An elastic–plastic and residual stress analysis steel reinforced thermoplastic composite cantilever beam

In the present study an analytical elastic–plastic stress analysis is carried out for a low-density homogeneous polyethylene thermoplastic cantilever beam reinforced by steel fibers. The beam is loaded by a constant single force at its free end. The expansion of the region and the residual stress component of σ_x are determined for 0°, 15°, 30°, 45°, 60°, 75° and 90° orientation angles. Yielding begins for 0° and 90° orientation angles at the upper and lower surfaces of the beam at the same distances from the free end. Although it starts first at the upper surface for 15°, 30° and 45°, it starts first at the lower surface for 60° and 75° orientation angles. The elastic–plastic analysis is carried out for both the plastic region which spreads only at the upper surface and the plastic region which spreads at the upper and lower surfaces together. The residual stress components of σ_x and τ_xy are also determined. The intensity of the residual stress component is maximum at the upper and lower surfaces of the beam, but the residual stress component of τ_xy is maximum on or around the х-axis. The beam can be strengthened by using the residual stresses. The distance between the plastically collapsed point and the free end is calculated for the same load in the beam for 0°, 15°, 30°, 45°, 60°, 75° and 90° orientation angles.     

Flexible time reduction method for burn-in of high-quality products

Burn-in is an effective method to screen out early failures of electronic devices. Typically, this is achieved by operating the devices under accelerated stress conditions. This paper focuses on a burn-in concept where a random sample of devices is drawn out of the running production, put to burn-in, and investigated for early failures. This procedure is called burn-in study. In parallel, as long as the burn-in study is ongoing, all other produced devices are subjected to burn-in screening. In this article, new flexible sampling plans for burn-in studies are introduced. These are based on the progress of these studies and defined quality targets. Furthermore, these sampling plans enable fast burn-in time reductions and various time reduction strategies. From a statistical point of view, this requires to combine the proportion of early failures in a population with their lifetime distribution function. The new model is illustrated by case studies and simulations. It contributes to burn-in cost reductions, while controlling quality levels at the same time.     

Bayesian calculation of cost optimal burn-in test durations for mixed exponential populations

The burn-in process is a part of the production process whereby manufactured products are operated for a short period of time before release. In this paper, a Bayesian method is developed for calculating the optimal burn-in duration for a batch of products whose life distribution is modeled as a mixture of two (denoted ‘strong’ and ‘weak’) exponential sub-populations. The criteria used is the minimization of a total expected cost function reflecting costs related to the burn-in process and to product failures throughout a warranty period. The expectation is taken with respect to the mixed exponential failure model and its parameters. The prior distribution for the parameters is constructed using a beta density for the mixture parameter and independent gamma densities for the failure rate parameters of the sub-populations. It is assumed that the optimal burn-in time is selected in advance and remains fixed throughout the burn-in process. When additional failure information is available prior to the burn-in process, the minimization of posterior total cost is used as the criteria for selecting the optimal burn-in time. Expressions for the joint posterior distribution and cost are provided for the case of both complete and truncated data. The method is illustrated with an example.     

Optimal burn-in time under cumulative free replacement warranty

In this paper, optimal burn-in time to minimize the total mean cost, which is the sum of manufacturing cost with burn-in and cumulative warranty-related cost, is studied. When the products with cumulative warranty have high failure rate in the early period (infant mortality period), burn-in procedure is considered to eliminate the early product failures. After burn-in, the posterior product life distribution and the cumulative warranty-related cost are dependent on burn-in time; long burn-in period decreases the warranty-related cost, but it increases the manufacturing cost. The paper provides a methodology to obtain the total mean cost under burn-in and cumulative warranty. Properties of the optimal burn-in time are analyzed here. Numerical examples and sensitivity analysis are used to demonstrate the applicability of the methodology derived in the paper.     

Dielectric properties and resistance to fatigue failure of different barrier layers prepared on flexible stainless-steel foils by ion-beam assisted deposition

A stainless-steel foil is an attractive candidate for the substrate of flexible display devices and integrated solar modules. For electrical insulation and ion diffusion reduction, a barrier layer should be coated on the stainless-steel foil surface. In this study, different barrier layers such as SiO_x, TaO_x, TiO_x and TaO_x/SiO_x were prepared on the flexible stainless-steel foils (SUS 304) by ion-beam assisted deposition. The dielectric properties of the barrier layers, including resistance, reactance, leakage current density, breakdown field strength and performance index, were investigated. The resistance to fatigue failure of the barrier layers was evaluated by insulating tests after the specimen foils were flattened. The results show that the dielectric properties and the resistance to fatigue failure of the TaO_x/SiO_x composite barrier layer are better than those of the SiO_x or the TaO_x barrier layer. The best dielectric properties and resistance to fatigue failure are achieved with the 4-μm thick TaO_x/SiO_x composite barrier layer.     

Excitation functions for 197Au(α, xn) reactions in the 10–40 MeV energy range

The stacked foil technique has been used to measure the excitation functions for the reactions ¹⁹⁷Au(α, xn), x = 1 to 3. A beam of alpha-particles of energy ≈ 40 MeV has been made to bombard a stack of ten gold foils. The thickness of the gold foils was selected so as to obtain an energy degradation of the order of 2 to 4 MeV. The induced activities in each foil were followed using a HPGe system. Theoretical excitation functions for these reactions based on the equilibrium decay model do not agree, in general, with the measured ones towards the high energy tails. Excitation functions have also been calculated simulating the pre-equilibrium emission by a hybrid model. The experimental excitation functions are best reproduced by taking a mixture of both the equilibrium and pre-equilibrium emissions.     

Opportunity-based age replacement policy with minimal repair

This paper proposes an opportunity-based age replacement policy with minimal repair. The system has two types of failures. Type I failures (minor failures) are removed by minimal repairs, whereas type II failures are removed by replacements. Type I and type II failures are age-dependent. A system is replaced at type II failure (catastrophic failure) or at the opportunity after age T, whichever occurs first. The cost of the minimal repair of the system at age z depends on the random part C(z) and the deterministic part c(z). The opportunity arises according to a Poisson process, independent of failures of the component. The expected cost rate is obtained. The optimal T^* which would minimize the cost rate is discussed. Various special cases are considered. Finally, a numerical example is given.     

Importance analysis considering time‐varying parameters and different perturbation occurrence times

Importance measures are integral parts of risk assessment for risk‐informed decision making. Because the parameters of a risk model, such as the component failure rates, are functions of time and a perturbation (change) in their values can occur during the mission time, time dependence must be considered in the evaluation of the importance measures. In this paper, it is shown that the change in system performance at time t, and consequently the importance of the parameters at time t, depends on the parameters perturbation time and their value functions during the system mission time. We consider a nonhomogeneous continuous time Markov model of a series‐parallel system to propose the mathematical proofs and simulations, while the ideas are also shown to be consistent with general models having nonexponential failure rates. Two new measures of importance and a simulation scheme for their computation are introduced to account for the effect of perturbation time and time‐varying parameters.     

An analytical elastic–plastic stress analysis in a woven steel reinforced thermoplastic cantilever beam loaded uniformly

In this investigation, an elastic–plastic stress analysis is carried out in a woven steel fiber reinforced thermoplastic (LDFE, F.2.12) composite cantilever beam loaded uniformly at the upper surface. Closed form solution is found satisfying both the governing differential equation and boundary conditions. The beam is loaded by a small uniform force at the upper surface, therefore during the solution of the problem for the elastic–plastic case, the normal stress σ_y is neglected in comparison with other stress components. The orientation angle of the fibers are chosen as 0, 15, 30 and 45°. The intensity of the residual stress component of σ_x is maximum at the upper and/or lower surfaces of the beam. The intensity of the residual stress component of the shear stress τ_xy is maximum on or around the x axis.     

Transformation of continuous‐time state equations to discrete‐time state equations

Abstract

A method is proposed for transforming a continuous‐time state equation, x(t)=Ax(t)+Bu(t), to a discrete‐time state equation, x[(k+1)τ]=ø(τ)x(kτ)+B(τ)u(kτ). It is based on expanding the matrix exponential exp (Aτ) into a shifted matrix Chebyshev series. An example is given to demonstrate the superiority of the method over other methods.     

Evaluation of three non-linear packing density models on micropowder mixtures

The formulation of powders often requires an optimized packing density of the granular skeleton which takes into account the desired properties. More accurate than the conventional linear models, three non-linear packing density models are evaluated from published data on binary or ternary mixtures of alumina powders, glass microbeads, siliceous microaggregates: the Compressible Packing Model (CPM), the 3-parameter Particle Packing Model (3PPM), the Theoretical Packing Density Model (TPDM). Depending on the models, they involve a compaction index K and certain particle interactions: the loosening effect a and possibly the critical cavity size ratio x₀ from which it appears, the wall effect b and the wedging effect c. The CPM (with a, b, K), by incorporating only 2 interaction functions for a and b, reduces its versatility but is efficient for siliceous. The 3PPM (with a, b, c), by incorporating 9 interaction functions, adapts well to the various micropowders with however a lower performance for the siliceous for which the packing densities predicted in “compacted” conditions are lower than in “uncompacted” conditions. The TPDM (with a, b, K, x₀) is effective for all types of micropowders and generates the best statistical indicators.     

Phase relations and microwave dielectric properties of vanadium modified Ba5Nb4O15 ceramics

Microwave dielectric ceramics of Ba₅Nb_4−xV_xO₁₅ (x = 0-1) were prepared by a solid-state reaction method. Vanadium substitution can markedly lower the sintering temperature of Ba₅Nb₄O₁₅ from 1450 to 1100 °C. The X-ray powder diffraction analysis reveals the multiphase nature of this system. A hexagonal-to-orthorhombic phase transition was also observed for the BaNb₂O₆ secondary phase. The microwave dielectric properties, such as τ_f, ε_r and Q × f value, decreased with increasing vanadium content for samples sintered at 1100 °C. There was an apparent increase in τ_f and Q × f value for samples (x ≥ 0.5) sintered at 1200 °C due to the hexagonal-to-orthorhombic phase transition of the BaNb₂O₆ phase. These results suggested that the microwave dielectric properties of multiphase ceramics strongly depended on the phase compositions and the phase transitions.     

Microwave dielectric characteristics of Mg(Ta1−xNbx)2O6 ceramics

The crystalline phase and the microwave dielectric properties of the Mg(Ta_1−xNb_x)₂O₆ ceramics have been investigated. Combining the positive temperature coefficient of the resonant frequency (τ_f) material (MgTa₂O₆, τ_f = +30 ppm/°C) with the negative one (MgNb₂O₆, τ_f = −70 ppm/°C) can produce the composite with τ_f ∼ 0 ppm/°C. The crystal structure of pure MgTa₂O₆ ceramic is the tetragonal structure. For x = 0.15, the crystal structure of the solid solution was the coexistence of the tetragonal structure and orthorhombic structure. Solid solutions with 0.25 ≦ x ≦ 1 exhibit the orthorhombic structure, which is like the structure of pure MgNb₂O₆ ceramic. The sintered morphologies of Mg(Ta_1−xNb_x)₂O₆ ceramics gradually change from the disk-typed grains (x = 0 and 0.15) to the disk-typed and bar-typed grains coexist (x = 0.35, 0.5, and 0.7), and then reveal the bar-typed grains (x = 0.85 and 1). The densities, dielectric constants (ɛ_r) and τ_f values of Mg(Ta_1−xNb_x)₂O₆ ceramics decrease with the increase of the MgNb₂O₆ content. The quality factor (Q × f) reaches the minimum value at x = 0.15, and then increases with the increase of the MgNb₂O₆ content. The Mg(Ta_1−xNb_x)₂O₆ ceramic with x = 0.25 sintered at 1450 °C exhibits a minimum τ_f value of −0.7 ppm/°C.     

The analysis of failure data in the presence of critical and degraded failures

Reported failures are often classified into severityclasses, e.g., as critical or degraded. The critical failures correspond to loss of function(s) and are those of main concern. The rate of critical failures is usually estimated by the number of observed critical failures divided by the exposure time, thus ignoring the observed degraded failures. In the present paper failure data are analyzed, applying an alternative estimate for the critical failure rate, also taking the number of observed degraded failures into account. The model includes two alternative failure mechanisms, one being of the shock type, immediately leading to a critical failure, another resulting in a gradual deterioration, leading to a degraded failure before the critical failure occurs. Failure data on safety valves from the OREDA (Offshore REliability DAta) data base are analyzed using this model. The estimate for the critical failure rate is obtained and compared with the standard estimate.     

Cooper pair breaking and isotope effect coefficient variation in high-T c superconductors

The effect of pair breaking on the isotope effect coefficientα=?d lnT _c/d lnM in La_2?x Sr _x CuO₄ and Pr-, Ca-, and Zn-doped YBa₂Cu₃O_7?x and EuBa₂Cu₃O_7?x is studied using the generalized Abrikosov-Gorkov theory recently employed by Singh and Kishore for superconductivity. It is argued that the isotope effect coefficientα can be further enhanced, in agreement with experimental observations, by considering the dependence of the characteristic scattering timeτ _s for Cooper pairs on the concentrationn of impurities (both magnetic and nonmagnetic) and the disorder ignored by them (J. Supercond. 8, 9 (1995).     

Superfluid Drops: Dynamics of Pinch-Off and Sliding Motion

We present high resolution and high speed (5 µs) photographs of ⁴He drops undergoing pinch-off and sliding down a cesiated inclined plane. When a fluid drop is stretched and pulled apart by gravity, a balance of surface tension and inertia resugts in a striking icicle-shaped column of fluid which connects the two separating parts. The narrowest point of the icicle is an example of a finite-time singularity in the equations of motion. The tip radius of the icicle L obeys a power law L～τ ^2/3, where τ is the time before the moment of pinch-off. We have verified this for both superfluid and normal drops. Because of the boundary condition requiring zero velocity at a solid wall, sliding and rolling motion of drops on a substrate is a subtle issue even for conventional fluids. For example, calculations of the dissipation yields nonphysical infinities. We have analyzed video images of sliding superfluid drop motion and measured the acceleration of ⁴He droplets on a Cesium substrate.     

Microwave dielectric properties of Ba[(Zn1−xCox)1/3Nb2/3]O3 ceramics

Microwave dielectric ceramics of Ba[(Zn_1−xCo_x)_1/3Nb_2/3]O₃ (x=0–0.8) were prepared by solid-state reaction method. The microwave dielectric properties, such as dielectric constants, Q×f values and τ_f (temperature coefficient of resonant frequency) were studied as a function of compositions and sintering temperatures. The results revealed that the dielectric constant and Q×f value decrease almost linearly with increasing x. With x increasing from 0 to 0.8, the dielectric constant decreases from 42 to 33, and Q×f value from 75,491 to 20,248 GHz. A nearly zero τ_f ceramic with dielectric constant of 33 and Q×f value of 20,248 GHz was obtained at x=0.8. The sintering temperature has slight effect on dielectric constant, but significant on Q×f value. The microstructures and crystal structures were characterized by using scanning electron microscopy (SEM) and X-ray diffraction (XRD) analysis techniques to reveal the mechanisms.     

Occurrence of common mode failure

In technical facilities, for example in nuclear power plants, redundant systems are used to prevent random failures from deleting the complete system function. However, although this redundancy concept is adequate to cope with random failures in single redundancies, its applicability is limited in case of multiple failures due to a systematic failure cause to which all redundancies are submitted due to their identical features.Some general considerations have been formulated to rule out the occurrence of such common mode failure (CMF) in redundant systems under certain circumstances. CMF means that in more than one redundancy the systematic failure cause is activated at the same time, or within the same frame of time (e.g. during the mission time for an accident). It therefore has to be distinguished between the systematic cause and the actual occurrence of CMF: a latently existing systematic cause does not necessarily lead to simultaneous failure; it must be activated and therefore is only the prerequisite for CMF.A systematic cause results in simultaneous failure if

• —the systematic cause is activated by specific circumstances associated with the accident: a triggering effect to which the redundancies are subjected due to their identical features.

• —previous failures have accumulated undetectedly before the accident.

They now appear on demand due to the accident.For exclusion of CMF, both exclusion of a triggering effect and of accumulation is necessary. A trigger can be excluded, if the components are not affected by the accident at all, or are not submitted to any ‘abnormal’ operation. Accumulation can be ruled out by self annuciation.From this a matrix for excluding CMF-susceptibility has been derived.     

Correlation of crystal structure and microwave dielectric properties for Zn(Ti1−xSnx)Nb2O8 ceramics

The correlation of crystal structure and microwave dielectric properties for Zn(Ti_1−xSn_x)Nb₂O₈ ceramics were investigated. The Zn(Ti_1−xSn_x)Nb₂O₈ ceramics contained ZnTiNb₂O₈ and an unknown Columbite-type phase. The columbite structure phase with increasing degree of ordering led to decrease of dielectric constant, increase of Qf and τ_f. The ZnTiNb₂O₈ with decreasing cation valence led to increase of τ_f. The typical values were: ? = 30.88, Qf = 43,500 GHz, τ_f = −54.32 × 10⁻⁶/ °C.     

Synthesis and microwave dielectric properties of Ca substituted SrLa4Ti4·93Zr0·07O17 ceramics

Microwave dielectric ceramics in Sr_1–x Ca _x La₄Ti_4·93Zr_0·07O₁₇ (0 ≤ x ≤ 0·5) composition series were processed via a solid-state sintering rout. X-ray diffraction revealed single phase ceramics. Ca substitutions for Sr tuned τ _f towards zero with increased Q _u f _o values. In the present study, ε _r ~ 55, Q _u f _o ~ 11960 GHz and τ _f ~ 5·2 ppm/°C were achieved for the composition with x = 0·3.