Traslaminar fracture of thinply composite laminates

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Faculdade de Engenharia da Universidade do Porto

Translaminar fracture of thin-ply

composite laminates

Márcio Ferraz da Costa Fernandes

MSc Thesis

Mestrado Integrado em Engenharia Mecânica Supervisor FEUP: Prof. Dr. Pedro Ponces Camanho

Supervisor EPFL: Prof. Dr. Ioannis Botsis

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Translaminar fracture of thin-ply composite

laminates

Márcio Ferraz da Costa Fernandes

Mestrado Integrado em Engenharia Mecânica

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"O homem é do tamanho do seu sonho."

Fernando Pessoa

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Acknowledgements

This dissertation was performed in the LMAF (Laboratory of Applied Mechanics and

Reliability Analysis), at EPFL (École Polytechnique Fédérale de Lausanne) under the

Eras-mus Program.

First of all, I would like to express my gratitude to Prof. Dr. Pedro P. Camanho, my advisor, for the opportunity to collaborate in this work.

I also express my gratitude to Prof. Dr. Ioannis Botsis for the opportunity to work at the Laboratory of Applied Mechanics and Reliability Analysis, in EPFL, for all his valuable supervision, and for the constructive and inclusive comments about this work.

I acknowledge to Prof. Dr. Thomas Gm¨ur for the comments given along this work.

I also would like to express my gratitude to Dr. Jo¨el Cugnoni, for the time spent in

multiple discussions, for his accessibility and contributions to make this work experience stimulating and motivating.

I would like to thank the help, valuable patience and advising provided by Guillaume Frossard, PhD student, during the development and execution of this entire dissertation. I would like also to thank to Dr. Roohollah Sarfaraz Khabbaz for his help on obtaining X-ray Tomography pictures and for his knowledge imparted. I acknowledge all the help provided by Ebrahim Farmand Asthiani, PhD student, for making possible the fulfillment of the experimental tests and for his help on obtaining SEM micrographs. I also would like to thank to all LMAF group for creating a pleasant work environment.

Lastly, I would like to express my gratitude to my family and friends for their encour-agement, support, and patience and for helping me going through all these years.

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Abstract

Thin-ply composite laminates are a promising field of development in composite ma-terials, and are expected to outperform conventional laminates in the near future.

In this dissertation, an experimental investigation was done in order to understand and characterize the translaminar fracture initiation and crack growth in cross-ply thin-ply laminates, [(90/0)m/90]S. Compact Tension (CT) tests were performed in four

differ-ent ply thickness laminates, from the same material and laminate thickness. Testing was monitored with digital image correlation (DIC). The compliance and area methods were considered to perform the data-reduction scheme.

A 2-D macro-scale finite element (FE) model was built and crack propagation was ulated using a layer of cohesive elements. The load-displacement curve predicted by sim-ulations was compared with experimental values. Moreover, bridging length, crack length and damage onset were also investigated. Fracture surface and through-the-thickness dam-age observations were also performed.

The study performed in this thesis showed that composite laminates show a brittle behavior, when decreasing the ply thickness. Moreover, it was observed that ply thick-ness depends on the energy release rate (ERR). The ERR changes linearly with the ply thickness.

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Resumo

Laminados compósitos ultrafinos são um promissor avanço realizado em materiais com-pósitos que se espera que no futuro venham a substituir os laminados convencionais.

Durante esta tese foi feito um estudo experimental com o intuito de caraterizar a tenacidade à fractura translaminar destes materiais, bem como a sua curva de resistên-cia. Assim, laminados cross-ply, [(90/0)m/90]S, foram reproduzidos em provetes compact

tension (CT). Estes provetes possuíam igual espessura e foram construídos a partir do mesmo material, variando apenas a espessura das lâminas entre provetes. Os testes real-izados foram monitorreal-izados com a técnica da correlação digital por imagem (DIC). Em termos de redução de dados, a tenacidade à fratura, G_Ic, foi avaliada através do método da área e da compliance.

Um modelo 2D à escala macro foi construído e inserido num software de elementos fini-tos. A propagação da fissura foi simulada utilizando uma camada de elementos coesivos. A curva carga-deslocamento prevista através das simulações foi seguidamente confrontada com os resultados experimentais. Além disso, o comprimento da fenda, o comprimento da zona dominada pelos efeitos de bridging e o momento correspondente à iniciação de dano, foram também avaliados.

Foram também realizados estudos das superfícies de fratura, bem como observações do dano ao longo da espessura de um provete selecionado.

Conclui-se que existe uma dependência da espessura das lâminas na tenacidade à fratura dos laminados compósitos. O estudo levado a cabo ao longo desta tese mostrou que, à medida que a espessura das lâminas é diminuída, os materiais laminados compósitos tendem a apresentar um comportamento mais frágil. Foi verificada uma variação linear entre a espessura das lâminas e a tenacidade à fratura.

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List of Figures

2.1 Schematic of tow-spreading process with a pneumatic method [1]. . . 6

2.2 Schematic of tow-spreading process with the help of airflow [1]. . . 7

2.3 In situ effect in laminated composites - In situ transverse strength vs total number of 90◦ plies clustered together (2n) [2]. . . 7

2.4 Overview of ply-level failure modes [3]. . . 8

2.5 Failure mechanisms in fiber reinforced polymers (FRPs): (a) fracture sur-face including (1) translaminar fiber tensile failure and (2) longitudinal ma-trix failure, (b) shear driven fiber compressive failure (the arrows indicate the loading direction), (c) fiber kinking (the arrows indicate the loading direction) [3]. . . 9

2.6 Estimated size of the plastic region according to Irwin’s model (adapted from [4]). . . 14

2.7 Dugdale’s model. . . 15

2.8 Schematic of cohesive zone model. Two examples of traction-separation laws [5]. . . 16

2.9 Trilinear softening law obtained by superposing two bilinear laws [6]. . . 17

4.1 Plate before being introduced in autoclave. . . 26

4.2 Configuration and nominal dimensions (in mm) of the CT specimen. . . 27

4.3 DIC measurement system and positioning of cameras used during the ex-perimental program. . . 28

4.4 Speckled CT specimen. . . 29

4.5 Load-displacement curve of the CT-150-a specimen. The small ’bumps’ on the loading curves are due to experimental error (see text for details). . . . 30

4.6 The two AOIs used, around the upper and lower pins. . . 31

4.7 Sigma [pixel] vs X [mm] plot along the path drawn, for a picture immedi-ately before crack propagation. . . 32

4.8 Sigma [pixel] vs X [mm] plot along the path drawn, for a picture immedi-ately after crack propagation. . . 32

4.9 Load-displacement curve of the CT-150-b specimen. The small ’bumps’ on the loading curves are due to experimental error (see text for details). . . . 33

4.10 Load-displacement curve of the CT-150-c specimen. The small ’bumps’ on the loading curves are due to experimental error (see text for details). . . . 34

4.11 Compliance vs crack length obtained from CT-150-a testing. . . 37

4.12 R-curve obtained from CT-150-a testing (the errorbar length represents twice the standard deviation among the three methods hereafter shown). . . 38

4.13 R-curve obtained from CT-150-a testing, using three different methods for smoothing fitted data. . . 39

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LIST OF FIGURES

4.14 Strain field along loading direction for the CT-150-a specimen before crack

propagation. . . 40

4.15 Strain field along loading direction for the CT-150-a specimen after 0.68 mm crack growth. . . 40

4.16 Compliance vs crack length obtained from CT-150-b testing. . . 41

4.17 R-curve obtained from CT-150-b testing (the errorbar length represents twice the standard deviation among the three methods hereafter shown). . . 42

4.18 R-curve obtained from CT-150-b testing, using three different methods for smoothing fitted data. . . 43

4.19 Compliance vs crack length obtained from CT-150-c testing. . . 44

4.20 R-curve obtained from CT-150-c testing (the errorbar length represents twice the standard deviation among the three methods hereafter shown). . . 45

4.21 R-curve obtained from CT-150-c testing, using three different methods for smoothing fitted data. . . 46

4.22 R-curves obtained from CT-150 tests. . . 47

4.23 Load-displacement curve of the CT-100 specimen. The small ’bumps’ on the loading curves are due to experimental error (see text for details). . . . 48

4.24 Compliance vs crack length obtained from CT-100 testing. . . 49

4.25 R-curve obtained from CT-100 testing (the errorbar length represents twice the standard deviation among the three methods hereafter shown). . . 50

4.26 R-curve obtained from CT-100 testing, using three different methods for smoothing fitted data. . . 51

4.27 Strain field along loading direction for the CT-100 specimen after 0.35 mm crack growth . . . 52

4.28 Strain field along loading direction for the CT-100 specimen after 3.37 mm crack growth . . . 52

4.29 Load-displacement curve of the CT-75 specimen. The small ’bumps’ on the loading curves are due to experimental error (see text for details). . . 53

4.30 Compliance vs crack length obtained from CT-75 testing. . . 53

4.31 R-curve obtained from CT-75 testing (the errorbar length represents twice the standard deviation among the three methods hereafter shown). . . 55

4.32 R-curve obtained from CT-75 testing, using three different methods for smoothing fitted data. . . 55

4.33 Load-displacement curve of the CT-30 specimen. . . 56

5.1 2-D finite element model used. . . 59

5.2 Traction-separation law used in the cohesive zone model. . . 60

5.3 AOIs and lines created to evaluate COD at the end of the bridging zone. . . 61

5.4 Vertical displacement (V) along the line immediately above (red line) and below (green line) the crack. . . 62

5.5 Comparison of load-displacement curves from simulations (K0= 60000 M P a/mm) and experiments. . . 67

5.6 Load-displacement curves from simulations and experiments. . . 68

5.7 Crack length measurements: experiments vs modeling. . . 69

5.8 Crack length vs applied displacement. . . 70

6.1 Load-displacement curves of the monotonic tests performed on the different ply thickness specimens. . . 72

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LIST OF FIGURES

6.2 X-ray Absorption (left), Refraction (middle) and Scattering (right) Tomog-raphy of a 90◦ layer at approximately 1/4 of the specimen thickness. . . . . 74

6.5 X-ray Absorption (left), Refraction (middle) and Scattering (right) Tomog-raphy of a 0◦ layer at approximately 1/4 of the specimen thickness. . . . 75

6.6 X-ray Absorption (left), Refraction (middle) and Scattering (right) Tomog-raphy of a 0◦ layer at approximately 3/4 of the specimen thickness. . . . 75

6.7 X-ray Refraction Tomography of a 90◦ layer (left) and the immediately adjacent 0◦ layer (right). . . 75

6.8 SEM fracture surface of CT-150-c specimen. . . 76

6.9 High magnification of the SEM fracture surface of CT-150-c specimen. . . . 76

6.10 ERR vs ply thickness. . . 77

A.1 3D segmented image of CT-150-a specimen using X-ray Tomography images. 81

A.2 3D segmented image of CT-150-a specimen using X-ray Tomography images (2). . . 82

A.3 3D segmented image of CT-150-a specimen using X-ray Tomography images (3). . . 82

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List of Tables

4.1 Properties of the cross-ply laminates used in this experimental program,

[(90/0)m/90]S. . . 26

4.2 Lamina material properties used in this work. . . 27

4.3 Laminate material properties obtained using CLT and homogenization prop-erties. . . 27

4.4 Configuration of the DIC system. . . 28

4.5 Experimental results obtained from CT-150-a testing. . . 37

4.6 ERR vs crack length results using different methods. . . 39

4.7 Experimental results obtained from CT-150-b testing. . . 41

4.9 Experimental results obtained from CT-150-c testing. . . 44

4.11 Experimental results obtained from CT-100 testing. . . 49

4.13 Experimental results obtained from CT-75 testing. . . 54

5.1 Evaluation of Gss_Ic, considering that steady-state is reached when a = 26.68 mm. . . 61

5.2 COD at the end of the bridging zone, considering that steady-state is reached when a = 26.68 mm. . . 63

5.7 Summary of the results obtained to Gss_Ic and δ_max, considering different ends for the bridging zone. . . 65

5.8 Summary of all required parameters to a complete characterization of the cohesive zone model (K0 = 60000 MPa/mm). . . 66

5.9 Semi-final cohesive zone model parameters. . . 67

5.10 Final cohesive zone model parameters. . . 68

6.1 Summary of the results obtained through area and compliance methods. . . 72

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Abbreviations

AOI Area of interest

CC Compliance Calibration CCD Charge-coupled device

CFRPs Carbon fiber reinforced polymers CLT Classical laminate theory

COD Crack opening displacement CT Compact-tension

DIC Digital image correlation ERR Energy release rate FBG Fiber Bragg grating FE Finite Element

FEA Finite Element Analysis FEM Finite Element Method

LEFM Linear elastic fracture mechanics LVDT Linear Variable differential transformer FRPs Fiber reinforced polymers

MCC Modified Compliance Calibration NLFM Nonlinear elastic fracture mechanics SEM Scanning electron microscope VCCT Virtual crack closure technique

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Notation

a Crack length ∆a Crack growth

C Compliance

G Energy release rate

Gc Critical strain energy release rate

GIc Mode-I critical strain energy release rate Gss_Ic Steady-state energy release rate

Gb_Ic Energy release rate due to the fiber bridging

Gi_Ic Initial energy release rate

GT_Ic Total energy release rate

KI Stress intensity factor

KIc Critical stress intensity factor t Specimen thickness

P Load

δ Displacement

δmax Maximum separation σc Damage initiation stress zmax Bridging length

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Chapter 1

Introduction

This dissertation reports results of how composite laminates build with thin plies respond in terms of fracture, when subjected to a mode I loading. Experimental and numerical studies were performed during this work and comparisons with the conventional composite laminates were also done.

In this chapter, a brief introduction to the spread tow thin-ply technology is presented, as well as the motivation and objectives from behind this thesis. Finally, the organization of this thesis is also herein presented.

1.1 Context

Composite materials are combinations of two or more different materials and are char-acterized by their constituent mechanical properties, owning generally high stiffness, high strength and low density. Their main applications range from aerospace and automotive industries to biomedical and recreational applications [7]. Recently, a new class of com-posite materials, with particular interest for the aircraft industry, has emerged and some recent research publications have been reported on the advantages of using these materi-als. This class of materials is produced from the spread tow thin-ply technology, which is able to produce flat and straight plies until a dry ply thickness as low as 0.02 mm [8]. Due to the inherent complexity of these materials, the application of fracture mechanics is a topic of great interest. Different techniques have been used to quantify fracture mechanics in composite materials, particularly into the fracture toughness of the material (GIc) and

the energy released per unit area of crack extension (G) during loading [7]. Therefore, this dissertation has as main goal to study the fracture response of thin-ply laminates. Ex-perimental tests were performed and observations were made to quantify and to describe the behavior of these materials in terms of its fracture response. Moreover, numerical

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Introduction

simulations were done. Finally, a study of the ply thickness effect was performed, from conventional laminates to thin-ply laminates.

1.2 Motivation and Objectives

Due to the increasing use of carbon fiber reinforced polymers (CFRPs) in airframes, when promising new composite technologies appear aircraft manufactures try to follow up their development, aiming to improve the performance of aircraft structures. One new technology of interest is the spread tow thin-ply technology. This technology is able to produce thin-ply composite laminates with ply thicknesses as low as 0.02 mm. The motivation for the trend towards thinner plies is not only to produce thinner and lighter structures but also to take advantage of the enhanced strength and damage resistance showed for these materials, due to the increased effective design space and the positive size effects. As main benefit of using thin-ply laminates for a given constant laminate thickness is the possibility of using larger number of ply orientations to achieve a better solution in terms of design, for a given load or set of load cases. Hence, using thin plies it becomes possible to design more complex and optimized laminates. Other advantages come from the positive size effects with respect to decreasing the ply thickness (e.g., improved damage resistance against matrix cracking and delamination).

The main purpose of this dissertation is then to understand and characterize the frac-ture initiation and crack growth in cross-ply thin-ply laminates. To be more precise, this thesis includes studies on the toughness and crack propagation of thin-ply composites and associated mechanistic studies, using fracture surface and through-the-thickness damage observations.

To achieve the main aim of this work, partial objectives needed to be completed, namely:

• Quantify experimentally the performance of thin-ply laminates, measuring its frac-ture toughness and crack propagation, with the help of DIC technique;

• Perform fracture surface and through-the-thickness damage observations;

• Accomplish numerical analysis, predicting toughness and simulating crack propaga-tion;

• Evaluate the contribution of the bridging fibers on fracture toughness; • Finally, study the ply effect in the fracture response of composite laminates.

1.3 Dissertation Outline

This dissertation is organized in seven chapters, including the introduction and conclu-sions. This first chapter introduces the work that was developed and that will be described

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Introduction

in the following chapters, taking into account the scope of this thesis. The motivation and the objectives of this work are described in this chapter.

Chapter 2 of this dissertation reports an introduction to the thin-ply composite lami-nates, as well as the methodology and manufacturing process from behind them. Due to its importance, a description of the in situ effect is also presented. Moreover, the main failure modes in composite materials are presented, with special highlighting for the translaminar fracture toughness, which is the main subject of this thesis. Examples of possible data reduction methods in compact tension tests are also described here. Finally, an overview of some common methods employed in composite materials analysis is presented.

Chapter3 of this thesis is devoted to present an overview of the DIC technique, which was used in this work.

Chapter 4describes the experimental test program performed along this work, as well as the experimental results. Emphasis is given to the fracture toughness and its variation with the crack growth (R-curve).

Chapter 5 gives emphasis to the numerical work performed along this thesis. Here, a 2-D FE model was built and crack propagation was simulated using a layer of cohesive elements. The load-displacement curve was predicted and crack and bridging length were investigated.

Chapter 6 shows the discussion performed concerning the experimental results. Here, the experimental results are summarized and compared to each other. The role of the bridging fibers is also investigated. Moreover, fracture surface and through-the-thickness damage observations performed in this work are also shown in this chapter.

Chapter7presents the main conclusions regarding the work carried out. Some consid-erations are also made here concerning the different methods used along this work. Finally, future works are suggested in order to fully characterize the behavior of these materials.

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Chapter 2

State-of-the-art and literature

review

In this chapter, thin-ply composite laminates are introduced, as well as the methodol-ogy and manufacturing process behind them. Due to its importance, a description of the

in situ effect is also presented. Moreover, the main failure modes in composite materials

are presented, with special highlighting for the translaminar fracture toughness, which is the main subject of this thesis. Examples of possible data reduction methods in compact tension tests are also described here. Finally, some techniques used to model composite materials, as well as a review of some possible methods to evaluate the energy release rate (ERR) due to the bridging fibers are also presented.

2.1 Thin-ply composite laminates

The use of composite materials in structures has significantly increased during the last years. This trend is mainly because composite materials have properties which are very different from conventional isotropic engineering materials, namely high strength-weight and high stiffness-strength-weight ratios, thermal stability, corrosion resistance and fatigue resistance, making them suited for structures in which the weight is a fundamental variable in the design process [9]. Aerospace, automotive and marine industries are taken the advantages of the special characteristics of these materials [9].

In the recent years, important progresses have been made in developing composite laminates using thinner plies. Nowadays, thin ply composite materials are commercially available down to about 0.02 mm per ply depending on the type of fiber [10].

In this field, the tow-spreading technology, according to Sihn et al. [1], has the ability to continuously and stably open fiber tows, where widely opened tows can be cost-effectively

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State-of-the-art and literature review

obtained from thick tows, such as 12K filament tows or higher, without damaging the filament fibers.

In addition to benefits regarding laminated composites design [11] and manufacturing [11,12], such as easier homogenization, continuous lay-up, better fiber dispersion and uniformity of plies, and potential to use heavier tow yarns, laminates incorporating ultra-thin plies also show tremendous advantages with respect to their mechanical response [11–

13], namely the suppression of subcritical damage such as microcracking and delamination [13], extraordinary improvement of fatigue life, and increased damage tolerance. Therefore, it is not surprising to see that the interest of the scientific and industrial communities in this new technology has increased considerably over the last few years [11–17].

Tow-spreading methodology

There are several known technologies to make a thin ply. Among them, a promising and cost-effective way is to use a tow-spreading technology that was developed by Kawabe et al. [18] at the Industrial Technology Center in Fukui Prefecture (Fukui-city, Japan).

According to Sihn et al. [1], this method uses the conventional thick tow, such as 12 K filament tow (see figure2.1), that passes through a spreading machine that is equipped with an air duct and a vacuum that sucks the air downward through the air duct.

Figure 2.1: Schematic of tow-spreading process with a pneumatic method [1].

Thus, the tow sags downward towards the air flow direction so that it loses tension and results in a tension-free state momentarily. Using the uniform airflow continuously operating on the tow, the tow can be spread continuously and stably. Furthermore, the airflow does not usually cause any damage to the fiber filaments during this processing because the airflow velocity is fairly low, being this characteristic essential to do thin-ply laminates using spread tows [1].

Figure 2.2shows how this method works when the air flows around both sides of the tow. Basically, the difference in the velocity of the airflow, near and away from the tow, results in the difference in the pressure at these locations, what by its turn creates an aerodynamic force that helps the filament fibers to lose the tension momentarily [1].

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Figure 2.2: Schematic of tow-spreading process with the help of airflow [1].

2.2 In situ strength

The in situ effect was originally detected in Parvizi’s tensile tests of cross-ply glass fiber reinforced plastics [2] and it is characterized by higher transverse tensile and shear strengths of a ply when it is constrained by plies with different fiber orientations in a laminate, compared with the strength of the same ply in a unidirectional laminate, once the crack growing is restrained. The in situ strength also depends on the number of plies clustered together, and on the fiber orientation of the constraining plies.

Figure 2.3: In situ effect in laminated composites - In situ transverse strength vs total number of 90◦ plies clustered together (2n) [2].

The accurate in situ strengths are necessary for any stress-based failure criterion for matrix cracking in constrained plies. Transverse matrix cracking is often considered a begin mode of failure because it normally causes such a small reduction in the over-all stiffness of a structure that it is difficult to detect during a test. Thus, to predict matrix cracking in a laminate subjected to in-plane shear and transverse tensile stresses, a failure criterion was established as a function of the in situ strengths [2]. The in situ strength theory proposed by Camanho et al. [2] provides a model based on linear elastic fracture

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mechanics (LEFM) to rescale the apparent in situ transverse tensile and in-plane shear properties of thin plies. This theory suggest a 1/t1/2relation (where t is the ply thickness).

2.3 Failure modes in laminated composites

The failure of a laminate will be governed by any one, or a combination of the following ply-level failure mechanisms [3]:

• Translaminar crack progression through fiber tensile/compressive failure; • Longitudinal/transverse intralaminar matrix cracking;

• Interlaminar cracking.

Figure 2.4: Overview of ply-level failure modes [3].

To be more precise, the failure modes which can arise through direct in-plane loadings are: translaminar fiber tensile failure, translaminar fiber compressive failure and intralam-inar matrix failure [3].

1. Translaminar fiber tensile failure

The translaminar fiber tensile failure is characterized by the dissipation of large amounts of strain energy, with fiber-matrix debonding and subsequent fiber pull-out, resulting in homogenised ply-level fracture toughness, as it can be seen in figure

2.5(a).

2. Translaminar fiber compressive failure

On the other hand, “under an applied compressive load, failure of the fibers aligned with the loading axis can initiate as either shear driven fiber failure, figure 2.5(b), or fiber kinking, figure2.5(c)”.

3. Intralaminar matrix failure

Ultimately, “the intralaminar matrix failure is characterized by matrix cracking ei-ther longitudinally or transversely with respect to the fibers”.

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Figure 2.5: Failure mechanisms in fiber reinforced polymers (FRPs): (a) fracture surface including (1) translaminar fiber tensile failure and (2) longitudinal matrix failure, (b) shear driven fiber compressive failure (the arrows indicate the loading direction), (c) fiber kinking (the arrows indicate the loading direction) [3].

The critical strain energy releases rates associated with these modes of failure are properties that are intrinsic to the material system, and need to be measured for complete characterization of the damage tolerance of the material system and response during dam-age propagation. To characterize these properties, there is a need for reliable experimental procedures and the results need to be reproducible and the test method itself should no introduce scatter [3,19].

Below, it is presented, with some detail, some issues about translaminar fracture tough-ness, namely its definition and possible ways to evaluate it.

Translaminar fracture toughness

The translaminar fracture toughness (G) of unidirectional (UD) fiber reinforced poly-mers (FRPs) is the energy required to fracture the material perpendicular to the fiber di-rection (per unit nominal area). This property governs the damage tolerance of structures with load-aligned fibers, as well as the strength of components with geometric discontinu-ities [20].

The characterization and prediction of the translaminar fracture toughness is an im-portant issue regarding the effect of ply thickness on damage tolerance of a composite structure and response during damage propagation [21].

According to M.J. Laffan et al. [3], “whilst the importance of translaminar fracture toughness measurement was recognized many years ago, it has received relatively little attention from the scientific community until now. This is at least partially due to (i) a lack of confidence in composites resulting in them not being used in primary structures where this type characterization is useful, and (ii) the lack of modeling capabilities which can use the parameters effectively. Nowadays, this has changed as large composite primary structures can be found on the latest aircraft, for example, and finite element analysis (FEA) is a common tool used for design”.

The fracture toughness can be characterized by parameters such as the critical stress intensity factor (K_Ic) or the critical energy release rate (G_Ic), but it may be presented more accurately in the form of a resistance curve (R-curve), showing the change in the critical energy release rate with crack growth. To plot the resistance curve becomes evident

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that the specimen configuration need to exhibit stable crack growth to capture the change in critical strain energy release rate with the evolution of damage [3].

There is a diversity of approaches to quantify the translaminar fracture [3]. Results need to be reproducible and the test method itself should not contribute significantly to the scatter [21]. A wide range of specimen configurations, sizes and data reduction strategies have been used, despite the existence of an ASTM standard (namely, ASTM E1922 – 04 for tensile tests). However, “of the specimen configurations found in the literature, only the compact tension (CT), three/four point bend (3/4 PB) and extended compact tension

(ECT) specimens exhibit stable crack growth, that it is necessary to capture the change in

critical strain energy release rate with the evolution of damage in the form of a resistance curve (R-curve) [3]”.

As the CT specimen is the specimen used in this work, next paragraphs are dedicated to it.

Compact tension (CT)

According to M.J. Laffan et al. [3], “the compact tension (CT) configuration is perhaps the most widely used specimen configuration for translaminar fracture toughness measure-ment of composites”. A range of approaches to data reduction have been used, but by far the most widely used has been through the determination of the critical stress intensity factor, KIc, as recommended by ASTM E399 testing standard:

KIc= Pc

t√wf (a/w) (2.1)

where Pc is the measured critical load that causes fracture, t is the thickness of the

specimen, w is the dimension from the load line to the right hand edge of the specimen,

a is the crack length, whose initial value is a0 and f (a/w) is a finite-width correction

factor. However, a number of studies have used f (a/w) values obtained from expressions developed for isotropic materials, which can lead to errors when they are used in composite materials. Known KIc, the critical strain energy release rate, GIc, can be obtained from

the following expression [3]:

GIc= KIc2 √ 2E₁₁E22 v u u t s E11 E22 + E11 2G₁₂− v12 (2.2) where E₁₁ and E₂₂ are the laminate elastic moduli in the 1 and 2 directions, respectively (1 is the direction of the load), G12 is the laminate shear modulus, and v12 the Poisson’s

ratio.

Alternatively, and less prone to error, “the critical strain energy release rate, G_Ic, can be determined directly from experimental data, if the rate of change of compliance, C, with crack length, a, is known”:

GIc= Pc2

2t

dC

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Note that this method is only applicable for linear elastic materials.

Other methods of data reduction for CT testing like the area method, J-integral/VCCT, and so on, can be found in [21].

R-curves can also be experimentally obtained, but it is necessary that the specimen exhibit stable crack growth for its characterization, as said before.

Laffan et al. [3] investigated data reduction methods for calculation of the translaminar fracture toughness, using the CT specimen configuration, with the aim of finding the best technique, in terms of reproducibility of results and simplicity. The different approaches used were the ASTM E399 testing standard (valid for isotropic metals), the area method, the compliance calibration method (CC), the J-integral/VCCT method and the modified compliance calibration method (MCC), using optically measured crack length and effective crack length. The results for all data reduction schemes were fairly consistent however, a modified experimental compliance calibration method (MCC), using an effective crack length determined through compliance measurements, was considered to be the most ap-propriate data reduction scheme, as it gives consistent results and does not require the use of an optically measured crack length or FEA. The main advantages and disadvantages of the different methods studied are here presented. Thus, according to this article it was concluded that the area method is the simplest method, but has as disadvantages the use of an optically measured crack growth, ∆a, becoming more sensitive to errors for low ∆a and insensitive to R-curve effects for large ∆a, and, for stick-slip crack growth, it requires interpolating the load vs displacement curve between critical loads. The ASTM E399 testing standard method allows to choose the initial (a/w) ratio which gives accu-rate initiation values, but relies on optically measured crack length and the use of the factor f (a/w) for isotropic materials is inappropriate. The J-integral/VCCT method has as main advantage the elimination of any error provided from differentiating a fitted curve such as that in the CC and MCC methods, but, as the ASTM E399 testing standard, relies on optically measured crack length and additionally the use of FE analysis adds complexity. The CC method works well if the compliance vs crack length curve can be sufficiently populated, but, once again, its use relies on optically measured crack length and points for compliance calibration curve are dictated by specimen crack jumps, may result in areas of curve not being populated. Lastly, the MCC method does not require optical crack length measurement, but requires additional experimental work or adds the complexity of using FE analysis to obtain the compliance vs crack length curve.

2.4 Modeling of composite materials

With the increasing use of composite materials in industry comes an increasing need of a better understanding of their behavior and improving their performance. Over the years, a tremendous amount of activity has been devoted to developing accurate and fast non-destructive evaluation techniques as well as numerical methodologies, which can

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quantitatively predict the performance and durability of composite structures [22]. The way to evaluate the performance and durability of composite materials generally consists of a mix of testing and analysis. While testing alone is prohibitively expensive and time consuming, analysis techniques alone are usually not enough to adequately predict results [23].

In order to reduce the cost of the overall effort while maintaining, or even increasing reliability, the development of accurate analytical and numerical tools that are able to predict the response of composites is extremely important, because in the absence of such tools, the design process will rely on costly matrices of mechanical tests based on a large number of test specimens and empirical knockdown factors [23].

Below, an overview of some common methods employed in the analysis of composite materials is presented.

2.4.1 Modeling scale

The ability of the models to predict physical phenomena strongly depends on the scale at which the mechanisms under consideration are modeled. Basically, the identifi-cation, characterization and formulation of the governing physical principles, may span from molecular dynamics scales to structural mechanics scales, including the intermediate micro and mesomechanics scales. In the case of composite materials, the most common scales used are the micromechanical, mesomechanical and macromechanical scales [24,25].

Micromechanical scale, the scale based in the constituent level, represents what is

normally the smallest scale of composite models. At this scale, experimental data on the properties of the fibers and matrix materials are used to predict the properties of the individual lamina, then the laminate and finally the structure [26–28]. On the other hand,

mesomechanical scale take the laminate layers or sublaminates as the basic homogeneous

building blocks and use the orthotropic material properties related to the directions of the fibers, determined from lamina-level characterization tests, to predict the behavior of the whole laminate [26–28].

Finally, macromechanical scale is the scale where performing analysis is easier and the computational effort required is more reduced. The material is considered homogeneous and the effects of the constituent materials are represented only by averaged apparent properties of the composite material [26–28]. Using these models it is possible to study stress patterns and stress concentration regions in components assuming the material as an homogeneous material. Predictions of the propagation of the crack could be based on a strain-softening law or a criterion based on the critical energy release rate [27,28].

2.4.2 Fracture Mechanics

Fracture mechanics is a subject of engineering science that deals with failure of solids caused by crack initiation and propagation. There are two basic approaches to establish

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fracture criteria, or crack propagation criteria: crack tip stress field (local) and energy balance (global) approaches [29].

In the crack tip field approach, the crack tip stress and displacement states are first analyzed and parameters governing the near-tip stress and displacements fields are identi-fied. All these parameters enable to determine the stress intensity factor, K. In the scope of the linear elastic fracture mechanics (LEFM), the stresses at crack tip vary according to r−1/2, where r is the distance from the crack tip [29].

The second approach for establishing a fracture criterion is based on the consideration of global energy balance during crack extension. Firstly, the potential energy of a cracked solid under a given load, Π, is determined and then, its variation with a virtual crack extension, dA, is examined [29]. The parameter obtained with this calculation is called the energy release rate, G:

G = −∂Π ∂A= −

∂(U − V )

∂A (2.4)

where:

Π - is the potential energy;

U – strain energy;

V – work done by the applied forces.

Linear elastic fracture mechanics (LEFM) characterizes crack behavior by means of the

crack-tip stress intensity factor (SIF), K. Although routinely used to predict the residual strength of cracked metallic structures, the ability to predict crack initiation and propaga-tion in composites based on LEFM only emerged with the development of computapropaga-tional methods, in particular the modified virtual crack closure technique (VCCT) and the im-plementation of the J-integral in the finite element method (FEM) [28,30].

According to LEFM theory, when the energy release rate (or the SIF) exceeds the corresponding value, Gc (or fracture toughness, Kc), the crack should propagates.

How-ever, LEFM assumes that the material response is elastic and that the mechanisms that consume the fracture energy act at the crack tip. So, LEFM theory is limited to applica-tions in which the fracture process zone is confined to the immediate neighborhood of the crack tip, and it cannot be applied to a number of important cracking problems involving some of the tougher, more ductile materials that fracture after extensive nonlinear defor-mation. This is the case of many composite materials and structures, where the fracture process zone may be relatively large compared to other structural dimensions. Further-more, if nonlinear behaviors exist in a model, difficulties arise when using the previously mentioned LEFM computational methods in determining the load at which the crack tip energy release rate equals its critical value [31].

In order to avoid some of these problems, and extend the LEFM theory to situa-tions where it cannot be directly applied, nonlinear fracture mechanics (NLFM) is able to

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provide a framework for characterizing crack growth resistance and for analyzing initial amounts of stable crack growth [28].

2.4.3 Nonlinear Fracture Mechanics

One of the most difficult concepts to accept in the linear elastic fracture mechanics (LEFM) is the fact that stresses at the crack tip are infinitely large, or singular. This stress singularity results from the linear elastic continuum representation of materials and the assumption of a perfectly sharp crack. Once stress singularity contradicts our intuition about failure of materials, there have been efforts in introducing ways to remove the stress singularity at the crack tip [29].

Adopting inelastic behavior in solids is a natural extension of the LEFM to avoid stress singularity [28,29]. Nonlinear Fracture Mechanics (NLFM) was initiated by Irwin with a model for ductile solids based on an elastic/perfectly plastic material response to describe the effect of plastic material behavior in the vicinity of the crack-tip on the fracture propagation [29,32]. By assuming that plasticity affects the stress field only in the vicinity of the crack tip, the size of the plastic region may be estimated by equating the yield strength to the stress of the elastic field ahead of the leading crack tip. However, such an approach often goes back to using the parameters employed by the LEFM such as stress intensity factor1 [29].

Figure 2.6: Estimated size of the plastic region according to Irwin’s model (adapted from [4]).

An alternative, simple NLFM model, but however again based on LEFM considera-tions, was proposed in 1960 by Dugdale [33]. According to Dugdale’s model, yielding in an ideal elastic-plastic infinite plate subjected to a uniform tensile stress must occur over some length c − a (c > a) measured from the crack tip. It is assumed that the plate may deform elastically under the action of the extern stress together with a tensile stress distributed

1

Note that the effective crack length used in the calculation of the SIF is now a + rY, instead of a.

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over the yielded (plastic) region. To account both effects, the principle of superposition is used. Assuming that plastic deformation occurs when the yield strength, σ_Y, is reached, this tensile stress distributed over part of an hypothetical crack may be equal to the yield strength. Accordingly, the size of the plastic region may be estimated assuming that the stress singularity in the hypothetical crack tip, |x| = c, ceases to exist, as the sum of the stress intensity due to the remote stress and the stress intensity due to the closure stresses must be zero.

Figure 2.7: Dugdale’s model.

Another NLFM approach with particular interest is the cohesive zone model. The cohesive zone model is a methodology that simulates the nonlinear fracture response near the crack tip [28,34]. Due to its importance, the cohesive zone model is described in the next section.

2.4.4 Cohesive zone models

A different approach is the cohesive zone model, which adds a zone of vanishing thick-ness ahead of the crack tip with the intention of describing more realistically the fracture process without the use of stress singularity. The cohesive zone is idealized as two cohesive surfaces, which are held together by a cohesive traction [29]. The material failure is char-acterized by the complete separation of the cohesive surfaces and the separation process is described by a cohesive law (or traction-separation law). A cohesive law describes the relationship between the cohesive traction and the separation displacement, as follows:

σ = σcf δ/_δ max (2.5) where σ_c is the peak cohesive traction, δ_max a characteristic separation, and f a dimen-sionless function describing the “shape” of the cohesive traction-separation curve (cohesive curve). The function f depends on the failure mechanism operative either at the micro-scopic or macromicro-scopic level [29]. Besides the cohesive parameters σ_cand δ_max, the cohesive

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energy density Γc, or the work of separation per unit area of cohesive surface, defined by:

Γc= δmax

Z

0

σ (δ) dδ (2.6)

is often used [5,29]. Once the shape of the cohesive curve is given, only two of the parameters σc, δmax, and Γc are independent [29].

A schematic normal traction-separation law is shown in figure 2.8. At the tip of the cohesive zone the opening is zero. Assuming that the crack is loaded to the point of incipient fracture at the back of the cohesive zone, the opening is equal to δmax and the

stress is zero. The most important parameters in the cohesive zone model are the strength,

σc, and the energy, Γc , that it is the energy required to propagate the crack, as one can

be seen if, for example, the J-integral is calculated for the cohesive zone model [5].

Figure 2.8: Schematic of cohesive zone model. Two examples of traction-separation laws [5].

Complete representation of fracture requires an ability to model both the initiation and growth of fracture. However, in composite materials, more than one physical phe-nomenon is often involved in the fracture process. Some phenomena act at small opening displacements, which are confined to correspondingly small distances from the crack tip, and others act at higher displacements, which will extend further into the crack wake. For example, when long-range friction effects are present, a softening law may have a peak at low crack displacements corresponding to the tip process zone and a long tail at high crack displacements representing the friction in the wake of the crack [6]. Carlos G. Dávila et al. [6] concluded that a single bilinear softening law was insufficient to account the multi-ple damage mechanisms and the toughening due to fiber bridging and fiber pull-out that occurs during the fracture of a composite laminate. In this case, they showed that by combining two or more bilinear cohesive elements of different properties, it was possible to represent the resistance curve, necessary for predicting the initiation and propagation of fracture, as illustrated in figure 2.9.

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Figure 2.9: Trilinear softening law obtained by superposing two bilinear laws [6].

The two underlying bilinear responses may be seen as representing different phenom-ena, such as quasi-brittle delamination fracture characterized by a short critical opening displacement δ_max1, combined with fiber bridging, characterized by a lower peak stress and a longer critical opening displacement δmax2. After, it becomes necessary to

deter-mine the proportions of the contributions of each bilinear law to the total critical energy release rate and the strength. Consequently, for the superposition shown in the last figure, it is possible to define the proportions: σc1 = nσc, σc2 = (1 − n)σc, G1 = mGc and G2 =

(1 − m)G_c, with 0 ≤ n, m ≤ 1, so that,

Gc = G1+ G2 and σc = σc1+ σc2 [6]

Procedures to determine the strength ratio n and the toughness ratio m that approximate an experimentally-determined R-curve can be seen in reference [6], for example.

Cohesive zone Embedded in Elastic Material

As a fracture criterion, the cohesive zone model is generally used in the context of a FEA. Nodes along the prospective fracture path are doubled and a special cohesive element is placed between the doubled nodes. The cohesive element encodes the traction-separation law. Loads are applied to the finite element (FE) model and the equilibrium solutions are incrementally solved for. The crack advances when the displacement at the crack tip reaches δmax. If the material outside of the cohesive zone is linearly elastic, then

the energy required to drive the crack is simply G = Γ_c.

Careful calibration of the strength, σc, energy, Γc and possibly the shape of the σ(δ)

curve is required to obtain accurate fracture predictions.

2.5 ERR due to the bridging fibers

Translaminar cracking in composites is often accompanied by fiber bridging in the wake of the crack [35]. Such fibers reduce the stress intensity at the crack tip thus contributing

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to the enhancement of toughness of such materials. This increase is usually described by the resistance curve (R-curve) representing the relationship between the crack length and the corresponding ERR [36].

Due to its importance, different attempts in the literature have been made to charac-terize the role of the bridging fibers. One approach consists of constructing models where the bridging fibers are treated phenomenological by an equivalent pressure on the crack faces [37]. Another method is to measure the crack opening displacement (COD) at the end of the bridging zone and calculate (or measure) the corresponding ERR for different crack lengths [38,39]. The derivative of the ERR with respect to the COD results in the so-called bridging law. In both approaches, it is necessary to measure the length of the bridging zone which is usually very difficult because it is not possible to discern its end precisely. Moreover, additional hypotheses regarding the density of bridging fibers or ligaments and the shape of these bridging ligaments may be needed [37].

The cohesive zone approach is also commonly used for modeling crack propagation in the presence of fiber bridging, see e.g. [40,41]. In this approach, crack bridging is represented by surface tractions along the crack face and the relationship between the local traction and the local opening is considered as being a material characteristic, following a so-called cohesive law. However identification of the cohesive law parameters requires significant computational efforts, once it is based on an iterative optimization process aiming at the ‘calibration’ of the cohesive model parameters in order to simulate the global specimen response, e.g., the load-displacement experimental curve [42,43], or the near the crack tip displacement field [44,45].

A semi-experimental approach has also been proposed to describe the bridging trac-tions with an analytical function which smears out the effect of individual fibers [46,47]. This method is based on longitudinal distributed strain measurements around the crack tip by an embedded fiber Bragg grating (FBG) sensor and a subsequent identification of the bridging tractions using the measured strain data as input.

Recently, an alternative semi-experimental method to measure the distributed strain in the proximity of the crack tip was proposed [37]. As before, an FBG serves as strain sensor, but this time, instead of a single long FBG, an array of several short FBGs at equal distances on the same fiber was embedded. The resulting strain distributions served as input in an inverse numerical identification scheme to calculate the bridging tractions. Using crack opening data from numerical simulations, the bridging traction distribution serves to determine the traction-separation or bridging law, which can be inserted in a cohesive zone FE model of the specimen test to predict the load-displacement curve.

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Chapter 3

Digital Image Correlation (DIC) –

An Overview

As a practical and effective tool for quantitative deformation measurement of an ob-ject surface, DIC is now widely accepted and commonly used in the field of experimental mechanics. In this chapter, methodologies of DIC technique for displacement field mea-surement and strain field estimation are systematically reviewed and discussed.

3.1 Introduction

“DIC is a technique which could measure the displacement field from consequent digital images before and after deformation (referred as the reference and deformed image, re-spectively). It is a versatile method that works for any measuring techniques that outputs digital images, with measuring scale ranging from nanoscopic to macroscopic. Due to its simple experimental setup, non-contacting measurement and high accuracy, DIC has been extensively investigated and has become a popular and powerful method for measuring surface or 3D deformation which is one of central topics in structural mechanics. Once the displacement field can be related to many mechanical parameters, DIC can be applied to evaluate some mechanical properties directly, such as the stress intensity factor” [48,49].

“The main idea of DIC is to select a subset of interest (usually rectangle) in the reference image, then use it as a template to find its new location in the deformed image. The criterion is that the correlation between matching subsets in reference and deformed image should reach its maximum to make a best match.” Then this becomes a parametric optimization problem, with the correlation as the only objective function, that could be solved efficiently by some iterative methods (Newton-Raphson, for example). For full-scope displacement field, just repeat this procedure independently for every interested subset in the reference image [48,49].

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Digital Image Correlation (DIC) – An Overview

3.2 Fundamentals of DIC

In general, the implementation of DIC method comprises three consecutive steps: (1) specimen and experimental preparations; (2) recording images of the specimen surface before and after loading; (3) processing the acquired images using a computer program to obtain the desired displacements and strain information.

3.2.1 Specimen and experimental preparation

• Specimen preparation

To achieve effective correlation, the specimen pattern must be non-repetitive, isotropic and has high contrast. In other words, the pattern should be random, should not exhibit a bias to one orientation and show dark blacks and bright whites [50].

The speckle pattern can be the natural texture of the specimen surface or artificially made by spraying black and/or white paints, or other techniques [51]. The most common technique for applying a speckle pattern is with ordinary paint. Typically, the surface is coated with white paint, in several very light coats, to do not change the shape of the surface. The speckle pattern is then applied after the base coat becomes at least tacky [50]. Speckles should be neither too small nor too large. In practice, there is a very wide range in how large a speckle pattern may be, and still achieve excellent results, but having an optimal pattern will give the best flexibility [50], because to perform the tracking, the subset is shifted until the pattern in the deformed image matches the pattern in the reference image as closely as possible. This match is calculated as the total difference in gray levels at each point. “If the pattern is too large, we may find that certain subsets may be entirely on a black field or entirely on a white field. This does not allow us to make a good match, as we have an exact match everywhere in the field. This can be compensated by increasing the subset size, but at the cost of spatial resolution. Conversely, if the pattern is too small, the resolution of the camera may not be enough to accurately represent the specimen (aliasing). Instead of appearing to move smoothly as the specimen moves, the pattern will show jitter as it interacts with the sensor pixels, where the resulting images often show a pronounced moiré pattern in the results. In addition, patterns that are too fine are very sensitive to defocus” [50].

• Set up the cameras

The distance between the cameras system and the specimen will be determined by the available lenses. Short lenses are generally easier to work with and can give somewhat better results [50]. The distance is set so that the specimen roughly fills the field of view. The entire area of interest must be visible in both cameras. Generally, the specimen should be made just a bit smaller than the field of view, so that pixel-perfect alignment is not necessary.

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“Once the lens and an approximate distance are selected, cameras can be pointed and positioned somewhat symmetrically about the specimen, which will keep the magnification level consistent. The angle between the cameras is not critical but selecting a correct stereo angle will give best results: the angle should be at least 25◦ for short lenses (8 mm, 12 mm), at least 20◦ for medium lenses (35 mm), and at least 15◦ for longer lenses (70 mm). By the other side, the angle should be kept below to approximately 60◦” [50].

• Adjusting focus

After the cameras have been positioned, the next step is to set focus. The focus achieved should be sharp on the entire specimen. To aid in focusing, the lens’s aperture should be opened all the way. This will reduce the depth of field and make any focus issues very obvious. Then, the aperture can be returned to the appropriate setting for the test [50].

• Aperture and exposure time

It is necessary to adjust the brightness of the image. Thus, there are two controls: the aperture setting on the lens, and the exposure setting time of the camera.

Opening the aperture (f-number) allows more light to fall on the sensor. Using a bigger aperture (lower f-number) will make the image brighter. However, it will also decrease the depth of field, or in other words, the range over which the focus is sharp. Note that the aperture may not be changed after the system is calibrated [50].

On the other hand, the exposure time is the amount of time the camera sensor gathers light before reading out a new image. In contrast to aperture, exposure time may be ad-justed after the system is calibrated if lighting conditions change or the specimen becomes brighter/darker [50].

When exposure and aperture settings are completed, the image should be bright and there should be no overdriven pixels [50]. On the other hand, when the ambient light is not enough to achieve this, supplemental light will be required.

• Calibration

Once the cameras positions have been set and the focus and aperture adjusted, cali-bration is the next step to be done. After this point, changing any aspect of the camera system will invalidate the calibration, so all adjustments should be carefully fixed at this point.

Firstly, it is chosen a grid that approximately fills the field of view. After, calibration images must be acquired. More calibration images will give a more accurate result. For a typical setup, 15-20 images will be a good number. To acquire calibration images, several images of the grid in different positions should be captured, covering as many degrees of freedom as possible.

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The calibration procedure calculates variables about the camera geometry and imaging, and it is not specific to a plane or volume in space. Therefore, it is not necessary to position the calibration grid in the exact same location as the intended specimen [50].

Distortion order option

“If the calibration results become significantly better when the order is increased from 1 to 2, or 2 to 3, then the lens does have higher-order distortions. Lenses with higher distortion orders require more images and it becomes even more important to take grid images where points are present in the corners of the field of view” [50].

High-magnification option

“For macro lenses and small fields of view, it will become very difficult to get significant off-axis tilt in the target without severe defocus. Because of this, the “center” values may be poorly estimated. The best solution is to attempt to get as much tilt as possible to get a better estimate, but failing this, the High magnification option will force the center values to be the numerical center of the lens” [50].

3.2.2 Recording images of the specimen surface before and after loading

Once calibration completed, the next step is to run the test. Note that the aperture, focus and position of the cameras must not be changed without recalibrating. For most tests, the first image taken will be the correct reference image. All displacements and strains will be relative to this reference image.

3.2.3 Processing the acquired images using a computer program to ob-tain the desired displacements and strain information

After recording the digital images of the specimen surface before and after deformation, the DIC computes the motion of each image point by comparing the digital images of the test object surface in different states [51].

Before running the correlation, it is necessary to define an area of interest (AOI). The AOI is the portion of the image that contains the speckle pattern and which will be analyzed for shape and displacement. Besides, it is also necessary to set the Subset and Step for this AOI. The default values work well for most speckle patterns. If the pattern is very coarse, larger subset values may be needed [50].

The reference image will be then divided into evenly spaced grids and the displacements will be computed at each point of the virtual grids to obtain the full-field deformation. To evaluate the similarity degree between the reference subset and the deformed subset, some correlation criterion will be used by the computer program (cross-correlation criterion, sum-squared difference correlation criterion, or others) [51].

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3.3 Displacement measurement error analysis

Although DIC has fewer requirements in experimental environment compared with other techniques for deformation measurement, this does not mean that the measurement accuracy of DIC is not or less affected by the measurement system. In contrast, it is noted that the displacement and strain measurement accuracy of DIC relies heavily on the quality of loading system, the perfection of the imaging system and the selection of a particular correlation algorithm [51]. Below, the errors related to various factors are summarized [51].

Errors related to specimen, loading and imaging:

– Speckle pattern;

– Non-parallel between the sensor and the object surface and out-of-plane

dis-placement;

– Imaging distortion;

– Noises during image acquisition and digitization.

Errors related to the correlation algorithm:

– Subset size;

– Correlation function; – Sub-pixel algorithm; – Shape function; – Interpolation scheme.

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Chapter 4

Experimental test program

A set of experimental tests were performed during this work in order to study the fracture toughness and crack propagation of different thin-ply laminates. In this chapter, the experimental program performed is described as well as the results obtained with these tests, with particular emphasis on the steady-state ERR and R-curve behavior. In order to perform the data-reduction scheme compliance and area methods were used.

4.1 Material characterization and experimental procedure

Materials and manufacture

In this experimental program, cross-ply prepregs with four different fiber areal weight (150, 100, 75 and 30 g/m2_{) were produced at North-TPT Switzerland using M40JB fibers}

and ThinPregT M 80EP/CF epoxy resin.

Cross-ply (CP) laminates, [(90/0)_m/90]S, with approximately the same nominal

thick-ness, were produced in autoclave. The curing cycle was conducted according to the fol-lowing steps: (i) ramp up to 25◦C, (ii) immediately afterward, ramp up to 58◦C for 33 minutes, (iii) hold at 58◦C for 2h30, (iv) ramp up to 82◦C for 24 minutes, (v) hold at 82oC for 8h30, and finally (vi) autoclave cooling. The peak pressure used was 3 atm and it was applied when the temperature reached 58◦C.

To achieve uniformity of the specimen thickness, two rigid and perfectly planar alu-minum plates separated by precisely machined spacers were used for the production.

Traslaminar fracture of thinply composite laminates

Faculdade de Engenharia da Universidade do Porto

Translaminar fracture of thin-ply

composite laminates

Márcio Ferraz da Costa Fernandes

MSc Thesis

Translaminar fracture of thin-ply composite

laminates

Márcio Ferraz da Costa Fernandes

Mestrado Integrado em Engenharia Mecânica

Acknowledgements

Abstract

Resumo

Contents

List of Figures

List of Tables

Abbreviations

Notation

Chapter 1

Introduction

1.1

Context

1.2

Motivation and Objectives

1.3

Dissertation Outline

Chapter 2

State-of-the-art and literature

review

2.1

Thin-ply composite laminates

2.2

In situ strength

2.3

Failure modes in laminated composites

2.4

Modeling of composite materials

2.5

ERR due to the bridging fibers

Chapter 3

Digital Image Correlation (DIC) –

An Overview

3.1

Introduction

3.2

Fundamentals of DIC

3.3

Displacement measurement error analysis

Chapter 4

Experimental test program

4.1

Material characterization and experimental procedure