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The purpose of the present article is to make a model using analytical equations, based on elasticity theory of continuous media for small deformations, with the aim of completely characterizing the material in their mechanical properties as well as the principal stresses-strains of thin films. The approach differs from the standard literature which usually brings crystal symmetries or is directly concerned with crystalline materials. It is entirely possible to define and to analyze anisotropy in elastic media from first principles in thin films. Therefore, the constitutive relation between strain and stress will be considered orthotropic, obeying the generalized Hooke's law. A new equation for the stress of the film-substrate system is proposed based on Newton's laws and energy conservation. As an application, it use the technique and data developed by Faurie et al (2005) in fiber-textured gold film deposited onto Kapton substrate by combining synchrotron X-Ray diffraction in situ tensile testing. As the gold thin film and substrate are considered transversely isotropic, therefore, is firstly required a texture analysis with the purpose of determining the possible Euler angles ($\phi$) and ($\psi$) for each crystallographic direction that can be used in the model equations. With the data, it is possible to make graphics, $\varepsilon$ (strain) X F, for every force applied to the sample. Comparing the experimental graphs with the theoretical equations it was possible obtained their mechanical properties and the principal stresses-strains of the anisotropic gold thin film. The results are compared with the results of Faurie et al (2005).

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Potential energy curves govern the properties of materials. A critical analysis of the potential energy curve helps better understand the properties of the material. Potential energy curve and in turn the properties of any material depend on the composition, bonding, crystal structure, their mechanical processing and microstructure. The type, strength, and directionality of atomic bonding controls the structure and material properties viz., melting temperature, thermal expansion, elastic stiffness, electrical properties, ductility and toughness etc. This paper attempts to bring out the correlation between the potential energy curves with the properties of materials.

This work examines mechanical properties of 50–300 nm gold thin films deposited onto micrometer-thick flexible polymer substrates
by means of tensile testing of the film–substrate system and modeling. The film properties are extracted from mechanical testing
of the film–substrate system and modeling of the bimaterial. Unlike materials in bulk geometry, the film elastic modulus and
yield strength present an important dependence with film thickness, with modulus and yield strength of about 520 and 30 GPa,
respectively, for the thinner films and decreasing toward the bulk value as the film thickness increases. The relation between
grain size, film thickness, and yield strength is examined. Finite element analysis provides further insight into the stress
distribution in the film–substrate system.

In this work we aim to develop expressions for the calculation of biaxial and triaxial stresses in polycrystalline anisotropic materials, and to determine their elastic constants using the theory of elasticity for continuum isochoric deformations; thus, we also derive a model to determine residual stress. The constitutive relation between strain and stress in these models must be assumed to be orthotropic, obeying the generalized Hooke's law. One technique that can be applied with our models is that of X-ray diffraction, because the experimental conditions are similar to the assumptions in the models, that is, it measures small deformations compared with the sample sizes and the magnitude of the tensions involved, and is insufficient to change the volume (isochoric deformation). Therefore, from the equations obtained, it is possible to use the sin
2ψ technique for materials with texture or anisotropy by first characterizing the texture through the pole figures to determine possible angles ψ that can be used in the equation, and then determining the deformation for each diffraction peak with the angles ψ obtained from the pole figures.

The elastic behavior of gold thin films deposited onto Kapton substrate has been studied using in situ tensile tester in a four-circle goniometer on a synchrotron beam line (LURE facility, France). The mechanical description of the substrate-thin film composite structure has been developed to determine the stress tensor in the film while the strong {111} fiber texture was taken into account using the crystallite group method (CGM). CGM strain analysis allowed us to forecast the nonlinear relationship between strain and sin2 Ψ obtained for the thin films due to the strong anisotropy of gold. A least-square method was used to fit the overall experimental data with good accuracy and allows determining all single-crystal elastic constants.

The purpose of the present article is to give a precise definition and analysis from first principals of anisotropy, as the term applies to elastic media, taking care to avoid unnecessary assumptions. Two fundamental concepts, material invariance and symmetry group of a material, are defined purely in terms of the stress-strain relation. The implications of material symmetry, or in other words, of anisotropy, for the structure of the stiffness tensor are then investigated. Using the reduced notation of Voigt, these results are presented as the well-known simplifications in the form taken by the six-by-six stiffness matrix that represents the material's stiffness tensor. A new, simple proof is given for the remarkable fact that an elastic medium cannot have rotational symmetry by an angle of less than 90 without being transversely isotropic. In addition, the mutual relation that the notions of elastic symmetry and crystal symmetry have with respect to the so-called orthogonal group is sketched. Despite the historical association between anisotropic elastic materials and the study of crystals, the given presentation shows that conceptually the notion of anisotropy in elastic media is entirely independent of that of crystal symmetry.

In this study, we have proposed a nondestructive method to simultaneously determine the Young's modulus (E) and Poisson's ratio (ν) of polycrystalline thin film materials. The method involved independent stress measurement by laser curvature technique and strain components determination by sin2ψ X-ray diffraction (XRD) method, and afterward, elasticity theory was employed to calculate E and ν. The proposed method was applied on two model specimens, TiN and ZrN thin films, using synchrotron X-ray and laboratory X-ray sources, respectively. The cos2αsin2ψ XRD method which measured the strain for diffraction planes at different location was performed on the same film, and the previously determined E and ν were used to calculate the stress. The residual stresses derived from cos2αsin2ψ method were close to the stresses from laser curvature measurements, which validated the measured values of E and ν. The depth profile of residual stress of the TiN thin film was assessed using cos2αsin2ψ method by appropriately adjusting the X-ray incident angle. In addition, the E value determined from nanoindentation (NIP) may depend on the indentation depth. Therefore, one should be cautious when employing the NIP-determined E in sin2ψ or cos2αsin2ψ methods to calculate the residual stress because the modulus may not always give correct stress value.

Measurements of Poisson's ratio and the Young's modulus of thin films have been problematic. In this work, evaluation of both Poisson's ratio and Young's modulus is conducted using grazing incidence X-ray diffraction combined with measurement of the induced stress. Poisson's ratio was evaluated from analysis of the X-ray diffraction data to obtain a strain—cos2α·sin2ψ plot. Moreover, the Young's modulus of the films could be also calculated from that plot as well as from the residual stress, which could be determined by a measurement of stress induced substrate curvature. The ternary nitride TiAlN is used as a model system for the evaluation. The films, prepared by cathodic arc plasma deposition, exhibited a strong (111) preferred orientation and a composition corresponding to Ti0.6Al0.4N. The measured Poisson's ratio and the Young's modulus of the films were 0.143±0.003 and 310±20 GPa, respectively, which are comparable to those reported in the literature.

Titanium carbide thin films show attractive mechanical properties for engineering applications. Thin films of TiC were deposited on a 〈100〉 silicon substrate by RF sputtering from a TiC target. Various sputtering pressures were carried out in order to observe the influence of this parameter on structural and mechanical properties. The sputtering pressure was varied from 0.35 to 1 Pa at a sputtering power of 300 W. Rutherford backscattering spectroscopy (RBS), X-ray diffraction (XRD) and atomic force microscopy (AFM) were used to characterize TiC thin films. Hardness was obtained by nanoindentation. Residual stress was determined by radius of curvature measurements. Lower pressures induce the formation of a distorted titanium carbide and a dense structure. In correlation to the lower pressure, large residual stress was measured and changed the TiC texture in XRD results. Both the compressive stress and the hardness exhibited a maximum value at a process pressure using pure argon at 0.35 Pa with a pressure of 1 Pa necessary to obtain TiC films with 〈111〉 texture.

We present a new type of electronic circuits: e-textiles. Such circuits are made by weaving together specialized component fibers. The fibers have electronic components integrated onto them. Various circuits can be formed by weaving these fibers in various patterns. Connections between fibers are made using contact pads, which are free to move against each other, thus keeping the fabric flexible. We use amorphous silicon thin-film transistors as the active devices and present their fabrication on fiber as well as an inverter circuit woven from the fibers.

ANSYS engineering analysis system theoretical manual

- P C Kohnke

P. C. Kohnke, ANSYS engineering analysis system theoretical manual, Ed. Houston Swanson Analysis Systems, Inc.,1989.