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

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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 loaddisplacement 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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10

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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11

Shibata, Taiju, Junya Sumita, Sinichi Baba, et al. "Basic Concept on Structural Design Criteria for Zirconia Ceramics Applying to Nuclear Components." Key Engineering Materials 297-300 (November 2005): 728–33. http://dx.doi.org/10.4028/www.scientific.net/kem.297-300.728.

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As an advanced in-core material in high temperature gas-cooled reactors (HTGRs), superplastic ceramics is attractive due to the possibility of the plastic working. For the application to the nuclear fields, the basic concept of design criteria was studied for typical superplastic ceramics, tetragonal zirconia polycrystals containing 3mol% yttria (3Y-TZP). The experimental results on 3Y-TZP showed that it is possible to apply the Weibull weakest-link theory to decide the stress limits in the criteria. The Weibull parameter m was evaluated as 9.5 for the bending and as 26.5 for the compressive.

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12

Oh, Sei Chang. "Estimation of Depth Effect on the Bending Strength of Domestic Japanese Larch Structural Lumber using Weibull Weakest Link Theory." Journal of the Korean Wood Science and Technology 42, no. 2 (2014): 112–18. http://dx.doi.org/10.5658/wood.2014.42.2.112.

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13

Park, Chanseok, and Min Wang. "Parameter Estimation of Birnbaum-Saunders Distribution under Competing Risks Using the Quantile Variant of the Expectation-Maximization Algorithm." Mathematics 12, no. 11 (2024): 1757. http://dx.doi.org/10.3390/math12111757.

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Competing risks models, also known as weakest-link models, are utilized to analyze diverse strength distributions exhibiting multi-modality, often attributed to various types of defects within the material. The weakest-link theory posits that a material’s fracture is dictated by its most severe defect. However, multimodal problems can become intricate due to potential censoring, a common constraint stemming from time and cost limitations during experiments. Additionally, determining the mode of failure can be challenging due to factors like the absence of suitable diagnostic tools, costly auto

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14

Duffy, S. F., and J. M. Manderscheid. "Noninteractive Macroscopic Reliability Model for Ceramic Matrix Composites With Orthotropic Material Symmetry." Journal of Engineering for Gas Turbines and Power 112, no. 4 (1990): 507–11. http://dx.doi.org/10.1115/1.2906196.

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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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15

Takashima, Yasuhito, Mitsuru Ohata, and Fumiyoshi Minami. "Analysis of Statistical Scatter in Charpy Impact Toughness." Materials Science Forum 783-786 (May 2014): 2394–99. http://dx.doi.org/10.4028/www.scientific.net/msf.783-786.2394.

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Charpy impact toughness values show large statistical scatter, particularly in the ductile-to-brittle transition temperature (DBTT) range. Although the statistical distribution of Charpy absorbed energy has not been clarified, critical values of the stress intensity factor, J-integral and crack-tip opening displacement (CTOD) at brittle fracture generally show the Weibull distribution with two or three parameters. This study proposes a brittle fracture model, based on the weakest link theory, for evaluating the scatter in Charpy absorbed energy KV. The numerical results show that the amplitude

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16

Takeo, Kyohei, Yuya Aoki, Toshio Osada, Wataru Nakao, and Shingo Ozaki. "Finite Element Analysis of the Size Effect on Ceramic Strength." Materials 12, no. 18 (2019): 2885. http://dx.doi.org/10.3390/ma12182885.

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The most prominent effect of the weakest link theory, which is used to derive the Weibull statistics of ceramic strength, is the size effect. In this study, we analyze the size effect on ceramic strength using the finite element analysis (FEA) methodology previously proposed by the authors. In the FEA methodology, the data of the microstructure distribution (i.e., relative density, size, and aspect ratio of the pore and the grain size) are considered as input parameters of a continuum damage model via a fracture mechanical model. Specifically, we examine five sizes of rectangular specimens und

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17

Suzuki, H., S. Kinugawa, and Hideki Sekine. "Load Carrying Capacity of Notched CFRP Laminates." Key Engineering Materials 430 (March 2010): 47–51. http://dx.doi.org/10.4028/www.scientific.net/kem.430.47.

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On the basis of a micromechanical study, a method for evaluating load carrying capacity of notched CFRP laminates is developed. The damage zone at a notch tip in CFRP laminates is modeled as a fictitious crack with a cohesive stress acting on the crack surface. Then, applying the Weibull weakest link theory to the strength of surviving fiber bundles on the crack surface, we derive the relationship between the cohesive stress and the crack opening displacement, i.e., the tension-softening relation. By incorporating it in a BEM scheme, the load-displacement relationship is simulated. The simulat

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18

Bosco, Nick, Martin Springer, Jiqi Liu, Sameera Nalin Venkat, and Roger H. French. "Employing Weibull Analysis and Weakest Link Theory to Resolve Crystalline Silicon PV Cell Strength Between Bare Cells and Reduced- and Full-Sized Modules." IEEE Journal of Photovoltaics 11, no. 3 (2021): 731–41. http://dx.doi.org/10.1109/jphotov.2021.3056673.

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19

Hosseini, Seyed Abdolkarim, Li-Ting Lin, and Frank Ko. "Investigation of the mechanical properties of lignin nanofibrous structures using statistical modeling." Textile Research Journal 88, no. 17 (2017): 1943–53. http://dx.doi.org/10.1177/0040517517715080.

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The growing use of nanomaterials, environmental concerns and related industrial applications have provided unique opportunities for the development of nanofibers from natural biopolymers such as lignin. The main purpose of this study was to develop a direct relationship between lignin single nanofiber, the aligned nanofiber mat and the twisted nanofiber yarn’s strength using the weakest link theory of strength and the statistical model proposed for parallel fiber bundles. Twisted yarn strength was obtained via in situ mechanical properties of yarn constituent nanofibers affected by the Weibull

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20

Sadananda, Ramana. "A probabilistic approach to bone fracture analysis." Journal of Materials Research 6, no. 1 (1991): 202–6. http://dx.doi.org/10.1557/jmr.1991.0202.

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Bones are biological structural materials made of dynamically adaptable tissues. They can be considered as complex natural composite materials with load bearing constituents such as osteons and interstitial lamellae cemented with weak bonding materials. In addition, they contain Haversian and Volkmann canals that are functionally needed but are structurally weak. Because of large variation in microstructure, the strength of a bone varies from bone to bone and animal to animal. In this study the applicability of Weibull statistics to fracture strength of bones has been evaluated. The statistics

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21

Fuis, Vladimír, and Premysl Janicek. "Stress Analysis of the Hip Joint Endoprosthesis Ceramic Head for Different Values of Shape Deviations." Advanced Materials Research 936 (June 2014): 770–75. http://dx.doi.org/10.4028/www.scientific.net/amr.936.770.

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The paper deals with the problems of ceramic head of hip joint endoprosthesis destructions, and with assessing the impact of shape deviations of conical surfaces on the tensile stress under ISO 7206-5 loading. The failure of the hip joint endoprosthesis ceramic head has always traumatic consequences for the patient, since a part of or even the whole endoprosthesis has to be reoperated. Hence, it is desired to reduce the number of implant re-operations to the minimum. Therefore the computational modelling of the stress of the head was realised. The shape deviations of the ideal contact cone are

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22

Wang, Yong, Weidong Yu, and Fumei Wang. "Experimental evaluation and modified Weibull characterization of the tensile behavior of tri-component elastic-conductive composite yarn." Textile Research Journal 88, no. 10 (2017): 1138–49. http://dx.doi.org/10.1177/0040517517698991.

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In order to clarify the effects of the extension rate and gauge length upon the distribution of tensile strength of tri-component elastic-conductive composite yarn (t-ECCY), experimental as well as theoretical studies have been performed in this paper. Influences of the extension rate and gauge length are highlighted. The yarn exhibits an extension-rate strengthening effect, and the higher extension rate results in a higher strength and fracture strain, irrespective of the gauge length considered, and vice versa. Expressed in terms of gauge length, yarn tenacity shows a drop for a longer testi

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23

Bažant, Zdeněk P. "Design of quasibrittle materials and structures to optimize strength and scaling at probability tail: an apercu." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2224 (2019): 20180617. http://dx.doi.org/10.1098/rspa.2018.0617.

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The objective in materials or structure design has been to maximize the mean strength. However, as generally agreed, engineering structures, such as bridges, aircraft or microelectromechanical systems must be designed for tail probability of failure less than 10 −6 per lifetime. But this objective is not the same. Indeed, a quasibrittle material or structure with a superior mean strength can have, for the same coefficient of variation, an inferior strength at the less than 10 −6 tail. This tail is unreachable by histogram testing. So, one needs a rational theory, physically based and experimen

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24

V., Fuis, and Navrat T. "Calculation of the Ceramics Weibull Parameters." October 20, 2011. https://doi.org/10.5281/zenodo.1073399.

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The paper deals with calculation of the parameters of ceramic material from a set of destruction tests of ceramic heads of total hip joint endoprosthesis. The standard way of calculation of the material parameters consists in carrying out a set of 3 or 4 point bending tests of specimens cut out from parts of the ceramic material to be analysed. In case of ceramic heads, it is not possible to cut out specimens of required dimensions because the heads are too small (if the cut out specimens were smaller than the normalised ones, the material parameters derived from them would exhibit higher stre

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25

Wang, Tianxing, Yan‐Feng Li, Hong‐Zhong Huang, and Song Bai. "A weakest link theory‐based probabilistic fatigue life prediction method for the turbine disc considering the influence of the number of critical sections." Quality and Reliability Engineering International, July 29, 2024. http://dx.doi.org/10.1002/qre.3629.

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AbstractThis study utilizes the rank correlation coefficient to examine the multi‐site failure correlation of turbine discs. Drawing from the stress‐strength interference model, reliability models both with and without factoring in the multi‐site failure correlation are constructed. Furthermore, the weakest link theory (WLT) within the context of the Weibull distribution function is invoked to develop a model for predicting the fatigue life of turbine discs, taking into account the quantity of critical sections. The variability in the low cycle fatigue (LCF) of turbine discs is scrutinized, le

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26

Le, Jia-Liang, and Zdeněk P. Bažant. "Scaling of Static Fracture of Quasi-Brittle Structures: Strength, Lifetime, and Fracture Kinetics." Journal of Applied Mechanics 79, no. 3 (2012). http://dx.doi.org/10.1115/1.4005881.

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The paper reviews a recently developed finite chain model for the weakest-link statistics of strength, lifetime, and size effect of quasi-brittle structures, which are the structures in which the fracture process zone size is not negligible compared to the cross section size. The theory is based on the recognition that the failure probability is simple and clear only on the nanoscale since the probability and frequency of interatomic bond failures must be equal. The paper outlines how a small set of relatively plausible hypotheses about the failure probability tail at nanoscale and its transit

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27

Wang, Zhijie, Caglar Oskay, and Alessandro Fascetti. "Multiscale Stochastic Modeling of Backward Erosion Piping Initiation, From Grain Kinetics to Weibull Statistics. Part II: Model Validation and Applications." International Journal for Numerical and Analytical Methods in Geomechanics, December 28, 2024. https://doi.org/10.1002/nag.3930.

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ABSTRACTBackward erosion piping (BEP) is a leading internal erosion mechanism for flood protection system failures. A model capable of predicting critical hydraulic conditions for BEP initiation at multiple scales while also incorporating soil variability is a pressing need. This study formulates and validates a novel multiscale probabilistic BEP initiation framework with incorporation of soil variability. The framework is based on a grain‐scale probabilistic model and the weakest link theory, and the theory of rate processes. The multiscale framework proposed herein is validated through a wid

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28

V., Fuis, Janicek P., and Navrat T. "Stress Analysis of the Ceramics Heads with Different Sizes under the Destruction Tests." November 4, 2014. https://doi.org/10.5281/zenodo.1097006.

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The global solved problem is the calculation of the parameters of ceramic material from a set of destruction tests of ceramic heads of total hip joint endoprosthesis. The standard way of calculation of the material parameters consists in carrying out a set of 3 or 4 point bending tests of specimens cut out from parts of the ceramic material to be analysed. In case of ceramic heads, it is not possible to cut out specimens of required dimensions because the heads are too small (if the cut out specimens were smaller than the normalised ones, the material parameters derived from them would exhibit

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