Failure Probability Curves Research Articles

Stochastic estimation of the number of fiber-break points in a CFRP by Markov process

A stochastic model based on Markov process is proposed to estimate the number of fiber-break points of a unidirectional fiber-reinforced composite. This model relies on the assumption that each state is assigned in the order of the fiber-break point number, and that it transits to two states from one state. The first state of the two is a state causing a composite fracture, and another is a state of survival while being damaged. Mini composites with 2–4 fibers were prepared using carbon fiber and epoxy resin to examine the applicability of the model. Predicted failure probability curves approach experimentally obtained data with an increase in the fiber-break point and ultimately agree with them. The fiber-break points till fracture are estimated with greater numbers than the number of fibers, which elucidates the significance of the experimental results higher than the average fiber strength. The validity of the model was finally discussed while considering the stress concentration around fiber-break point(s).

Evaluation of failure probability for RC slabs subjected to low-velocity impacts

This study presents a procedure to evaluate the failure probabilities of reinforced-concrete (RC) slabs subjected to low-velocity impacts considering the uncertainties existing in slab features and impactor properties. A two-degree-of-freedom (2-DoF) non-linear model using a dynamic load–displacement curve is adopted to simulate the impact response of RC slabs because of its accuracy and efficiency. This model can effectively consider punching shear behaviour, which dominates the response of most RC slabs under impact loading. The 2-DoF is coupled with a correlation-controlled Latin hypercube sampling method to assess the failure probability. A sensitivity analysis is performed to identify significant random variables and a comprehensive parametric study is conducted to investigate the effect of different parameters in slab design and impactor properties on the failure probability of the impacted slab. The failure probabilities were found to fit a normal distribution under different impact velocities. This result is used in a simple procedure to derive the impact-induced failure probability curves with the distribution means estimated at the mean parameters, and the coefficients of variation ranged between 0·15 and 0·20.

A sampling-based method for high-dimensional time-variant reliability analysis

Abstract A new sampling-based method is proposed for high-dimensional time-variant reliability analysis with both random variables and random process as inputs. The new method employs the series expansion methods, e.g., the Karhunen-Loeve expansion, to represent the input random process into a set of random variables. Based on the concepts of composite limit state, the time-variant reliability analysis is converted into a series system reliability problem with multiple responses. Then the generalized subset simulation is applied to compute cumulative failure probabilities which are further used to interpolate a completely cumulative failure probability curve for a given time interval. The advantage of the proposed method is that only a single run can provide a cumulative failure probability curve instead of repeated runs. Two high-dimensional time-variant reliability problems with input random process are used to demonstrate the performance of the proposed method.

Isothermal bending fatigue response of solder joints in high power semiconductor test structures

Fatigue and cyclic delamination behavior of PbSnAg solders which are typically used as die attach material in power semiconductors was investigated. Isothermal bending fatigue tests were performed by using multilayered model test structures consisting of Si chips soldered on ceramic substrates and failure probability curves were obtained up to 1e8 loading cycles. The fatigue experiments were conducted by using an ultrasonic fatigue testing machine equipped with a three point bending set-up at a constant testing temperature of 80°C. Detailed failure analysis of the fatigued samples revealed a dependency of the failure mode on the chemical composition of the high-Pb soft solders. The main failure modes included interfacial delamination of the Si-chip from the die attach, degradation due to crack propagation in the solder layer and in some cases partial fracture of the chip. Finally the feasibility of high frequency mechanical fatigue testing for screening and evaluation of solder joints in multilayered electronic systems is discussed.

On the evaluation of multiple failure probability curves in reliability analysis with multiple performance functions

Many systems have multiple failure modes that result in multiple performance functions. In this paper, a new stochastic simulation based approach is proposed for evaluation of multiple failure probability curves in a reliability problem with multiple performance functions. The state-of-the-art stochastic simulation based techniques, such as subset simulation and auxiliary domain method, are efficient in evaluating a failure probability curve but only consider a single performance function. Standard Monte Carlo simulation is robust to the type and dimension of the problem and is applicable to evaluate multiple failure probability curves for a problem with multiple performance functions but is computationally expensive especially while estimating small probabilities. The proposed approach for simultaneous consideration of multiple performance functions generalizes the subset simulation and is an improvement of the generalized subset simulation. The output of an analysis using the proposed approach is multiple failure probability curves with each corresponding to one performance function. The proposed approach is robust with respect to the dimension of the failure probability integral, model complexity, the degree of nonlinearity, number of performance functions, and efficient in cases involving the computation of small failure probabilities. The effectiveness and efficiency of the proposed approach are demonstrated by three numerical examples.

Estimación del potencial de rollover de vehículos pesados usando principios de confiabilidad

Rollover is defined as a moving vehicle’s abrupt loss of the trajectory of the center of gravity. In horizontal curves, it refers to overturning by an unbalance of the lateral acceleration. The likelihood that this turnover occurs can be estimated by studying the static rollover potential, which is calculated with lateral acceleration thresholds that, when being exceeded, make the vehicle to suffer a rollover. These models consider the geometry of the vehicle, the road and operating speed, and sometimes the vehicle’s suspension system. This approach is suitable for analyzing the rollover potential of individual vehicles, but it is not very practical when analyzing vehicle fleets driving at operating speeds that follow a probability distribution according to the geometrical conditions of the environment and the type of vehicle. This work analyzes the rollover phenomenon through a probabilistic approach based on the reliability theory, which allows estimating the rollover risk considering random variables. It applies the Hasofer-Lind First-Order Reliability Method to calculate the rollover probability, based on the geometry, type of vehicle, and operating speed when taking horizontal curves. Additionally, it discusses three rollover calculation methods and presents the reliability theory concepts used herein. This paper describes the construction of limit state functions, experimental design, input data, and the failure probability curves for 4 types of vehicle and 3 input speeds. It was concluded that it is not recommendable to use a horizontal curve radius of less than 170 m, especially because heavy vehicles run the risk of suffering rollover.

In-plane shear characteristics of unidirectional glass fiber/epoxy functionally graded (FG) and nonfunctionally graded (NFG) composite laminates with statistical analysis

In this paper, a modified Iosipescu test fixture has been designed and fabricated to investigate the in-plane shear characteristics of unidirectional glass fiber/epoxy composite laminates which are functionally graded in the thickness direction ( z). Two functionally graded and three non-functionally graded unidirectional glass fiber/epoxy composite laminates with a total fiber volume fraction of 39.9 ± 0.3% and a total thickness of 6 mm were fabricated using hand lay-up technique. The effects of unidirectional arrangement of glass fiber layers and the number of layers on shear characteristics of functionally graded and non-functionally graded composites were studied experimentally. It was observed that the layer arrangement and the number of layers have a great effect on the shear properties of the tested composites. The specimen failure modes were recorded and discussed. Two-parameter Weibull distribution function was used to statistically analyze the in-plane shear test results. The failure probability curves were plotted for all tested composites which can be used by design engineers.

PROBABILISTIC SEISMIC ASSESSMENT OF BASE-ISOLATED NPPS SUBJECTED TO STRONG GROUND MOTIONS OF TOHOKU EARTHQUAKE

The probabilistic seismic performance of a standard Korean nuclear power plant (NPP) with an idealized isolation is investigated in the present work. A probabilistic seismic hazard analysis (PSHA) of the Wolsong site on the Korean peninsula is performed by considering peak ground acceleration (PGA) as an earthquake intensity measure. A procedure is reported on the categorization and selection of two sets of ground motions of the Tohoku earthquake, i.e. long-period and common as Set A and Set B respectively, for the nonlinear time history response analysis of the base-isolated NPP. Limit state values as multiples of the displacement responses of the NPP base isolation are considered for the fragility estimation. The seismic risk of the NPP is further assessed by incorporation of the rate of frequency exceedance and conditional failure probability curves. Furthermore, this framework attempts to show the unacceptable performance of the isolated NPP in terms of the probabilistic distribution and annual probability of limit states. The comparative results for long and common ground motions are discussed to contribute to the future safety of nuclear facilities against drastic events like Tohoku.

Zadoff-Chu Sequence Based Signature Identification for OFDM

A signature identification algorithm is a method to obtain the cell identification information for wireless cellular systems or determine the intended user for wireless local area network. In this paper, we propose a simple and efficient signature identification algorithm on the basis of Zadoff-Chu sequence in orthogonal frequency division multiplexing systems. In addition, we prove that the proposed algorithm achieves a maximum likelihood solution if the receiver knows the channel length. Also, the exact probabilities of signature identification failures of the proposed algorithm are provided for different power delay profiles. To demonstrate efficacy of the proposed algorithm in fading channels, we derive the failure probability at high signal-to-noise ratio (SNR). Through a high SNR expression, it is shown that the proposed algorithm fully exploits frequency selective fadings. Especially, we reveal that the slope of the failure probability curves at high SNR is determined by the channel length regardless of power delay profiles. Simulation results show that the proposed algorithm outperforms conventional signature algorithms in frequency selective fading channels. Also, we confirm that our analysis matches well with the empirical results of the proposed signature identification algorithm.

Failure of multimode optical fibers nano-structured by near ablation threshold single-shot femtosecond laser procedure

The present paper deals with the study of the failure probability of nano-structured optical fibers when submitted to uniaxial tensile loading. A nano-structuration procedure of optical fibers thanks to near ablation threshold single shot femtosecond laser has been proposed. The ablation threshold energy Ep0 for silica fiber is such that: NA2Ep0=15.5nJ, where NA is the numerical aperture of the objective to focus the laser inside the fibers. The rupture strength of the impacted fibers can be controlled through the pulse energy Ep, the numerical aperture NA, the number Nl of nano-craters depending on the step dz of the position of the fiber surface into the focal region, the interval dx between each crater and the number nl of flaw lines. An additive combination of two classical Weibull's laws allows a good representation of the failure probability of the impacted fibers. A phenomenological model for the evolutions of the Weibull's parameters (exponents and scaling stresses) has been proposed and the experimental tendencies of the failure probability curves are fairly well described by the set of the model's equations (Eq. (27)).

S‐N‐P curves in 7075 T7351 and 2024 T3 aluminium alloys subjected to surface treatments

ABSTRACTThe S‐N‐P (stress, number of cycles, failure probability) curves for 2024 T3 and 7075 T7351 aluminium alloys were obtained. Previously, surface treatments of degreasing and different types of anodizing were applied to samples, evaluating the influence of these treatments on the fatigue life of the alloys. The determination of the S‐N‐P curves was done using Maennig's method. Rotary fatigue was used because this technique produces greater stress on the sample surfaces, the zone in which it is important to evaluate fatigue resistance. Both the transition range and the finite life range were evaluated, calculating the 1, 50 and 99% fracture probability. SEM was performed in order to characterize the fracture micromechanism. The conclusions were that Maennig's method is useful to evaluate fatigue life of these materials in a fast and efficient manner. Moreover, surface treatments produce a decrease in the fatigue life of both alloys, associating this effect with the surface damage produced on each sample during the treatment.

Statistical failure analysis of brittle coatings by spherical indentation: theory and experiment

The mode of failure and failure probability of a brittle coating on a compliant substrate subjected to a static load through a spherical indenter is investigated experimentally and theoretically. We extend our recent study (2003, J Mat Sci 38:1589) of surface crack initiation in a monolithic solid to the layered system, and account for the multi axial stress state of the indentation in the failure probability analysis. Two modes of failure, a Hertzian cone crack initiating from the contacting surface and a half-penny-shaped crack initiating from the interface, are investigated and the probability of failure initiation for both surfaces are theoretically predicted and compared with experimental data.The effect of interface debonding on failure phenomena is investigated. For a given load the failure probability for debonded specimens is significantly higher than that of well-bonded samples. For the debonded case the theoretical failure probability curve falls within the 90% confidence interval of the experimental data, while the experimental values for the completely bonded case show somewhat lower failure probabilities than that predicted. This may be attributed to the possible bridging effect by the adhesive on interfacial surface defects in the ceramic that is not accounted for in our model.

ENGINEERING ESTIMATION OF THE LOWER BOUND TOUGHNESS IN THE TRANSITION REGIME OF FERRITIC STEELS

A simple engineering method for estimating a lower bound fracture toughness in the ductile‐to‐brittle transition region is presented. It is based on empirical evidence that the lower tail of the failure probability versus fracture toughness curve tends to be a straight line rather than a Weibull curve. Fitting the lower tail by a straight line, however, gives an engineering lower bound at a theoretical failure probability of zero. The method enables one to obtain lower bounds using small data sets of three or four specimens.

The Weibull distribution applied to post and core failure

In this study, data on initial failure loads of direct post and core-restored premolar teeth were analyzed using the Weibull distribution. Restorations consisted of a prefabricated titanium alloy post, and an amalgam, composite or glass cermet core buildup in human upper premolar teeth. The specimens were subjected to compressive forces until failure at angles of 10, 45 and 90° to their long axis. The two- and three-parameter Weibull distributions were compared for applicability to the failure load data. For estimation of the parameters of the two-parameter distribution: σ 0 (reference stress) and m (Weibull modulus), linear regression was used. In this distribution, it is assumed that the third parameter, σ u (cut-off stress), equals 0. The Maximum Likelihood (MLH) method was used to estimate all three parameters. It was found that the choice of distribution has a strong influence on the estimated values and that the three-parameter distribution is best fitted for the failure loads in this study. Comparisons were made between the failure probability curves as found by MLH estimation for the different core materials and loading angles. The results indicated that the influence of loading angle on the failure mechanism was stronger than that of core material.

Extensions of Models for Transistor Failure Probability Due to Neutron Fluence

Models developed in the Hardening Options for Neutron Effects (HONE) program for predicting transistor failure probability are extended to include probability distributions for the initial current gains and to allow non-zero origins for all random variables concerned. Further, these models are generalized to consider two-transistor combinations. Test cases are calculated to compare the failure probability curves generated by these models with previous results.

Determination of transformer life expectancy

Evaluation of transformer life in reliability and economic studies involves a changing life expectancy and failure rate. The relation of loading to temperature and insulation life is reasonably defined. The problem is to establish means of assigning values to added transformer life or reduced failure rates. A user can predict the return on transformer investment and the reduction in failure rates by use of relative aging and failure probability curves applied to the present age of existing installations