THE USE OF MARKOV CHAINS THEORY FOR APPROXIMATION OF ATIGUE CURVE OF COMPOSITE MATERIAL
Some simple mathematical model for fatigue life of composite m aterial consisting mainly of parallel rigidd components (strands) is offered.. The model,, whi chh is foundedd onn the use of Markov chainn theory,, allows too get S-type curve of internal stress growthh and, finally,, too s ee the connectionn betweenn static strengthh distributionn parameters andd S-N fatigue curve (Wholer curve).. The model is tooo simple andd does not provide numerica l coincidence with experimental fatigue test data but by the use of some additional parameters we cann fit the model too actual fatigue datasets,, we can use it for nonlinear regressionn model of S-N fatigue curveandd predict consequence of static strengthh parameter changes.
Estimating the parameters of fatigue curve of a composite material
By using the method of maximum likelihood, the parameters of two versions of a mathematical model for fatigue damage accumulation in a laminate are estimated. The models, which are founded on the Markov chain theory, are very simple: they do not take into account the specific structural features of a composite and therefore cannot provide numerical coincidence with experimental fatigue test data, but they can be used for a nonlinear regression analysis of fatigue curves. A simple method is offered for approximately estimating model parameters, some of which characterize the distribution of the local static strength. By using such models, we can predict the relative changes in fatigue curves from known relative variations in the parameters of static strength and also predict the distribution function of fatigue life in program fatigue tests.
A bifunctional Cr/Yb/Tm:Ca3Ga2Ge3O12 phosphor with near-infrared long-lasting phosphorescence and upconversion luminescence.
Currently, upconversion nanocrystals and long-lasting phosphorescent particles have attracted extensive research interest for their possible applications as bioimaging probes. However, there are few reports concerning the achievement of both upconversion luminescence of lanthanide ions and long-lasting phosphorescence of transition metal ions in a sole host so far. Herein, we demonstrate a novel calcium gallium germanium garnet (Ca3Ga2Ge3O12) host where lanthanide ions such as Tm(3+)/Yb(3+) and transition metal ions such as Cr(3+) can be easily incorporated through substituting the Ca(2+) and Ga(3+) respectively. This Cr/Yb/Tm:Ca3Ga2Ge3O12 phosphor exhibits both broadband near-infrared long-lasting phosphorescence of Cr(3+) with an afterglow time of more than 7000 s and near-infrared to near-infrared upconversion luminescence of Tm(3+). Impressively, it is evidenced that the addition of Yb(3+)/Tm(3+) into Cr:Ca3Ga2Ge3O12 not only results in Tm(3+) upconversion luminescence but also greatly increases Cr(3+) afterglow time. Based on excitation/emission, three-dimensional thermoluminescence, and time-resolved luminescence spectra, the related long-lasting phosphorescence and upconversion luminescent mechanisms are systematically discussed as well.