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16 pages, 4110 KB

Open AccessArticle

Evaluation of 3-Point and 4-Point Bending Tests for Tensile Strength Assessment of GFRP Bars

by Philip Prakash Lochan and Maria Anna Polak

Materials 2024, 17(21), 5261; https://doi.org/10.3390/ma17215261 - 29 Oct 2024

Cited by 2 | Viewed by 2386

Glass Fiber Reinforced Polymer (GFRP) bars are used as reinforcement for structural concrete, especially in cases where corrosion of traditional steel reinforcement is a problem. The tensile strength of these reinforcing bars is the primary characteristic on which the design of concrete members [...] Read more.

Glass Fiber Reinforced Polymer (GFRP) bars are used as reinforcement for structural concrete, especially in cases where corrosion of traditional steel reinforcement is a problem. The tensile strength of these reinforcing bars is the primary characteristic on which the design of concrete members reinforced with GFRP bars relies. Determination of the tensile strength of the bars using a direct tensile test is a time and resource-intensive task and therefore is not routinely conducted for quality control. The tensile strength can also be measured from flexure tests, which are much simpler than direct tensile tests, and use appropriate correlation formulations. In this paper, the applicability of flexure testing for the identification of bars’ tensile strength is investigated by conducting and analyzing both 3-point and 4-point flexure testing. The correlation formulations are presented that allow the determination of tensile strength from the modulus of rupture. The Weibull weakest link model and the assumption of the same flaw distribution in tensile and flexure tests is adopted. The results of the 3-point and the 4-point bending are presented and compared. Comparisons are also conducted to select direct tensile test results. The work shows that 3-point and 4-point bending tests provide very similar results, with the difference between the results being 2% to 10%, suggesting both tests can be used for tensile strength determination of GFRP bars. Full article

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17 pages, 760 KB

Open AccessFeature PaperArticle

Parameter Estimation of Birnbaum-Saunders Distribution under Competing Risks Using the Quantile Variant of the Expectation-Maximization Algorithm

by Chanseok Park and Min Wang

Mathematics 2024, 12(11), 1757; https://doi.org/10.3390/math12111757 - 5 Jun 2024

Cited by 2 | Viewed by 1261

Abstract

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, [...] Read more.

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 autopsy procedures, and other obstacles, collectively referred to as the masking problem. In this paper, we investigate the distribution of strength for multimodal failures with censored data. We consider both full and partial maskings and present an EM-type parameter estimate for the Birnbaum-Saunders distribution under competing risks. We compare the results with those obtained from other distributions, such as lognormal, Weibull, and Wald (inverse-Gaussian) distributions. The effectiveness of the proposed method is demonstrated through two illustrative examples, as well as an analysis of the sensitivity of parameter estimates to variations in starting values. Full article

(This article belongs to the Special Issue Significant Applications in Economics, Business, Management and Industrial Statistics)

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22 pages, 1284 KB

Open AccessFeature PaperArticle

Kaniadakis Functions beyond Statistical Mechanics: Weakest-Link Scaling, Power-Law Tails, and Modified Lognormal Distribution

by Dionissios T. Hristopulos and Anastassia Baxevani

Entropy 2022, 24(10), 1362; https://doi.org/10.3390/e24101362 - 26 Sep 2022

Cited by 6 | Viewed by 3285

Abstract

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 [...] Read more.

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

-Weibull suitable for modeling the mechanical strength distribution of materials. Finally, we introduce the

κ

-lognormal probability distribution and calculate the generalized (power) mean of

κ

-lognormal variables. The

κ

-lognormal distribution is a suitable candidate for the permeability of random porous media. In summary, the

κ

-deformations allow for the modification of tails of classical distribution models (e.g., Weibull, lognormal), thus enabling new directions of research in the analysis of spatiotemporal data with skewed distributions. Full article

(This article belongs to the Special Issue Twenty Years of Kaniadakis Entropy: Current Trends and Future Perspectives)

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10 pages, 1253 KB

Open AccessArticle

Influence of Test Specimen Geometry on Probability of Failure of Composites Based on Weibull Weakest Link Theory

by Rajnish Kumar, Bo Madsen, Hans Lilholt and Lars P. Mikkelsen

Materials 2022, 15(11), 3911; https://doi.org/10.3390/ma15113911 - 31 May 2022

Cited by 8 | Viewed by 2112

Abstract

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 [...] Read more.

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 failure in the gauge section. For unidirectional carbon fibre composites with Weibull modulus m in the range 10–40, it can be calculated by the model that strength measured with a straight-sided specimen will be 1–2% lower than the strength measured with a specific waisted butterfly-shaped specimen solely due to the difference in test specimen shape and volume. Full article

(This article belongs to the Special Issue Mechanical Characterization of FRP Composite Materials)

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13 pages, 4444 KB

Open AccessArticle

Evaluation of Anti-Adhesion Characteristics of Diamond-Like Carbon Film by Combining Friction and Wear Test with Step Loading and Weibull Analysis

by Hiroki Mano and Tsuguyori Ohana

Materials 2021, 14(11), 2746; https://doi.org/10.3390/ma14112746 - 22 May 2021

Cited by 3 | Viewed by 2356

Abstract

Anti-adhesion characteristics are important requirements for diamond-like carbon (DLC) films. The failure load corresponding to the anti-adhesion capacity varies greatly on three types of DLC film (hydrogen-free amorphous carbon film (a-C), hydrogenated amorphous carbon film (a-C:H), and tetrahedral hydrogen-free amorphous carbon film (ta-C)) [...] Read more.

Anti-adhesion characteristics are important requirements for diamond-like carbon (DLC) films. The failure load corresponding to the anti-adhesion capacity varies greatly on three types of DLC film (hydrogen-free amorphous carbon film (a-C), hydrogenated amorphous carbon film (a-C:H), and tetrahedral hydrogen-free amorphous carbon film (ta-C)) in the friction and wear test with step loading using a high-frequency, linear-oscillation tribometer. Therefore, a new method that estimates a representative value of the failure load was developed in this study by performing a statistical analysis based on the Weibull distribution based on the assumption that the mechanism of delamination of a DLC film obeys the weakest link model. The failure load at the cumulative failure probabilities of 10% and 50% increased in the order ta-C < a-C:H < a-C and ta-C < a-C < a-C:H, respectively. The variation of the failure load, represented by the Weibull slope, was minimum on ta-C and maximum on a-C:H. The rank of the anti-adhesion capacity of each DLC film with respect to the load obtained by a constant load test agreed with the rank of the failure load on each DLC film at the cumulative failure probability of 10% obtained by Weibull analysis. It was found to be possible to evaluate the anti-adhesion capacity of a DLC film under more practical conditions by combining the step loading test and Weibull analysis. Full article

(This article belongs to the Special Issue DLC (Diamond-Like Carbon) Film Formation and Application)

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14 pages, 3988 KB

Open AccessArticle

Probabilistic Estimation of Fatigue Strength for Axial and Bending Loading in High-Cycle Fatigue

by Tomasz Tomaszewski, Przemysław Strzelecki, Adam Mazurkiewicz and Janusz Musiał

Materials 2020, 13(5), 1148; https://doi.org/10.3390/ma13051148 - 5 Mar 2020

Cited by 18 | Viewed by 3486

Abstract

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 [...] Read more.

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. For this purpose, an analytical model and a numerical model based on the finite element method were used. The model that gives the lowest error implemented in specific test conditions was determined on the basis of high-cycle fatigue analysis. For the analyzed materials, it was a highly-stressed volume model based on the weakest link theory. Full article

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13 pages, 4088 KB

Open AccessArticle

Finite Element Analysis of the Size Effect on Ceramic Strength

by Kyohei Takeo, Yuya Aoki, Toshio Osada, Wataru Nakao and Shingo Ozaki

Materials 2019, 12(18), 2885; https://doi.org/10.3390/ma12182885 - 6 Sep 2019

Cited by 27 | Viewed by 4168

Abstract

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 [...] Read more.

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 under three types of loading conditions. Then, we simulate the fracture stresses of sets of 30 specimens under each size and loading condition and obtain the relationship between the scale parameter and effective volume using the Weibull distribution. The results suggest that the proposed FEA methodology can be applied to the analysis of the fracture probability of ceramics, including the size effect. Full article

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20 pages, 905 KB

Open AccessArticle

Weakest-Link Scaling and Extreme Events in Finite-Sized Systems

by Dionissios T. Hristopulos, Manolis P. Petrakis and Giorgio Kaniadakis

Entropy 2015, 17(3), 1103-1122; https://doi.org/10.3390/e17031103 - 9 Mar 2015

Cited by 13 | Viewed by 6985

Abstract

Weakest-link scaling is used in the reliability analysis of complex systems. It is characterized by the extensivity of the hazard function instead of the entropy. The Weibull distribution is the archetypical example of weakest-link scaling, and it describes variables such as the fracture [...] Read more.

Weakest-link scaling is used in the reliability analysis of complex systems. It is characterized by the extensivity of the hazard function instead of the entropy. The Weibull distribution is the archetypical example of weakest-link scaling, and it describes variables such as the fracture strength of brittle materials, maximal annual rainfall, wind speed and earthquake return times. We investigate two new distributions that exhibit weakest-link scaling, i.e., a Weibull generalization known as the κ-Weibull and a modified gamma probability function that we propose herein. We show that in contrast with the Weibull and the modified gamma, the hazard function of the κ -Weibull is non-extensive, which is a signature of inter-dependence between the links. We also investigate the impact of heterogeneous links, modeled by means of a stochastic Weibull scale parameter, on the observed probability distribution. Full article

(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)

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