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Probabilistic Mechanical Fatigue and Fracture of Materials

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A special issue of Materials (ISSN 1996-1944). This special issue belongs to the section "Advanced Materials Characterization".

Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 41276

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Special Issue Editors

Prof. Alfonso Fernández-Canteli

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Guest Editor

Department of Construction and Manufacturing Engineering, Universidad de Oviedo, Oviedo, Spain
Interests: probabilistic modeling of fatigue and fracture; material characterization using local models; structural integrity
Special Issues, Collections and Topics in MDPI journals

Dr. Miguel Muniz-Calvente

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Guest Editor

Department of Construction and Manufacturing Engineering, Universidad de Oviedo, Oviedo, Spain
Interests: non-local probabilistic approaches; probabilistic fatigue damage; phenomenological models; scale effect; structural integrity
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

When designing structural and mechanical engineering components, general structural integrity criteria must be met. This ensures that the component will satisfactorily perform its designed function, supporting loads or resisting any kind of action causing stress and strains to the material without catastrophic failure. Consequently, during the last decades a large number of works were performed to allow fatigue and fracture to be reliably predicted. Nevertheless, the diversity of test conditions, failure mechanisms, damage evolution, component functionalities and loading types, as well as the specificity of material properties and the difficulty of achieving unambiguous material characterization, have impeded the discovery of a satisfactory solution to all failure questions.

With this aim, we invite other researchers to participate with relevant works that contribute to updating the state-of-the-art in this domain, through a Special Issue entitled “Probabilistic Mechanical Fatigue and Fracture of Materials”. Its scope encompasses methodologies that facilitate an objective material characterization, to advanced damage models that guarantee the transfer from experimental results to the design of real components. We expect to attract papers with some probabilistic background related to innovative experimental methodologies, theoretical and applied fracture and fatigue theories, advanced numerical models, and examples of real applications related to advanced materials. Nevertheless, other topics related to fracture and fatigue are also welcome.

Prof. Alfonso Fernández-Canteli
Dr. Miguel Muniz-Calvente
Guest Editors

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Keywords

Fatigue
Fracture mechanics
Phenomenological models
Failure criterion
Generalized driving force
Elastic and plastic materials
Probabilistic life prediction
Environmental assisted fatigue

Published Papers (14 papers)

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Editorial

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5 pages, 201 KiB

Open AccessEditorial

Special Issue: Probabilistic Mechanical Fatigue and Fracture of Materials

by Miguel Muñiz-Calvente and Alfonso Fernández-Canteli

Materials 2020, 13(21), 4901; https://doi.org/10.3390/ma13214901 - 31 Oct 2020

Cited by 1 | Viewed by 1225

Abstract

When designing structural and mechanical components, general structural integrity criteria must be met in order to ensure a valid performance according to its designed function, that is, supporting loads or resisting any kind of action causing stress and strains to the material without catastrophic failure. For these reasons, the development of solutions to manage the test conditions, failure mechanism, damage evolution, component functionalities and loading types should be implemented. The aim of this Special Issue “Probabilistic Mechanical Fatigue and Fracture of Materials” is to contribute to updating current and future state-of-the-art methodologies that promote an objective material characterization and the development of advanced damage models that ensure a feasible transferability from the experimental results to the design of real components. This is imbricated in some probabilistic background related to theoretical and applied fracture and fatigue theories, and advanced numerical models applied to some real application examples. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

Research

Jump to: Editorial

19 pages, 10316 KiB

Open AccessArticle

Defects in Electron Beam Melted Ti-6Al-4V: Fatigue Life Prediction Using Experimental Data and Extreme Value Statistics

by Viktor Sandell, Thomas Hansson, Sushovan Roychowdhury, Tomas Månsson, Mats Delin, Pia Åkerfeldt and Marta-Lena Antti

Materials 2021, 14(3), 640; https://doi.org/10.3390/ma14030640 - 30 Jan 2021

Cited by 14 | Viewed by 2483

Abstract

Electron beam melting is a powder bed fusion (PBF) additive manufacturing (AM) method for metals offering opportunities for the reduction of material waste and freedom of design, but unfortunately also suffering from material defects from production. The stochastic nature of defect formation leads to a scatter in the fatigue performance of the material, preventing wider use of this production method for fatigue critical components. In this work, fatigue test data from electron beam melted Ti-6Al-4V specimens machined from as-built material are compared to deterministic fatigue crack growth calculations and probabilistically modeled fatigue life. X-ray computed tomography (XCT) data evaluated using extreme value statistics are used as the model input. Results show that the probabilistic model is able to provide a good conservative life estimate, as well as accurate predictive scatter bands. It is also shown that the use of XCT-data as the model input is feasible, requiring little investigated material volume for model calibration. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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20 pages, 2728 KiB

Open AccessArticle

On the Influence of Ultimate Number of Cycles on Lifetime Prediction for Compression Springs Manufactured from VDSiCr Class Spring Wire

by Max Benedikt Geilen, Marcus Klein and Matthias Oechsner

Materials 2020, 13(14), 3222; https://doi.org/10.3390/ma13143222 - 20 Jul 2020

Cited by 6 | Viewed by 2183

Abstract

For the generation of fatigue curves by means of fatigue tests, an ultimate number of cycles must be chosen. This ultimate number of cycles also limits the permissible range of the fatigue curve for the design of components. This introduces extremely high costs for testing components that are to be used in the Very High Cycle Fatigue regime. In this paper, we examine the influence of the ultimate number of cycles of fatigue tests on lifetime prediction for compression springs manufactured from VDSiCr class spring wire. For this purpose, we propose a new kind of experiment, the Artificial Censoring Experiment (ACE). We show that ACEs may be used to permissibly extrapolate the results of fatigue tests on compression springs by ensuring that a batch-specific minimum ultimate number of cycles has been exceeded in testing. If the minimum ultimate number of cycles has not been exceeded, extrapolation is inadmissible. Extrapolated results may be highly non-conservative, especially for models assuming a pronounced fatigue limit. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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15 pages, 9808 KiB

Open AccessArticle

A Novel Approach to Describe the Time–Temperature Conversion among Relaxation Curves of Viscoelastic Materials

by Adrián Álvarez-Vázquez, Alfonso Fernández-Canteli, Enrique Castillo Ron, Pelayo Fernández Fernández, Miguel Muñiz-Calvente and María Jesús Lamela Rey

Materials 2020, 13(8), 1809; https://doi.org/10.3390/ma13081809 - 11 Apr 2020

Cited by 7 | Viewed by 3643

Abstract

Time and temperature, besides pressure in a lesser extent, represent the most significant variables influencing the rheological behavior of viscoelastic materials. These magnitudes are each other related through the well-known Time–Temperature Superposition (TTS) principle, which allows the master curve referred to relaxation (or creep) behavior to be derived as a material characteristic. In this work, a novel conversion law to interrelate relaxation curves at different temperatures is proposed by assuming they to be represented by statistical cumulative distribution functions of the normal or Gumbel family. The first alternative responds to physical considerations while the latter implies the fulfillment of extreme value conditions. Both distributions are used to illustrate the suitability of the model when applied to reliable derivation of the master curve of Polyvinil–Butyral (PVB) from data of experimental programs. The new approach allows not only the TTS shift factors to be estimated by a unique step, but the whole family of viscoelastic master curves to be determined for the material at any temperature. This represents a significant advance in the characterization of viscoelastic materials and, consequently, in the application of the TTS principle to practical design of viscoelastic components. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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13 pages, 1241 KiB

Open AccessArticle

Numerical Study on the Variability of Plastic CTOD

by Pedro André Prates, Armando Eusébio Marques, Micael Frias Borges, Ricardo Madeira Branco and Fernando Ventura Antunes

Materials 2020, 13(6), 1276; https://doi.org/10.3390/ma13061276 - 11 Mar 2020

Cited by 3 | Viewed by 2445

Abstract

This paper presents a numerical study on the influence of material parameters and loading variability in the plastic crack tip opening displacement (CTOD) results. For this purpose, AA7050-T6 was selected as reference material and a middle-cracked tension specimen geometry was considered. The studied input parameters were the Young’s modulus, Poisson’s ratio, isotropic and kinematic hardening parameters and the maximum and minimum applied loads. The variability of the input parameters follows a Gaussian distribution. First, screening design-of-experiments were performed to identify the most influential parameters. Two types of screening designs were considered: one-factor-at-a-time and fractional factorial designs. Three analysis criteria were adopted, based on: main effect, index of influence and analysis of variance. Afterwards, metamodels were constructed to establish relationships between the most influential parameters and the plastic crack tip opening displacement (CTOD) range, based on two types of designs: Face-Centered Central Composite Design and Box-Behnken design. Finally, the metamodels were validated, enabling the expeditious evaluation of the variability in the plastic CTOD range; in addition, the variability in the fatigue crack growth rate was also evaluated. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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14 pages, 6551 KiB

Open AccessArticle

Influence of the Elastoplastic Strain on Fatigue Durability Determined with the Use of the Spectral Method

by Michał Böhm, Mateusz Kowalski and Adam Niesłony

Materials 2020, 13(2), 423; https://doi.org/10.3390/ma13020423 - 16 Jan 2020

Cited by 9 | Viewed by 2274

Abstract

The paper presents experimental static and fatigue tests results under random loading conditions for the bending of 0H18N9 steel. The experimental results were used in performing calculations, according to the theoretical assumptions of the spectral method of fatigue life assessment, including elastoplastic deformations. The presented solution extends the use of the spectral method for material fatigue life assessment, in terms of loading conditions, above Hooke’s law theorem. The work includes computational verification of the proposal to extend the applicability of the spectral method of determining fatigue life for the range of elastoplastic deformations. One of the aims of the proposed modification was to supplement the stress amplitudes used to calculate the probability density function of the power spectral density of the signal with correction, due to the plastic deformation and its use for notched elements. The authors have tested the method using four of the most popular probability density functions used in commercial software. The obtained results of comparisons between the experimental and calculation results show that the proposed algorithm, tested using the Dirlik, Benasciutti–Tovo, Lalanne, and Zhao–Baker models, does not overestimate fatigue life, which means that the calculations are on the safe side. The obtained results prove that the elastoplastic deformations can be applied within the frequency domain for fatigue life calculations. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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12 pages, 18411 KiB

Open AccessArticle

A Study on Fatigue Crack Propagation for Friction Stir Welded Plate of 7N01 Al-Zn-Mg Alloy by EBSD

by Wenyu Liu, Dongting Wu, Shuwei Duan, Tao Wang and Yong Zou

Materials 2020, 13(2), 330; https://doi.org/10.3390/ma13020330 - 10 Jan 2020

Cited by 13 | Viewed by 2689

Abstract

EBSD (electron backscattered diffraction) was used to study the fatigue crack propagation mechanism in a friction stir welding joint of a 15 mm-thick 7N01 aluminum alloy plate. Crack tips with detailed features were clearly characterized by EBSD images. The plastic zone caused by crack was small in the stir zone. Due to the fine grain strengthening in the stir zone, there were several lattice distortion regions which were observed in the BC (band contrast) map but disappeared in the SEI (secondary electron image). In the stir zone, fatigue crack tends to awake and grow along grain boundaries, and propagate with little deformation of the grains. When the crack tries to grow across a boundary, the deformation of the plastic zone at the crack tip shows little correlation to the cyclic loading direction. However, the plastic zone in base metal, the rolled plate, is large and continuous, and no obvious lattice distortion region was found. According to Schmidt factor, the base metal near crack is fully deformed, lots of low angle boundaries parallel to the cyclic force can be observed. The base metal showed a better ability for fatigue crack propagation resistance. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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12 pages, 7181 KiB

Open AccessArticle

A Probabilistic Approach to Assessing and Predicting the Failure of Notched Components

by Miguel Muñiz-Calvente, Lucas Venta-Viñuela, Adrián Álvarez-Vázquez, Pelayo Fernández Fernández, María Jesús Lamela Rey and Alfonso Fernández Canteli

Materials 2019, 12(24), 4053; https://doi.org/10.3390/ma12244053 - 05 Dec 2019

Cited by 5 | Viewed by 1942

Abstract

This work presents a probabilistic model to evaluate the strength results obtained from an experimental characterisation program on notched components. The generalised local method (GLM) is applied to the derivation of the primary failure cumulative distribution function (PFCDF) as a material property (i.e., independent of the test type, load conditions and specimen geometry selected for the experimental campaign), which guarantees transferability in component design. To illustrate the applicability of the GLM methodology, an experimental program is performed using specimens of EPOLAM 2025 epoxy resin. Three different samples, each with a specific notch geometry, are tested. As a first scenario, a single assessment of each sample is obtained and the PFCDFs are used to perform cross predictions of failure. Some discrepancies are noticeable among the experimental results and cross-failure predictions, although they are within the expected margins. A possible reason for the disagreement can be assigned to the inherent statistical variability of the results and the limited number of tests per each sample. As a second scenario, a joint assessment of the three samples is performed, from which a unique PFCDF is provided, according to the GLM. In the latter case, a more reliable assessment of the experimental results from the geometry conditions is achieved, the suitability of the selected driving force is verified, and the transferability of the present material characterisation is confirmed. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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17 pages, 4195 KiB

Open AccessArticle

Fatigue Assessment Strategy Using Bayesian Techniques

by Enrique Castillo, Miguel Muniz-Calvente, Alfonso Fernández-Canteli and Sergio Blasón

Materials 2019, 12(19), 3239; https://doi.org/10.3390/ma12193239 - 03 Oct 2019

Cited by 14 | Viewed by 2199

Abstract

Different empirical models have been proposed in the literature to determine the fatigue strength as a function of lifetime, according to linear, parabolic, hyperbolic, exponential, and other shaped solutions. However, most of them imply a deterministic definition of the S-N field, despite the inherent scatter exhibited by the fatigue results issuing from experimental campaigns. In this work, the Bayesian theory is presented as a suitable way not only to convert deterministic into probabilistic models, but to enhance probabilistic fatigue models with the statistical distribution of the percentile curves of failure probability interpreted as their confidence bands. After a short introduction about the application of the Bayesian methodology, its advantageous implementation on an OpenSource software named OpenBUGS is presented. As a practical example, this methodology has been applied to the statistical analysis of the Maennig fatigue S-N field data using the Weibull regression model proposed by Castillo and Canteli, which allows the confidence bands of the S-N field to be determined as a function of the already available test results. Finally, a question of general interest is discussed as that concerned to the recommendable number of tests to carry out in an experimental S-N fatigue program for achieving “reliable or confident” results to be subsequently used in component design, which, generally, is not adequately and practically addressed by researchers. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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19 pages, 2422 KiB

Open AccessArticle

On the Statistical Size Effect of Cast Aluminium

by Roman Aigner, Sebastian Pomberger, Martin Leitner and Michael Stoschka

Materials 2019, 12(10), 1578; https://doi.org/10.3390/ma12101578 - 14 May 2019

Cited by 15 | Viewed by 2536

Abstract

Manufacturing process based imperfections can reduce the theoretical fatigue strength since they can be considered as pre-existent microcracks. The statistical distribution of fatigue fracture initiating defect sizes also varies with the highly-stressed volume, since the probability of a larger highly-stressed volume to inherit a potentially critical defect is elevated. This fact is widely known by the scientific community as the statistical size effect. The assessment of this effect within this paper is based on the statistical distribution of defect sizes in a reference volume

V_{0}

compared to an arbitrary enlarged volume

V_{α}

. By implementation of the crack resistance curve in the Kitagawa–Takahashi diagram, a fatigue assessment model, based on the volume-dependent probability of occurrence of inhomogeneities, is set up, leading to a multidimensional fatigue assessment map. It is shown that state-of-the-art methodologies for the evaluation of the statistical size effect can lead to noticeable over-sizing in fatigue design of approximately

10 %

. On the other hand, the presented approach, which links the statistically based distribution of defect sizes in an arbitrary highly-stressed volume to a crack-resistant dependent Kitagawa–Takahashi diagram leads to a more accurate fatigue design with a maximal conservative deviation of

5 %

to the experimental validation data. Therefore, the introduced fatigue assessment map improves fatigue design considering the statistical size effect of lightweight aluminium cast alloys. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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11 pages, 2924 KiB

Open AccessArticle

Vickers Micro-Hardness of New Restorative CAD/CAM Dental Materials: Evaluation and Comparison after Exposure to Acidic Drink

by Marco Colombo, Claudio Poggio, Alessandro Lasagna, Marco Chiesa and Andrea Scribante

Materials 2019, 12(8), 1246; https://doi.org/10.3390/ma12081246 - 16 Apr 2019

Cited by 73 | Viewed by 6174

Abstract

CAD/CAM (computer-aided design/computer-aided manufacturing) for indirect restorative materials has been recently introduced in dentistry. The purpose of this study was to evaluate the change of the surface micro-hardness of different restorative CAD/CAM materials after exposure to a carbonated acidic drink (Coca-Cola, Coca-Cola Company, Milan, Italy). One hundred and eighty specimens of identical size (2 mm thickness) were obtained by sectioning each tested CAD/CAM block of four materials: a hybrid ceramic (CERASMART™, GC Corporation, Tokyo, Japan), a resin nano ceramic (Lava™ Ultimate, 3M, Monrovia, CA, USA), a nanohybrid composite (Grandio blocs, VOCO GmbH, Cuxhaven, Germany), and a zirconia-reinforced lithium silicate glass ceramic (VITA SUPRINITY^® PC; VITA Zahnfabrik, Bad Sackingen, Germany). Forty-five specimens of each material were tested. Micro-hardness was measured at baseline, after 7 days and after 28 days. The data were analyzed. The micro-hardness of each material varied significantly after immersion in Coca-Cola. The nanohybrid composite had a high initial micro-hardness and the greatest percentage loss after acid exposure. The hybrid ceramic and the resin nano ceramic had similar percentage losses of micro-hardness values even if the second material had higher initial values. The zirconia-reinforced lithium silicate glass ceramic had the highest baseline values and the lowest percentage loss of micro-hardness. The different CAD/CAM materials presented different micro-hardness values before and after acid exposure. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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13 pages, 9063 KiB

Open AccessArticle

The Effect of Plasma Nitriding on the Fatigue Behavior of the Ti-6Al-4V Alloy

by Michele C. B. de Castro, Antônio A. Couto, Gisele F. C. Almeida, Marcos Massi, Nelson B. de Lima, Argemiro da Silva Sobrinho, Mariano Castagnet, Gleicy L. Xavier and Rene R. Oliveira

Materials 2019, 12(3), 520; https://doi.org/10.3390/ma12030520 - 09 Feb 2019

Cited by 17 | Viewed by 3635

Abstract

The Ti-6Al-4V alloy is widely used in the manufacture of components that must have low density and high corrosion resistance and fatigue strength. The fatigue strength can be improved by surface modification. The aim of this study was to determine the influence of plasma nitriding on the fatigue behavior of a Ti-6Al-4V alloy with a lamellar microstructure (Widmanstätten type). Nitriding was executed at 720 °C for 4 h in an atmosphere with N₂, Ar, and H₂. Microstructure characterization of the samples was carried out by X-ray diffraction analysis, optical microscopy, and scanning electron microscopy. The average roughness of the specimens was determined, and fatigue tests were executed in a bending–rotating machine with reverse tension cycles (R = −1). X-ray diffraction analysis of the nitrided alloy revealed the following matrix phases: α, β, ε-Ti₂N, and δ-TiN. A nitrogen diffusion layer was formed between the substrate and the titanium nitrides. Plasma nitriding resulted in an increase in low-cycle fatigue strength, whereas at high cycles of 200 MPa, both conditions exhibited similar behaviors. The fracture surface of the fatigue-tested specimens clearly revealed the lamellar microstructure. The fracture mechanism in the non-nitrided specimens appears to be due to cracking at the interface of the α and β phases of the lamellar microstructure. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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10 pages, 3807 KiB

Open AccessArticle

Mechanical Properties of Gas Main Steels after Long-Term Operation and Peculiarities of Their Fracture Surface Morphology

by Volodymyr Hutsaylyuk, Pavlo Maruschak, Ihor Konovalenko, Sergey Panin, Roman Bishchak and Mykola Chausov

Materials 2019, 12(3), 491; https://doi.org/10.3390/ma12030491 - 05 Feb 2019

Cited by 14 | Viewed by 2673

Abstract

Regularities of steel structure degradation of the “Novopskov-Aksay-Mozdok” gas main pipelines (Nevinnomysskaya CS) as well as the “Gorky-Center” pipelines (Gavrilovskaya CS) were studied. The revealed peculiarities of their degradation after long-term operation are suggested to be treated as a particular case of the damage accumulation classification (scheme) proposed by prof. H.M. Nykyforchyn. It is shown that the fracture surface consists of sections of ductile separation and localized zones of micro-spalling. The presence of the latter testifies to the hydrogen-induced embrittlement effect. However, the steels under investigation possess sufficiently high levels of the mechanical properties required for their further safe exploitation, both in terms of durability and cracking resistance. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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16 pages, 2478 KiB

Open AccessArticle

Flexural Strength Prediction Models for Soil–Cement from Unconfined Compressive Strength at Seven Days

by Alaitz Linares-Unamunzaga, Heriberto Pérez-Acebo, Marta Rojo and Hernán Gonzalo-Orden

Materials 2019, 12(3), 387; https://doi.org/10.3390/ma12030387 - 26 Jan 2019

Cited by 26 | Viewed by 4396

Abstract

Soil–cement is an environmentally friendly road construction technique for base and subbase materials, which allows employing soils placed in the right-of-way of the road or in the surroundings, by improving its engineering properties. With this technique, it is possible to reduce the over-exploitation of quarries, the necessity of landfills and the pollutant gas emission due to the reduction of aggregate fabrication and transport. The manufacturing of soil–cement is generally controlled by means of the Uniaxial Compressive Strength (UCS) test at seven days, according to the regulations of each country. Nonetheless, one of the properties that best defines the performance of soil–cement is the Flexural Strength (FS) at long term, usually at 90 days. The aim of this paper is to develop new equations to correlate the UCS and the FS at long term and the UCS at seven days and at 90 days. Obtained results validate the proposed models and, hence, the flexural strength can be predicted from the Uniaxial Compressive Strength at seven days, allowing, if necessary, correcting measures (recalculation or rejection) in early stages of the curing time to be taken. Full article

(This article belongs to the Special Issue Probabilistic Mechanical Fatigue and Fracture of Materials)

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