Relevant bibliographies by topics / Weibull's weakest-link theory

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  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Weibull's weakest-link theory'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Weibull's weakest-link theory"

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Carpinteri, Alberto, Pietro Cornetti, and Simone Puzzi. "Scale effects on strength and toughness of grained materials: An extreme value theory approach." Strength, Fracture and Complexity: An International Journal 3, no. 2-4 (2005): 175–88. https://doi.org/10.3233/sfc-2005-057.

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The present paper provides a statistical model to the size effect on grained materials tensile strength and fracture energy. It has been already demonstrated by using extreme value theory that the scaling law obtained for the tensile strength introducing a doubly truncated distribution of flaws, under the hypothesis of Weibull's weakest link, resembles the Multi-Fractal Scaling Law (MFSL), already proposed by the first Author through fractal concepts. Since the weakest link in grained materials is usually represented by the interface between the matrix and the grains, in the present paper we a
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Zok, Frank W. "On weakest link theory and Weibull statistics." Journal of the American Ceramic Society 100, no. 4 (2017): 1265–68. http://dx.doi.org/10.1111/jace.14665.

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Daum, Benedikt, Gerrit Gottlieb, Nabeel Safdar, Martin Brod, Jan-Hendrik Ohlendorf, and Raimund Rolfes. "A numerical investigation of the statistical size effect in non-crimp fabric laminates under homogeneous compressive loads." Journal of Composite Materials 56, no. 5 (2021): 665–83. http://dx.doi.org/10.1177/00219983211057346.

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The compressive strength of fiber reinforced composites is typically limited by a shear localization phenomenon known as microbuckling and is very sensitive to local imperfections of fiber alignment. Local misalignments act as randomly distributed flaws and introduce a dependence of the compressive strength on the size of material volume element under consideration. For homogeneously loaded material elements, weakest-link theory in combination with a Weibull power law is a frequently employed statistical model for microbuckling strength. This implies a dependence of strength on the size of vol
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Hristopulos, Dionissios T., and Anastassia Baxevani. "Kaniadakis Functions Beyond Statistical Mechanics: Weakest-Link Scaling, Power-Law Tails, and Modified Lognormal Distribution." Entropy 24, no. 10 (2022): 1362. http://dx.doi.org/10.3390/e24101362.

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Probabilistic models with flexible tail behavior have important applications in engineering and earth science. We introduce a nonlinear normalizing transformation and its inverse based on the deformed lognormal and exponential functions proposed by Kaniadakis. The deformed exponential transform can be used to generate skewed data from normal variates. We apply this transform to a censored autoregressive model for the generation of precipitation time series. We also highlight the connection between the heavy-tailed κ-Weibull distribution and weakest-link scaling theory, which makes the κ-Weibul
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Lam, Frank. "Length effect on the tensile strength of truss chord members." Canadian Journal of Civil Engineering 27, no. 3 (2000): 481–89. http://dx.doi.org/10.1139/l99-084.

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Length effects on the tensile strength of multiple member truss chords have been studied. Simulation and reliability studies have been presented to evaluate the impact of length and multiple member effects on the target safety index for tensile failure. Results indicate significant length effect can be expected for long multiple tension chord members. Based on the Weibull weakest link theory, length effect adjustment parameters have been established. Further simulation and reliability studies have demonstrated the robustness of the proposed length effect adjustment procedures. A procedure has
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Vu, Chi Cong, Jérôme Weiss, Olivier Plé, and David Amitrano. "Statistical Size Effects on Compressive Strength and Mechanical Behavior of Concrete." Key Engineering Materials 754 (September 2017): 317–20. http://dx.doi.org/10.4028/www.scientific.net/kem.754.317.

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The size effect on strength of concrete has been studied for a long time from various approaches. In particular, the weakest-link theory remains nowadays the basic tool to interpret statistical size effects, i.e. how the probability of failure under a given stress depends on external size. The main shortcoming of Weibull’s theory is that the activation of fracture from the weakest flaw is assumed to set the final strength, i.e. possible interactions between microcracks and defects during progressive damage are implicitly neglected. The objective of this study is to determine experimentally the
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Kumar, Rajnish, Bo Madsen, Hans Lilholt, and Lars P. Mikkelsen. "Influence of Test Specimen Geometry on Probability of Failure of Composites Based on Weibull Weakest Link Theory." Materials 15, no. 11 (2022): 3911. http://dx.doi.org/10.3390/ma15113911.

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This paper presents an analytical model that quantifies the stress ratio between two test specimens for the same probability of failure based on the Weibull weakest link theory. The model takes into account the test specimen geometry, i.e., its shape and volume, and the related non-constant stress state along the specimen. The proposed model is a valuable tool for quantifying the effect of a change of specimen geometry on the probability of failure. This is essential to distinguish size scaling from the actual improvement in measured strength when specimen geometry is optimized, aiming for fai
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Tomaszewski, Tomasz, Przemysław Strzelecki, Adam Mazurkiewicz, and Janusz Musiał. "Probabilistic Estimation of Fatigue Strength for Axial and Bending Loading in High-Cycle Fatigue." Materials 13, no. 5 (2020): 1148. http://dx.doi.org/10.3390/ma13051148.

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In this paper, the sensitivity to the type of loads (axial and bending loading) of selected construction materials (AW6063 T6 aluminum alloy, S355J2+C structural steel, and 1.4301 acid-resistant steel) in high-cycle fatigue was verified. The obtained S-N fatigue characteristics were described by a probabilistic model of the 3-parameters Weibull cumulative distribution function. The main area of research concerned the correct implementation of the weakest link theory model. The theory is based on a highly-stressed surface area and a highly-stressed volume in the region of the highest stresses.
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Moses, D. M., and H. G. L. Prion. "A three-dimensional model for bolted connections in wood." Canadian Journal of Civil Engineering 30, no. 3 (2003): 555–67. http://dx.doi.org/10.1139/l03-009.

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Recent criticism of the bolted connection requirements in the Canadian wood design code CSA Standard O86 indicates that the code lacks consideration of the different modes of failure, particularly as they relate to multiple-bolt connections. A finite element model is proposed to predict load–displacement behaviour, stress distributions, ultimate strength, and mode of failure in single- and multiple-bolt connections. The three-dimensional (3-D) model uses anisotropic plasticity for the wood member and elastoplasticity for the bolt. The Weibull weakest link theory is used to predict failure at g
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He, Xi Xi, and Zhi Hui Xie. "Experimental Study on Statistical Parameters of Concrete Strength Based on Weibull Probability Distribution." Key Engineering Materials 477 (April 2011): 224–32. http://dx.doi.org/10.4028/www.scientific.net/kem.477.224.

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Along with deterministic size effect theory statement, Weibull distributed size effect has been neglected generally. The author believes that, deterministic size effect is not established to the basic strength index of plain concrete without notches. Definite size effect has an application limitation on the large-size zone. The most recent development of size effect is the fracture size effect theory based on probability in modern times. As a result of stress concentration caused by the notches, failure mechanism is bond to be affected. Therefore, the existing fracture theory needs to be teste
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Dissertations / Theses on the topic "Weibull's weakest-link theory"

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Kovář, Jaroslav. "Pravděpodobnosti porušení keramické součásti s využitím Weibullovy teorie nejslabšího článku." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-382549.

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This thesis compares Weibull weakest link theory with inclusion of one and all three principal stresses. Principal stresses needed for this theory were calculated with finite element method. The informational research is in the introduction of this thesis. It includes ceramic materials, Weibull weakest link theory, Gaussian quadrature over spherical surface and ceramic head of hip joint endoprothesis. Theoretical part is used for next calculations of probability of failure. The probability of failure of ceramic rod loaded by four-point bending is calculated in first calculations. This task is
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Book chapters on the topic "Weibull's weakest-link theory"

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Bažant, Zdeněk P., Jia-Liang Le, and Marco Salviato. "Probabilistic Theory of Quasibrittle Fracture." In Quasibrittle Fracture Mechanics and Size Effect. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192846242.003.0006.

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The foregoing models of quasibrittle fracture are incomplete because the actual behavior is always random. The weakest-link model, leading the Weibull probability distribution of structure strength, is discussed first, as the simplest approach, and is shown to follow from the stability postulate of extreme value statistics. The power law mean size effect of Weibull distribution and constancy of its coefficient of variation are derived. Then it is emphasized that real quasibrittle structures have rarely sufficient size for considering the number of links to be infinite, and a geometry-independe
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Conference papers on the topic "Weibull's weakest-link theory"

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Schneider, Markus, Dennis Wawoczny, and Kevin Haffke. "The Size Effect Of The Strength Of Sintered Nd2Fe14B Hard Magnets." In Euro Powder Metallurgy 2024 Congress & Exhibition. EPMA, 2024. http://dx.doi.org/10.59499/ep246319979.

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Ceramics and intermetallic compounds, e.g. sintered Nd2Fe14B hard magnets, are hard and brittle. The lack of any macroscopic plasticity yields to the fact that all defects exhibit its sharpest effect as predicted with the methods of the classical Linear Elastic Fracture Mechanics (LEFM) and Neuber’s theory of notch stresses. Residual stresses from the processing do not relax. The lack of any peak stress or stress intensity reducing plasticity explains its stronger scattering and Probability Density Function’s (PDF) loss of symmetry. The PDF of common ceramics are skewed and broader which leads
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Smart, John, and Siu L. Fok. "Determining Failure Laws for Ceramic Materials." In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-085.

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For determining the failure probability of ceramic components in a varying stress field, there are many theories which are based on the Weibull “weakest-link” ideas. However, the difference between the predictions for many stress systems is small and because of the scatter in the failure loads for ceramic materials and the inevitable experimental errors, it has been difficult to decide which is most suitable. In this paper, a testing regime is described which spreads the predictions from the various theories to allow the most suitable theory for a given material to be chosen. This will give mo
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Noronha, Silvester J. "A New Rationale for Scatter in Fracture Toughness Measurements." In ASME 2008 Pressure Vessels and Piping Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/pvp2008-61058.

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The observed scatter in fracture toughness is investigated based on a dislocation simulation model that has been proposed to predict the brittle ductile transition in ferritic steels. We carried out a series of Monte-Carlo simulations using uniform distribution of microcracks on the crack plane of macrocrack. Detailed statistical analysis of the simulation results showed that the fracture is always initiated at one of the largest microcracks, whose size correspond to the tail of the size distribution function, and the inherent scatter arises from the distribution in the size of the critical mi
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Duffy, Stephen F., and Jane M. Manderscheid. "Noninteractive Macroscopic Reliability Model for Ceramic Matrix Composites With Orthotropic Material Symmetry." In ASME 1989 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/89-gt-129.

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A macroscopic noninteractive reliability model for ceramic matrix composites is presented. The model is multiaxial and applicable to composites that can be characterized as orthotropic. Tensorial invariant theory is used to create an integrity basis with invariants that correspond to physical mechanisms related to fracture. This integrity basis is then used to construct a failure function per unit volume (or area) of material. It is assumed that the overall strength of the composite is governed by weakest link theory. This leads to a Weibull type model similar in nature to the principle of ind
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Cicero, Sergio, and Sergio Arrieta. "On the Validity of the Weibull Parameters Used in the Master Curve in Ferritic Steels Containing Notches." In ASME 2022 Pressure Vessels & Piping Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/pvp2022-78263.

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Abstract The Master Curve (MC) is a valuable well-known characterization tool of the fracture behaviour of ferritic steels operating within their ductile-to-brittle transition zone (DBTZ). It assumes weakest link statistics in the cleavage process and it is based on a 3 parameter Weibull distribution analysis of the experimental results. Besides, it takes into account the scatter of the fracture resistance, the size effect and the temperature dependence. The methodology has been widely validated and has been standardised in ASTM 1921. This paper analyses whether the Weibull parameters used by
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Sjödin, Björn. "A Non-Local Theory for the Assessment of Multiaxial High Cycle Fatigue Failure." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-509.

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Looking at HCF, the most critical component on the turbine is the blade. At the present moment there is a need for a HCF criterion suitable for evaluation of stresses calculated with the Finite Element Method. Today there are some, such criterions e.g. Sines. However the criterion does not include important aspects such as the influence of; ‘geometrical size’, ‘stressed volume’ or ‘stress gradient’. A better understanding of the HCF phenomena would give an increase in the design precision and an opportunity to increase the load on the blades. A proposal is made for a new theory for HCF assessm
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Chen, Xiaoming, and Thanasis D. Papathanasiou. "A Computational Study of Interfacial Stress Distribution in Unidirectional Composites and Its Use in Prediction of Brittle Failure." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-55046.

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A computational investigation has been conducted to examine the effect of key microstructural and material parameters, namely the minimum inter-fiber spacing (δ) and the fiber/matrix stiffness ratio (Ef/Em), on the interfacial stress distributions in unidirectional composites subjected to transverse uniaxial tensile load. Representative Volume Elements (RVE’s) containing 144 fibers are constructed using a Monte-Carlo (MC) algorithm, imitating random composite structures. The boundary element method is then used to solve the multi-region elasticity problem on these microstructures. We pay parti
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Dutta, B. K., S. Guin, M. K. Sahu, and M. K. Samal. "Temperature Dependency of Beremin’s Parameters for 20MnMoNi5-5 Material." In 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/icone14-89710.

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The mechanism of cleavage fracture in reactor structural material is significantly different from ductile fracture. The cleavage fracture in a material usually originates from micro-cracks, which are formed by different mechanisms. The micro-cracks are formed due to non-homogeneous distribution of plastic deformation within the grains, called slip-initiated cleavage. The cracked grain boundary carbides also are the sources to originate the micro-cracks. This occurs when the stress normal to the planes of carbide particles is sufficiently high. The fracture takes place by the formation of micro
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