Nuevas aportaciones estadísticas al estudio de la fiabilidad de materiales

Abstract

he aim of this PhD thesis is the contribution of new techniques and statistical methodologies for the study of the reliability of materials subjected to thermal efforts and mechanical fatigue. Specifically two procedures have been introduced for immediate application in the fields of applied physics and material engineering. The first is an alternative to conduct studies of Time Temperature Superposition (TTS) while the second is a new flexible approach for estimating the distribution of lifetimes of materials subjected to mechanical fatigue. Both methodologies represent useful and competitive contributions for the resolution of problems of materials characterization and prediction of their physical properties during its lifetime, from the point of view of statistical modeling of degradation data obtained by thermal analysis and mechanical techniques. In the following lines the two proposed procedures are briefly described. a) TTS procedure based on the shifting of first derivative curves: A new methodology for estimating the viscoelastic properties of polymeric materials as a function of time and temperature has been introduced. Specifically, the proposed method provides an estimation and predictions of the viscoelastic properties of amorphous polymer at a given temperature and time of observation outside the experimental range, starting from a set of experimental curves of elastic modulus E0(t), taken each one at different temperatures and obtained by Dynamic Mechanical Analysis (DMA). The procedure introduced here is based on the TTS principle, like the existing parametric models Arrhenius and William-Landel-Ferry (WLF), and it can be summarized in the following steps: (1) First, we choose a reference temperature at which we want to estimate the viscoelastic properties of a material in a wide range of time/frequency for which gets its experimental curve, in this case E0(t), in a range of times/frequencies much narrower. This will be the basis of the curve called master. (2) New curves of time dependent viscoelastic properties are obtained, each one at a different temperature (higher or lower than the corresponding to the master curve). (3) The experimental curves are interpolated using spline curves to make then smooth and differentiable. (4) First derivative of each experimental curve is calculated using spline procedures. (5) Following the TTS physical principle, we apply horizontal displacements to derived curves in order to overlap them at the reference temperature, and thus building the required master curve. At this point, it is important to note that another innovation that provides this PhD thesis is the criterion for obtaining the so called optimum displacement factors, which are calculated through the distance L1 between the first derivative curves of viscoelastic property. The estimates of master curve are obtained by adjusting a B-spline basis to the shifted curves, with corresponding IX bootstrap pointwise confidence intervals. So you can estimate the, e.g. storage module, beyond the experimental range of times. (7) Finally, the master curve obtained using non parametric method is compared with those obtained by adjusting the parametric models WLF and Arrhenius. Making use of the bootstrap resampling, medium quadratic error and simulation study of TTS principle, the accuracy of the estimates have been evaluated. b) Estimation of the lifetime distribution under mechanical fatigue: The main cause (90% of cases) of degradation and subsequent failure of structural materials is the phenomenon of mechanical fatigue (Dowling, 2013). This study presents a new method to accurately estimate the time of failure distribution occurred due to mechanical fatigue efforts, in practice regardless of the time of censorship. The proposed methodology allows you to adjust both crack growth curves corresponding to different specimens, materials subjected to efforts of mechanical fatigue, using mixed effects linear models (lme) with smoothing B-splines and subsequently the linearized model of Paris-Erdogan. Once defined the failure to a determined crack length, the fatigue lifetime distribution function of an specific material is estimated by applying nonparametric techniques, in particular kernel estimator of the distribution function (kda). The proposed procedure was evaluated using real data and different simulation scenarios for which were obtained crack growth curves using Monte Carlo method, according to different values of the Paris C and m parameters. In addition, the results of the new nonparametric method (SEP-lme) have been compared with those obtained by the method proposed by Meeker and Escobar, on the one hand, and Pinheiro and Bates, based on mixed effects nonlinear regression (nlme), also using techniques of functional data analysis. Estimates of the lifetime distribution function equivalent or better are obtained using the SEP-lm method. Finally, the influence of the adjustment of various types of materials and other important parameters of the model has been evaluated. Importantly, one of the objectives of this thesis is to provide to professionals, users from academia and industry, easy access, the automation and implementation of methodologies and tools presented here. Therefore, two R packages have been developed, TTS and FCGR. The currently represent two alternatives fully accessible to estimate the lifetime of materials due to thermal and mechanical stresses.