Nondestructive Evaluation (NDE) is an effective way for determining material properties. More specifically, ultrasonic waves along with visual measurements from a microscope can be used to systematically determine the elastic modulus of single ply composites that are subject to an altered manufacturing process. In this approach, the magnitudes of specific ultrasonic wave velocities are applied through Chirstoffel’s equations to determine the necessary five elastic constants that describe the elastic modulus of transversely isotropic composites. On the other hand, fiber misalignment measurements are taken through via digital microscopy to satisfy a statistical approach for the determination of the same elastic modulus. The Paper Physics Approach (PPA) and Laminate Analogy Approach (LAA) are utilized to predict the elastic modulus of unidirectional carbon fiber samples. A two parameter Weibull distribution is expected to satisfy the probability density of the fiber length and fiber orientation variation which will then be implemented into the Halpin-Tsai equations that will determine the elastic modulus. In terms of results, the mean fiber length from the visual approach is approximately 250 μm and the mean fiber misalignment is just over 3°. The elastic moduli range from 7 GPa to 9 GPa depending on the approach. Destructive mechanical testing led to an average elastic modulus value of 8.49 GPa.

The reliability of experimental data obtained in friction welded titanium alloy and stainless steel with copper interlayer by using various interlayer thicknesses and upset time are investigated using the maximum likelihood method for the estimation of the Weibull parameters of the results. The results indicate that among the various process parameters, interlayer thickness was significant. Further the reliability of the tensile strength was estimated using weibull distribution. Using this technique in conjunction with the experimental data, we can predict the output, in this case tensile strength more accurately and minimize their impact. Titanium alloy when directly bonded to stainless steel, improper bonding happens. Hence an interlayer in the form of copper is added to have successful joints.

The State of Kuwait is considering diversifying its energy sector and not entirely depend on oil. This desire is motivated by Kuwait commitment to reducing its share of pollution, as a result of burning fossil fuel, and to extend the life of its oil and gas reserves. The potential for solar energy in Kuwait is quite obvious; however, it is not the case when it comes to wind energy. The aim of this work was to analyze wind data from several sites in Kuwait and assess their suitability for building large-scale wind farms. The analysis of hourly averaged wind data showed that some sites can have an average wind speed as high as 5.3 m/s at 10 m height. The power density using Weibull distribution function was calculated for the most promising sites. The prevailing wind direction for these sites was also determined using wind-rose charts. The power curves of several Gamesa turbines were used in order to identify the best turbine model in terms of specific power production cost. The results showed that the area of Abraq Al-Habari has the highest potential for building a large-scale wind farm. The payback period of investments was found to be around 7 years and the cost of electricity production was around US Cent 4/kWh.

In our previous paper [1], four material constants required for Low-Cycle Fatigue under drop impact modeling in ABAQUS were obtained. This study aimed to validate that technique using conventional JEDEC drop test results. Several test boards were subjected to drop test at 3000G/0.28ms, close to the most severe condition of JEDEC Standard. During repetitive drops, the overall electrical resistance of daisy-chained solder joints of each package on the test board was monitored to detect the failure. Weibull distribution were obtained for edge and center package. The numerical model was then built in ABAQUS Low-cycle Fatigue, the set of constant obtained from previous study [1] was used as a reference source for the model. Fatigue life of the package extracted from the numerical model was compared with experiment results. The validation was finally reported.

Air pollution has been proven as a significant risk factor for multiple health conditions. A major portion of urban air pollution is attributed to vehicle emissions. In this study, a high school which is close to an interstate highway is numerical simulated to estimate the impact of traffic emissions on air quality. Two probability density functions, Weibull distribution and Rayleigh distribution, were used in wind data statistical analysis. A numerical method was used to estimate the wind speed at study site based on the wind data in meteorology stations. Both indoor and outdoor environment were simulated using computational fluid dynamics (CFD). The airflow and the dispersion of particulate air pollutants emitted from the highways surrounding the high school building were analyzed. The wind flow was simulated using Reynolds-Averaged Navier Stokes (RANS) model. The particulate matters are tracked using Lagrangian model. For the indoor simulation, the standard k-ε model is employed to model the air-phase turbulence. Discrete phase model (DPM) and Eulerian multiphase model were utilized for the particle phase, respectively. The comparison shows that the Lagrangian approach has better agreement since the dispersed-phase volume fractions are less than 10%.

The inclusion of 0.25 and 0.5 wt.% functionalized multi-walled carbon nanotubes (MWCNTs) into a vinyl ester (VE) resin has been studied. To investigate the effect of carbon nanotubes (CNTs) dispersion, the sonication process has been performed under a variety of parameters including mixing time and sonication amplitude. Differential scanning calorimetry (DSC) and 3-point flexural testing methods have been employed to explore the thermo-mechanical properties of materials. Differential scanning calorimetry results show up to 13°C increase in the glass transition temperature (T g ) of the VE polymer by introducing 0.25 wt.% CNTs with a total sonication energy of 60 KJ. It is also established that the flexural modulus of the polymer can be improved up to 24%. An array indentation technique has been used to evaluate the hardness and elastic modulus variations in the regions of nanoparticle concentration. The resulting variations along the indentation array have been statistically studied using three-parameter Weibull distribution. Based on the resulting dispersion conditions, the optimum sonication parameters and nanoparticle concentration have been determined.

An improved program of previous optimization work is put forward for analyzing and optimizing the spatial configurations of wind turbines in offshore wind arrays. It applies Ainslie’s wake model in which the wake profile is dependent on wind speed, turbulence intensities and the turbine’s thrust coefficient. Models of single wakes and multiple wakes are employed. Weibull distributions and turbulence intensities of wind are applied. A real wind turbine power curve is used to estimate power out of the turbines. The annual power output of the wind array for the North Sea’s Horns Rev wind array is evaluated and compared with the optimization results. Disagreement is observed between the simulated results using different angular discretizations of the possible wind directional probabilities. An analysis and possible explanation are discussed.

In this paper Fouling and Erosion damages as two main sources of deterioration in the engine performance are modelled for a single spool engine. The effects of these phenomena on the Low Cycle Fatigue (LCF) and Creep status of the engine turbine blades are studied. A Matlab/Simulink model is developed for the LCF and Creep damages evaluation based on the available measured outputs. Several simulations are performed to investigate the effects of different levels of the Fouling and the Erosion degradations on the LCF and Creep damages propagation in the take-off mode of the flight. The probability of failure is calculated in each simulation scenario according to the Weibull distribution. The obtained results can be used as a prognostic tool to predict an appropriate next cycle for the engine maintenance schedule.

In this study, the nanophased epoxy with 2 wt.% clay was utilized in a vacuum assisted resin transfer molding (VARTM) set up with carbon fabric to fabricate laminated composites. The effectiveness of clay addition on mechanical properties of composites has been evaluated by tensile, flexural and fatigue test. The tensile and flexural strengths improved by 5.7% and 13.5%, respectively as compared to the neat composite. The fatigue strength was also improved significantly. Based on the experimental result, a linear damage model combined with the Weibull distribution function has been established to describe static failure processing of neat and nanophased carbon/epoxy. The simulated stress strain curves from the model are in good agreement with the test data. Simulated results show that damage processing of neat and nanophased carbon/epoxy described by bimodal Weibull distribution function.

The explosively loaded right-circular tube geometry is used as the basis for dynamic fracture and fragmentation modeling. Details of the cylinder configuration are investigated to prescribe controlled loading conditions of uniaxial stress and plane strain. Earlier works by Goto et al [1] had used thin-walled tubes to provide plane strain loading and shorter “rings” to establish uniaxial stress conditions. This paper extends on that work to look at alternative cylinder dimensions and metals of interest. A tungsten alloy, Aero-224, and a high strength steel, Eglin Steel (ES-1), are the subject metals. Transient continuum-mechanics simulations evaluated whether the stress triaxiality conditions were being met as design parameters of cylinder material, cylinder wall-thickness, cylinder length, and initiation configuration were varied. Design analysis shows that the thin cylinders of ES-1 steel do establish the desired plane strain conditions as it expands to failure. Ultra-high speed photography experiments verify the time of fracture and correlate casewall expansion and velocity measurements. Synchronization of the code and diagnostics measurements is presented as a valuable analysis method. On the other hand, rings (i.e. uniaxial stress) of the Aero-224 tungsten alloy were failing just short of uniaxial stress approximating conditions. Analysis of the Aero-224 rings indicated it must be capable of achieving at least a 25% strain to failure in order to have the triaxiality condition satisfied. Strain to failure measurements directly from recovered fragments were less than 14%. Nevertheless, a Weibull distribution was fit to the empirical data set and used to drive a statistically compensated fracture model. Results and discussion of the failure strain distribution and the ability for continuum codes to adequately conduct such simulations are presented.

Reliability growth curves are modeled using the results of Weibull distribution regression analysis. The Weibull Learning Curve (WLC) model is useful because it provides an early statistical indication of wear out issues. The vibration, thermal, humidity and corrosion environments of the F-22 are severe. It is prudent to be concerned about wearout problems in severe aircraft environments. The power of Weibull is the ability to predict the characteristic life and distribution shape with a small amount of data. The proposed model is compared to the traditional Duane Learning Curve approach. Statistical model validity is evaluated using numeric and graphical methods, including coefficients of determination (r 2 ) and residuals. The WLC model provides insight into interdisciplinary issues, including supplier quality control, qualification testing, physics of failure, and reliability engineering. In addition, the WLC model quantifies the number of items with removal statistics consistent with wearout; therefore, this study helps to quantify successes and shortfalls of durability analysis and testing approaches.

Engineering structures such as aircraft, bridges, dams, nuclear containments and ships, as well as computer circuits, chips and MEMS, should be designed for failure probability < 10 −6 –10 −7 per lifetime. The safety factors required to ensure it are still determined empirically, even though they represent much larger and much more uncertain corrections to deterministic calculations than do the typical errors of modern computer analysis of structures. The empirical approach is sufficient for perfectly brittle and perfectly ductile structures since the cumulative distribution function (cdf) of random strength is known, making it possible to extrapolate to the tail from the mean and variance. However, the empirical approach does not apply to structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared to structure size. This paper presents a refined theory on the strength distribution of quasibrittle structures, which is based on the fracture mechanics of nanocracks propagating by activation energy controlled small jumps through the atomic lattice and an analytical model for the multi-scale transition of strength statistics. Based on the power law for creep crack growth rate and the cdf of material strength, the lifetime distribution of quasibrittle structures under constant loads is derived. Both the strength and lifetime cdf’s are shown to be size- and geometry-dependent. The theory predicts intricate size effects on both the mean structural strength and lifetime, the latter being much stronger. The theory is shown to match the experimentally observed systematic deviations of strength and lifetime histograms of industrial ceramics from the Weibull distribution.

A new constitutive equation is presented to describe the damage evolution process in parallel fibered collagenous tissues such as ligaments and tendons. The model is formulated by accounting for the fibrous structure of the tissues. The tissue’s stress is defined as the average of the collagen fiber’s stresses. The fibers are assumed to be undulated and straighten out at different stretches that are defined by a Weibull probability density function. After becoming straight each fiber is assumed to be linear elastic. Its waviness is defined by a Weibull distribution. Tissue’s damage is assumed to occur at the fiber level and is defined as a reduction in the fiber’s stiffness. The proposed model is validated by using experimental data published in the biomechanics literature by Provenzano et al. [1].

Tensile mechanical behavior of T700 fiber bundles have been studied in the strain rate range from 0.001 l/s to 1000 l/s and complete stress strain curves were obtained. Results show that both ultimate strength and failure strain are strain rate insensitive, and T700 carbon fiber can be regarded as strain rate insensitive materials. On basis of the fiber bundles model and the statistic theory of fiber strength, a statistical constitutive model based on Weibull distribution function has been developed to describe mechanical behavior of T700 fiber. And a method for determine the statistic parameters of fibers by tensile tests of fiber bundles is established, too. The simulated stress strain curves from the model are in good agreement with the test data. Simulated results show that the strength of T700 fiber can be described by single Weibull distribution function.

In many applications such as computers and telecommunications, the IC chip sizes are very big, the on-chip frequency and power dissipation are very high, and the number of chip I/Os is very large. The CCGA (ceramic column grid array) package developed by IBM is one of the best candidates for housing these kinds of chips [1–7]. There are two parts in this study. One is to show that the 2-parameter Weibull life distribution is adequate for modeling the thermal-fatigue life of lead-free solder joints. This is demonstrated by comparing the 2-parameter and 3-parameter Weibull distributions with life test data of an 1657-pin CCGA package with the 95.5wt%Sn3.9wt%Ag0.6wt%Cu lead-free solder paste on lead-free PCBs (printed circuit boards) under thermal cycling conditions. The other part of this study is to determine the time-history creep strain energy density of the 1657-pin CCGA solder column with two different solder paste materials, namely, 95.5wt%Sn3.9wt%Ag0.6wt%Cu and 63wt%Sn37wt%Pb and under three different thermal cycling profiles, namely, 25 ↔ 75°C, 0 ↔ 100°C, and −25 ↔ 125°C. The effects of these solder pastes and temperature conditions on the thermal-fatigue life of the high-lead (10wt%Sn90wt%Pb) solder columns of the CCGA package are provided and discussed.

This study was performed to develop the accelerated life test method using Weibull-IPL (Inverse Power Law) model for power train components that are running on cyclic loads. Weibull-IPL model is concerned with determining the assurance life with confidence level and the accelerated life test time. From the relation of weibull distribution factors and confidence limit, the testing times on the no or some number of failure acceptance criteria are determined. The power train components under cyclic loads generally represent wear and fatigue characteristics as a failure mode. IPL based on the cumulative damage theory is applied effectively the mechanical components to reduce the testing time and to achieve the accelerating test conditions. The proposed Weibull-IPL model is an approach to improve the reliability assessment on the statistical distribution and wear out failure mechanism concepts. As the actual application example, accelerated life test method of agricultural tractor transmission was described. Life distribution of agricultural tractor transmission was supposed to follow Weibull distribution and life test time was calculated under the conditions of average life (MTBF) 3,000 hours and 90% confidence level for one test sample. According to IPL, because test time can be shorten in case increase test load, test time could be reduced by 482 hours when we put the load 1.1 times of rated load than 0.73 times of rated load that is equivalent load calculated by load spectrum of the agricultural tractor. This time, acceleration factor was 11.7. This Weibull-IPL model can be used to develop accelerated test method of gear reducer, hydraulic hose, bearing and etc.

Surface micromachining (SMM) techniques produce complex microscale polysilicon features on the surface of a silicon wafer using a patterned maultilayer film deposition process. Failure characteristics of SMM polysilicon obtained from testing series of 2 μm and 4 μm wide ligaments fabricated using standard SMM processing techniques, fit a Weibull distribution, suggesting a behavior governed by a distribution of flaws, similar to brittle ceramic materials. However, positive identification of critical flaws that dictate the failure distribution within the ligaments remains unclear. Likely candidates are flaws associated with surface roughness or gain boundary intersections with the polysilicon microstructure. To address the possible connection between microstructure and failure behavior of SMM polysilicon, templates, based on observed polysilicon microstructure were subjected to deformation simulations using polycrystal elasticity modeling. Series of simulations were performed to capture the statistical failure of polysilicon due to local elastically driven stress concentrations between grains with different crystallographic orientations.. Simulated results are presented and discussed in the context of experimental failure data.

A comparative evaluation of the leading lead-free solder candidate (95.5Sn3.8Ag0.7Cu) and traditional tin-lead solder (63Sn37Pb) under thermal cycling conditions was carried out. A test vehicle consisting of four daisy chained 10×10 array 0.8mm pitch plastic micro ball grid arrays (microBGA) mounted on an 8-layer FR4 printed wiring board was designed. The board finish was organic solder preservative (OSP) for the lead-free devices and hot air solder levelled (HASL) in the case of the eutectic devices. An event detector was used to monitor the continuity of each daisy chain during accelerated temperature cycling, where the test vehicles were cycled with a ramp rate of approximately 3°C per minute from −40°C to 125°C, with 10-minute dwells and a total cycle time of 2 hours 10 minutes. Results to date plotted using a Weibull distribution indicate that the SnAgCu solder is more reliable under these conditions. Experiments were also carried out on large-scale lead-free solder specimens to determine the parameters required for the Anand viscoplasticity model. The Anand model was then implemented in finite element analysis using ANSYS ® , where the submodelling technique was employed to determine the viscoplastic work per thermal cycle for each solder joint along the package diagonal. Schubert’s fatigue life model was used to predict the number of cycles to failure of each joint, although it should be noted that the necessary model parameters for the may need to be calibrated. Results indicate that the joint under the die edge is likely to fail first and that the SnAgCu solder is more fatigue resistant. The numerical predictions underestimate the fatigue life in both cases.

This study was performed to develop the assurance life prediction method using modification of shape parameter for the latch spring of vehicle door. The shape parameter β is a main parameter with scale parameter, number of sample, confidence level, in determining the predicted assurance life and testing time. The proposed the modification of shape parameter is an approach to verify the life prediction procedures based on the life testing data and to improve the reliability assessment on the statistical distribution. The latch spring generally represent fatigue and fracture characteristics as a failure mode. Firstly, life distribution of latch spring was supposed to follow Weibull distribution and life test time was calculated under the conditions of average life (B 5 ) 300,000 cycles and 95% confidence level for 60 test samples with value of shape parameter 2.07 from reference data. Secondly, after the life test, the value of shape parameter 2.26 can be obtained by using MINITAB. Finally, the assurance life of latch spring could be predicted by the relation of mean life and the scale parameter which is achieved also from the analysis of sample failure data.

In this paper, loading and loading-unloading tests of carbon fiber reinforced aluminum laminates (CRALL) have been carried out in a tensile impact apparatus, and quasi-static tensile tests have been performed on a MTS-810 machine. Complete stress-strain curves of composite in the strain rate range from 0.001–1200 1/s have been obtained. Experimental results show that CRALL composite is a strain rate sensitivity material, the tensile strength and failure strain both increased with increasing strain rate. A linear strain hardening model has been combined with Weibull distribution function to establish a constitutive equation for CRALL. The simulated stress-strain curves from model are in good agreement with the test data. The analysis of the model shows that the Weibull scale parameter, σ 0 , increased with increasing strain rate, but Weibull shape parameter, β, can be regarded as a constant.