Weibull Statistical Analysis Research Articles

Ocena wytrzymałości mechanicznej kompozytów ściernych z mikrokrystalicznego tlenku glinu zbrojonych wiskerami z wykorzystaniem analizy statystycznej Weibulla

Ocena wytrzymałości mechanicznej kompozytów ściernych z mikrokrystalicznego tlenku glinu zbrojonych wiskerami z wykorzystaniem analizy statystycznej Weibulla

Evolution of dislocation loops in He ion irradiated nickel under different temperature

The effect of temperature on the evolution of loops in nickel was investigated under 30 keV He+ irradiation. The size, Burgers vector, and nature of loops were analyzed by a transmission electron microscope (TEM). In addition, the Weibull statistical analysis was introduced to analyze the size distributions of the loops. The TEM results indicate that the sizes of loops increase with increasing irradiation temperature, where they are mainly in the range of 10–30, 20–50, and 30–80 nm at 300, 400, and 500 °C, respectively. In the irradiation temperature range of 300–500 °C, the size distributions of loops fit Weibull distribution very well, which suggests that the loops tend to grow larger and/or be merged. In addition, almost all the loops formed under He+ irradiation are the interstitial loops with Burgers vectors b = a2⟨110⟩, which is ascribed to the assistance of the He atom on the formation process of loops.

Análise da resistência mecânica de vigas de mármore sintético através da teoria estatística de Weibull

RESUMO No presente trabalho, adotou-se a análise estatística de Weibull para avaliação da resistência mecânica à flexão, e sua repetibilidade, de mármores sintéticos, tanto puros quanto reforçados com fibra vidro-E. O objetivo foi observar o comportamento do módulo de Weibull e da resistência mecânica, à medida que se introduz fibra de vidro picotada na composição do mármore sintético. Para isso foram avaliados quatro diferentes teores, em massa, de fibra de vidro, para estabelecer uma curva padrão do comportamento mecânico, à medida em que se alterou a fração de fibra do compósito. A metodologia de Weibull viabiliza esta análise, uma vez que, além dos corpos de prova possuírem grande semelhança dimensional de espessura com os produtos fabricados em mármore sintético, ela quantifica a ocorrência de imperfeições devido ao processo de fabricação. Os resultados demonstraram que a inserção de fibra de vidro, em uma massa de 3 Kg de mármore sintético, em proporções de 12,5 a 100 gramas provocou, dependendo da quantidade de fibra inserida, uma variação na resistência intrínseca, que inicialmente diminuiu (0 a 25 g) e depois aumentou até o valor máximo com 100 gramas. Outro resultado importante foi o tempo de desmoldagem, que influenciou fortemente a dispersão dos resultados, que quando diminuído de 24h para 2h, provocou uma diminuição do módulo de Weibull (i.e. aumento na variação da tensão de ruptura), de até 60%.

Lifetime Assessment Method using Multiple-Stress Acceleration Aging for Flexible Cable of Portable Electric Machines

In this study, in order to analyze the lifetime for flexible cables used in portable electric machines, artificial accelerating aging was carried out for VCT(Vinyl Cab-Tire) cables in consideration of thermal, mechanical and electrical multiple-stresses. Accelerated aging factors were calculated with aging temperatures based on the Arrhenius relationship. Through Weibull statistical analysis in the AC breakdown voltages for aged cables after low-temperature mechanical tests, it was analyzed that AC breakdown voltages were proportional to the elongation rates and 19kV of the scale parameter in Weibull analysis was suggested as limit value of lifetime. Using this criterion, it was deduced that the lifetimes with thermal and mechanical multiple-stresses for 70℃, 50℃ and 40℃ continuous operation were calculated to be 3.3 years, 9.9 years and 15.7 years respectively. Based on these analysis procedure, it is possible to suggest the lifetime assessment technique with multiple-stresses for low voltage cables.

산 및 알칼리 용액에 부식된 SiC의 기계적 특성에 대한 와이블 통계 해석

산 및 알칼리 용액 속에 침지한 SiC 세라믹의 기계적 특성은 와이블 통계로 해석하였다. 시험편은 1373K에서 열처리를 행하였다. SiC의 부식은 KSL1607 방법에 의한 산 및 알칼리 용액 속에서 수행하였다. 부식된 균열치유재의 굽힘 강도는 부식되지 않은 균열치유재의 굽힘강도보다 산 및 알칼리 용액 속에서 각각 47% 및 70% 감소하였다. SiC 세라믹의 부식은 산 용액 속에서보다 알칼리 용액 속에서 더 빨랐다. 척도 파라미터 및 형상 파라미터는 모재와 부식재에서 평가하였다. 산 및 알칼리 용액에서 부식된 모재의 형상 파라미터는 산용액에서 크게 나타났다. 그러나 열처리재는 산용액에서 크게, 알칼리 용액에서 작게 나타났다. 모재 및 열처리재의 척도 파라미터는 산 및 알칼리 용액에서 모두 작게 나타났다.

Rolling Bearing Service Life Based on Probable Cause for Removal—A Tutorial

ABSTRACTIn 1947 and 1952 G. Lundberg and A. Palmgren developed what is now referred to as the Lundberg-Palmgren model for rolling bearing life prediction based on classical rolling-element fatigue. Today, bearing fatigue probably accounts for less than 5% of bearings removed from service for cause. A bearing service life prediction methodology and tutorial indexed to eight probable causes for bearing removal, including fatigue, are presented that incorporate strict series reliability; Weibull statistical analysis; available published field data from the Naval Air Rework Facility; and ∼224,000 rolling-element bearings removed for rework from commercial aircraft engines. Bearing service life Lserv can be benchmarked and calculated to the bearing L10 fatigue life as follows: Lserv = X1/m L10, where X is the number of bearings removed from service because of fatigue divided by the total of all bearings removed from service regardless of cause and m is the Weibull modulus of the bearings removed from service. The most conservative bearing L10 service life calculation is obtained assuming an exponential distribution where m = 1.1. Of the ∼224,000 commercial engine bearings removed from service for rework, 1,977 or 0.88% were rejected because of fatigue. From the Naval Air Rework Facility bearing data, eliminating rolling–element fatigue as a cause for removal, the L10 service life of these bearings would increase by approximately 3%.

Effect of interface type on the static and dynamic mechanical properties of 3D braided SiCf/SiC composites

The static and dynamic mechanical properties of three dimensional (3D) braided SiCf/SiC composites with pycrocarbon (PyC) and SiC and without an interphase layer prepared by polymer infiltration and pyrolysis (PIP), were investigated using static and dynamic bending tests as well as microstructural characterization. Test results indicated that the interfacial shear stress, flexural strength, elastic modulus, and storage modulus of 3D braided SiCf/SiC composites with an interphase layer were superior to those the composites without an interlayer; the former also showed a lower internal friction than the latter. Results from Weibull statistical analysis also indicated that the scale parameter σ0 (337.1MPa and 630.6MPa, respectively) and Weibull modulus m (16.85 and 19.91, respectively) of 3D braided SiCf/SiC composites with SiC and PyC interphase were higher than those of composites without an interphase (103.2MPa, 14.02). The composite with the PyC interphase presented the highest flexural strength and the most ductile fractures because it featured relatively ideal interfacial bonding and a layered interphase structure, leading to effective energy-dissipation mechanisms, such as fiber pull-out. The composite with the SiC interphase exhibited highest elastic and dynamic moduli because of strong interfacial bonding and a non-layered rough interphase structure, which enhanced its ability to resist strain. The ideal interface improves load transfer and did not contribute to damping. The occurrence of interfacial damping in the 3D braided SiCf/SiC caused the internal friction to become more sensitive to temperature, frequency and amplitude. The static and dynamic mechanical properties, including internal friction and storage modulus, as well as failure behavior of the 3D braided composites were remarkably affected by the interface type.

Effect of fiber directionality on the static and dynamic mechanical properties of 3D SiCf/SiC composites

The static and dynamic mechanical properties of three-dimensional (3D) 4-directional and 3D 5-directional braided SiCf/SiC composites fabricated by polymer infiltration and pyrolysis (PIP) were investigated using static and dynamic bending tests, as well as microstructural characterization. X-ray diffraction revealed that polycarbosilane was converted into a matrix of crystalline β-SiC after PIP cycling. Test results indicated that the density, flexural strength, elastic modulus, fracture toughness, and storage modulus of 3D 5-directional SiCf/SiC composites were superior to those of 3D 4-directional braided SiCf/SiC composites; the former also showed a smaller internal friction than the latter. Results from Weibull statistical analysis indicated that the scale parameter σ0 (736.9MPa) and Weibull modulus m (21.7) of the 3D 5-directional specimen were higher than those of 3D 4-directional braided SiCf/SiC composites (629.6MPa, 14.7). Both 3D braided composites demonstrated good toughness and avoided catastrophic brittle fractures under loading because of the effective crack energy dissipating mechanisms of crack deflection, interface debonding, and fiber pull-out. The internal friction and storage modulus of the 3D braided composites were sensitive to temperature. The cross angle of fiber placement in the preform and the direction of the applied force, as well as the pre-crack propagation remarkably influenced the static mechanical properties and failure behavior of the 3D braided SiCf/SiC composites. The dynamic mechanical properties of the 3D braided composites, including internal friction and storage modulus, were also considerably affected by fiber directionality in their preforms.

Properties of Geopolymer Composites Reinforced with Basalt Chopped Strand Mat or Woven Fabric

Geopolymers or polysialates are inorganic polymeric, ceramic‐like materials composed of alumina, silica, and alkali metal oxides that can be made without any thermal treatment. Additions of reinforcing phases vastly improve the mechanical properties and high‐temperature stability of the geopolymer. The processing and mechanical properties of both chopped strand mat as well as 2‐D woven fabric‐reinforced potassium geopolymer composites have been evaluated. Hand lay‐up and hydraulic press processing methods were used to produce composite panels. The room‐temperature tensile and flexural strength of chopped strand mat composites was 21.0 ± 3.1 and 31.7 ± 4.4MPa, respectively, while those of basalt weave‐reinforced geopolymer composites reached 40.0 ± 5.9 and 45.2 ± 9.3MPa, respectively. Composite microstructures were examined using optical microscopy as well as scanning electron microscopy (SEM). Mass, volume, and porosity fractions were also determined. The effect of high‐temperature treatments at 25°C, 300°C, 600°C, and 800°C were analyzed. Finally, Weibull statistical analysis was performed, which showed an increase in reliability when a reinforcement phase was added to K‐geopolymer.

Analysis of the impact of position in fatigue cracks on the fracture toughness of thick-walled pressure vessel material

The testing of fracture toughness thick-walled pressure vessel material showed a vast range of different results. Pressure vessels were made by hot plastic deformation treatment. Three sets of specimens were cut-out from the vessel, each having a same orientation of fatigue cracks in relation to the vessel axis. Fracture toughness tests were performed on the SENB specimens in accordance with ASTM 1820-11. The results showed a large range of different results, even within each sets of specimens. The results of fracture toughness in the initiation zone of stable crack growth were processed by means of Weibull statistical analysis. Based on these results of a direction distribution coefficient m was obtained and results reliability interval of fracture toughness was defined.

Fique Fiber Tensile Elastic Modulus Dependence with Diameter Using the Weibull Statistical Analysis

Fique is a plant native of Colombia with fibers extracted from its leaves presenting relevant physical characteristics and mechanical properties for possible engineering applications, such as reinforcement of polymer composites. The main physico-mechanical properties of the fique fiber have already been investigated for both untreated and mechanically treated fibers. The statistical distribution of the fique fiber diameter was analyzed and the effect of microfibrillar angle on the tensile strength and elongation was determined. However, the correlation of mechanical properties with the fiber diameter is yet to be determined. Thus, the present work evaluated the tensile elastic modulus dependence of the fique fiber as a function of its diameter. By means of the Weibull statistical analysis, it was found that an inverse correlation adjusted the elastic modulus with the equivalent diameter through a hyperbolic type of mathematical relationship. Similar correlation have been found for several lignocellulosic fibers not only by the research group of the present work but also other international groups The results are compared and discussed.

Chemistry effects on the compressive property and Weibull modulus of Zr-based bulk metallic glasses

ABSTRACT In this study, the variations in compressive mechanical properties of a variety of Zr-based bulk metallic glasses (BMGs) were analyzed. Systematic changes in composition were employed to modify the compressive malleability of the Zr-based BMGs. The enhancement on the malleability of investigated Zr-based BMGs could be correlated with the variations in Poisson's ratio. Two-parameter Weibull statistical analysis was performed on their compressive strengths over a statistically significant number of specimens. High compressive strength reliability demonstrated by its high uniformity in strength was found on the Zr-based BMGs. Malleable Z4 (Zr 66 Al 9 Ni 8.3 Cu 16.7 ) BMG showed a higher Weibull modulus ( m = 71) as compared with the less malleable Z1 (Zr 53 Al 16 Co 23.25 Ag 7.75 ) BMG ( m = 38), implying a more uniform distribution of compressive failure strength and a higher reliability. The correlation of m with the intrinsic malleability of Zr-based BMGs was discussed by the variations in the Poisson's ratio, the shear modulus or the glass transition temperature.

Comparison of Three-Parameter Weibull Statistical Analysis of the Flexural Strength of Dense and Porous Sintered Clay

Reliability analysis of dense and porous sintered clay-based ceramic was compared using three-parameter Weibull model. The raw and the sintered clay at temperatures 900-1300°C were characterized using XRF and XRD. The raw clay (dense) and clay mixed with cassava starch (porous) were compacted and sintered at 1300°C. Flexural strength of the dense (24.11-46.56MPa) and the porous (13.58-23.26MPa) sintered clay were determined using three-point bending test. The results were analyzed by three-parameter Weibull probability distribution using Minitab 15 software at 95% confidence interval. Scale and threshold parameters of the dense sintered clay were higher than that of the porous sintered clay. However, the Weibull modulus of the porous ceramic was higher than the dense ceramic. The morphology of the porous sintered clay shows a relative distribution of porosity while the dense ceramic shows a random distribution of cracks. Three- parameter Weibull is a suitable tool to model the reliability of dense and porous sintered clays.

SiC 첨가한 ZrO<sub>2</sub>의 기계적 특성에 대한 와이블 통계 해석

비커스 경도 실험은 세라믹스 재료의 경도를 특성화하는데 사용되는 일반적인 실험법이다. 그러나 경도도 하나의 확률변수로 취급하는 것이 일반적이다. 본 연구의 목적은 단상 ZrO₂ 와 SiC 첨가한 ZrO₂/SiC 복합 세라믹스의 굽힘강도와 비커스 경도의 통계적 성질을 조사하는 것이다. 본 연구에서는 와이블 통계 해석에 기초하여 그들의 결과를 특성치와 변동을 비교 고찰하였다. 굽힘강도 및 비커스 경도는 모두 와이블 분포에 비교적 잘 적합할 수 있음을 알았다. 또한 단상 ZrO₂ 와 SiC 첨가한 ZrO₂/SiC 복합 세라믹스와 그들의 열처리재에 대한 비커스 경도의 확률분포에 대한 척도 및 형상 파라메터 값을 평가하였다.

Thermomechanical Properties of Cycled Ceramic/Glass Composite Seals for Solid Oxide Fuel Cells

The present research focuses on a novel ceramic/glass composite seal. These seals first underwent a curing cycle. The cycled seal was then characterized with a laser dilatometer to identify the glass transition, softening temperature, and thermal expansion properties. High temperature ring-on-ring (RoR) experiments were performed to study the effect of glass transition and softening temperatures on mechanical response. X-ray diffraction (XRD) techniques in conjunction with post-test micrographs were used to understand the observed mechanical response. In addition, Weibull statistical analysis performed on cycled seals showed that Weibull modulus had decreased and Weibull characteristics strength had increased with multiple thermal cycles.

Statistical aspects of fatigue crack growth life of base metal, weld metal and heat affected zone in FSWed 7075-T651 aluminum alloy

The statistical aspects of fatigue crack growth life of base metal (BM), weld metal (WM) and heat affected zone (HAZ) in friction stir welded (FSWed) 7075-T651 aluminum alloy has been studied by Weibull statistical analysis. The fatigue crack growth tests were performed at room temperature on ASTM standard CT specimens under three different constant stress intensity factor range controls. The main objective of this paper is to investigate the effects of statistical aspects of fatigue crack growth life on stress intensity factor ranges and material properties, namely BM, WM and HAZ specimens. In this work, the Weibull distribution was employed to estimate the statistical aspects of fatigue crack growth life. The shape parameter of Weibull distribution for fatigue crack growth life was significantly affected by material properties and the stress intensity factor range. The scale parameter of WM specimen exhibited the lowest value at all stress intensity factor ranges.

Effect of dissolved hydrogen on removal of double oxide film defects from Al melt

Effect of increasing the hydrogen content of the melt on the removal of double oxide (bifilm) defects in commercial purity Al melt was investigated using Weibull statistical analysis of mechanical properties of solidified castings and a semiempirical mathematical model that had been developed previously. The results of the Weibull analysis revealed that increasing the H content of the melt from 0·2 to 0·4 mL/100 g and holding the melt in furnace for 30 min caused the Weibull modulus of the casting to increase by ∼73%. Studies (SEM and EDX) of fracture surfaces of the test bars indicated that the number of oxide defects in the melt decreased due to this treatment. The mathematical model suggested that increasing the H content of the melt to ∼0·8 mL/100 g would force all the oxide defects to expand rapidly and float out of the liquid metal in a very short time.

The effect of size on the strength of coarse rock aggregates and large rockfill samples through experimental data

Testing the mechanical response of coarse granular materials requires very large and expensive laboratory equipments. During the 1960s, pioneering experimental programs were carried out on several rockfill dam materials, and those results are still a reference for engineers and researchers. However, only few experimental works have been reported to this day, and due to the scarcity of empirical data, the role of the size effect caused by grain crushing is not well known. To improve understanding of this rarely studied issue and the influence of individual particle strength, this paper analyzes the size effect on rock aggregate crushing strength and its connection with the shear envelope of rockfills. The suitability of the 4-parameter Weibull equation to describe size effects on the crushing strength reported in the literature is discussed. Furthermore, a Weibull statistical analysis was carried out for a wide number of experimental results on rock aggregates, where it has been observed that strength decreases with particle size. In parallel, the results of large triaxial tests on homothetic scaled rockfill samples of 250 and 1,000 mm in diameter reveal that the coarser the material, the higher the amount of grain breakage and the lower the shear strength. The impact of size effects obtained from the experiments is analyzed and discussed in terms of the factor of safety of rockfill slope stability. Furthermore, the results are compared with the only existing theoretical method that links the rock aggregate with the strength of the granular assembly. Good agreement between the empirical results and this theoretical method has been confirmed.

Chacterization of Tensile Strength Dependence with Diameter of Sponge Gourd Fibers by Weibull Statistical Analysis

Lignocellulosic fibers with relatively unknowns mechanical properties such as those extracted from the sponge gourd, are being investigated as polymer composites reinforcement. The use of natural fibers are related to environmental , technical, economical and social advantages. An important possibility of improving the mechanical properties is the fact that lignocellulosic fibers may present tensile strength inversely correlated with their diameter. Therefore, this possibility was investigated in the present work regarding sponge gourd fibers by means of the Weibull statistic analysis. The results supported a hyperbolic inverse correlation between the strength of sponge gourd fibers with their diameter. Scanning electron microscopy observation of fibers with different diameters revealed possible mechanisms for the strength inverse correlation with diameter.

마찰교반용접된 7075-T651 알루미늄 합금 용접부의 피로균열전파율의 공간적 불규칙성 (LT 방향의 시험편에 대하여)

본 연구의 목적은 마찰교반용접된 7075-T651 알루미늄 합금 용접부에 대한 피로균열전파율의 공간적 불규칙성을 고찰하기 위한 것이다. 본 연구에서는 이전의 피로균열전파 실험 데이터를 활용하였다. 피로균열전파율의 공간적 불규칙성을 명확히 이해하기 위하여, 피로균열전파 실험은 일정 응력확대계수범위 제어하에서 수행되었다. 재질, 즉 마찰교반용접된 7075-T651 알루미늄 합금 용접부의 용접재와 모재에 대하여 피로균열전파율의 공간적 불규칙성을 조사하기 위하여 실험 데이터가 해석되었다. 결론적으로 용접재의 변동성이 모재의 변동성보다 높게 나타났으며, Weibull 통계 해석에 의하여 변동성을 평가할 수 있음을 알았다.