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Keywords = parabolic notch

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41 pages, 17064 KB  
Article
Fatigue Probabilistic Approach of Notch Sensitivity of 51CrV4 Leaf Spring Steel Based on the Theory of Critical Distances
by Vítor M. G. Gomes, Miguel A. V. de Figueiredo, José A. F. O. Correia and Abílio M. P. de Jesus
Appl. Sci. 2025, 15(17), 9739; https://doi.org/10.3390/app15179739 - 4 Sep 2025
Viewed by 560
Abstract
The mechanical and structural design of railway vehicles is heavily influenced by their lifetime. Because fatigue is a significant factor that impacts the longevity of railway components, it is imperative that the fatigue resistance properties of crucial components, like leaf springs, be thoroughly [...] Read more.
The mechanical and structural design of railway vehicles is heavily influenced by their lifetime. Because fatigue is a significant factor that impacts the longevity of railway components, it is imperative that the fatigue resistance properties of crucial components, like leaf springs, be thoroughly investigated. This research investigates the fatigue resistance of 51CrV4 steel under bending and axial tension, considering different stress ratios across low-cycle fatigue (LCF), high-cycle fatigue (HCF), and very-high-cycle fatigue (VHCF) regimes, using experimental data collected from this work and prior research. Data included fractographic analyses aiming to help in understanding some of failures for different loads. The presence of geometric discontinuities, such as notches, amplifies stress concentrations, requiring a probabilistic approach to fatigue assessment. To address notch effects, the theory of critical distances (TCD) was employed to evaluate fatigue strength. TCD model was integrated in fatigue statistical models, such as the Walker model (WSN) and the Castillo–Fernández-Cantelli model adapted for mean stress effects (ACFC). Extending the application of the TCD theory, this research provides an improved probabilistic fatigue model that integrates notch sensitivity, mean stress effects, and fatigue regimes, contributing to more reliable design approaches of railway leaf springs or other components produced in 51CrV4 steel. Full article
(This article belongs to the Special Issue Fracture and Fatigue Analysis of Metallic Materials)
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16 pages, 3287 KB  
Article
Interference Effect Between a Parabolic Notch and a Screw Dislocation in Piezoelectric Quasicrystals
by Yuanyuan Gao, Guanting Liu, Chengyan Wang and Junjie Fan
Crystals 2025, 15(7), 647; https://doi.org/10.3390/cryst15070647 - 15 Jul 2025
Viewed by 2284
Abstract
This study investigates the coupling mechanism between a parabolic notch and dislocations in one-dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs) based on the theory of complex variable functions. By applying perturbation techniques and the Cauchy integral, analytical solutions for complex potentials are derived, yielding [...] Read more.
This study investigates the coupling mechanism between a parabolic notch and dislocations in one-dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs) based on the theory of complex variable functions. By applying perturbation techniques and the Cauchy integral, analytical solutions for complex potentials are derived, yielding closed-form expressions for the phonon–phason stress field and electric displacement field. Numerical examples reveal several key findings: significant stress concentration occurs at the notch root, accompanied by suppression of electric displacement; interference patterns between dislocation cores and notch-induced stress singularities are identified; the J-integral quantifies distance-dependent forces, size effects, and angular force distributions reflecting notch symmetry; and the energy-driven dislocation slip toward free surfaces leads to the formation of dislocation-free zones. These results provide new insights into electromechanical fracture mechanisms in quasicrystals. Full article
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10 pages, 5272 KB  
Article
Determination of the Fracture Locus of a Cor-Ten Steel at Low and High Triaxiality Ranges
by Axel Baruscotti, Nicholas Miori and Franco Concli
Appl. Sci. 2025, 15(7), 3569; https://doi.org/10.3390/app15073569 - 25 Mar 2025
Cited by 1 | Viewed by 520
Abstract
Cor-Ten steels, also known as weathering steels, are construction materials of growing importance in the field of architecture and crash barriers, not only due to their good mechanical and corrosion resistance properties but also for the appealing color of their oxides. However, a [...] Read more.
Cor-Ten steels, also known as weathering steels, are construction materials of growing importance in the field of architecture and crash barriers, not only due to their good mechanical and corrosion resistance properties but also for the appealing color of their oxides. However, a complete description of the fracture locus of Cor-Ten steels in both low and high triaxiality ranges is still lacking. The present study aims at integrating and extending the data available in the literature for this peculiar material by evaluating four different planar specimens with a mixed numerical–experimental methodology. A non-notched specimen was tested in terms of tension to calibrate the true stress–strain curve of the material after necking by means of an iterative process involving the FEM. Once the model had been calibrated, a tensile test of each specimen was simulated, and the corresponding results were validated using the experimental test data. From the FEM results, the quantities of interests, namely, the stress triaxiality, the equivalent plastic strain, and the normalized Lode angle, were extrapolated. Subsequently, the fracture locus of the Cor-Ten steel was determined through the interpolation of the experimental data collected in the present study as well as data available in the literature for low triaxiality ranges. The results confirmed the parabolic trend characterizing the fracture locus at low triaxiality suggested in the literature, and an exponential decreasing trend was found at higher triaxiality values after reaching a local maximum. The results thus confirm that the fracture locus of Cor-Ten steels, as generally found for metallic materials, cannot be completely described by a monotonic function. Moreover, it was found that the highly ductile behavior of the material induces a significant topology change in the specimens before failure, thus making it more complex to forecast the location of crack nucleation and, as a consequence, the stress state. Full article
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22 pages, 3301 KB  
Article
Cyclic Elasto-Plastic Behaviour of 51CrV4 Steel for Railway Parabolic Leaf Spring Design
by Vítor M. G. Gomes, Rita Dantas, José A. F. O. Correia and Abílio M. P. de Jesus
Appl. Sci. 2025, 15(5), 2549; https://doi.org/10.3390/app15052549 - 27 Feb 2025
Cited by 1 | Viewed by 560
Abstract
Parabolic leaf springs are components typically found in suspensions of freight railway rolling stock. These components are produced in high-strength alloyed steel, DIN 51CrV4, to resist severe loading and environmental conditions. Despite the material’s good mechanical characteristics, the geometric notches and high surface [...] Read more.
Parabolic leaf springs are components typically found in suspensions of freight railway rolling stock. These components are produced in high-strength alloyed steel, DIN 51CrV4, to resist severe loading and environmental conditions. Despite the material’s good mechanical characteristics, the geometric notches and high surface roughness that features its leaves might raise local stress levels to values above the elastic limit, with cyclic elasto-plastic behaviour models being more appropriate. In this investigation, the parameters of the Chaboche model combining the kinematic and isotropic hardening models are determined using experimental data previously obtained in strain-controlled cyclic tests. Once the parameters of the cyclic hardening model are determined, they are validated using a finite element approach considering the Chaboche cyclic plasticity model. As a result, the material properties specified in this investigation can be used in the fatigue mechanical design of parabolic leaf springs made with 51CrV4 (local approaches to notches and at surface roughness level) or even in other components produced with the same steel. Full article
(This article belongs to the Section Mechanical Engineering)
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27 pages, 4912 KB  
Review
Recent Advances in the Analytical Stress Field Solutions for Radiused Notches in Orthotropic Solids
by Alessandro Pontefisso, Matteo Pastrello and Michele Zappalorto
Materials 2023, 16(11), 3915; https://doi.org/10.3390/ma16113915 - 23 May 2023
Cited by 2 | Viewed by 1578
Abstract
The main aim of this work is to provide a brief overview of the analytical solutions available to describe the in-plane and out-of-plane stress fields in orthotropic solids with radiused notches. To this end, initially, a brief summary on the bases of complex [...] Read more.
The main aim of this work is to provide a brief overview of the analytical solutions available to describe the in-plane and out-of-plane stress fields in orthotropic solids with radiused notches. To this end, initially, a brief summary on the bases of complex potentials for orthotropic elasticity is presented, with reference to plane stress or strain and antiplane shear problems. Subsequently, the attention is moved to the relevant expressions for the notch stress fields, considering elliptical holes, symmetric hyperbolic notches, parabolic notches (blunt cracks), and radiused V-notches. Eventually, examples of applications are presented, comparing the presented analytical solutions with the results from numerical analyses carried out on relevant cases. Full article
(This article belongs to the Special Issue Manufacturing and Mechanics of Materials, Volume II)
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15 pages, 7496 KB  
Article
Investigation of Notch-Induced Precise Splitting of Different Bar Materials under High-Speed Load
by Yuanzhe Dong, Yujian Ren, Shuqin Fan, Yongfei Wang and Shengdun Zhao
Materials 2020, 13(11), 2461; https://doi.org/10.3390/ma13112461 - 28 May 2020
Cited by 16 | Viewed by 3188
Abstract
A notch-induced high-speed splitting method was developed for high-quality cropping of metal bars using a new type of electric-pneumatic counter hammer. Theoretical equations and FE models were established to reveal the crack initiation and fracture mode. Comparative tests were conducted for notched and [...] Read more.
A notch-induced high-speed splitting method was developed for high-quality cropping of metal bars using a new type of electric-pneumatic counter hammer. Theoretical equations and FE models were established to reveal the crack initiation and fracture mode. Comparative tests were conducted for notched and unnotched bars of four types of steels, i.e., AISI 1020, 1045, 52100, and 304, and the section quality and microfracture mechanism were further investigated. The results show that damage initiates at the bilateral notch tips with peak equivalent plastic strain, and propagates through the plane induced by the notch tip; the stress triaxiality varies as a quasi-sine curve, revealing that the material is subjected to pure shearing at the notch tip, and under compression at the adjacent region. High precision chamfered billets were obtained with roundness errors of 1.1–2.8%, bending deflections of 0.5–1.5mm, and angles of inclination of 0.7°–3.4°. Additionally, the notch effectively reduced the maximum impact force by 21.6–23.9%, splitting displacement by 7.6–18.6%, and impact energy by 27.8–39.1%. The crack initiation zone displayed quasi-parabolic shallow dimples due to shear stress, and the pinning effect was larger in AISI 52100 and 1045 steel; the final rupture zone was characterized by less elongated and quasi-equiaxial deeper dimples due to the combination of shear and normal stress. Full article
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15 pages, 4019 KB  
Article
Determination of Fracture Energy of Early Age Concrete through a Uniaxial Tensile Test on an Un-Notched Specimen
by Dongya Ren and Lambert Houben
Materials 2020, 13(3), 496; https://doi.org/10.3390/ma13030496 - 21 Jan 2020
Cited by 5 | Viewed by 3337
Abstract
Unlike the notched specimens for conventional concrete fracture tests, this paper introduces a deformation-controlled uniaxial tensile test on an un-notched specimen. The surface of the dog bone-shaped specimen is a second order parabolic curve, and the gradual change in the specimen shape does [...] Read more.
Unlike the notched specimens for conventional concrete fracture tests, this paper introduces a deformation-controlled uniaxial tensile test on an un-notched specimen. The surface of the dog bone-shaped specimen is a second order parabolic curve, and the gradual change in the specimen shape does not lead to extreme stress concentrations. Another significant feature of the tension test set-up is that it is built with three hinges, to accommodate the alignment of the specimens. The specimen preparation, test conditions, and the tension test set-up are explained in detail. The fracture energy of the concrete is determined by the obtained complete softening curves. The fracture energy is found to increase with age, going towards a horizontal asymptote as concrete hardened in a tested age range of 1 day to 90 days. Moreover, the rate of development of the fracture energy was found to be higher when compared to tensile strength and stiffness. Full article
(This article belongs to the Section Construction and Building Materials)
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