination
The present studies on the misalignment angle determination, as well as on the tensile and 4PB tests, which will be presented in Sec. 4.1, were carried out as part of a collaborative research project with the racing team MACIF, and the design office Gsea Design. Their objective was, on the one hand, to design a new version for their hydrofoils, and on the other hand, to evaluate their calculation methods. For this purpose, 7 different prepreg materials were selected which form the basis of the following investigations. The misalignment angles of those seven prepregs were determined using Yurgartis’ method. The prepregs, whose main characteristics are listed in Tab. 3.1, were all made of IM carbon fibres and epoxy resins whose glass transition temperatures were at 120 C. They were manufactured to panels with a [+45/ 09/-45/011/-45/09/+45] stacking sequence by CDK Technologies in Lorient and cut into several specimens by water jet for 4PB testing after autoclave curing. More information concerning the fabrication process of these specimens will be given in Sec. 4.1.
The coordinate system in Fig. 3.1 will be used in the following to define the in- and outof- plane directions of (mis-)aligned fibres. In the following Sec. 3.2, the implementation of Yurgartis’ method to determine the fibre misalignment angles of the presented specimens will be demonstrated.
Determination of the misalignment angles in in- and out-of-plane direction
The estimation of the fibre misalignment angles in out-of-plane (in-plane) direction required the knowledge of three parameters: the length of the major axes of the ellipses ai (a0 i), and the fibre diameter to calculate the angles between the sectioning plane and the axes of the (mis-)aligned fibres !i (!0i), as well as the plane cut angle PC (PC) to determine the out-of-plane (in-plane) fibre misalignment angles i (i). In Yurgartis [1987], the fibre diameter was determined through specimen sectioning perpendicularly to the fibre direction and by calculating the mean value of the overall fibres diameters d90,mean on the section surface. Hence, Yurgartis found a mean diameter of 6.93 μm with a SD of 0.31 μm measured from 742 XAS carbon fibres. The ai (a0 i) data
were measured by a microcomputer program, and the sectioning angle PC (PC) was defined as the mean value !i,mean (!0 i,mean) of the overall !i (!0i ). The same approach was applied in the scope of this study, with the following supplement.
On the one hand, the fibre diameter was determined as it was done in the research work of Yurgartis [1987] (perpendicularly specimen sectioning and fibre diameter mean value determination d90,mean). On the other hand, the fibre diameter was referred to the minor axes lengths bi (b0 i) of the ellipses or to the mean value of all minor axes lengths bi,mean (b0 i,mean). As last option, the fibre diameter dDS was taken directly from the data sheet. The choice of determining the fibre misalignment angles from four different diameter sources was done, since Yurgartis’ method requires an additional step, specimen sectioning at 90, whereas the fibre diameters are directly indicated on the data sheet or can, when the fibre diameter is set equal to the minor axes, be determined individually for each ellipse and from this the resulting mean value when using the image processing software ImageJ.Thus, within this study, four different fibre diameters d90,mean, bi (b0 i), bi,mean b0 i,mean) and dDS were applied to estimate the fibre misalignment angles i (i). The major axes of the ellipses ai (a0 i) were also determined using ImageJ. This part will be presented in more detail in Sec. 3.3.4.
Table of contents :
Part I Introduction
1 Thesis context and problem description
1.1 The compressive strength Xc and the interlaminar tensile strength (ILTS) in hydrofoil design
1.2 Motivation and objective of Part II
1.3 Motivation and objective of Part III
Part II The Compressive Strength XC
2 Role of 0 in the design of laminate composites with regard to Xc
2.1 Significance of the misalignment angle 0 in the determination of the compressive strength Xc
2.2 Source of fibre misalignment in composite materials
2.2.1 Definition of fibre misalignment and fibre waviness
2.2.2 Review of the origin of fibre misalignment, fibre waviness and other material defects related to the manufacturing process .
2.2.3 Consequences of fibre misalignment and fibre waviness on the mechanical properties of the composites
2.2.4 Composite materials in the marine sector
2.3 Review on methods for fibre misalignment and fibre waviness determination
2.3.1 Ultrasound scanning method
2.3.2 (Micro) X-ray computed technology
2.3.3 Structure tensor method
2.3.4 Direct tracking method
2.3.5 Fourier transformation method
2.3.6 Hough transformation method
2.3.7 Stereological method (Yurgartis [1987]’ method)
2.3.8 The Multiple field image analysis (MFIA) method
2.3.9 Other methods
2.3.10 Assessment on the methods to determine the fibre misalignment angle
3 Determination of the in- and out-of-plane fibre misalignment angles using Yurgartis’ method
3.1 Presentation of the material for fibre misalignment angle determination
3.2 Introduction to Yurgartis’ method
3.2.1 Definition of the in- and out-of-plane fibre misalignment orientations
3.2.2 Definition of the sectioning directions
3.2.3 Determination of the misalignment angles in in- and out-of-plane direction
3.3 Practical implementation of Yurgartis’ method
3.3.1 Sectioning of specimens along the width and the thickness
3.3.2 Resin coating and polishing of specimens
3.3.3 Image recording
3.3.4 Image post-processing with ImageJ
3.3.5 Determination of the in- and out-of plane misalignment angles
3.4 Results of fibre misalignment determination
3.4.1 In- and out-of- plane fibre misalignments of mould and sealant side for series 3 to 7 from four different fibre diameter sources
3.5 Conclusion
4 Confrontation of two experimental methods to measure or estimate the compressive strengths
4.1 Four point bending (4PB) and tensile tests of ±45 laminates to determine XEXP c and XANA c
4.1.1 ±45 tensile specimens and test procedure
4.1.2 Analysis of tensile tests on ±45 specimens
4.1.3 4PB test specimens and test procedure
4.1.4 Analysis of 4PB tests
4.2 Data for the calculation of the compressive strength XANA c .
4.3 Creation of cartographies of fibre alignment distribution
4.4 Confrontation of XANA c and XEXP c , cartographies of fibre alignment distribution
4.5 Analysis and discussion on XEXP c /XANA c -i, XEXP c /XANA c -i diagrams with regard to fibre alignment distribution
4.5.1 Categories for classification of cartographies . . .
4.5.2 Questioning procedure
4.5.3 Series 5, out-of-plane fibre misalignment (i), mould/sealant sides
4.5.4 Series 5, in-plane fibre misalignment (i), mould/sealant sides .
4.5.5 Series 3, out-of-plane fibre misalignment (i), mould/sealant sides
4.5.6 Series 3, in-plane fibre misalignment (i), mould/sealant sides
4.6 Conclusion on the observations
4.7 Synthesis about the applied method and perspectives
Part III The InterLaminar Tensile Strength (ILTS)
5 Bibliographic review on the Interlaminar tensile strength (ILTS)
5.1 Out-of-plane strength 33 determination with regard to the specimen production
5.2 Classical hand lay-up and Automated fibre placement (AFP) technology .
6 Setting up of the analytical, the experimental and the numerical tool
6.1 Presentation of the analytical tool ANA
6.1.1 Validation of the analytical tool
6.2 Presentation of the experimental tool EXP
6.2.1 Design of the test setup
6.2.1.1 Geometrical and mechanical design of 4PB test setup
6.2.1.2 Technological design of 4PB test setup .
6.2.2 Experimental test setup and instrumentation
6.3 Presentation of the numerical tool NUM
6.3.1 Validation of the numerical tool
6.3.2 Sensibility studies on the influence of the mesh and the material choice of the loading bars on the numerical results
6.3.2.1 Sensibility study on the influence of the mesh on the numerical results
6.3.2.2 Sensibility study on the influence of the material chose for the loading bars on the numerical results .
6.4 Summary of the present chapter 6
7 4PB study on L-beam specimens manufactured by AFP technology
7.1 Material properties and fabrication process of AFP L-beam specimens .
7.1.1 Stacking generation and autoclave curing
7.2 Test realisation of AFP L-beam specimens
7.3 Results of AFP L-beam specimens tested in 4PB
7.3.1 Experimental results of AFP L-beam specimens tested in 4PB
7.3.1.1 Reproducibility and stiffness
7.3.1.2 First failure cracks
7.3.1.3 Acoustic emissions (AE)
7.3.1.4 Digital image correlation (DIC) images and strain gauge
7.3.2 FE results of AFP L-beam specimens tested in 4PB
7.3.2.1 Non-linearity of load-displacement diagrams
7.3.2.2 FE calculations on AFP L-beam specimens .
7.3.3 Analytical results of AFP L-beam specimens tested in 4PB .
7.3.3.1 Confrontation of ILTSKedward et al. and ILTSLekhnitskii to S33
7.3.3.2 Normalized stresses Sij , 33,Kedw. and 33,Lekhn. along the specimen thickness and width
7.3.3.3 Analytically calculated radial position rmax .
7.4 Summary of AFP specimens tested in 4PB
8 4PB study on L-beam specimens manufactured by traditional hand lay-up (MAN)
8.1 Material properties of Manually laid-up (MAN) L-beam specimens
8.2 Fabrication process of MAN L-beam specimens
8.3 Test realisation of MAN L-beam specimens
8.4 Results of MAN L-beam specimens tested in 4PB
8.4.1 Experimental results of MAN L-beam specimens tested in 4PB
8.4.1.1 Reproducibility and stiffness
8.4.1.2 First failure cracks
8.4.1.3 Acoustic emissions (AE)
8.4.1.4 DIC images and strain gauge
8.4.2 FE results of MAN L-beam specimens tested in 4PB
8.4.3 Analytical results of MAN L-beam specimens tested in 4PB
8.4.3.1 Confrontation of ILTSKedward et al. and ILTSLekhnitskii to S33
8.4.3.2 Normalized stresses Sij , 33,Kedw. and 33,Lekhn. along the
specimen thickness and width
8.4.3.3 Analytically calculated radial position rmax .
8.5 Summary of MAN L-beam specimens tested in 4PB
9 Confrontation of results of AFP and MAN L-beam specimens tested in 4PB
9.1 Test reproducibility
9.2 Metrology, CBS and stiffness
9.2.1 Influence of specimen metrology on the Interlaminar tensile strength
9.2.2 Confrontation of stiffnesses of AFP and MAN L-beam specimens
9.2.3 Impact of corrected i calculation on the ILTS
9.3 First failure crack locations
9.3.1 Analytically estimated first first failure crack locations
9.3.2 Numerically calculated first failure crack locations
9.3.3 Experimentally observed first failure crack locations
9.4 Load at failure and ILTS
9.5 Macroscopic defects
9.6 Investigation of the cross sections of AFP and MAN L-beam specimens
9.7 Influence of the manufacturing processes on the ILTS .
9.8 Conclusion on the present study
Part IV Summary and Perspectives
A.1 Misalignment angle results soural andces of series 4, 6 and 7 determined
from different diameter
B.2 Design drawing of 4PB testing setup
B.3 Results AFP L-beam specimens
B.3.1 Crack localisations of AFP L-beam specimens tested in 4PB .
B.3.2 EXP/NUM correlation of load-displacement diagrams of AFP Lbeam specimens
B.3.3 Normalized stresses Sij as a function of the normalized thickness/width for AFP L-beam specimens
B.3.4 ANA, EXP and NUM results of AFP L-beam specimens tested in 4PB
B.4 Results MAN L-beam specimens
B.4.1 Crack localisations of MAN L-beam specimens tested in 4PB .
B.4.2 EXP/NUM correlation of load-displacement diagrams of MAN Lbeam specimens
B.4.3 Normalized stresses Sij as a function of the normalized thickness/width for MAN L-beam specimens
B.4.4 ANA, EXP and NUM results of MAN L-beam specimens tested in 4PB
Bibliography
