Investments promotion and agglomeration economy in regional development: «valmiera+» investment area case study

Секция 4. Теоретические аспекты регионального социально-экономического развития в современных условия

Biaxial fragmentation of thin silicon oxide coatings on poly(ethylene terephthalate)

Crack patterns of 53 nm and 103 nm thick silicon oxide coatings on poly(ethylene terephthalate) films are analyzed under equibiaxial stress loading, by means of a bulging cell mounted under an optical microscope with stepwise pressurization of film specimens. The biaxial stress and strain are modeled from classical elastic membrane equations, and an excellent agreement is obtained with a finite element method. In the large pressure range, the derivation of the biaxial strain from force equilibrium considerations are found to reproduce accurately the measured data up to 25% strain. The examination of the fragmentation process of the coating under increasing pressure levels reveals that the crack onset strain of the oxide coating is similar to that measured under uniaxial tension. The fragmentation of the coating under biaxial tension is also characterized by complex dynamic phenomena which image the peculiarities of the stress field, resulting in considerable broadening of the fragment size distribution. The evolution of the average fragment area as a function of biaxial stress in the early stages of the fragmentation process is analyzed using Weibull statistics to describe the coating strengt

Influences of roll-to-roll process and polymer substrate anisotropies on the tensile failure of thin oxide films

The influence of internal stress anisotropy resulting from anisotropic loading in a roll-to-roll (R2R) process, and polymer substrate anisotropy on the crack onset strain (COS) of thin oxide coatings was analyzed. Experimental data obtained for R2R processed films were compared with data obtained using an isotropic sheet-to-sheet (S2S) process with the same anisotropic substrate. In the R2R case the COS was found to increase by 20% between the transverse direction and the machine direction. In the S2S case the COS was found to be independent of orientation, except at a 45° in-plane orientation with respect to the machine direction, where it was 15% higher. The internal stress in the machine direction could not be determined, presumably due to deposition-induced curvature changes of the polymer substrate, and was therefore fitted to the COS data. Fracture mechanics analysis and finite element modeling of the experimental data showed that the influence of substrate anisotropy was marginal, and that it was the process-induced internal strain in the coating which controlled the COS. © 2010 Elsevier B.V

Analysis of brittle coating fragmentation under uniaxial tension for Weibull strength distributions

We investigate the sequential cracking of thin brittle coatings attached adhesively to substrates. The focus of our study are uniaxial tensile loading conditions, where we monitor the behavior in a continuous picture and the coating strength follows a two-parameter Weibull distribution. For fracture well under way we derive an approximate analytical expression for the distribution of fragment lengths. We recover that the distribution scales with the average fragment length $\left\langle l\right\rangle$ and that $\left\langle l\right\rangle$ is a power function of the applied strain ε, i.e. $\left\langle l\right\rangle\propto\varepsilon^{-\kappa}$, where κ depends on the distribution of the strength of the coating and on the adhesive's nonlinearity. Furthermore we compare our approximate analytical expression with numerical solutions and with simulations' findings