Fracture properties of silicon carbide thin films by bulge test of long rectangular membrane

This paper reports the mechanical properties and fracture behavior of silicon carbide (3C-SiC) thin films grown on silicon substrates. Using bulge testing combined with a refined load-deflection model of long rectangular membranes, which takes into account the bending stiffness and prestress of the membrane material, the Young's modulus, prestress, and fracture strength for the 3C-SiC thin films with thicknesses of 0.40 and 1.42 mu m were extracted. The stress distribution in the membranes under a load was calculated analytically. The prestresses for the two films were 322 +/- 47 and 201 +/- 34 MPa, respectively. The thinner 3C-SiC film with a strong (111) orientation has a plane-gstrain moduli of 415 +/- 61 GPa, whereas the thicker film with a mixture of both (111) and (110) orientations exhibited a plane-strain moduli of 329 +/- 49 GPa. The corresponding fracture strengths for the two kinds of SiC films were 6.49 +/- 0.88 and 3.16 +/- 0.38 GPa, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over edge, surface, and volume of the specimens and were fitted with Weibull distribution function. For the 0.40-mu m-thick membranes, the surface integration has a better agreement between the data and the model, implying that the surface flaws are the dominant fracture origin. For the 1.42-mu m-thick membranes, the surface integration presented only a slightly better fitting quality than the other two, and therefore, it is difficult to rule out unambiguously the effects of the volume and edge flaws.

Bulge testing and fracture properties of plasma-enhanced chemical vapor deposited silicon nitride thin films

The mechanical properties and fracture behavior of silicon nitride (SiNx) thin film fabricated by plasma-enhanced chemical vapor deposition is reported. Plane-strain moduli, prestresses, and fracture strengths of silicon nitride thin film; deposited both oil a bare Si substrate and oil a thermally oxidized Si substrate were extracted using bulge testing combined with a refined load-deflection model of long rectangular membranes. The plane-strain modu i and prestresses of SiNx thin films have little dependence on the substrates, that is, for the bare Si substrate, they are 133 +/- 19 GPa and 178 +/- 22 MPa, respectively, while for the thermally oxidized substrate, they are 140 +/- 26 Gila and 194 +/- 34 MPa, respectively. However, the fracture strength values of SiNx films grown on the two substrates are quite different, i.e., 1.53 +/- 0.33 Gila and 3.08 +/- 0.79 GPa for the bare Si substrate a A the oxidized Si substrate, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over the edge, Surface, and volume of the specimens and fitted with the Weibull distribution function. For SiNx thin film produced oil the bare Si Substrate, the Volume integration gave a significantly better agreement between data and model, implying that the volume flaws re the dominant fracture origin. For SiNx thin film grown on the oxidized Si substrate, the fit quality of surface and edge integration was significantly better than the Volume integration, and the dominant surface and edge flaws could be caused by buffered HF attacking the SiNx layer during SiO2 removal. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.

Fracture properties of PECVD silicon nitride thin films by long rectangular memrane bulge test

Bulge test combined with a refined load-deflection model for long rectangular membrane was applied to determine the mechanical and fracture properties of PECVD silicon nitride (SiNx) thin films. Plane-strain modulus E-ps prestress s(0), and fracture strength s(max) of SiNx thin films deposited both on bare Si substrate and on SiO2-topped Si substrate were extracted. The SiNx thin films on different substrates possess similar values of E-ps and s(0) but quite different values of s(max). The statistical analysis of fracture strengths were performed by Weibull distribution function and the fracture origins were further predicted.

Fracture properties of silicon carbide thin films charcterized by bulge test of long membranes

The mechanical properties and fracture behavior of silicon carbide (3C-SiC) thin films grown on silicon substrates were characterized using bulge testing combined with a refined load-deflection model for long rectangular membranes. Plane-strain modulus E-ps, prestress so, and fracture strength s(max) for 3C-SiC thin films with thickness of 0.40 mu m and 1.42 mu m were extracted. The E, values of SiC are strongly dependent on grain orientation. The thicker SIC film presents lower so than the thinner film due to stress relaxation. The s(max) values decrease with increasing film thickness. The statistical analysis of the fracture strength data were achieved by Weibull distribution function and the fracture origins were predicted.

Tensile strength of radio frequency cold plasma treated PET fibers - Part 1: Influence of environment and treatment time

This article reports on a series of experiments with polyethylene terepthalate (PET) treated in a radio frequency plasma reactor using argon and oxygen as a gas fuel, for treatment times equal to 5 s, 20 s, 30 s, and 100 s. The mechanical strength modification of PET fibers, evaluated by tensile tests on monofilaments, showed that oxygen and argon plasma treatment resulted in a decrease in the average tensile strength compared with the untreated fibers. This reduction in tensile strength is more significant for argon plasma and is very sensitive to the treatment time for oxygen plasma. Scanning electron microscopy (SEM) used to analyze the effects of cold plasma treatment on fiber surfaces indicates differences in roughness profiles depending on the type of treatments, which were associated with variations in mechanical strength. Differences in the roughness profile, surveyed through an image analysis method, provided the distance of roughness interval, D-ri. This parameter represents the number of peaks contained in a unit length and was introduced to correlate fiber surface condition, before and after cold plasma treatments, and average tensile strength. Statistical analysis of experimental data, using Weibull cumulative distribution and linear representation, was performed to explain influences of treatment time and environmental effects on mechanical properties. The shape parameter, alpha, and density parameter, beta, from the Weibull distribution function were used to indicate the experimental data range and to confirm the mechanical performance obtained experimentally.

A Note on the Prior Distributions of Weibull Parameters for the Reliability Function

In Bayesian Inference it is often desirable to have a posterior density reflecting mainly the information from sample data. To achieve this purpose it is important to employ prior densities which add little information to the sample. We have in the literature many such prior densities, for example, Jeffreys (1967), Lindley (1956); (1961), Hartigan (1964), Bernardo (1979), Zellner (1984), Tibshirani (1989), etc. In the present article, we compare the posterior densities of the reliability function by using Jeffreys, the maximal data information (Zellner, 1984), Tibshirani's, and reference priors for the reliability function R(t) in a Weibull distribution.

Fracture statistics of brittle materials: Weibull or normal distribution

The fit of fracture strength data of brittle materials (Si3N4, SiC, and ZnO) to the Weibull and normal distributions is compared in terms of the Akaike information criterion. For Si3N4, the Weibull distribution fits the data better than the normal distribution, but for ZnO the result is just the opposite. In the case of SiC, the difference is not large enough to make a clear distinction between the two distributions. There is not sufficient evidence to show that the Weibull distribution is always preferred to other distributions, and the uncritical use of the Weibull distribution for strength data is questioned.

Characterization of Probability Distributions Using the Residual Entropy Function

The present study on the characterization of probability distributions using the residual entropy function. The concept of entropy is extensively used in literature as a quantitative measure of uncertainty associated with a random phenomenon. The commonly used life time models in reliability Theory are exponential distribution, Pareto distribution, Beta distribution, Weibull distribution and gamma distribution. Several characterization theorems are obtained for the above models using reliability concepts such as failure rate, mean residual life function, vitality function, variance residual life function etc. Most of the works on characterization of distributions in the reliability context centers around the failure rate or the residual life function. The important aspect of interest in the study of entropy is that of locating distributions for which the shannon’s entropy is maximum subject to certain restrictions on the underlying random variable. The geometric vitality function and examine its properties. It is established that the geometric vitality function determines the distribution uniquely. The problem of averaging the residual entropy function is examined, and also the truncated form version of entropies of higher order are defined. In this study it is established that the residual entropy function determines the distribution uniquely and that the constancy of the same is characteristics to the geometric distribution

Improved likelihood inference for the shape parameter in Weibull regression

We obtain adjustments to the profile likelihood function in Weibull regression models with and without censoring. Specifically, we consider two different modified profile likelihoods: (i) the one proposed by Cox and Reid [Cox, D.R. and Reid, N., 1987, Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B, 49, 1-39.], and (ii) an approximation to the one proposed by Barndorff-Nielsen [Barndorff-Nielsen, O.E., 1983, On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.], the approximation having been obtained using the results by Fraser and Reid [Fraser, D.A.S. and Reid, N., 1995, Ancillaries and third-order significance. Utilitas Mathematica, 47, 33-53.] and by Fraser et al. [Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple formula for tail probabilities for frequentist and Bayesian inference. Biometrika, 86, 655-661.]. We focus on point estimation and likelihood ratio tests on the shape parameter in the class of Weibull regression models. We derive some distributional properties of the different maximum likelihood estimators and likelihood ratio tests. The numerical evidence presented in the paper favors the approximation to Barndorff-Nielsen`s adjustment.

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998) This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Gawk 2009) which contains several lifetime models such as exponential geometric (Adamidis and Loukas 1998) exponential Poisson (Kus 2007) and exponential logarithmic (Tahmasbi and Rezaei 2008) distributions The hazard function of our class can be increasing decreasing and upside down bathtub shaped among others while the hazard function of an EPS distribution is only decreasing We obtain several properties of the WPS distributions such as moments order statistics estimation by maximum likelihood and inference for a large sample Furthermore the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints Special distributions are studied in some detail Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions (C) 2010 Elsevier B V All rights reserved

Análise clássica e bayesiana do modelo Weibull modificado generalizado

Pós-graduação em Matematica Aplicada e Computacional - FCT

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

The negative binomial-beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial-beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

The McDonald extended distribution: properties and applications

We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments, quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and Gini concentration index. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The applicability of the new model is illustrated by means of a real data set.