Study of adhesively bonded repairs in aircraft CFRP primary structures

Study of adhesively bonded repairs in aircraft CFRP primary

structures

Mémoire

Aris Khechen

Maîtrise en génie mécanique

Maître ès Sciences (M.Sc.)

Québec, Canada

Résumé

Afin de développer un protocole d’essai standardisé et des outils analytiques facilitant la conception de réparations collées en biseau pour des structures composites aéronautiques primaires, le présent mémoire se concentre sur la caractérisation et la modélisation des performances de joints collés en composite de type lisse-escalier soumis à un effort de traction uni-axiale. Dans un premier temps, deux matériaux composites tissés, une toile (PW) et un satin (8-HS) pré-imprégnés de type plastique à renfort de fibre de carbone ont été testés en traction uni-axiale à température ambiante sec (TAS) et à température élevée sec (TES). Les données issues de cette caractérisation ont permis la modélisation numérique des réparations. Dans un deuxième temps, des réparations de type lisse-escalier ont été fabriquées sur des stratifiés en utilisant les matériaux composites PW et 8-HS en suivant la même séquence de plis quasi-isotrope ([+45°/0°/-45°/90°]2s) pour le parent et pour la

réparation. Le film adhésif utilisé est le Cytec FM300-2M. L’effet des conditions environnementales et de l’angle de biseau (3°, 5.5° et 7.5°) sur les performances des réparations a été étudié. Les résultats des essais de traction ont révélé que l’angle de biseau a un impact significatif sur le mode de rupture de la structure réparée. Alors que la rupture s’est produite dans le composite pour les réparations avec un angle de biseau de 3°, une rupture en cisaillement de type cohésive a été observée pour les réparations pour les biseaux à 5.5° et 7.5°. Ce changement de mode de rupture a été retrouvé pour les deux conditions environnementales (TAS et TES). Comparativement au stratifié intact, une baisse non-significative de la rigidité a été notée pour tous les angles de biseau. Toutefois, l’augmentation de l’angle de biseau a conduit à une baisse significative de la restitution de la contrainte à la rupture comparativement à celle du stratifié d’origine, indiquant l’importance de l’angle de biseau sur l’intégrité de la structure des réparations adhésives de type lisse-escalier. Les essais de tractions à TES suggèrent qu’il n’y a qu’une très faible diminution de la rigidité et de la contrainte à la rupture pour les réparations à TES comparativement à TAS. Finalement, des analyses par éléments finis 2D dans l’épaisseur ont été conduites en utilisant ABAQUS Standard et Explicit. Une analyse élastique a tout d’abord été menée afin de prédire les distributions des contraintes de pelage et de cisaillement normalisées au milieu de l’adhésif, le long de la ligne adhésive, pour trois différentes configurations géométriques de jointure (lisse-lisse, lisse-escalier, escalier-escalier). Contrairement aux distributions de contraintes uniformes observées le long de la ligne adhésive de la configuration lisse-lisse, de forts et fréquents pics de contraintes de

pelage et de cisaillement ont été observés pour les deux autres configurations. Ces observations ont mené à conclure que la modélisation d’un joint de réparation collé en biseau doit être conduite avec précaution. Émettre l’hypothèse que la surface adhésive du stratifié patch est lisse (i.e.: configuration lisse) alors qu’elle est en fait de type lisse-escalier implique de ne pas prendre en compte les pics de contraintes causés par les irrégularités géométriques de la surface adhésive du stratifié. Cela peut mener à la surestimation de la contrainte à la rupture de la réparation. Pour finir, une analyse élastique-plastique a été conduite en utilisant les modèles de plasticité et d’endommagement par cisaillement déjà implémentés dans ABAQUS. Ces modèles de plasticité et d’endommagement ont été utilisés pour le film adhésif seulement. Le matériau composite a été supposé linéaire élastique jusqu’à la rupture. Le critère des déformations maximales a été utilisé pour prédire la rupture du premier pli dans le composite. Les prédictions obtenues avec le modèle et les résultats expérimentaux ont montré de très bonnes corrélations.

Abstract

This master’s degree thesis focuses on testing and modeling the bonded scarf-stepped composite joint performance under uniaxial tensile loading as part of the effort to develop testing protocols and analytical tools for the design of scarf bonded repair for primary aeronautical composite structures. First, plain weave (PW) and 8-harness satin (8-HS) carbon fiber-reinforced plastic (CFRP) pre-preg composite materials were tested under uniaxial tensile loading at room temperature dry (RTD) and elevated temperature dry (ETD) conditions. The gathered characterization data was later used for the numerical modeling of the repairs. Furthermore, smoothed parent laminate bonding surface and stepped patch laminate bonding surface (scarf-stepped repairs were performed using both PW and 8-HS composite materials with matching quasi-isotropic ([+45°/0°/-45°/90°]2s) ply stacking

sequence between the parent and the patch. The adhesive film that was used is the Cytec FM300-2M. The effects of environmental conditions and the influence of the scarf angle (i.e. 3˚, 5.5° and 7.5˚) on the performance of the bonded repairs were investigated. The tensile test results revealed that the scarf angle has a significant impact on the failure mode of the repaired composite part. While substrate failure occurred with a 3˚ scarf angle, cohesive shear failure was observed for the 5.5° and 7.5˚ angles. This change in failure mode is consistent both at RTD and ETD. When compared with the pristine laminate, an insignificant drop in stiffness was found regardless of the scarf angle. Although, increasing the scarf angle led to a significant drop in strength restitution in comparison with the pristine laminate. This indicates the importance of the scarf angle on the structural integrity of a scarf-step bonded repair. The tensile test results in ETD conditions suggest a slight decrease in stiffness and strength for both materials at ETD. Eventually, 2D through-thickness finite-element analyses were also conducted using both ABAQUS Standard and Explicit. An elastic analysis was first performed to predict the distribution of normalized shear and peel stresses in the middle of the adhesive along the bondline for three different joint geometries (scarf-scarf, scarf-step and step-step). As opposed to the uniform stress distributions found along the bondline of the scarf-scarf configuration, high and frequent peaks of peal and shear stresses were found for both scarf-step and step-step configurations. These observations led to the conclusion that one must be particularly cautious when modeling a scarf joint bonded repair. Assuming that the patch laminate bonding surface is smoothed (i.e., scarf-scarf configuration) while it is actually stepped (i.e., scarf-step configuration) can

lead to overestimating the overall repair strength since the high stress peaks caused by the geometric irregularities of the stepped patch laminate bonding surface would then be ignored. Furthermore, an elastic-plastic analysis was conducted using the already implemented plasticity and shear damage models in ABAQUS. These plasticity and damage models were used for the adhesive film only. The composite material was supposed to behave linear-elastically up to failure. The maximum strain criterion was used to predict the first ply failure in the composite. The predictions obtained with the model correlated very well with the experimental results.

Table of content

Résumé iii

Abstract v

Table of content vii

List of tables x

List of figures xii

Acknowledgments xv

Introduction 1

Characterization and numerical modeling of the composite materials

Characterization and numerical modeling of the repairs mechanical behavior 40

Conclusion and future work 79

List of tables

Table 2.1: Composite materials general properties. ... 17

Table 2.2: Characterization test matrix for the CYCOM 5320 T650 3k PW. ... 17

Table 2.3: Characterization test matrix for the CYCOM 5320 T650 3k 8HS... 18

Table 2.4: In-plane axial properties for the PW at RTD. ... 22

Table 2.5: In-plane transverse properties for the PW at RTD and ETD. ... 24

Table 2.6: In-plane shear properties for the PW at RTD. ... 26

Table 2.7: In-plane axial properties for the 8HS at RTD. ... 28

Table 2.8: In-plane transverse properties for the 8HS at RTD and ETD. ... 30

Table 2.9: In-plane shear properties for the 8HS at RTD. ... 32

Table 2.10: Summary of experimental results for the PW material. ... 33

Table 2.11: Summary of experimental results for the 8HS material. ... 34

Table 2.12: Elastic properties of a PW CFRP at RTD. ... 35

Table 2.13: Effective elastic modulus prediction for a quasi-isotropic laminate using different modeling approaches... 39

Table 3.1: Mechanical properties of the 0.25mm-thick CYTEC FM300-2M adhesive film at RTD and ETD. ... 42

Table 3.2: Characterization test matrix for the CYCOM 5320 T650 3k PW repairs. ... 42

Table 3.3: Characterization test matrix for the CYCOM 5320 T650 3k 8HS repairs. . 43

Table 3.4: Axial properties for the 3° scarf angle PW repair at RTD and ETD. ... 47

Table 3.5: Axial properties for the 7.5° scarf angle PW repair at RTD and ETD. ... 49

Table 3.6: Axial properties for the 3° scarf angle 8HS repair at RTD and ETD. ... 52

Table 3.7: Axial properties for the 6° scarf angle 8HS repair at RTD and ETD. ... 54

Table 3.8: Summary of experimental results for the 3° scarf angle PW repairs. ... 55

Table 3.9: Summary of experimental results for the 7.5° scarf angle PW repairs. ... 55

Table 3.10: Summary of experimental results for the 3° scarf angle 8HS repairs. ... 55

Table 3.11: Summary of experimental results for the 6° scarf angle 8HS repairs. ... 56

Table 3.12: Elastic properties of the 0.25 mm-thick CYTEC film adhesive at RTD and ETD. ... 59

Table 3.13: Stiffness prediction of repaired quasi-isotropic laminates using different bonded joint configurations. ... 60

Table 3.14: Plasticity data implemented in ABAQUS/Explicit for the adhesive film at RTD and ETD. ... 66 Table 3.15: Shear failure model data implemented in ABAQUS/Explicit for the

adhesive film at RTD and ETD. ... 67 Table 3.16: Summary of explicit elastic-plastic analysis results for 3˚ and 7.5˚ scarf angle quasi-isotropic PW repairs for C1, C2 and C3 geometric configurations at RTD. ... 69 Table 3.17: Summary of experimental and numerical results for the 3˚ scarf angle quasi-isotropic scarf-step (C2) PW repair specimens tested under uniaxial tension at RTD and ETD. ... 69 Table 3.18: Summary of experimental and numerical results for the 7.5˚ scarf angle quasi-isotropic scarf-step (C2) PW repair specimens tested under uniaxial tension at RTD and ETD. ... 72 Table 3.19: Summary of experimental and numerical results for the 3˚ scarf angle quasi-isotropic scarf-step (C2) 8HS repair specimens tested under uniaxial tension at RTD and ETD. ... 74 Table 3.20: Summary of experimental and numerical results for the 6˚ scarf angle quasi-isotropic scarf-step (C2) 8HS repair specimens tested under uniaxial tension at RTD and ETD. ... 76

List of figures

Figure 1.1 : Representation of different joint geometries [2] ... 2

Figure 1.2 : Lap joint representation – Volkersen/shear-lag model ... 7

Figure 1.3 : Volkersen’s adhesive shear stress distribution ... 8

Figure 1.4 : Lap joint representation – Goland and Reissner model ... 8

Figure 1.5 : Goland and Reissner's adhesive peel and shear stress distributions ... 9

Figure 2.1: Fiber architecture pattern for a) a PW fabric and b) an 8HS fabric. ... 17

Figure 2.2: Debulk time and cure cycle of the composite material. ... 19

Figure 2.3: Axial stress vs. axial strain for the PW composite material tested under uniaxial tension at RTD. ... 22

Figure 2.4: Picture of the PW failed specimens for the in-plane axial test at RTD. ... 23

Figure 2.5: Transverse stress vs. transverse strain for the PW composite material tested under uniaxial tension at RTD. ... 24

Figure 2.6: Transverse stress vs. transverse strain for the PW composite material tested under uniaxial tension at ETD. ... 24

Figure 2.7: Picture of the PW failed specimens for the in-plane transverse test at RTD. ... 25

Figure 2.8: Picture of the PW failed specimens for the in-plane transverse test at ETD. ... 25

Figure 2.9: Shear stress vs. shear strain for the PW composite material tested under uniaxial tension at RTD. ... 26

Figure 2.10: Picture of the PW failed specimens for the in-plane shear test at RTD. . 27

Figure 2.11: Axial stress vs. axial strain for the 8HS composite material tested under uniaxial tension at RTD. ... 28

Figure 2.12: Picture of the 8HS failed specimens for the in-plane axial test at RTD. . 29

Figure 2.13: Transverse stress vs. transverse strain for the 8HS composite material tested under uniaxial tension at RTD. ... 30

Figure 2.14: Transverse stress vs. transverse strain for the 8HS composite material tested under uniaxial tension at ETD. ... 30

Figure 2.15: Picture of the 8HS failed specimens for the in-plane transverse test at RTD. ... 31

Figure 2.16: Picture of the 8HS failed specimens for the in-plane transverse test at ETD. ... 31

Figure 2.17: Shear stress vs. shear strain for the 8HS composite material tested

under uniaxial tension at RTD. ... 32

Figure 2.18: Picture of the 8HS failed specimens for the in-plane shear test at RTD. 33 Figure 2.19: Stiffness matrices swapping procedure according to the modeling convention ... 37

Figure 2.20: Representation of the 16-plies quasi-isotropic laminate. ... 38

Figure 3.1: Shear stress vs. shear strain for the 0.25mm-thick CYTEC FM300-2M epoxy adhesive film. ... 42

Figure 3.2: Uncured laminate after hand-laying the plies. ... 44

Figure 3.3: Parent laminate after sanding. ... 45

Figure 3.4: Assembly of the parent, the adhesive and the patch before curing. ... 45

Figure 3.5: 2D trough-the-thickness representation of the bonded repair. ... 46

Figure 3.6: Axial stress vs. axial strain for 3° scarf angle PW repair specimens tested under uniaxial tension at RTD ... 47

Figure 3.7: Axial stress vs. axial strain for 3° scarf angle PW repair specimens tested under uniaxial tension at ETD. ... 48

Figure 3.8: Picture of 3˚ scarf angle PW repair specimens at RTD. ... 48

Figure 3.9: Picture of 3˚ scarf angle PW repair specimens at ETD. ... 48

Figure 3.10: Axial stress vs. axial strain for 7.5° scarf angle PW repair specimens tested under uniaxial tension at RTD. ... 50

Figure 3.11: Axial stress vs. axial strain for 7.5° scarf angle PW repair specimens tested under uniaxial tension at ETD. ... 50

Figure 3.12: Picture of 7.5˚scarf angle PW repair specimens at RTD (in-plane view). 51 Figure 3.13: Axial stress vs. axial strain for 3° scarf angle 8HS repair specimens tested under uniaxial tension at RTD. ... 52

Figure 3.14: Axial stress vs. axial strain for 3° scarf angle 8HS repair specimens tested under uniaxial tension at RTD. ... 52

Figure 3.15: Picture of 3˚ scarf angle 8HS repair specimens at RTD. ... 53

Figure 3.16: Picture of 3˚ scarf angle 8HS repair specimens at ETD. ... 53

Figure 3.17: Axial stress vs. axial strain for 6° scarf angle 8HS repair specimens tested under uniaxial tension at RTD. ... 54

Figure 3.18: Axial stress vs. axial strain for 6° scarf angle 8HS repair specimens tested under uniaxial tension at ETD. ... 54

Figure 3.19: Picture of 6° scarf angle 8HS repair specimens at RTD (in-plane view). .. 55

Figure 3.20: Geometry of a 16-ply 3° scarf angle quasi-isotropic scarf-scarf (C1) repair. ... 59

Figure 3.21: Geometry of a 16-ply 3° scarf angle quasi-isotropic scarf-step (C2) repair. ... 59

Figure 3.22: Geometry of a 16-ply 3° scarf angle quasi-isotropic step-step (C3) repair. ... 59 Figure 3.23: Representation of load and boundary conditions used for the modeling of the repair laminate. ... 60 Figure 3.24: Normalized peel and shear stresses vs. normalized bondline distance for a 3˚ scarf angle quasi-isotropic scarf-scarf (C1) repair. ... 61 Figure 3.25: Normalized peel and shear stresses vs. normalized bondline distance for a 3˚ scarf angle quasi-isotropic scarf-step (C2) repair ... 62 Figure 3.26: Normalized peel and shear stresses vs. normalized bondline distance for a 3˚ scarf angle quasi-isotropic step-step (C3) repair ... 62 Figure 3.27: Normalized shear stresses vs. normalized bondline distance for 3˚ scarf angle quasi-isotropic scarf-scarf (C1), scarf-step (C2) and step-step (C3) repairs ... 63 Figure 3.28: Normalized peel stresses vs. normalized bondline distance of 3˚ scarf angle quasi-isotropic scarf-scarf (C1), scarf-step (C2) and step-step (C3) repairs ... 64 Figure 3.29: Diagram of the post-processing analysis used for determining the correct failure mode and failure stress of a quasi-isotropic repaired laminate. ... 68 Figure 3.30: Comparison between experimental and numerical results for the 3° scarf angle scarf-step (C2) PW repair specimen at RTD. ... 70 Figure 3.31: Comparison between experimental and numerical results for the 3° scarf angle scarf-step (C2) repair specimen at ETD. ... 71 Figure 3.32: Representation of the failure location for the 3° scarf angle scarf-step PW repair ... 71 Figure 3.33: Comparison between experimental and numerical results for the 7.5° scarf angle scarf-step (C2) PW repair specimen at RTD. ... 72 Figure 3.34: Comparison between experimental and numerical results for the 7.5° scarf angle scarf-step (C2) PW repair specimen at ETD. ... 73 Figure 3.35: Through-the-thickness micrography view of a 7.5° scarf angle scarf-step (C2) PW repair specimen. ... 73 Figure 3.36: Comparison between experimental and numerical results for the 3° scarf angle scarf-step (C2) 8HS repair specimen at RTD. ... 74 Figure 3.37: Comparison between experimental and numerical results for the 3° scarf angle scarf-step (C2) 8HS repair specimen at ETD. ... 75 Figure 3.38: Comparison between experimental and numerical results for the 6° scarf angle scarf-step (C2) 8HS repair specimen at RTD. ... 76 Figure 3.39: Comparison between experimental and numerical results for the 6° scarf angle scarf-step (C2) 8HS repair specimen at ETD. ... 77

Acknowledgments

I would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC), the Consortium for Research and Innovation in Aerospace in Quebec (CRIAQ), Bombardier Aerospace and L3-MAS for the financial support and materials.

I would also like to thank Marie-Laure Dano who gave me the opportunity to work on this project.

I would like to thank Augustin Gakwaya, Yves Jean, and Charles-Olivier Amyot for their help and resourceful advices.

To my father, mother and brother.

Introduction

Context

Carbon fiber reinforced polymer (CFRP) composite materials have been increasingly used for primary aircraft components because of their superior structural performances such as high specific strength and stiffness, long fatigue life, and lightness.

Composite structures offer many advantages over traditional metallic structures such as immunity to corrosion and cracking. However, these structures are more sensitive to other types of service damage such as mechanical impact. Impact can cause delamination, matrix cracks, fiber failure and material crushing which can induce severe reductions in strength and stiffness and may lead to structural failure. Other types of service damage include mishandling, delamination caused by inadequate shimming during component assembly or by fastener removal or reinstallation and local overheating caused impingement by hot exhaust gases or by lightning strike [1]. Therefore, it is crucial to have effective repair methods to restore the stiffness and strength of damaged composite structures.

Some repair methodologies have been developed for secondary structures, but these technologies will be very difficult to adapt for primary structures. Primary structures are often quite thick in order to carry structural loads and have to meet high damage tolerance requirement. For such structures, it is crucial to design repairs that provide a significant level of recovery of residual strength. However, engineers responsible for damage assessment and repair designs currently do not have sufficient reliable methodology and analysis tool to design high confidence repairs. In order to design reliable repairs, it is essential to develop a robust computational tool that allows engineers to analyze and predict the behavior of the repaired component.

This thesis presents the work conducted as part of a large research project on composite repair. The objective of the project was the development of finite-element tools and protocols for the design of CFRP composite bonded repair for primary aerospace structures manufactured with out-of-autoclave processing. In the project, two types of structures were studied: sandwich and monolithic (stiffened and non-stiffened) panels.

The work presented in this thesis focuses exclusively on monolithic non-stiffened repairs. The finite element model developed constitutes a stepping stone for further modeling tool development.

Literature review

Over the years, an increasing number of both experimental and numerical studies have been conducted in order to better understand the behavior of adhesively bonded joints. The growing interest on the now widespread adhesively bonding technology has been driven by its increased use in the aeronautical as well as other industries. Adhesive joining technique has shown to have numerous advantages over the conventional mechanical joining method, such as lower cost, smoother geometry, higher specific stiffness and strength, more uniform stress distributions.

The geometries of bonded joints (see Figure 1.1) and type of structures that have been joined have evolved over the years from simple ones such as the lap joint between two metal adherends to more complex ones such as circular step joints between composite adherends. This evolution in complexity of joining methods has been accompanied by an increase in the number of parameters involved in their behavior.

Figure 1.1 : Representation of different joint geometries [2]

This thesis focuses on bevel joints, which includes three types of joint geometries, performed on monolithic structures and subjected to a uniaxial tensile loading. The three

types of joint geometry will be presented in further detail within this chapter. Therefore, the literature review will remain within this scope.

First, experimental works conducted on scarf joints will be presented. The effects of scarf angle, joint geometry, adhesive thickness will be discussed.

Next, different elastic models to predict the scarf joint mechanical behavior will be summarized and the results obtained for the peel and shear stress distributions along the bondline will be discussed. Also, the different approaches used to predict failure will be presented. For each, the advantages and limitations will be assessed in order to select the most appropriate model in our context.

This literature review will provide an as updated as possible state of the art on the subject of scarf joints subjected to tensile loading. It will also assess the boundaries of the work that has been conducted so far and set the objectives of the present research to fill some gaps regarding the study of scarf joints.

Both classical analytical and finite element methods have been largely used to analyze the stress distributions within the adhesive and to predict the joint strength and the type of failure. The following literature review is presented as an overview of the most relevant studies related to adhesively bonded joints.

1.2.1. Experimental work on scarf joints

Many parameters may have an impact on the mechanical performance of adhesive scarf joints such as the processing conditions, the scarf angle, the adhesive thickness, the adherends stacking sequences, the environmental conditions, etc. Given the seemingly infinite list of influential factors, focus will be placed on the most important ones, namely the scarf angle of a repair, its geometry and its bondline thickness. These parameters have been found to have a profound effect on the mechanical properties of adhesive joints.

Effect of the scarf angle

The scarf angle of an adhesively bonded scarf repair is one of the most influential parameters. Numerous papers have shown the direct correlation between the strength of a scarf repair and its scarf angle.

The adhesive films used for scarf repairs are designed to be performant primarily under shear loading. Thus, depending on the scarf angle used for the repair, the type of loading that the adhesive will be subjected to will vary, and its mechanical performance will be impacted accordingly.

In the case of a butt joint, where the scarf angle is equal to 90°, when the scarf repair is subjected to a uniaxial tensile load, the adhesive will be loaded only in tension and therefore will provide its least achievable mechanical performance. On the other hand, in the case of a single lap joint as the one presented in [3], where the scarf angle is equal to 0°, the adhesive will be loaded only in shear and therefore will provide its best achievable mechanical performance.

These observations appear in the literature where it was shown experimentally that for smaller scarf angles higher tensile strength of scarf repairs loaded in tension was achieved.

Kumar et al. [4] tested adhesively bonded scarf joints with [0°]16 unidirectional CFRP

adherends and a 0.15 mm-thick AF-163-2 film adhesive under uniaxial tension for various scarf angles ranging from 0.8° to 4.0°. The tensile strength of each tested scarf repairs was respectively ranging from 900 MPa to 400 MPa. Moreover, the failure mode was also investigated. Experiments showed that for very small angles (below 2°), the repair’s mode of failure shifted from shear failure in the adhesive to fibre fracture and fibre pull-out.

Similarly, but with [0°/90°]8S unidirectional CFRP adherends and the Araldite 2015 adhesive

film, Campilho et al. [5] tested scarf repairs with scarf angles ranging from 3° to 45° under uniaxial tension. The tensile strength was respectively ranging from 420 MPa to 40 MPa. The type of failure was also investigated and showed that for scarf angles above 15°, only pure cohesive failure within the adhesive layer was obtained. For scarf angles below 15°, a mix of both cohesive and interlaminar/intralaminar failures was observed, showing that the more the adhesive is loaded under shear the more likely the failure path will travel through the adherends.

In [6], the same trend of results was found, although the adherends were made with quasi-isotropic laminates. Although it appears that the highest strength of a scarf repair is achieved using the smallest scarf angle, the authors point out that the smaller the scarf angle, the more material will have to be removed from the parent laminate, which may result in weakening the structure due to the very small amount of material left at the ends of the scarf repair.

Effect of joint geometry

As it can be found in the literature, there are many types of adhesively bonded joints. A non-exhaustive list of these joints includes butt joint, lap joints, double lap joints, scarf joints, etc. However, the scope of this thesis is to investigate and predict the mechanical behaviors of adhesively bonded scarf joints. Therefore, the following review will present results from studies conducted exclusively on scarf joints.

Scarf joints are a category of adhesively bonded joints on their own. Their geometry consists of two beveled pieces of material, the parent and the patch adherends, that are bonded together by an adhesive layer. The bevel angle is called the scarf angle.

There are three sub-categories of scarf joints. The following denominations were used to describe these joints through-out this thesis:

1. Scarf-scarf joint 2. Scarf-step joint 3. Step-Step joint

The scarf-scarf joint designates a scarf joint for which the bonding surface of both adherends was sanded down to a smooth bevel.

The scarf-step joint designates a scarf joint for which the bonding surface of the parent adherend was sanded down to a smooth bevel. The bonding surface of the patch adherend was left as a stepped bevel.

The step-step joint designates a scarf joint for which the bonding surface of both adherends was left as a stepped bevel.

Most of the experimental and numerical studies available in the literature have been conducted on the first sub-category, i.e., the scarf-scarf joint [5-9]. Despite being relevant for the aerospace industry, not a lot of focus has been placed on investigating the differences between these three categories. As a matter of fact, the three sub-categories are related to the machining method and the bonding technology used for the composite patch [10].

For step-step joints, the damaged layers are removed in steps from the parent laminate. Then, the uncured repair plies are stacked to fit into each step and are cured in place following a co-bonding technique.

For scarf-step joints, the damaged layers are removed by machining a scarf angle through the parent laminate. Then, the uncured repair plies are stacked to fit along the scarf angle and are cured in place following a co-bonding technique.

For scarf-scarf joints, the damaged layers are removed by machining a scarf angle through the parent laminate. Then, the uncured repair plies are stacked to fit along the scarf angle and are precured in an oven or an autoclave. The cured composite patch is then sanded down to a smooth bevel and bonded to the parent using a secondary bonding technique.

Given the lack of detailed analyses presenting the differences between the three categories, this thesis will be focusing on investigating those differences to better understand the influence of the joint geometry on the performance of scarf repairs.

Effect of adhesive thickness

The effect of adhesive thickness on the strength of the joints has also been investigated in multiple studies [4,7,11,12]. In general, it has been shown that the strength and stiffness of the joints subjected to uniaxial tensile loading decrease when the bondline thickness increases.

In [7], quasi-isotropic scarf repairs were tested under tensile loading with various adhesive thicknesses ranging from 0.1-1mm. It was found that using an adhesive film thickness of about 0.15-0.25mm the scarf repair reached its highest strength (i.e., 360 MPa for 0.2mm thickness). This study points out that although the mechanical properties of a scarf joint are found to be reduced under tensile loading as the bondline thickness increases, if the latter is too thin (i.e., 0.1mm), then the mechanical properties of the scarf joints were found to be impacted negatively. A thin adhesive film will be stiff and brittle and will lead premature shear failure at the parent/patch interface. The damage will propagate to the whole bondline rapidly, resulting in the failure of the repaired structure at lower ultimate stress (i.e., 280MPa for 0.1mm thickness). A thick adhesive film will rapidly follow a plastic behavior and show large deformation. The decrease in ultimate strength is caused by the fact that the parent is carrying most of the applied tensile load due to the large deformation in the adhesive film preventing the load to efficiently propagate to the patch. For thicknesses of 0.4-1mm, the ultimate failure was found to decrease from 330MPa to 280MPa.

In [4], scarf repairs with unidirectional adherends were tested under tensile loading with 0.15mm, 0.3mm and 0.5mm adhesive thicknesses. It was found that for a given scarf angle,

increasing the thickness of the adhesive decreases the strength of the scarf joint. The reduction in strength was more pronounced for larger scarf angles. Similar results were found in both [11] and [12].

1.2.2. Classical analytical models

The first classical analytical methods that studied adhesively bonded joints were developed back in the 30’s and 40’s. These methods were developed for bonded metal joints and have been later on modified for composite materials. Moving forward, the finite element method allowed solving problems that were insoluble by using the classical methods.

The Volkersen model

In 1938, Volkersen [13] proposed the first known study on bonded joints. In this study, he developed the shear-lag model. This analytical tool was first developed to analyze the shear stress distributions on mechanical lap joints using fasteners but was later on used for adhesively bonded lap joints. The Volkersen method assumes that the adherends are elastic and can therefore deform in tension and that the adhesive can deform in shear only. It does not take into consideration the bending effect and shear deformation on the adherends caused by the eccentric load path. Figure 1.2 shows a representation of the lap joint as per the Volkersen/shear-lag model.

Figure 1.2 : Lap joint representation – Volkersen/shear-lag model

Figure 1.3 shows a representation of the adhesive shear stress distribution given by the Volkersen’s model. As can be observed, the maximum shear stress occurs at the two ends of the overlap.

Figure 1.3 : Volkersen’s adhesive shear stress distribution

The Goland and Reissner model

In 1944, Goland and Reissner [14] developed a model that took into consideration the bending deformation of the adherends in order to predict the peel stress distribution in the adhesive. Goland and Reissner accounted for the bending moment M and the

transverse force V at the joints ends caused by the eccentric load path in addition to the applied tensile load P, as shown in Figure 1.4.

Figure 1.4 : Lap joint representation – Goland and Reissner model

Figure 1.5 shows a representation of the adhesive peel and shear stresses distribution given by the Goland and Reissner’s model. The peel and shear peak stresses are at the overlap ends.

Figure 1.5 : Goland and Reissner's adhesive peel and shear stress distributions

The Hart-Smith model

In 1973, Hart-Smith developed a solution that accounted for adhesive plasticity using an elastic-plastic shear stress model, as opposed to Volkersen and Goland and Reissner who used an elastic model. A solution was developed for single lap joints [15] and double lap joint [16]. The solution showed that the joint strength predictions were higher when the adhesive plasticity was taken into consideration compared to an elastic analysis. The maximum shear strain criterion was used to calculate the maximum lap joint strength. Also, stiffness imbalances and thermal mismatch between the adherends were considered. The solution showed a strength decrease in the joint when the adherends were not each made of the same material. A decrease in strength was also shown for any thermal mismatch between the adherends, which was even more important with an increased adherend stiffness and thickness.

He also formulated an analytical elastic analysis on scarf joints and stepped joints. These analyses were conducted for metallic adherends, with matching stiffness. He observed that smooth bonding adherend surfaces led to uniform shear stress distributions in the bondline as opposed to stepped surfaces. The latter led to non-uniform shear stress distribution along the bondline characterized by peak stresses corresponding to each step.

1.2.3. Numerical work on scarf joints

Elastic modeling of scarf joints

The main objective of studying the elastic behavior of a scarf joint is to analyze the stresses distributions within its bondline and understand their effect on the performance of the joint later during the failure analysis. By using an appropriate finite element elastic model, one can analyze the peel and shear stresses within the bondline to predict where the onset of failure will most likely occur but also study the influence of the parameters presented in the previous section.

Multiple studies [5, 8, 9] have analyzed the distributions of peel and shear stresses in the bondline of scarf joints subjected to tensile loading using a finite element elastic model. These studies have been using these results to conduct parametric analysis to determine the effect and weight of parameters individually and in conjunction, but also to better understand the reason for failure further on in their analysis.

For example, Gunnion and Herszberg [9] developed a finite element elastic model to better understand the effect of parameters such as the stacking sequence of the adherends, the laminate thickness, mismatched adherends, the adhesive thickness, the scarf angle, the addition of plies over the repair (i.e., over-laminate plies), etc. Both peel and shear stress distributions along the middle of the bondline were extracted from the elastic model. Stresses were gathered from nodes, using a local coordinate system, following the path of the bondline. Stress distributions have been normalized by the far-field applied stress and then multiply by 1000 for ease of comparison purposes. The quantity measured and compared through the study were average peel and shear stresses, and peak peel and shear stresses in the adhesive. Out of all the parameters that were investigated, the two most important observations were that mismatched adherends lay-ups have a very little effect on both peak and shear stresses in the adhesive and that the addition of an over-laminate significantly reduces peak stresses in the adhesive. The conclusions drawn from these observations were that in order to achieve an optimal repair, the importance of the patch lay-up is minimal, and that the addition of over-laminates to a repair to improve its durability is highly recommend when their usage is possible.

What this study [9] and [5, 8] demonstrate is that once a valid numerical elastic model is established, it can be used as a design tool to try different combinations between parameters

that are involved in scarf repairs and study their effects on the repair elastic behavior and on the bondline stress distributions.

Failure prediction modeling of scarf joints

As per [8], to predict failure of a scarf repair it is essential to consider the elastic-plastic deformation behavior of the adhesive since the majority of structural adhesive plastically deform prior to failure, especially in shear. By accounting for the plastic yielding of the adhesive, the bondline stresses found in the elastic analysis are redistributed before failure of the scarf repair.

Unlike the elastic analysis, there are multiple ways to develop a failure prediction model for scarf joints. In a nutshell, the two main models used in the literature to predict the failure of scarf joint are the cohesive zone model (CZM) and the elastic-plastic model with failure criterion.

In [5, 17-21], the CZM model was used to predict failure of various joints including scarf joints. The CZM model is an energy-based approach available in various finite element software such as ABAQUS. It can only be applied to interfaces (i.e., between two elements). Elements with infinitesimal thicknesses are placed between the two interfaces and are removed from the analysis once they fulfill the law that they are associated with (e.g., bilinear, trapezoidal, exponential, etc.). These elements are called interfacial cohesive elements. The parameters used in the cohesive zone model that define the law associated with each interfacial cohesive element are the energy release rates at failure for normal and shear modes. As described more in detail

in [16], these parameters are determined experimentally from DCB and ENF tests.

Campilho et al. [5] added interfacial cohesive element layers along the parent/adhesive and patch/adhesive interfaces. A cohesive layer was also added in the middle of the adhesive. This allows taking into account both interfacial (i.e., adhesive) failure and cohesive failure of the joint by simulating the onset and growth of the crack during failure. The joint studied was a scarf joint, assuming that the patch and the parent bonding surfaces are smooth. Both parent and patch laminates were made out of CFRP laminates using seven different stacking sequences (quasi-isotropic and unidirectional). The adhesive film was defined as an elastic-plastic material according to the von Mises yield criterion. The model presented good correlation with experimental results but is descriptive instead of predictive. As a matter of fact, the energy release rates at failure for normal and shear modes were determined

experimentally from DCB and ENF tests and assumed to be equal for the interfacial cohesive elements as well as the ones in the adhesive.

The CZM presents multiple limitations, the first being that the parameters governing the energy-based law that will be used in the model are difficult to determine and are descriptive in nature rather than predictive. Another limitation of this approach is that the onset and growth of the crack can only take place where the interfacial cohesive layers are being placed in the model, which therefore assumes knowing where the failure could take place. Moreover, for more complex joint geometries, such as a scarf-stepped bevel joint, it can become very challenging for the user to include the interfacial cohesive elements at the adhesive/patch interface.

As mentioned previously, Campilho et al. used an elastic-plastic material according to the von Mises yield criterion [19] in order to take into account the plastic deformation of the adhesive before failure. Cheng Xiaoquan et al. [6], Wang and Gunnion [8] and Chou Shih-Pin [22] also used the von Mises yield criterion as an effective way to model the plastic behavior of the adhesive film of a scarf repair. However, alternatively to using interfacial cohesive elements, the models developed in [6, 8, 22] were coupled with the shear failure criterion that is already implemented in Abaqus to predict failure. These models presented very good correlations with the experimental results, and very easy to implement, regardless of the type of joint geometry. Unfortunately, these models have so far not being used to conduct a comparative study between the three main types of scarf joints described earlier in this chapter (i.e., scarf-scarf joint, scarf-step joint and step-step joint).

Conclusion

Amongst the variety of existing joints, scarf joints are predominantly used in the aerospace industry as a means to repair compromised structures. Depending on the damage that needs to be repaired, it can quickly become very challenging to achieve a durable and trust-worthy repair. It is therefore important to understand the mechanisms involved in these types of repairs that are governed by a multitude of parameters. By having a clear understanding of the influence of these parameters on the mechanical behavior of a scarf joint, one can get closer to achieving the perfect repair. The influence of these parameters can be studied through experimental testing, but also through analytical models and numerical analysis. Classical analytical models such as the Volkersen model, the Golland and Reisnner model and the Hart-Smith model can be a very useful first stepping stone into understanding the mechanical behaviors of adhesively bonded joints but are limited to specific shapes of

repairs. A finite element elastic model is another great tool to supplement experimental results. Once validated using experimental results as a comparison point, it can be used to run multiple parametric analyses to better understand the effect of a larger array of parameters on the stress distributions in the bondline of a scarf repair at no cost but the computational cost of running the analysis. In addition to the saving in time and material cost, a finite element elastic analysis allows very easy extraction of the peel and shear stress distributions along the bondline, which cannot be done experimentally. On the other hand, an elastic analysis should not be conclusive of a repair final performance and should be used along-side with a failure prediction model as a preliminary tool to understand the onset of failure in a scarf joint. Amongst failure prediction models, the CZM and elastic-plastic model with a failure criterion are commonly used for the prediction of failure of scarf joints. Through defining its parameters, the CZM is a descriptive energy-based approach that is only suitable for simple geometries. Also, the potential crack onset and growth is assumed to be known in advance. The elastic-plastic with failure criterion approach is suitable for more complex joint geometries (e.g., scarf-step joint) and it is a predictive tool rather than descriptive.

Objectives

The need to study the effect of the joint geometry (scarf-scarf vs. scarf-step vs. step-step joint) subjected to uniaxial tensile loading has arisen from the absence of data regarding this topic in the literature. Hence, the main goal of this study is to provide a parametrical finite element tool that can predict the strength, failure mode and stress distributions along the bondline of adhesively bonded scarf joint repairs subjected to uniaxial tensile loading, performed on non-stiffened monolithic CFRP panels. The objectives of this study are therefore twofold: experimental and numerical.

On the experimental side, the objectives are as follows:

- Characterize the mechanical properties of the out-of-autoclave CFRP composite materials that will be used for the parent and patch adherend laminates at different environmental conditions.

- Characterize the mechanical properties of scarf-step repairs specimens with various scarf angles at different environmental conditions, in order to obtain different types of failure modes.

- Validate a 2D linear elastic ply-by-ply through-the-thickness numerical model of the quasi-isotropic adherends by comparing the calculated global mechanical properties to the ones determined experimentally.

- Provide an elastic finite element model of the scarf repair, using different geometric configurations (i.e., scarf-scarf, scarf-step, step-step) and predict the shear and peel stress distributions along the bondline in the middle of the adhesive. This part will point out the importance of modeling properly the joint geometric configuration by showing the differences in stress distributions between the three configurations. - Provide a finite element model that takes into account the non-linear behavior of the

adhesive film and able to predict the correct failure mode and strength value of various scarf angle scarf-step repairs.

- Finally, compare the results with the experimental ones for both material at room temperature dry (RTD) and elevated temperature dry (ETD) conditions.

Thesis work plan

In order to satisfy the above objectives, we will adopt a work plan comprising three chapters. The first chapter will address the issue of material characterization and numerical modeling of the composite material mechanical behavior. In this chapter, the in-plane tensile and shear mechanical properties measured at RTD conditions for the CYCOM 5320 epoxy/resin composite material, both with a PW and a 8HS fiber architectures, will be presented. The in-plane tensile mechanical properties will also be presented for ETD conditions. These properties are then implemented in a 2D linear elastic ply-by-ply through-the-thickness model of a quasi-isotropic laminate using Abaqus/Standard. Furthermore, they are compared to Classical Lamination Theory (CLT) prediction results in order to validate the modeling approach of the repair quasi-isotropic adherends.

The second chapter will address the problem of material characterization and numerical modeling of the repair mechanical behavior. In this chapter, the focus is on the influence of various scarf angle, namely 3°, 6° and 7.5°, for a scarf-step bonded repair. Using both PW and 8HS composite materials as adherends and 0.25 mm-thick CYTEC FM300-2M epoxy adhesive film, the experimentally determined tensile mechanical properties will be presented for RTD and ETD conditions. Moreover, a 2D linear elastic, ply-by-ply and through-the-thickness model of 3°-scarf angle repair will be developed using Abaqus/Standard for three different geometric joint configurations. The effect of those configurations (i.e., scarf-scarf, scarf-step and step-step) on the shear and peel stress distributions along the bondline in the middle

of the adhesive will also be investigated. Furthermore, the three joint configurations will be modeled using Abaqus/Explicit and their effect on the repair strength and failure mode will be analyzed. The adherends material properties will be assumed as linear elastic, as opposed to the adhesive film, whose elastic-plastic mechanical behavior and failure will be taken into account. The experimental results will then be compared with the predictions of the finite element model.

Finally, a third chapter will be devoted to the conclusion. In the last chapter, a review of the results and conclusions assessed in previous sections will be presented. Furthermore, a discussion of the future work regarding the modeling of bonded repairs will be presented.

Characterization and numerical

modeling of the composite

materials mechanical behavior

Introduction

This chapter presents the experimental results from tensile tests conducted under various environmental conditions on both plain weave (PW) and 8-harness satin (8HS) carbon/epoxy composite materials. For each composite material, both in-plane tensile and in-plane shear properties were determined experimentally.

Moreover, a 2D linear elastic ply-by-ply through-the-thickness model was developed using the software Abaqus/Standard to predict the elastic behavior of a quasi-isotropic laminate. The results were then compared to the classical lamination theory prediction results in order to validate the finite element model.

2.1.1. Materials

Tests were conducted to characterize CYCOM 5320 PW epoxy/resin with a plain weave fiber architecture composite material and CYCOM 5320 8HS epoxy/resin with an 8-harness satin fiber architecture composite material. The general properties of both composites can be found in Table 2.1.

Table 2.1: Composite materials general properties.

Material Areal Weight [g/m2_{] Resin Content [%] Ply Thickness [mm]}

T650-35 3K PW 196 36 0.19

T650-35 3K 8HS 370 36 0.38

PW and 8HS are two of the three types of dry woven fabrics used to produce composite laminates. A PW is a simple balanced fabric where both yarns cross along the length and the width of the fabric. The warp (x-direction) and the fill (y-direction) are made of threads of the same number, size and weight; therefore, forming a chessboard-like pattern as shown in Figure 2.1 (a). An 8HS is a more complex and unbalanced fabric. As shown in Figure 2.1 (b), the warp passes over seven filling yarns.

Figure 2.1: Fiber architecture pattern for a) a PW fabric and b) an 8HS fabric.

2.1.2. Test matrices

Table 2.2 and Table 2.3 summarize the test matrix respectively for the two fiber architectures. These tables indicate which tests were conducted for each material, the test method used and the number of valid tested specimens.

Table 2.2: Characterization test matrix for the CYCOM 5320 T650 3k PW.

Test

Test Method

RTD

1

_ETD

2

0° Tensile Testing

D 3039

4

90° Tensile Testing

D 3039

5

3

±45° Tensile Testing

D 3518

3

5

1_{RTD: Room Temperature (20°C), Dry humidity levels.}

2_{ETD: Elevated Temperature (82°C), Dry humidity levels.}

Table 2.3: Characterization test matrix for the CYCOM 5320 T650 3k 8HS.

Test

Test Method

RTD

ETD

0° Tensile Testing

D 3039

5

90° Tensile Testing

D 3039

5

4

±45° Tensile Testing

D 3518

4

5

ASTM standards

2.2.1. In-plane tensile properties (ASTM standard D3039/D3039M)

In order to determine the in-plane (0° and 90°) tensile properties of both the PW and the 8HS composite materials, the ASTM standard D3039/D3039M, also known as the Standard Test Method for Tensile Properties of Polymer Matrix Composite Material, was used. This method is suited for polymer matrix composite materials reinforced by high-modulus fibers. The composite materials forms are limited to continuous fiber or discontinuous fiber-reinforced composites for which the laminate is balanced and symmetric with respect to the test direction [23].

2.2.2. In-plane shear properties (ASTM standard D3518/D3518M)

In order to determine the in-plane shear response of both the PW and the 8HS composite materials the ASTM standard D3518/D3518M, also known as the Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a ±45° Laminate, was used. This method is also suited for polymer matrix composite materials reinforced by high-modulus fibers. The test consists in conducting a tensile test in the x-direction of a ±45° composite laminate. Although the ASTM standard D3518/D3518M has specific restrictions regarding the stacking sequence and the specimen’s thickness, the uniaxial tension tests of the ±45° laminates were performed in accordance with the D30518/D3518M test method [24].

Specimen manufacturing

The specimens were manufactured at Laval composite materials laboratory. The plies were cut from pre-preg composite material rolls and stacked according to the needs of the experiment. For the 0° and 90° uniaxial specimens, they were cut from the same laminate to ensure similar manufacturing conditions. A PW ply thickness was reported to be equal to 0.19 mm and to 0.38 mm for an 8HS ply. The layups for the characterization specimens were [0°]7S, for a total of fourteen plies corresponding to 2.66 mm thickness, and [0°]4S, for a

total of eight plies corresponding to a 3.04 mm thickness, respectively for the PW and the 8HS composite material. Therefore, the total thickness was higher than 2.5mm recommended by the ASTM D3039/D3039 Test Method. The laminates were cured in an oven and under vacuum. After a 6-hour debulk, the following cure cycle was used to cure the composite material plates: 55-minute ramp to 122°C, 2-hour at 122°C, 1.5-hour ramp to 177°C, 2.5-hour at 177°C and finally a 2.5-hour ramp to 26°C. Figure 2.2 presents the debulk time and cure cycle used for the manufacturing.

Figure 2.2: Debulk time and cure cycle of the composite material.

After cure, the specimens were cut using a high-pressure waterjet to a dimension of 254 mm x 25.4 mm each in accordance with the ASTM D3039/D3039M Test Method.

The same procedure was followed for the ±45° PW and 8HS specimens with a layup sequence of [+45/-45]2s. In agreement with the ASTM D3518/D3518M Test Method, each laminate

counted a total of eight plies. 0 20 40 60 80 100 120 140 160 180 200 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T em pera tu re (˚ C ) Time (h) Cure Cycle Debulk

Test Methodology

Once the specimens were cut from each panel, their cross-sectional area A was then determined using five points per measure.

Every specimen was tested until failure. A 100 kN MTS load frame with a displacement rate of 4 mm/min applied the tensile load. In accordance with the ASTM D3039/D3039M Test Method, this displacement speed was selected to ensure specimen failure within 1 to 10 minutes.

2.4.1. In-plane tensile test methodology

According to the test matrices presented in Table 2.2 and Table 2.3, the specimens tested for the in-plane tensile properties of both materials were tested under RTD and ETD environmental conditions. Aluminum tabs were added to the 0° and 90° specimens in order to avoid failure at the grips. The force F was acquired during each test and the corresponding tensile stress σ was calculated using:

𝜎 =𝐹

𝐴 (2.1)

Mechanical extensometers were used to measure axial and transverse strains and evaluate the elastic modulus E1 and Poisson ratio ν12 at RTD using:

𝐸1= ∆𝜎1 ∆𝜀1 (2.2) 𝜈12 = − ∆𝜀2 ∆𝜀1 (2.3) where σ1 is the axial stress applied in the 0o-direction, ε1 is the axial strain and ε2 is the

transverse strain.

The elastic modulus E2 was evaluated at RTD using:

𝐸2= ∆𝜎2 ∆𝜀2

(2.4) where σ2 is the axial stress applied in the 90o-direction and ε2 is the corresponding axial

Once enough data were recorded within the elastic range by the mechanical extensometers, the test was paused and the mechanical extensometers were replaced by a video-extensometer that recorded only the axial strain ε1. The test was then resumed until failure

of the coupon.

In the case of ETD environmental condition, the specimens were tested in an environmental chamber at the desired temperature of 82°C. A thermocouple was fixed on the specimen to ensure that the material had reached the desired temperature. Testing began five minutes after the thermocouple indicated the desired temperature. The axial strain was recorded using a video-extensometer.

2.4.2. In-plane shear test methodology

Again, in accordance with the test matrices of Table 2.2 and Table 2.3, the in-plane shear tests were realized under RTD and ETD environmental conditions. Emery cloth was used for the ±45° specimens as stipulated by the ASTM standard D3518/D3518M. It should be noted that the force F was acquired during each test and the corresponding shear stress τ was calculated using:

𝜏12= 𝐹

2𝐴 (2.5)

The axial and transverse strains, respectively εx and εy, were measured using a

video-extensometer for the ±45˚ specimens. The shear strain γ12 and the shear modulus G12 was

then calculated using:

𝛾12= 𝜀x− 𝜀y (2.6)

𝐺12= ∆𝜏12 ∆𝛾12

(2.7)

In the case of ETD environmental condition, the specimens were tested in an environmental chamber at the desired temperature of 82°C. A thermocouple was fixed on the specimen to ensure that the material had reached the temperature. Testing began five minutes after the thermocouple indicated the desired temperature. The axial strain ε1 and transverse strains

PW experimental results

2.5.1. In-plane axial properties at RTD

Figure 2.3 shows the axial stress 𝜎1 (MPa) versus the axial strain 𝜀1 (%) for the PW specimens tested under uniaxial tension at RTD. The axial strain 𝜀1 presented in Figure 2.3 was measured using a video-extensometer. Due to the important differences observed between the specimens in terms of strain, the data presented Figure 2.3 was used only to compute the average axial strength 𝜎1𝑚𝑎𝑥 of the material. The average axial modulus E1 was calculated

using the data from the mechanical extensometer. The variations are most likely caused by the inaccuracy of the video-extensometer and not by the material’s mechanical behavior. Stress increased linearly until abrupt failure of the specimens occurred. Table 2.4 lists the average axial properties 𝜎1𝑚𝑎𝑥, E1 and ν12 as well as the standard deviation and covariance

calculated between the specimens.

Figure 2.3: Axial stress vs. axial strain for the PW composite material tested under uniaxial tension at RTD.

Table 2.4: In-plane axial properties for the PW at RTD.

Properties Average Std. Dev.

Cov. %

𝝈

𝟏𝒎𝒂𝒙

[MPa]

782.8

34.4

4.39

E

1

[GPa]

62.66

1.77

2.82

ν

12

[-]

0.047

0.003

6.83

0 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Ax ial St re ss (M P a) Axial Strain (%) PW-0D-RTD-1 PW-0D-RTD-2 PW-0D-RTD-3 PW-0D-RTD-4

A

B

C

D

Figure 2.4 shows the specimens after failure for the in-plane axial test at RTD. Specimen B failed exclusively near the grips. The other coupons failed near the grips, yet they presented a failure further away from the grips as recommended by the ASTM standard D3039/D3039M in order for the results to be valid. The different failure locations are well represented in the Figure 2.4. As a matter of fact, the strength B is slightly lower than the rest. However, since this difference is insignificant, the specimen B was considered as valid even though it does not respect the ASTM standard D3039/D3039M guidelines.

Figure 2.4: Picture of the PW failed specimens for the in-plane axial test at RTD.

2.5.2. In-plane transverse properties at RTD and ETD

Figure 2.5 and Figure 2.6 show the transverse stress 𝜎2 (MPa) versus the transverse strain 𝜀2 (%) for the PW specimens tested under uniaxial tension, respectively at RTD and ETD. The axial strain 𝜀2 presented in Figure 2.5 and Figure 2.6 was measured using a video-extensometer. For both conditions, no significant variations were found between the specimens. Therefore, the data presented in in Figure 2.5 and Figure 2.6 were used to evaluate the average transverse modulus E2 and the transverse strength 𝜎2𝑚𝑎𝑥 of the material. It should be noted that curves waviness presented in Figure 2.6 is due to strain recording issues. The specimens were tested in an environmental chamber with a 5-layered glass door that created an optical distortion that affected the video-extensometer’s measurements. Again, stress increased linearly until abrupt failure of the specimens occurred. Table 2.5 lists the average transverse properties 𝜎2𝑚𝑎𝑥 and E2 as well as the standard deviation and

covariance calculated between the specimens for both RTD and ETD conditions.

A

B

C

Figure 2.5: Transverse stress vs. transverse strain for the PW composite material tested under uniaxial tension at RTD.

Figure 2.6: Transverse stress vs. transverse strain for the PW composite material tested under uniaxial tension at ETD.

Table 2.5: In-plane transverse properties for the PW at RTD and ETD.

Properties

RTD

ETD

Average Std. Dev.

Cov. % Average Std. Dev.

Cov. %

𝝈

𝟐𝒎𝒂𝒙

[MPa]

799.3

26.2

3.27

798.6

46.2

5.78

E

2

[GPa]

66.93

2.94

4.40

61.61

3.75

6.09

Figure 2.7 shows the specimens after failure for the in-plane transverse test at RTD. Specimen A failed near the grips as well as close to the center line. Coupons B to D, on the

0 100 200 300 400 500 600 700 800 900 1000 0 0.5 1 1.5 T ran sve rs e Stre ss (M Pa) Transverse Strain (%) PW-90D-RTD-1 PW-90D-RTD-2 PW-90D-RTD-3 PW-90D-RTD-4 PW-90D-RTD-5 0 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 T ran sv er se St re ss (M P a) Transverse Strain (%) PW-90D-ETD-1 PW-90D-ETD-2 PW-90D-ETD-3

A

B

C

D

E

A’

B’

C’

other end, presented failure exclusively near the grips. Specimens C and D do have slightly lower strength values compared to the other ones.

Figure 2.8 shows the specimens after failure for the in-plane transverse test at ETD. Specimen A’ failed near the grips and near the center line. Unfortunately, the two other coupons presented failure exclusively near the grips.

Despite these observations, no significant difference was noted between the strengths of the specimens. Therefore, all coupons were considered as valid for both RTD and ETD conditions.

Figure 2.7: Picture of the PW failed specimens for the in-plane transverse test at RTD.

Figure 2.8: Picture of the PW failed specimens for the in-plane transverse test at ETD.

2.5.3. In-plane shear properties at RTD

Figure 2.9 shows the shear stress 𝜏12 (MPa) versus the shear strain 𝛾12 (%) for the PW specimens tested under uniaxial tension at RTD. The axial ε1 and transverse strains ε2

A

B

C

D

E

A'

B’

C’

presented in Figure 2.9 were measured using a video-extensometer. The shear strain γ12 was then calculated using equation (2.6). No significant variations were found between the specimens. Therefore, the data presented in Figure 2.9 was used to calculate both the average shear modulus G12 and strength 𝜏12𝑚𝑎𝑥of the material. The stress-strain curve is a typical representation of the shear behavior of a composite material, with a linear behavior at the beginning, followed by a non-linear hardening of the matrix, until abrupt failure. Table 2.6 lists the average shear properties 𝜏12𝑚𝑎𝑥 and G12 as well as the standard deviation and

covariance calculated between the specimens.

Figure 2.9: Shear stress vs. shear strain for the PW composite material tested under uniaxial tension at RTD.

Table 2.6: In-plane shear properties for the PW at RTD.

Properties Average Std. Dev.

Cov. %

𝝉

𝟏𝟐𝒎𝒂𝒙

[MPa]

130.2

8.0

6.14

G

12

[GPa]

4.93

0.41

8.25

Figure 2.10 shows the specimens after failure for the in-plane shear test at RTD. All specimens failed near the center line. Therefore, they were all considered as valid in accordance with the ASTM standard D3518/D3518M.

0 20 40 60 80 100 120 140 160 0 10 20 30 40 Sh ear St re ss (M P a) Shear Strain (%) PW-45D-RTD-1 PW-45D-RTD-2 PW-45D-RTD-3

A

B

C

Figure 2.10: Picture of the PW failed specimens for the in-plane shear test at RTD.

8HS experimental results

2.6.1. In-plane axial properties at RTD

Figure 2.11 shows the axial stress 𝜎1 (MPa) versus the axial strain 𝜀1 (%) for the 8HS specimens tested under uniaxial tension at RTD. The axial strain 𝜀1 presented in Figure 2.11 was measured using a video-extensometer. No significant variations were found between the specimens. Therefore, the data presented in Figure 2.11 was used to evaluate both the average axial modulus E1 modulus and axial strength 𝜎1𝑚𝑎𝑥 of the material. Stress increased linearly until abrupt failure of the specimens occurred. Table 2.7 lists the average axial properties 𝜎1𝑚𝑎𝑥, E1 and ν12 as well as the standard deviation and covariance calculated

between the specimens.

A

B

Figure 2.11: Axial stress vs. axial strain for the 8HS composite material tested under uniaxial tension at RTD.

Table 2.7: In-plane axial properties for the 8HS at RTD.

Properties Average Std. Dev.

Cov. %

𝝈

_𝟏𝒎𝒂𝒙

[MPa]

811.2

40.4

4.98

E

1

[GPa]

66.27

1.52

2.30

ν

12

[-]

0.043

0.006

13.11

Figure 2.12 shows the specimens after failure for the in-plane axial test at RTD. Specimens A and C presented failure exclusively near the grips. The other coupons failed near the grips, yet they presented a failure further away from the grips as recommended by the ASTM standard D3039/D3039M in order for the results to be valid. Despite this observation, no significant differences were to be noted for the strength of each specimen except for specimen E where a slightly lower strength value was reported.

0 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Ax ial St re ss (M P a) Axial Strain (%) 8HS-0D-RTD-1 8HS-0D-RTD-2 8HS-0D-RTD-3 8HS-0D-RTD-4 8HS-0D-RTD-5

A

B

C

D

E