Processes of deposition and testing of mechanical properties of polymers and metal coated polymers

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THESE

Pour l'obtention du Grade de

DOCTEUR DE L'UNIVERSITE DE POITIERS

(Faculté des Sciences Fondamentales et Appliquées)

(Diplôme national - arrêté du 7 août 2006)

Ecole doctorale: Sciences pour l'Ingénieur & Aéronautique

Secteur de recherche: Physique: Milieux denses, materiaux et composants

Présentée par:

Brigita ABAKEVIČIENĖ

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Processes of Deposition and Testing of Mechanical

Properties of Polymers and Metal Coated Polymers

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Directeurs de thèse:

_{Joël BONNEVILLE}

Sigitas TAMULEVIČIUS

Soutenue le 16 Dècembre 2008 devant la Commission d'Examen

JURY

Maris KNITE Professeur Université de Rige, Lettonie Rapporteur

Jacek TYCZKOWSKI Professeur Université de Lodz, Pologne Rapporteur Arvaidas GALDIKAS Professeur Université de Technologique de Kaunas, Lituanie Examinateur Liudvikas PRANEVIČIUS Professeur Université de Vytautas Magnus, Lituanie Examinateur Claude TEMPLIER Professeur Université de Poitiers, France Examinateur Joël BONNEVILLE Professeur Université de Poitiers, France Examinateur Sigitas TAMULEVIČIUS Professeur Université de Technologique de Kaunas, Lituanie Examinateur

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Dedicated to

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ACKNOWLEDGEMENTS

Most of the experimental work presented in this Thesis has been performed in the Laboratoire Physique des Matériaux (PHYMAT) - Université de Poitiers (France) and the Institute of Physical Electronics of Kaunas University of Technology (Lithuania) in the framework of a common supervising agreement between both universities. I want to thank Professors Rolly Gaboriaud and Sigitas Tamulevičius, the directors of both laboratories involved in this common supervising thesis work.

This work would have been impossible without the help, support and understanding of many people, who made my life much easier, brighter and enjoyable.

Special thanks are addressed to:

 Professors Sigitas Tamulevičius, Joël Bonneville and Claude Templier as my supervisors for many insightful conversations during the development of the ideas in this thesis, for helpful comments and suggestions on the text and for their patience.

 Professor Philippe Goudeau, who taught me how to operate the Seifert apparatus and use four-cycle X ray diffractometer for the XRD measurements.

 The engineers Bruno Lamongie, Yannick Diot and electician Fabrice Berneau for the design of the microtensile device and for the help to adapt it for tensile measurements.

 Dr. Jérôme Colin for teaching the finite element method and interesting discussions.

 Dr. Jean-Christophe Dupré from Laboratoire de Méchanique des Solides (CNRS) for the mark-tracking technique realisation in my tensile experiments.

 All Laboratoire Physique des Matériaux, Physics Department and Institute of Physical Electronics of Kaunas University of Technology Staff.

 Professor Giedrius Laukaitis for remarks and kind review of the thesis.

 Dr. Liudvikas Augulis for introduction to electronic speckle pattern interferometry.  All my colleagues and students who contributed to this study.

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LIST OF FIGURES

Figure 1. Important coating/substrate properties for technological application [10]

Figure 2. (a) Schematic description of how speckles appear in a detector, (b) a typical speckle pattern, and (c) a random walk in the complex [69]

Figure 3. Shows interferometric speckle patterns obtained (a) before object deformation and (b) after object deformation from a shearography system. In (c) is the displacement gradient correlation fringes obtained from subtracting image (a) from image (b). The correlation fringes are sensitive to out-of-plane displacement gradient [73]

Figure 4. Modified Michelson interferometer for speckle interferometry. The reference mirror is replaced by diffuse scatterers [77]

Figure 5. Low-strain region of the engineering stress-strain curve for annealed polycrystalline copper; this curve is typical of that of many ductile metals [125]

Figure 6. Full engineering stress-strain curve for annealed polycrystalline copper [125] Figure 7. Stress-strain curve for polyamide (nylon) thermoplastic [125]

Figure 8. Comparison of engineering and true stress-strain curves for copper. An arrow indicates the position on the “true” curve of the UTS on the engineering curve [125]

Figure 9. Log-log representation of the plastic stress-strain data for copper [125] Figure 10. Stages of structure (a) and stress (b) evolution in thin films [131]

Figure 11. (a) drawing of tensile specimen, (b) photograph of Kapton®HN (dark sample is 125 µm thick, light sample is 25 µm thick) specimens (All dimension are given in mm)

Figure 12. The principal scheme of evaporator

Figure 13. Photomask patterns with x = 2mm, y = 1.5mm

Figure 14. (a) “DYNAPERT PRECIMA” centrifugal machine: 1–sample holder; 2–time speed control button, 3–“ON” button; 4–“OFF” button, 5–vacuum, 6–speed monitoring button. (b) Infrared soft bake machine “LADA”: 1–IR light system, 2-soft-baking temperature control (at the Institute of Physical Electronics Kaunas University of Technology, LITHUANIA)

Figure 15. Optical contact lithography and exposure machine

Figure 16. SEM photographs of freestanding Al film: (a) the top side of freestanding film, (b) the bottom side of freestanding film (Scale bars are: (a) 1000 µm, (b) 100 µm)

Figure 17. The photo of the four-circle Seifert XRD300 diffractometer (a) and the general schema of the four-circle diffractometer (b)

Figure 18. Instrumental peak broadening obtained from XRD θ - 2θ spectra of a standard LaB6

sample. The experimental integral peak width was fitted by polynomial of forth degree Figure 19. Scanning electron microscope scheme

Figure 20. In the inside of the sample chamber on the far left of the backscatter detector is the lens, in the centre is the secondary electrons detector. To collect electrons, the backscatter detector moves under the lens so the electron beam can travel through the hole in its centre

Figure 21. Principles of formation of composition image and topography image Figure 22. Principles of formation of composition, topography and shadow image

Figure 23. SEM backscattered electron images of PET sample: (a) shadow image (SHADOW), (b) composition image (COMPO), (c) topography image (TOPO)

Figure 24. Interatomic force vs. distance curve: (a) repulsive force, (b) attractive force Figure 25. X-rays photoelectron spectrometer

Figure 26. Schematic presentation of four-point probe when probes are in the same line and between them is the same distance [148]

Figure 36. Scheme of the ESPI system: 1-lens; 2-optical objective; 3-sample; 4-fixed grip; 5-moving grip; 6-load cell; BS-beam-splitter; M1 and M2-mirrors; CCD camera; PC 1-personal computer

Figure 37. Example of the speckle interference pattern of the Kapton® HN sample 25 µm thick. (Four bright fringes are visible in cross-sectional area 25 x 10-9 m2)

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temperatures

Figure 47. Rocking curves of the (111) reflection of Ag/PET samples for 20°C and 120°C deposition temperatures

Figure 48. Variation of the CDD size and microstrains, ε, as a function of deposition temperatures for Ag/PET structure: IB is the integral breadth method, WA is the Warren-Averbach method. The uncertainties are 2 nm and 0.005% for CDD and microstrains, respectively

Figure 49. sin2ψ plots for the Ag/PET {331} planes (red line-20°C, blue line-120°C) Figure 50. sin2ψ plots for the Ag/PET {420} planes (red line-20°C, blue line-120°C) Figure 51. sin2 Ψ plots for the PET/Ag {422} planes (brown line– 40°C, green line -80°C)

Figure 52. XRD pattern of Ag films on PET substrate of different thickness as deposited and under annealing at 140°C for 30 min: a) 20 nm, b) 50 nm, c) 100 nm

Figure 53. XRD Al peak d111 profile on PET before (1-20 nm, 3-50 nm, 5-100 nm thickness), and

after annealing at T = 140°C for 30min (2-20 nm, 4-50 nm, 6-100 nm)

Figure 54. AFM contact-force images of Ag on PET deposited at 20°C (a), 40°C (b) and 120°C (c) Figure 55. AFM images of Ag film on PET with thickness: (a) 20 nm and (c) 50 nm (as deposited), (b) 20 nm and (d) 50 nm (annealed at 1400C for 30 min)

Figure 56. AFM image of Al films on PET of various thickness (20, 50 and 100 nm) deposited at 20°C and later annealed at 140°C for 30 min (lateral force image)

Figure 57. (a) AFM image of 200 nm Al on PET at 20°C, (b) AFM image of 500 nm Al on PET at 20°C, (c) AFM image of 1 µm Al on PET at 20°C

Figure 58. Fitted XPS Ag 3d spectra for 1 µm thick silver film deposited on PET at 20o_{C: spheres -}

acquired data, dashed line – fitted data, thin line - metallic silver, thick line - silver bounded to oxygen, “sat.” - satellite signal is due to nonmonochromatized Al Kα radiation

Figure 59. Fitted XPS Ag 3d spectra for 20 nm thick Ag film deposited on PET at 20°C and annealed at 140oC for 30 min: crosses - acquired data, dashed line - fitted data, thin line – metallic silver, thick line - silver bounded to oxygen, ‘‘sat.’’ - satellite signal is due to nonmonochromatized Al Kα radiation

Figure 60. XPS C 1s spectra for 20 nm thick Ag film on PET deposited at 20°C and annealed at 140°C for 30 min: dashed line with crosses - acquired data

Figure 61. XPS spectra Al 2p of 1 µm thick Al film on PET Figure 62. XPS spectra O 1s of 1µm thick Al film on PET

Figure 63. C 1s peak of XPS for PET film coated with Al (20 nm thick): first curve, after film deposition; second curve, after thermal treatment at 140°C for 30 min

Figure 64. Drawing of half of a tensile specimen. Here, L1 = 1mm, L2 = 1mm, L3 = 8mm, l1 = 1mm,

l3 = 10mm, R = 1mm, n = 1, L1 = 2L0, L0 - the length of the right part of the sample

Figure 75. The pattern differences generated from the use of positive and negative resist [223] Figure 76. The three types of flood exposures used in photolithographic processing. Far left is contact printing, middle is proximity printing which employs about a 0.5-1 micron gap and projection printing is at the far right. Projection printing focuses the pattern of the optical mask through a lens [224]

Figure 77. The response curves for negative and positive resist after exposure and development [224]

Figure 78. The difference between anisotropic and isotropic wet etching [227]

Figure 79. The average roughness, Ra, is an integral of the absolute value of the roughness profile. It is the shaded area divided by the evaluation length, L

Figure 80. The amplitude distribution function (ADF) Figure 81. Relation between surface profile and Rsk value

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LIST OF TABLES

Table 1. Representative Young’s modulus values for different thin films with different thickness Table 2. The physical properties of substrates [29]

Table 3. The main process parameters of photoresist preparation used in our experiments Table 4. Process flow for the fabrication of the Al freestanding film

Table 5. Summary of mechanical properties obtained from tension test combined with MTT. (Values in bold font correspond to the bulk material [151])

Table 6. The results obtained by the integral breadth method using three hypothesis Table 7. The results obtained by the Warren-Averbach method

Table 8. The residual stress results obtained using sin2ψ method

Table 9. The crystallite size and microstrain of Ag films on PET (as deposited and annealed at 140°C for 30min)

Table 10. XRD analysis results of Al films on PET

Table 11. AFM analysis results of the Ag films (thickness 1 µm) on PET at different deposition temperatures

Table 12. Morphology and grain size of Ag films on PET (as deposited and annealed at 140°C for 30min).

Table 13. AFM analysis results of the Al films on PET at 20°C deposition temperatures

Table 14. Resistivity of different metallic films with thickness 1µm on PET and on Kapton®HN Table 15. Resistivity of different thickness Al films on PET

Table 16. Results of Kapton foils obtained with the ESPI and MTT Table 17. Results of PET foils obtained with ESPI and MTT

Table 18. Results of the Young’s moduli obtained with ESPI and MTT; Poisson’s ratio obtained with MTT

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LIST OF SYMBOLS

β integral breadth

βtrue integral breadth on the angular scale βt integral breadth of total experimental βgrain integral breadth of grain size

βstrain integral breadth of strain

βintrinsic integral breadth of intrinsic (convolution of grain size and strain)

βinstrumental integral breadth of instrumental profiles βC Cauchy component of the integral breadth βG Gaussian component of the integral breadth βP Voigt (parabolic) component of the integral

σy yield stress

σUTS ultimate tensile strength, σM dispersion of matrices M

σN dispersion of matrices N

σr residual stress

σ11tot total stress applied to the film (metal) - substrate (polymer) composite

σ11f,σ22f deduce the applied stresses to the film

< ε2>1/2 the root mean square strain (or the microdistortion) εAB strain between two points A and B

εx, εy, εxy strain tensor components ε1, ε2 eigenvalues of the strain tensor

ρ resistivity

ν Poisson’s ratio

νs Poisson’s ratio of substrate νf Poisson’s ratio of film

λ wavelength

ω width of the composite

φ Euler angle

Δφ relative phase between the two beams

θ angle between the surface normal in the z-plane and the incident wave fronts

θB Bragg angle of {hkl} planes of the crystal

ψ Euler angle

a_ψ,_ϕ lattice parameter

a0 stress-free lattice parameter

A0 initial specimen cross-sectional area (in Chapter 1) A specimen cross-sectional area (in Chapter 1) A cross-sectional area (in Chapter 2)

A maximum height (in Chapter 3)

A matrix

B matrix

C correlation matrix

D average size of the coherently diffracting domains (CDD) d reference length measured on the surface along the x-axis

Δd displacement

dAB relative displacement between two sampling points A and B

d0 interplanar spacing

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Ef Young’s modulus of film

Etot Young’s modulus of the coated polymer Es Young’s modulus of the polymer foil alone Ef Young’s modulus of the metallic film Erecom Young’s modulus of bulk materials

I speckle pattern intensity distributions obtained prior to displacement of the sample

I’ speckle pattern intensity distributions obtained after the displacement of the sample

I(x, y) light intensity of the pixel whose coordinates are (x, y) Is lower limit of the light intensity

F11tot resultant load along the longitudinal direction supported by the specimen film substrate

hf thicknesses of the thin film hs thicknesses of the substrate

K geometrical factor related to the shape of the crystallites L0 gauge length (in Chapetr 1)

L “apparent” domain size (in Capetr 2)

lAB elongation between to sample points (in Chapter 3)

M matrix

<M> average of matrix M

N matrix

<N> average of matrix N

N number of fringes forming the interference pattern NAB number of fringes between A and B

n the average speckle size

P load corresponding to the displacement

Ra average roughness

Rq root-mean-square (rms) average roughness

Rs sheet resistance

s scattering vector (in Chapter 2) s measuring sensitivity (in Chapter 3)

t sample thickness

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INTRODUCTION

Nowadays most materials used in Microelectromechanical systems (MEMS) and electronic devices are usually in the form of metallic thin films on rigid substrates or freestanding metallic films. An understanding of the relationship between the microstructure and the mechanical properties of these materials and the interfaces between them is crucial in optimising their performance and reliability. Interfaces between ductile thin films and brittle materials as substrates are very common in the microelectronics industry.

In addition to microelectronic and MEMS devices, thin films are widely used in other applications such as wear-resistant coatings for tools, thermal barrier coatings for jet engines and protective coatings for magnetic disks, etc [1-3]. The knowledge of the mechanical characteristics of thin films for such applications is important since these films are often subjected to very large mechanical stresses during both manufacturing and operation. These high mechanical stresses often lead to device failure.

Metallic films on polymers also have a wide range of applications in the field of MEMS and especially in the field of optical devices such as diffractive optical elements [3, VI]. Polymers are widely used in complex multilayered systems and the nature of the interfaces with metallic materials plays a major role in the definition of mechanical, electrical and chemical properties of the whole system [5]. In particular, the adhesion between the polymer and metal layer depends on the chemical interactions occurring at the molecular level at the metal/polymer interface. For instance, the adhesion of metallic films increases sharply with the polymer deposition temperature above 100 °C [6]. For temperatures above the glass transition temperature, rearrangement of the polymer chains may occur, leading to an improvement of film adhesion.

Determining adhesion of thin metallic films on polymers as well as determining their mechanical properties has become increasingly important as some application shift from hard metallic and ceramic films to more cost effective polymeric films. The importance of mechanical analyses of coated polymers, in terms of coating strength, internal stress sate, adhesion to the substrate, extend physical and chemical analyses. These features are nevertheless among the most important coating/substrate properties, as it is shown in Figure 1. Almost all films on substrate are stressed (under compression or tension) - the elastic stress in thin film is an inherent part of the deposition process. Typical values of the stress in thin metallic films can change in the range 107 - 109 Pa, in the insulator films these stresses are a bit lower and as a rule they are compressive [7]. It is very important to be able to monitor and control stress in the growing film and substrate to avoid undesirable effects to and investigate the stress dependence on technological parameters.

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Introduction

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Figure 1. Important coating/substrate properties for technological application [10]

Fundamental interest arises from the fact that the mechanical properties of geometrically constrained materials, such as thin films, often differ significantly from those of their bulk counterparts, which is usually ascribed to a size effect [8, 9].

The study of fracture mechanisms, such as fracture strength, fatigue behaviours and flow stresses are of great interest, because they are required to guarantee product reliability.

Mechanical properties of material are particularly sensitive to the microstructural length scale. The mechanical properties of thin films are often tested on a substrate, for example by radius-of-curvature measurements during thermal cycling [11, 12] or nano-indentation [13]. The constraint provided by the substrate provides good geometrical definition of the film and in many applications film properties have to be known under just such conditions.

The mechanical behaviour of a freestanding thin film is expected to be different from that of bulk material or a conventional thin film on substrate [14, 15]. In a freestanding thin film, the grain size is typically very small and the absence of a substrate leads to both its top and bottom surfaces being unconstrained. These microstructural characteristics may result in unique mechanical properties of a freestanding thin film. The elastic and inelastic properties of freestanding thin films can be measured by dynamic methods [16]. To know the stiffness or to achieve the large strains required for yield of fracture, other methods are necessary, such as the tensile test [17-19], the bulge test [20, 21]. The main difficulty with these is a reliable measurement of the strain.

The mechanical properties of most bulk materials are well documented. However, as a rule, thin film properties cannot be extracted from bulk properties, because their dimensional restrictions result in specific effects. The effect of surfaces becomes more important because the surface-to-volume ratio increases with decreasing dimensions. As a result, much effort has been devoted in the recent years on thin films testings. New techniques have been developed to perform tests at a reduced

Coating Interface Substrate • Roughness • Erosion • Corrosion/Oxidation • Electronic properties • Frictional characteristics • Porosity • Residual stress • Cohesion • Cracking/Defects • Multilayers • Graded composition • Adhesion • Adhesion • Substrate properties • Expansion mismatch • Interdiffusion • Diffusion barriers • Cleanliness/Roughnes s

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length scale.

Recent developments in the fabrication methods of thin films utilize the microfabrication techniques, including lithography [22], deposition and etching in order to produce micrometer sized tensile specimens. Microfabrication techniques offer the advantage that a large number of specimens with uniform thickness, chemical composition, geometry and structure can be fabricated in a single process run. Tensile tests can be carried out on as-fabricated, as well as heat-treated, specimens, which are easy to handle. Different specimen grips and loading devices have been used by the researchers, such as electrostatic or direct pin-like grip. Different techniques also have been used to obtain the actual sample strain, such as image correlation or different specimen lengths to correct for load-train compliance.

The task of the measurement of mechanical properties of thin films is carried out using various experimental techniques. Tensile tests provide several parameters, such as Young’s modulus, yield stress, ultimate strength and ductility [23]. These properties are specific of a given material and used for defining material applications, development of new materials and quality control. In addition, tensile properties are the input parameters for structural design, numerical modelling and computation of material mechanical behaviour in structures. Specimens used in conventional tensile tests are typically several millimetres or even centimetres thick for parallelepipedic specimens or in diameter for cylindrical specimens, which are a few orders of magnitude larger than the thin films used in microelectronics. The testing machines, grip devices and specimen preparation procedures prescribed for standard testing methods are not applicable for thin films, which have thicknesses in the micrometer or submicrometer range. Thin films of micrometer or submicrometer size have microstructures and properties, which are influenced by their fabrication processes that are different from bulk materials of the same nominal chemical composition. Extrapolations of properties of films prepared by one process often cannot be made from films prepared by other processes or from bulk specimens. The properties of thin films must be measured in the dimensions and conditions at which their are used in actual applications. Specimen fabrication, preparation and more specially specimen mounting on the loading devices were considered as an issue in the early developed techniques. Other indirect methods, such as the instrumented indentation test and the bulge test, have also been used to derive Young’s modulus and material strength. A variety of microtensile devices have been reported in the literature, each of them having their own disadvantages and advantages.

For the tensile test, it is essential that this measurement can be made in situ, i.e. on the specimen itself, as one uses a strain gauge in a conventional make the strain values unreliable. Sensitive displacement measurement techniques are needed for the mechanical property measurements, because the elastic displacements of thin film specimens are small. A number of in situ methods have been developed, such as speckle interferometry [24], the interferometric strain/displacement gauge

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Introduction

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[25], or X-ray diffraction [26]. Electronic Speckle Pattern Interferometry (ESPI), also called TV Holography or Digital Holography, where a laser beam is expanded by a lens and illuminates the surface to be measured, is a well-established optical technique for the measurement of in-plane displacement [27].

Scientific Novelty and Practical Value of the Dissertation

This thesis describes two original computer control piezo-actuated microtensile devices, where the deformation measurements are based on optical methods either ESPI or mark tracking method [28, V]. The microtensile devices were specially designed for investigating the elastic and plastic properties of thin films or multilayers structures. The performance of equipment has been first evaluated by preliminary tensile test on metallic films, polymers, metal coated polymers and freestanding aluminium thin films.

Principal Objectives of the Dissertation

The principal objectives of this work are twofold:

1. To design and perform of two original computer control microtensile deformation apparatus combined a piezo-actuated microtensile testing device with either an electronic speckle pattern interferometer or an optical mark-tracking device to test both the elastic and plastic properties of thin metallic, polymers, coated polymers and freestanding films.

2. Since the mechanical properties of materials are greatly influenced by their microstructures, a systematic study is necessary to evaluate the effect of interface formation between metal/polymer structure and the microstructure on the mechanical behaviour of thin films.

Tasks of the Dissertation

1. To modify the electronic speckle pattern interferometer set-up for measurements of in-plane displacements of different points of the sample gauge surface under tensile testing conditions and to combine with the first (1st) piezo-actuated microtensile testing device (developed at Kaunas University of Technology, Physics Department).

2. To adapt the ESPI algorithm of data analysis based on the speckle correlation matrix calculation at a microscopic scale.

3. To combine the mark-tracking technique (MTT) with the second (2nd

) piezo-actuated microtensile testing device (developed at University of Poitiers, Laboratoire de Physique des Matériaux, France) and to perform the stress-strain measurements of thin metallic films (Al, Cu) for the validation the microtensile system and measurement method (MTT).

4. Using developed microtensile devices combined with either an electronic speckle pattern interferometer or an optical mark-tracking device, to measure the elastic properties (Young’s

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modulus, Poisson’s ratio) and plastic behaviour of polymers (Kapton®_{HN and polyethylene}

terephthalate (PET)), metal coated (with Al, Ag, Ni, Cr) polymers and freestanding (Al) films.

5. To analyse the effect of the deposition temperatures of metal/polymer (Ag/PET) structures in order to understand how the microstructure, the residual stress, chemical composition and morphology of metal/polymer (Ag/PET) structures can be affected.

6. To investigate the mechanism of the interface formation between metallic (Ag) layers and polymer (PET) at temperature close to the polymer (PET) glass transition temperature.

7. To investigate the processes of the nucleation and shaping of nanostructures on polymer (PET) substrate during deposition and after thermal annealing by analysing the morphology and composition of ultra thin metallic (Al) films.

Structure of the Dissertation

The dissertation is composed of four chapters (introduction, experimental techniques, experimental procedures and results, conclusions), list of references, list of publications and abstracts in English and French languages. The dissertation consists of 138 pages, including 81 figures and 18 tables. The total list of references contains 228 references.

Approbation of the Research Results

The results of the research were prublished in 23 scientific publications: 3 of them in the Master List of the Institute for Scientific Information (ISI), 2 in proceedings of the ISI, 1 published in the periodicals in Lithuania and presented in 15 international and 2 national conferences.

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1. LITERATURE REVIEW

1.1. Introduction to Small Scale Testing

Any mechanical structure under loading can exhibit elastic, plastic, fracture, fatigue, anelastic or viscoelastic behaviour. These responses can be distinguished on the basis of complete recoverability, linearity and instantaneity in response that can be analyzed from the stress-strain relationship [29, 30]. At present, much of the micromaterial development is concerned with evaluating elastic, plastic and fracture behaviour. Mechanical material properties of interest include the Young’s modulus, Poisson’s ratio, yield stress, fracture stress and coefficient of thermal expansion (CTE). These measurements enable information about the residual stresses and stress gradients in the material resulting from fabrication and operation to be evaluated [31].

In the design of MEMS structures and devices, knowledge of mechanical material properties at small scales is necessary to understand the different failure mechanisms and achieve performance. Some materials can be manufactured only as small structures and cannot be produced in bulk form. In addition, the bulk specimens of the same nominal composition may have significantly different microstructure from that of the microscale, resulting in different mechanical response. Hence, direct measurement at small scales is extremely important for mechanical material characterization.

Thin films at micrometer and submicrometer level develop intrinsic loads during the deposition processes [32] and extrinsic loads due to operational and environmental conditions of the devices [33]. They may fail to maintain mechanical integrity, as observed by cracking, delamination, and void/hillock formation under stresses [34]. Accurate prediction of thin film materials response is a challenging problem because bulk testing methods, such as uniaxial tension test, are very difficult to apply directly to thin films, and extrapolation of bulk materials properties to the microscale is not scientifically reliable [35]. The problem is further complicated by the fact that mechanical properties of thin films are significantly affected by the fabrication processes [36] and are very sensitive to the influences of interfaces and adjoining materials [37]. Uniaxial tensile test, a popular method in bulk testing, is difficult to perform on thin films because of the challenges in 1) generating small forces (on the order of micronewtons), 2) gripping of the specimen, and 3) preventing bending force component in the specimen. While it is difficult to ensure no bending during tests the problems of fine force resolution and specimen gripping can be approached by using a substrate layer (usually very compliant, and with known materials properties) along with the actual film to be tested. This is demonstrated by [38], in which aluminium films were tested with thickness from 60 to 240 nm on

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Literature Review

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polymer substrates. However, introduction of the substrate complicates the experimental analysis because: 1) the microscale materials properties of the substrate itself may not be known accurately and 2) the interface may influence the mechanical behaviour of the film. Therefore, it is desirable to test freestanding thin films. This has been attempted by researchers who designed experimental setups with larger specimen sizes to cope with the coarser load resolutions. The tensilometer reported by Hoffman (1993) [39] is capable of generating 0.1 N force and was used to test (0.5 - 0.5)mm x 150 µm x 100 nm aluminium films. Ruud et.al [40] used motor-driven micrometers to produce elongation in freestanding films, then used a load cell to read the force and laser spots diffracted from the gratings on the specimen surface to determine the strain. The force resolution of their set up was 2 mN, and specimens could be tested with 1cm x (3.3 - 0.013) mm x (1.9 - 2.6) µm dimensions. Read [41] developed a piezo-actuated tensile testing apparatus with force and displacement resolutions of 200 µN and 20 nm, respectively, and demonstrated it on (700 x 200 x 1.2) µm multilayered film specimens. Piezoelectric actuators have been previously utilized by [42] and [43], who used load cell-laser interferometry and strain gauge-optical encoder assemblies, respectively, to measure force and displacements. They tested polysilicon structures with thickness of 3.5 and 2 µm, respectively.

1.2. Testing Methods for Thin Films

During the past decade, several experimental techniques have been developed for measuring thin film mechanical properties. Techniques to study thin films’ response to mechanical loading are diverse and can be classified as static or dynamic. Although both will yield the thin films’ mechanical properties, they accomplish it in completely different manner. Within the static group are nanoindentation (in standard DC mode) [44, 45], micro-tensile [46], bending [47, 48, 49] and bulge test [50, 51, 52]. Nanoindentation, when the continous stiffness measurement feature is used, resonance and fatigue methods [53, 54] belong to the dynamic group.

The dynamic techniques, such as the vibrational reed method, use acoustic waves to probe the elastic response of the sample [55]. For example, the vibration frequency can be correlated with the stress. These methods can be measure the tensor components of the stiffness (or compliance), but requires complicated and indirect schemes to measure the strain. Accuracy may suffer due to the numerous assumptions involved in data conversion. Furthermore, due to the infinitesimal nature of the applied strains, they are intrinsically incapable of probing large-strain phenomena such as the yield stress and the creep rate.

Most films are used on their substrates. Radius of curvature [56] and nanoindentation [57, 58] are among the most popular methods for on-substrate mechanical measurements. A variation of the radius of curvature is the microbeam deflection method [59], in which a thin film is micro-machined

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in such a way that only one end is attached to the substrate. Some measurements, however, such as those involving large deformation, can only be on freestanding films. The data from freestanding films are easier to interpret because the measured properties are intrinsic to the films, and therefore free from any substrate effects. Furthermore, substrate effects can be simulated to some extent with the introduction of hard passivation layers on the thin film surfaces.

For example, cantilever bending test is also a popular bulk testing method and is equally difficult to implement on freestanding thin films. Since the bending stiffness of freestanding thin films is much smaller than their tensile stiffness, the force resolution of the loading device must be high, and its spring constant must be comparable to that of the specimen. The cantilever bending test was first applied to thin films by [60], who used a nanoindenter as the loading device. The thinnest freestanding film tested by this method was a 0.87 µm thick gold film.

The tensile test [61, 62] and the bulge test are among the most popular static techniques. They use a slowly increasing applied stress to determine how a sample deforms. The major advantages in that they can measure large strain phenomena. The results are easier to interpret but typically have lower accuracy than those from the dynamic measurements. For example, the compliance of the apparatus or sample slippage may be erroneously recorded as part of the sample deformation. Even more importantly, these methods have been mostly developed for testing bulk samples. They are ill-suited for testing thin films or multilayers because the sample sizes are often orders of magnitude smaller.

The Development of Non-Destructive Testing Material characterization and structure evaluation is a fundamental task in many fields. Experimental measurement methods should have a high sensitivity without affecting, with their presence, the results. This is particularly true when small-size specimens are studied.

Optical methods are inherently non-intrusive and non-contacting. Furthermore, they are highly sensitive and provide full-field measurement data.

Laser and holographic interferometry are now well-established techniques in optical non-destructive testing. However, shortcomings such as stringent stability requirements, high costs, and the need for optically skilled operators hindered the spread of these methods in hostile and/or industrial situations.

Review of the literature shows that several indirect strain measurements techniques have been developed to meet the needs of micromaterial measurements. Other indirect measurement tests involved the use of a micrometer stage that is capable of inducing a known amount of strain to the sample [63]. The smallest displacement allowable by a micrometer often will plastically deform the sample with no measure of the elastic region. In addition, slipping or rigid body motion is not

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distinguishable from strain in such crosshead displacement measurements. Microscale material characterization calls for strain measurement over small gage meters. Li et. al. [64] measured strain in sections ranging from 10 to a few 100 microscale specimen using the Moiré technique. The technique involved using Focused Ion Beam (FIB) to write a ‘nanograting’ on top of the microscale by ion milling. The strain was measured by counting the Moiré fringes that were formed after deformation of the structure in a scanning electron microscope. The strain is calculated after the experiment is performed and does not provide a real-time measurement. The Moiré fringes provide a full field strain but the drawback to this technique is that improved measurement resolution is achieved by increasing the density of the gratings and is limited by FIB [64]. Bremand et. al. [65] made non-contact measurements of local strains using a master grid marked on the sample and diffraction technique based on the diffraction of a laser beam by orthogonal grating. The diffracting light spots characterize the grating geometry on the surface. The comparison between the undeformed and deformed state allows the determination of the magnitude and orientation of principal strains. Fast Fourier Transform (FFT) techniques were demonstrated to enable direct mechanical material characterization of the sample. Although the technique was completely non-contact in nature the technique required post processing precluding real-time measurements [65].

A number of non-contact real-time direct strain measurement techniques have been developed. Bell [66, 67] used lines on the surface of the specimen to produce an optical diffraction pattern. The spatial frequency of the diffraction pattern is monitored providing direct strain measurement in the gage section marked by the ruled lines. Yang et. al. [68] constructed a universal digital laser micro-interferometer capable of measuring displacements based on laser interferometry using a modified Michelson Interferometer. The technique uses ESPI to extract phase information [68], and the interferometer is capable of measuring shape, displacement, in-plane and out-of-plane strain of microscale specimen. A drawback in this test setup is the low spatial resolution and the inability to measure small displacements. In the ESPI, an optical lens is used to focus the CCD on the specimen which can lead to errors from aberrations in the optics and negatively affects the resolution limit. 1.3. Speckle Pattern Interferometry

Speckle pattern interferometry is an important and growing part of optical measuring techniques in experimental mechanics. Speckle techniques use the random pattern of dark and bright spots (speckles) that are formed in space when a diffusely reflecting object is illuminated by coherent laser light (laser speckles), or when a random pattern exists naturally at the object’s surface (white light speckles). The speckle formation depends on the form of the surface, which must be rough

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compared with the laser wavelength. The speckles contain phase information about the object surface added to a speckle noise term, which depends on the object surface in a complex way. Speckle pattern interferometry uses this phase information to perform measurements. To avoid analysis of an individual speckle pattern, two speckle patterns are correlated, often by subtraction, to obtain the optical phase change when a perturbation is applied to the system.

Laser speckle is the granular appearance of the light intensity, formed by illuminating an optically rough surface with a laser. An optically rough surface has a roughness of the order of, or greater than, the optical wavelength. To be more precise this speckle pattern is an objective speckle pattern as the intensity pattern depends on viewing direction. This type of speckle pattern depends on the optical wavelength and the illumination and viewing parameters. Alternatively a subjective speckle pattern can be obtained by imaging of the speckle pattern. The spatial distribution of the speckles in this type of speckle pattern is limited by the diffraction limit of the imaging system and the optical wavelength.

A noisy, random granular speckle pattern is observed when looking at or imaging a laser illuminated, diffusely reflecting surface with the eye or with a camera (see Figure 2(a) and (b)). Fully developed speckles appear only if the height variations of the surface are greater than the wavelength, λ, of the light. Such surfaces are said to be optically rough. If the object is imaged, each point P on the detector will gain contribution of light coming from a coherence volume, determined by at least the airy spot and the roughness of the surface. A summation of these wave packages that illuminates point P is illustrated in Figure 2(c), describing a so-called random walk. As long as the complex amplitude A follows the statistics indicated in the figure, the speckle field is fully developed.

The observed speckle pattern could be thought of as a “fingerprint” of the illuminated area in the sense that the observed pattern is unique for the microstructure of the specific surface area. Another area will give rise to a totally different random speckle pattern. When the surface area is moved or deformed, the observed speckles in the image plane will also move accordingly. This is the reason why speckle correlation techniques are so good at determining in-plane motions of an object.

In speckle correlation techniques, the movement of the speckle pattern in the image plane is studied, i.e. the movement of the surface. Speckle pattern interferometry systems on the other hand study the phase information of the speckles. As opposed to classical interferometry where optically smooth surfaces are studied and no speckle pattern appears, speckle interferometry uses the phase information carried by the speckles to determine the deformation of the object. Classical interferometry obtain the shape of a polished part by comparing the deformed reflected wave with a plane reference wave, no speckles are present. The difference between the waves will give rise to

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(a) _(b) _(c)

Figure 2. (a) Schematic description of how speckles appear in a detector, (b) a typical speckle pattern,

and (c) a random walk in the complex [69]

interference fringes describing the shape of the object, i.e. only one interferogram is needed. In speckle interferometry optically rough surfaces are studied and therefore the interference pattern obtained when the reflected wave and the reference wave interfere will be a random speckle pattern with varying phase and amplitude. Therefore, in speckle interferometry a second interferogram after the object has deformed in some way is captured. The fringes obtained when these two interferograms are compared describe the deformation of the object. The reference wave can be either a smooth wave (as in out-of-plane set-ups) or a speckle pattern (used in shearography and in-plane set-ups), as long as it is constant in time. One could say that speckle correlation and speckle interferometry methods complement each other in this respect, explaining why the combined speckle interferometry/speckle correlation technique is investigated.

The principal speckle interferometry techniques are ESPI and shearography. ESPI utilising a smooth reference beam is a technique sensitive to displacement [71] or surface shape [72] depending on the optical configuration used. Shearography is a subtechnique of ESPI, utilising a common path speckle reference formed using a shearing interferometer, and is an optical configuration that is sensitive to displacement derivative [74] or surface slope. The sensitivity to displacement gradient, a parameter closely related to surface strain, and insensitivity to rigid body motion [70] are advantages of shearography for surface strain measurement. Both ESPI and shearography have variable sensitivity vectors depending on the illumination and imaging directions.

ESPI, although it is also called video holography, TV holography or electronic holography (EH). The basic concepts of ESPI were developed almost simultaneously by Macovski, Ramsey, and Schaefer (1971) in the United States and by Butters and Leendertz (1971) in England [72]. The advantages of the ESPI technique are the accuracy and spatial resolution of the measurement (in the micron meter range), a larger measuring area than the measurement area of strain gages, and non-contact measurement.

The major features of electronic speckle techniques are:

• It is a non-contact measurement method with wavelength order accuracy.

Aperture

Surface Roughness P

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• A full field measurement. It is not limited to single points as for a contact sensor.

• It is well suited for computer aided measurements since the information is acquired and evaluated electronically.

• The sensitivity is much higher than that of holographic plates and thus allows one to use shorter exposure times than those in classical holography. The vibration isolation requirement cab thus is relaxed a bit.

• Almost a real-time operation. The correlation fringes can be displayed on a monitor without the recourse to any form of photographic processing, or plate relocation.

• The resolution of the recording medium used, need not to be high compared with that required for traditional holography.

ESPI is a technique that can measure optical path length differences of the order of the optical wavelength, or below, in full-field across the surface of the object under investigation. The full-field aspect of the measurement is due to the recording of the intensity of the interferometric speckle pattern across the field of view of the camera. A speckle pattern is a distribution of intensities formed by the interference of coherent light scattered from different points on an optically rough surface. In speckle pattern interferometry the speckle pattern formed in this way is optically mixed with a reference beam, or reference speckle pattern, originating from the same optical source to form an interferometric speckle pattern that may be recorded by a camera. In the interferometric speckle pattern the intensity of the light contains information on the optical phase and hence on the optical path length difference between the two paths through the interferometer. Recording interferometric speckle patterns obtained before and after applying a perturbation to the system and then correlating the interferometric speckle patterns, commonly by subtraction, yields correlation fringes that can be processed to recover the measuring.

An example of the formation of correlation fringes is shown in Figure 3. The images were recorded by a shearography system with the shear applied in the horizontal direction. Figure 3 shows speckle patterns recorded (a) before and (b) after a point deformation to a flat plate, normal to the object surface and approximately in the centre of the field of view, (c) shows the correlation fringes sensitive to out-of-plane displacement gradient obtaining by subtracting image (a) from image (b).

The sensitivity of speckle interferometry is given by the geometry of the set-up and the wavelength. Speckle decorrelation limits the range of motion or deformation that can be recorded with speckle interferometry. Many different speckle interferometer configurations have been proposed and used for a variety of different applications [75]. Depending on the optical configuration, the speckle interferometer can be made sensitive to out-of-plane displacements, in-plane displacement, or both. In early experiments [76], the Michelson interferometer configuration was used, but the mirror was replaced by diffuse scatters. Figure 4 shows a diagram of the set-up

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[77]. An imaging system is now needed so that the two superimposed wave fields from the object and reference surfaces can be recorded photographically.

(a) (b)

(c)

Figure 3. Shows interferometric speckle patterns obtained (a) before object deformation and (b) after

object deformation from a shearography system. In (c) is the displacement gradient correlation fringes obtained from subtracting image (a) from image (b). The correlation fringes are sensitive to

out-of-plane displacement gradient [73]

Figure 4. Modified Michelson interferometer for speckle interferometry. The reference mirror is

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ESPI experimental set-ups can be divided, mainly, into two major groups depending on the type of deformations that can be measured: out-of-plane or in-plane interferometers. The direction in which the measurements can be carried out is defined by the arrangement of the coherent light sources employed in the experiment [78]. As is obvious the change from one configuration to another is neither a simple neither a fast process; in fact, it is quite time consuming. An in-plane set-up can only determine the displacements that take place in one direction of the plane. This direction is determined by the intersection of the plane formed by the two illuminating beams with the object and perpendicular to the optical axis of the imaging system. The change of position of the beams is usually a complicated and time-consuming process. Another possibility is the change of position of the object, though in some cases this is impossible because the dimensions of the object make it complicated.

1.4. Effects of Size on Mechanical Properties of Thin Films

The mechanical properties of thin films can be very different from those of bulk materials. The mechanical behaviour of a material is determined by its microstructure, which is described by an arrangement of defects at a microscopic scale. This length scale is far below the macroscopic dimensions of bulk samples, but in thin films, the film thickness is often below that length scale. Therefore, film surface and the interface between film and substrate or between multilayers will influence the processes that control the mechanical behaviour of the films [79]. For example, micrometer scale thin films are often found to support much higher stresses than bulk samples of the same material. This has been attributed to constraints on dislocation motion imposed by the interfaces with surrounding layers and to the small (nano) grain size, that is typically encountered in thin films [80]. Dimensional constraints are imposed by interfaces and the small dimensions typically encountered in thin films, whereas microstructural constraints arise from the very fine grains often found in thin films [81]. In bulk materials, microstructural constraints dominate the plastic behaviour of the material. However, when material dimensions are comparable with microstructural length scales, as for thin films, free surfaces and interfaces are important as well. For example, dislocations can exit the material through free surfaces, and strong interfaces can prevent them from doing so. Consequently, interfaces may lead to a higher cumulative dislocation density in the film, resulting in higher flow stresses and greater strain hardening rates.

Another example is that recent measurements of Young’s modulus on freestanding thin films show that the measured values are smaller that the values for bulk materials [82].

A lot of theoretical and experimental works have been conducted to explain the mechanical properties of thin films such as Young’s modulus, yield stress and strain hardening behaviour.

The yield stress of thin films is usually much larger than that of their bulk counterparts. The strengthening effect in thin films is usually attributed to two kinds of constraints: dimensional

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constraints, which are usually indicated as film thickness effects, and microstructural constraints, such as grain boundary strengthening. The presence of the film-substrate interface and film passivation layer interface belongs to the dimensional constraints, and the small grain size typically found in thin films belongs to the latter [79 - 82].

The film thickness effect has been modelled by various researchers. Theoretical models can be roughly classified into two main categories.

The macroscopic models are based on the continuum theory of plasticity, such as the strain gradient plasticity theories developed by Aifantis [83, 84] or Fleck and Hutchison [85, 86].

The microscopic models are based on dislocation mechanisms, such as the one dislocation model proposed by Nix [79] or the discrete dislocation dynamics simulations by Needleman and Van der Giessen [87, 88].

Compared with dimensional constraints, the effects of microstructural constraints have been widely studied in bulk materials, and various models are well established. For example, the Taylor equation provides a relationship between flow stress and dislocation density, while the well-known Hall-Petch equation quantifies the effect of the grain size [89]. Some of these models developed for bulk materials break down for materials with ultra fine microstructures. Spaepen and Yu [90], for instance, recently compared the effect of microstructural length scales on the yield stress of various Cu-based materials including multilayers, thin films, and nanocrystalline compacts. They found that the classical Hall-Petch relation tends to overestimate the yield strength when the relevant microstructural length scale decreases below 1µm. Furthermore, research on nanocrystalline materials reveals that when the grain size decreases below a critical value (on the order of 10nm), some materials may exhibit an inverse Hall-Petch behaviour, where the flow stress decreases with decreasing grain size [91, 92]. This behaviour has been attributed to grain boundary deformation mechanisms such as grain boundary sliding and rotation that become dominant at very small grain sizes [93].

Table 1 lists the test methods and results from representative works in which the Young’s moduli were measured.

In addition to thin film plastic behaviour, elastic properties are of interest as well. Recent measurements of Young’s modulus of various freestanding metal films and multilayers, including Cu [93-98], Ag [95], Al [95, 97, 99], W [97], Au [100, 101] and Cu/Ag multilayers [95] have yielded experimental values that are 20–50 % smaller than for bulk materials, and other researchers have reported values similar to those of bulk materials [100-106]. This modulus decrease is observed mainly for films deposited with electron beam evaporation and tested using the microtensile technique [95, 96, 99, 100] although sputtered Au films with ultrafine grains [101] and some electroplated Cu films [98] have also been reported to have lower Young’s moduli.

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One of the surprising results for thin films is that the measured Young’s moduli are significantly smaller than bulk values. In this case, the modulus deficit can be partially explained by the fact that thicker films are less dense, so a lower modulus reading maybe expected. Also the surface roughness increases significantly with the film thickness, which affects the contact area determination in the indentation analysis for example.

Table 1. Representative Young’s modulus values for different thin films with different thickness

Material Thickness of the film (µm) Young’s Modulus (GPa) Testing Methods References Bulk Young’s Modulus (GPa) 0.01 – 0.07 ∼154 Bulge test [106] 0.2 43 ± 13 1.0 43 ± 12 Indentation test [107] 73 Bulge test [108] 69 Beam bending test [109] 71 Indentation test [108] ∼1.0 69 Tensile test [109] 2.0 60 Tensile test [110] Al 3.0 57 Tensile test [111] 70 0.1 – 0.3 78.5 Bulge test [112] 57 Beam bending test Au 0.87 74 Indentation test [113] 78 0.07 – 0.5 124 Bulge test [114] 0.99 – 1.73 99-110 Tensile test [115] 0.2 133 2.0 110 Indentation test [29] 3.0 102 Tensile test [111] Cu 18 – 70 105 Tensile test [116] 110 - 128

TiCuTi 0.05 + 1.1 + 0.05 107 Tensile test [117] 105 – 120 (for Ti) 1.5 – 3.5 162 Tensile test [118] 2.0 (×2 µm) 167 Tensile test [119] Poly-Si 3.5 169 Tensile test [120] - 222 0.29 216 Indentation test [121] 0.5 255 Tensile test [122] Si nitride 0.7 150 -

SiO2 0.65 70 Tensile test [119] -

1.5. Introduction to Stress and Strain

Stress is defined as a force per unit area and strain as the relative change in sample length, usually expressed in percent. In a uniaxial test using the initial sample dimensions yield engineering stress and strain; while using the true dimensions lead to the true stress and true strain. In the current study, we ignore this difference in tensile testing because the maximum sample elongation was less

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than 2% at room temperature.

How a sample deforms (strain) under load (stress) has always been the central problem to solid mechanics. Deformation of a solid may be instantaneous or time –dependent. In either case, the deformation may be permanent or recoverable, or a combination of the two.

Most metallic alloys and thermoset polymers are considered isotropic, where by definition the material properties are independent of direction. Such materials have only 2 independent variables (i.e. elastic coeffients) in their stiffness and compliance matrices, in contrast with the 21 elastic coefficients in the more general anisotropic case.

The two elastic coefficients are usually expressed as the Young's modulus, E and the Poisson's ratio, ν. However, alternative elastic constants K (bulk modulus) and/or G (shear modulus) can also be used. For isotropic materials, G and K can be deduced from E and ν by a set of equations, and vice-versa.

Hooke's law for isotropic materials in compliance matrix form is given by [123]:

! ! ! ! ! ! ! ! " # $ $ $ $ $ $ $ $ % & ! ! ! ! ! ! ! ! " # $ $ $ $ $ $ $ $ % & + + + ' ' ' ' ' ' = ! ! ! ! ! ! ! ! " # $ $ $ $ $ $ $ $ % & xy zx yz zz yy xx xy zx yz zz yy xx E ( ( ( ( ( ( ) ) ) ) ) ) ) ) ) * * * * * * 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 _{. (1)}

A factor 2 can be found in literature, which multiply the shear modulus in the compliance matrix; it results from the difference between shear strain and engineering shear strain, where

xy yx xy

xy ! ! !

" = + =2 , etc.

The stiffness matrix is equal to the inverse of the compliance matrix, and is given by

! ! ! ! ! ! ! ! " # $ $ $ $ $ $ $ $ % & ! ! ! ! ! ! ! ! " # $ $ $ $ $ $ $ $ % & ' ' ' ' ' ' ' + = ! ! ! ! ! ! ! ! " # $ $ $ $ $ $ $ $ % & xy zx yz zz yy xx xy zx yz zz yy xx E ( ( ( ( ( ( ) ) ) ) ) ) ) ) ) ) ) ) ) ) * * * * * * 2 1 0 0 0 0 0 0 2 1 0 0 0 0 0 0 2 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 ) 2 1 )( 1 ( . (2)

Accordingly, a factor 1/2 may exist that multiply the shear modulus in the stiffness matrix resulting again from the difference between shear strain and engineering shear strain.

“Engineering” stress-strain curves

The tensile test is the most important test for investigating material’s mechanical response [124]. It consists to clamp one end of specimen to a loading frame while the other is subjected to a

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controlled displacement δ. A transducer connected in series with the specimen provides an electronic reading of the load P(δ) corresponding to the displacement. Alternatively, modern servo-controlled testing machines permit using load rather than displacement as the controlled variable, in which case the displacement δ(P) would be monitored as a function of load. The engineering measures of stress and strain, referred to as σe and εe in the following, are determined from the measured load and elongation using the initial specimen cross-sectional area A0 and the gauge length L0:

0 A P e = ! and 0 L e ! " = . (3) Plotting the stress σe as a function of the strain εe, provides the engineering stress-strain curve, such as the one shown in Figure 5.

In the early (low strain) portion of the curve, many materials obey Hooke’s law to a reasonable approximation, that means the stress is proportional to strain with a proportionality coefficient, which is the elastic modulus or Young’s modulus, denoted by E, such as:

e

e E!

" = . (4)

Figure 5. Low-strain region of the engineering stress-strain curve for annealed polycrystalline copper;

this curve is typical of that of many ductile metals [125]

As strain is increased, materials either break or deviate from this linear behaviour, the point of departure being termed the yield stress. The nonlinear behaviour is usually associated with stress-induced “plastic” flow in the specimen. Here, the material is undergoing a rearrangement of its internal molecular or microscopic structure, in which atoms are being moved to new equilibrium positions. The stress-strain curve for brittle materials is typically linear over their full range of strain, eventually terminating in fracture without appreciable plastic flow [125].

Note that an increase in stress is needed to increase the strain beyond the yield stress (Figure 5).

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The microstructural rearrangements associated with plastic flow are usually not recovered when the load is removed, so that the yield stress upon reloading is often the same as or at least close to the material’s elastic limit. Elasticity is the property of complete and immediate recovery from an imposed deformation on the load release. The elastic limit is the stress value at which the material experiences a permanent residual strain, which is not recovered upon unloading. The residual strain induced by a given stress can be determined by drawing an unloading line from the ultimate flow stress reached on the σe-εe curve with a slope equal to that of the initial elastic loading stage. This is because there are no driving forces for the molecular structure to go back to its original position.

A closely related term is the yield stress, denoted by σY in the following; this is the stress needed to induce plastic deformation in the specimen. Since it is often difficult to define the exact stress at which plastic deformation begins, a proof stress or “offset yield stress” is taken to be the stress needed to induce a specified amount of permanent strain, typically 0.2%. The construction used to find this “offset yield stress” is shown in Figure 5, in which a line of slope E is drawn from the strain axis at εe=0.2%. This is the unloading line that would result in the specified permanent strain of 0.2%. The stress at the intercept with the σe-εe curve is the “offset yield stress”.

Figure 6 shows the engineering stress-strain curve for copper with an enlarged scale, showing now strains from zero up to specimen fracture. Here, it appears that the rate of strain hardening (the strain hardening rate is the slope of the stress-strain curve) decrease up to a point labelled UTS, for Ultimate Tensile Strength (denoted by σf in these modules). Beyond that point, the material exhibit strain softening, that is each strain increment requires a smaller stress.

Figure 6. Full engineering stress-strain curve for annealed polycrystalline copper [125]

The apparent change from strain hardening to strain softening is an artefact of calculations of the stress. Beyond the yield stress, molecular flow causes a reduction in the specimen cross-sectional area A, so that the true stress σt = P/A actually sustained by the material is larger than the engineering

Processes of deposition and testing of mechanical properties of polymers and metal coated polymers

THESE

DOCTEUR DE L'UNIVERSITE DE POITIERS

Brigita ABAKEVIČIENĖ

Processes of Deposition and Testing of Mechanical

Properties of Polymers and Metal Coated Polymers

Joël BONNEVILLE

Sigitas TAMULEVIČIUS

JURY

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

LIST OF SYMBOLS

INTRODUCTION

1. LITERATURE REVIEW

_{Joël BONNEVILLE}