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20 pages, 3455 KiB  
Article
Chemical Equilibrium Fracture Mechanics—Hydrogen Embrittlement Application
by Andreas G. Varias
Corros. Mater. Degrad. 2025, 6(1), 5; https://doi.org/10.3390/cmd6010005 - 6 Feb 2025
Viewed by 287
Abstract
Chemical Equilibrium Fracture Mechanics (CEFM) studies the effect of chemical reactions and phase transformations on crack-tip fields and material fracture toughness under chemical equilibrium. An important CEFM direction is hydrogen-induced embrittlement of alloys, due to several industrial applications, including those within the industrial [...] Read more.
Chemical Equilibrium Fracture Mechanics (CEFM) studies the effect of chemical reactions and phase transformations on crack-tip fields and material fracture toughness under chemical equilibrium. An important CEFM direction is hydrogen-induced embrittlement of alloys, due to several industrial applications, including those within the industrial value chain of hydrogen that is under development, which, according to European and international policies, are expected to contribute significantly to the replacement of fossil fuels by renewable energy sources. In the present study, the effect of hydrogen on the crack-tip fields of hydride- and non-hydride-forming alloys is examined. The crack-tip stress and hydrogen concentration distributions are derived under hydrogen chemical equilibrium, which is approached by considering the coupling of the operating physical mechanisms. In all cases, analytic relations are derived, thus facilitating integrity assessments, i.e., without the need to rely on complicated numerical methods, expected to lead to the development of respective tools in industrial applications. It is shown that, in the case of hydride precipitation, there are significant deviations from the K, HRR, and Prandtl fields, and, thus, the well-known approaches of Linear Elastic Fracture Mechanics (LEFM) and Elastic–Plastic Fracture Mechanics (EPFM) need to be accordingly modified/extended. Full article
(This article belongs to the Special Issue Hydrogen Embrittlement of Modern Alloys in Advanced Applications)
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<p>Chemical Equilibrium Fracture Mechanics is a multidisciplinary approach for the evaluation of structural integrity under chemical equilibrium and steady-state energy transfer.</p>
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<p>Hydrogen concentration in interstitial lattice sites ahead of a crack tip on the crack plane of ASTM A 106 Grade B steel at 20 °C, normalized by remote hydrogen concentration in interstitial lattice sites. Distances have been normalized by J-integral [<a href="#B78-cmd-06-00005" class="html-bibr">78</a>] over yield stress.</p>
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<p>Hydrogen concentration in interstitial lattice sites on the plane of deformation, normal to the crack edge, for an ASTM A 106 Grade B steel at 20 °C. Hydrogen concentration has been normalized by remote hydrogen concentration in interstitial lattice sites. Distances have been normalized by J-integral [<a href="#B78-cmd-06-00005" class="html-bibr">78</a>] over yield stress.</p>
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<p>Variation in the ratio of hydrogen concentration in trap sites over hydrogen concentration in interstitial lattice sites with the remote hydrogen concentration in interstitial lattice sites, for different stress trace levels, expected ahead of a crack tip; ASTM A 106 Grade B steel at 20 °C.</p>
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<p>Variation in the ratio of hydrogen concentration in trap sites over hydrogen concentration in interstitial lattice sites with the remote hydrogen concentration in interstitial lattice sites, for different stress trace levels, expected ahead of a crack tip; X-750 Ni-Cr-Fe alloy at (<b>a</b>) 25 °C and (<b>b</b>) 285 °C.</p>
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<p>Change in hydride precipitation zone shape as the deformation behavior of the metal changes from linear elastic to elastic–plastic with power-law hardening and perfectly plastic deformation. With the exception of the hardening exponent, the properties of the material correspond to α-Ti, given in <a href="#cmd-06-00005-t003" class="html-table">Table 3</a>.</p>
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<p>Angular variation in the singular stress field before, <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mover accent="true"> <mrow> <mi>S</mi> </mrow> <mo>~</mo> </mover> </mrow> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msubsup> </mrow> </semantics></math>, and after hydride precipitation, <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mover accent="true"> <mrow> <mi>σ</mi> </mrow> <mo>~</mo> </mover> </mrow> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>e</mi> <mi>l</mi> </mrow> </msubsup> </mrow> </semantics></math>, ahead of the crack tip in the sector [−45°, 45°] when material deformation is described by linear elasticity. The properties of the material correspond to α-Ti, given in <a href="#cmd-06-00005-t003" class="html-table">Table 3</a>.</p>
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<p>Angular variation in the singular stress field before, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>S</mi> </mrow> <mo>~</mo> </mover> </mrow> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>, and after hydride precipitation, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>σ</mi> </mrow> <mo>~</mo> </mover> </mrow> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>, ahead of the crack tip in the sector [−45°, 45°] under elastic–plastic power-law hardening behavior with <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. The properties of the material correspond to α-Ti, given in <a href="#cmd-06-00005-t003" class="html-table">Table 3</a>.</p>
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<p>Angular variation in the stress field before, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>, and after hydride precipitation, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>, ahead of the crack tip in the sector [−45°, 45°] under perfect plastic deformation; stresses are normalized by yield stress. Remote hydrogen concentration corresponds to <math display="inline"><semantics> <mrow> <mrow> <mrow> <msub> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>h</mi> <mi>z</mi> </mrow> </msub> </mrow> <mo>/</mo> <mrow> <msub> <mrow> <mi>σ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>2</mn> </mrow> </mrow> </mrow> </semantics></math>. The properties of the material correspond to α-Ti, given in <a href="#cmd-06-00005-t003" class="html-table">Table 3</a>.</p>
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<p>Angular variation in the stress field, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>, ahead of the crack tip in the hydride precipitation sector [−45°, 45°] under perfect plastic deformation for various levels of hydride precipitation zone stress trace, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>h</mi> <mi>z</mi> </mrow> </msub> </mrow> </semantics></math>; stresses are normalized by yield stress. The properties of the material correspond to α-Ti, given in <a href="#cmd-06-00005-t003" class="html-table">Table 3</a>.</p>
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18 pages, 10071 KiB  
Article
Crack Propagation in Axial-Flow Fan Blades Under Complex Loading Conditions: A FRANC3D and ABAQUS Co-Simulation Approach
by Mariem Ben Hassen, Slim Ben-Elechi and Hatem Mrad
Appl. Sci. 2025, 15(3), 1597; https://doi.org/10.3390/app15031597 - 5 Feb 2025
Viewed by 305
Abstract
Since fan blades are exposed to fatigue, and in some cases harsh loading conditions, they may exhibit fracture failures due to crack propagation, resulting in significant losses. Previous studies of crack propagation in blades are mainly confined to either simplified blade geometry or [...] Read more.
Since fan blades are exposed to fatigue, and in some cases harsh loading conditions, they may exhibit fracture failures due to crack propagation, resulting in significant losses. Previous studies of crack propagation in blades are mainly confined to either simplified blade geometry or loads, resulting in a significant discrepancy between the simulated crack propagation and the real blade propagation behavior, while it is lacking for challenging shapes and loads. A co-simulation approach of FRANC3D and ABAQUS was developed to study the crack propagation of an axial-flow fan blade subjected to centrifugal, aerodynamic, and combined loads. The projected approach is validated with results obtained from analytical calculations and experiments. Meanwhile, making use of benchmarks, the Stress Intensity Factor (SIF) and the prediction of mixed-mode crack growth path are validated. Considering various loads, the crack propagation path response for the fan blade is computed for different growth steps. The results pinpoint that the crack propagation length of the crack tip center is maximum under centrifugal loading. However, the aerodynamic load led to a maximum propagation length of the crack tip endpoints. In addition, the combined force of centrifugal and aerodynamic loads limits the crack from growing. Full article
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<p>Finite element model illustration of the specimen: (<b>a</b>) without crack, (<b>b</b>) with center double slant crack.</p>
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<p>Comparison of the theoretical and numerical results of stress intensity factors: KI and KII with different initial crack lengths: (<b>a</b>) for φ = 30°, and (<b>b</b>) for φ = 45°.</p>
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<p>The polymethyl methacrylate (PMMA) beam specimens: (<b>a</b>) the finite element model without holes, (<b>b</b>) the crack growth path for specimen A, (<b>c</b>) the crack growth path for specimen B, (<b>d</b>) the crack growth path for specimen C.</p>
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<p>The PMMA specimen: (<b>a</b>) the finite element model with holes, (<b>b</b>) the crack growth path for specimen D, (<b>c</b>) the crack growth path for specimen E, (<b>d</b>) the crack growth path for specimen F.</p>
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<p>Comparison of the crack propagation paths obtained using the proposed method with the experimental [<a href="#B24-applsci-15-01597" class="html-bibr">24</a>] and Abaqus self-method for the first three PMMA beam specimens (A, B, C).</p>
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<p>Comparison of the crack propagation paths obtained using the proposed method with the experimental [<a href="#B24-applsci-15-01597" class="html-bibr">24</a>] and the Abaqus self-method for the last three PMMA beam specimens (D, E, F).</p>
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<p>Crack propagation flow chart using FRANC3D code.</p>
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<p>Boundary conditions acting on the blade: (<b>a</b>) centrifugal load, (<b>b</b>) aerodynamic load, (<b>c</b>) combined centrifugal and aerodynamic loads.</p>
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<p>Equivalent (von Mises) stress distribution along the blade: (<b>a</b>) centrifugal load, (<b>b</b>) aerodynamic load, (<b>c</b>) combined centrifugal and aerodynamic loads.</p>
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<p>Crack propagation path under: (<b>a</b>) centrifugal load, (<b>b</b>) aerodynamic load, (<b>c</b>) combined centrifugal and aerodynamic loads.</p>
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<p>Stress intensity factor KI for: (<b>a</b>) centrifugal load, (<b>b</b>) aerodynamic load, (<b>c</b>) combined centrifugal and aerodynamic loads.</p>
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<p>The crack propagation lengths of both ends of the crack tip for the three equal subdivisions of the step number.</p>
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<p>The crack propagation lengths of the center of the crack tip for the three equal subdivisions of the step number.</p>
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<p>Comparison of the total crack length for the different loads.</p>
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23 pages, 5227 KiB  
Article
Mechanisms of Strength Degradation of Dental Zirconia Due to Glazing: Dependence on Glaze Thickness
by Kazumichi Nonaka, Mitsuji Teramae and Giuseppe Pezzotti
Materials 2025, 18(3), 684; https://doi.org/10.3390/ma18030684 - 4 Feb 2025
Viewed by 354
Abstract
Glazing is a common method for smoothing the surface of zirconia and imitating the appearance of natural teeth. Several authors have previously reported that glazing reduces the strength of zirconia. However, the dependence of strength on glaze thickness and the mechanism of strength [...] Read more.
Glazing is a common method for smoothing the surface of zirconia and imitating the appearance of natural teeth. Several authors have previously reported that glazing reduces the strength of zirconia. However, the dependence of strength on glaze thickness and the mechanism of strength reduction remains unclear. Clarifying these factors is particularly important for improving the reliability of zirconia prostheses. In this study, three types of zirconia were glazed with various thicknesses, and their strength was evaluated. The results showed that the strength of the materials decreased with increasing glaze thickness. The decrease in the fracture load of the glazed test specimen stopped at a load where the stress necessary to fracture the glaze material was applied to the surface of the glaze layer. Furthermore, the strength reduction mechanism was investigated using FEM analysis, fractography, and Raman spectroscopy. The results suggested that the strength reduction due to glazing was a consequence of the crack-tip stress concentration developed upon the preliminary fracture of the glaze layer. Full article
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<p>The specimen preparation procedure.</p>
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<p>FEM analysis model.</p>
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<p>Photomicrographs of fractured 3Y and 4Y zirconia specimens. The top and bottom are porcelain surface and side views, respectively. The arrows indicate channel cracks. The red circles indicate delamination of the glaze material.</p>
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<p>Principal stress distribution calculation results in three-point flexural test using FEM (glaze thickness: 40 μm). The red area indicates stress concentrations.</p>
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<p>Calculated maximum stress applied to the base material and glaze layer during a three-point flexural test (Load: 100N). The stress distribution in each material changes depending on the glaze thickness.</p>
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<p>Calculated maximum stress applied to the base material and glaze layer during a three-point flexural test (glaze thickness: 40 μm).</p>
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<p>Representative stress–strain curves for each specimen. The arrows in <a href="#materials-18-00684-f007" class="html-fig">Figure 7</a> indicate the fracture points.</p>
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<p>Relationship between flexural strength calculated from Equation (1) and glaze thickness of each material. The figure on the right shows the measured values normalized by the glaze-removed strength of each material. The bar-shaped elements are specimens in which the glaze material delaminated during the test and deviated from the strength reduction curve.</p>
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<p>Average three-point flexural strength for each glaze thickness range. The asterisks refer to statistical significance according to the Tukey–Kramer multiple comparison test (*: <span class="html-italic">p</span> &lt; 0.05, **: <span class="html-italic">p</span> &lt; 0.01).</p>
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<p>Relationship between fracture load and glaze thickness of each material (data from delaminated specimens were excluded). The blue shading indicates the load range at where the fracture stress of the glaze material is applied to the glaze layer, estimated from <a href="#materials-18-00684-f006" class="html-fig">Figure 6</a>.</p>
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<p>SEM image of the fracture surface of the 3Y zirconia specimen. The white arrows indicate the direction of crack propagation. The inset shows a high-magnification image of the area outlined in red. The red arrow indicates the fracture origin.</p>
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<p>SEM image of the fracture surface of the 4Y zirconia specimen. The white arrows indicate the direction of crack propagation. The inset shows a high-magnification image of the area outlined in red. The red arrow indicates the fracture origin.</p>
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<p>SEM image of the fracture surface of the 5Y zirconia specimen. The white arrows indicate the direction of crack propagation. The inset shows a high-magnification image of the area outlined in red. The red arrow indicates the fracture origin.</p>
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<p>SEM images of the fracture surface of the glaze layer on a 3Y zirconia specimen (glaze thickness: 45.2 μm, three-point flexural strength: 653 MPa). The white, black, and red arrows indicate the direction of crack propagation, hackles, and rib marks, respectively.</p>
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<p>Raman spectrum on glazed 3Y zirconia surface. No typical peaks indicative of the monoclinic phase (176 cm<sup>−1</sup> and 183 cm<sup>−1</sup>) are observed.</p>
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<p>Map of the monoclinic peak (~176 cm<sup>−1</sup>) intensity on the fracture surface of glazed 3Y zirconia. The red line indicates the area where the average monoclinic phase content was calculated (<a href="#materials-18-00684-f017" class="html-fig">Figure 17</a>).</p>
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<p>Relationship between average monoclinic phase content of fracture surface calculated from Equation (2) and flexural strength of glazed 3Y zirconia.</p>
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16 pages, 21224 KiB  
Article
Dynamic Responses and Crack Propagation of Rock with Crossed Viscoelastic Joints Under Blasting Loads
by Chengyang Li, Dongju Jiang, Jinhai Zhao, Tuo Zhang and Renfei Kuang
Materials 2025, 18(3), 548; https://doi.org/10.3390/ma18030548 - 25 Jan 2025
Viewed by 417
Abstract
To investigate the propagation of stress waves in viscoelastic joints under blasting loads, and their impact on crack propagation and dynamic response in rock masses, a numerical model incorporating intersecting viscoelastic joints was developed using LS-DYNA. This study focuses on the influence of [...] Read more.
To investigate the propagation of stress waves in viscoelastic joints under blasting loads, and their impact on crack propagation and dynamic response in rock masses, a numerical model incorporating intersecting viscoelastic joints was developed using LS-DYNA. This study focuses on the influence of various joint geometric parameters, including thickness and angle, on stress wave propagation and damage patterns in rock. The Riedel–Hiermaier–Thoma (RHT) model was employed to simulate the dynamic behavior of rock, while the Poynting–Thomson model was used to describe the viscoelastic properties of the joint fillings. The simulation results provide detailed insights into the principal stress, displacement, and particle vibration velocity around the joints. Based on the stress wave propagation theory, the velocity transmission coefficients were calculated to quantify the attenuation of stress waves across the joints. The findings demonstrate that viscoelastic joint properties significantly affect the damage patterns in the rock mass. Specifically, the area of the crushed zone and the width of cracks on the blasting side are proportional to joint thickness, while crack propagation at the joint tips is governed by differences in principal stress. Moreover, the propagation of vibration velocity is notably weakened at the second joint, highlighting the critical role played by joint characteristics in stress wave dynamics. These results underscore the complex interaction between joint properties and stress wave behavior in rock masses, providing valuable insights for optimizing blasting designs and improving the safety of underground engineering projects. Full article
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<p>Methodology flowchart.</p>
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<p>Crack patterns of Barre granite sample under blasting loads. (<b>a</b>) Numerical simulation; (<b>b</b>) blast experiment [<a href="#B30-materials-18-00548" class="html-bibr">30</a>].</p>
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<p>Schematic diagrams of the charge and joints in the models.</p>
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<p>Crack propagation of rock under D = 10 mm with (<b>a</b>) θ = 10°; (<b>b</b>) θ = 15°; (<b>c</b>) θ = 20°; (<b>d</b>) θ = 25°; (<b>e</b>) θ = 30°.</p>
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<p>Propagation of the effective stress 0.3 ms after detonating with (<b>a</b>) θ = 10°; (<b>b</b>) θ = 15°; (<b>c</b>) θ = 20°; (<b>d</b>) θ = 25°; (<b>e</b>) θ = 30°.</p>
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<p>Velocity transmission coefficients of models with different angles: (<b>a</b>) 10 mm joints; (<b>b</b>) 20 mm joints; (<b>c</b>) 30 mm joints.</p>
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<p>Crack propagation of rock under θ = 20° with (<b>a</b>) D = 10 mm; (<b>b</b>) D = 20 mm; (<b>c</b>) D = 30 mm.</p>
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<p>Propagation of the effective stress 0.3 ms after detonating with (<b>a</b>) D = 10 mm; (<b>b</b>) D = 20 mm; (<b>c</b>) D = 30 mm.</p>
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<p>Positions of reference points A, B, C, and D.</p>
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<p>Time–history of effective stress at (<b>a</b>) reference A; (<b>b</b>) reference B; (<b>c</b>) reference C; (<b>d</b>) reference D.</p>
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<p>Time–history of effective stress at the ends of different joint thicknesses: (<b>a</b>) Joint I; (<b>b</b>) Joint II.</p>
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<p>Arrangement of the measurement points (MPs) surrounding the right tips of two joints.</p>
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<p>Principal stress distribution surrounding the tip of the D = 20 mm joints 0.4 ms after detonating (MPa): (<b>a</b>) θ = 10°; (<b>b</b>) θ = 15°; (<b>c</b>) θ = 20°; (<b>d</b>) θ = 25°; (<b>e</b>) θ = 30°.</p>
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<p>Displacements around the tip of the joints under D = 10 mm, θ = 20° conditions: (<b>a</b>) shear displacement μ; (<b>b</b>) normal displacement υ.</p>
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18 pages, 9042 KiB  
Article
Ab Initio Molecular Dynamics Insights into Stress Corrosion Cracking and Dissolution of Metal Oxides
by Levi C. Felix, Qin-Kun Li, Evgeni S. Penev and Boris I. Yakobson
Materials 2025, 18(3), 538; https://doi.org/10.3390/ma18030538 - 24 Jan 2025
Viewed by 402
Abstract
Oxide phases such as α-Fe2O3 (hematite) and α-Al2O3 (corundum) are highly insoluble in water; however, subcritical crack growth has been observed in humidity nonetheless. Chemically induced bond breaking at the crack tip appears unlikely due [...] Read more.
Oxide phases such as α-Fe2O3 (hematite) and α-Al2O3 (corundum) are highly insoluble in water; however, subcritical crack growth has been observed in humidity nonetheless. Chemically induced bond breaking at the crack tip appears unlikely due to sterically hindered molecular transport. The molecular mechanics of a crack in corundum with a reactive force field reveal minimal lattice trapping, leading to bond breaking before sufficient space opens for water transport. To address this, we model a pre-built blunt crack with space for H2O molecule adsorption at the tip and show that it reduces fracture toughness by lowering the critical J-integral. Then, we explore stress-enhanced dissolution to understand the mechanism of crack tip blunting in the oxide/water system. Density functional theory combined with metadynamics was employed to describe atomic dissolution from flat hematite and corundum surfaces in pure water. Strain accelerates dissolution, stabilizing intermediate states with broken bonds before full atom detachment, while the free energy profile of unstrained surfaces is almost monotonic. The atomistic calculations provided input for a kinetic model, predicting the shape evolution of a blunt crack tip, which displays three distinct regimes: (i) dissolution primarily away from the tip, (ii) enhanced blunting near but not at the apex, and (iii) sharpening near the apex. The transition between regimes occurs at a low strain, highlighting the critical role of water in the subcritical crack growth of oxide scales, with dissolution as the fundamental microscopic mechanism behind this process. Full article
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<p>Crystal structure of (<b>a</b>) anti-ferromagnetic <math display="inline"><semantics> <mi>α</mi> </semantics></math>-Fe<sub>2</sub>O<sub>3</sub> and (<b>b</b>) <math display="inline"><semantics> <mi>α</mi> </semantics></math>-Al<sub>2</sub>O<sub>3</sub> with the <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>001</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>012</mn> <mo>)</mo> </mrow> </semantics></math> cleavage planes being labeled. (<b>c</b>) Top view of corundum <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>110</mn> <mo>)</mo> </mrow> </semantics></math> plane. (<b>d</b>) Octahedral units of both materials with long and short bond lengths, from our DFT calculations.</p>
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<p>Fracture energy <span class="html-italic">R</span> values for all cleavage planes considered, computed with DFT. Each surface termination is marked by dashed line arrows pointing to their corresponding <span class="html-italic">R</span> values.</p>
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<p>(<b>a</b>) Geometric setup for the crack tip analysis for <math display="inline"><semantics> <mi>α</mi> </semantics></math>-Al<sub>2</sub>O<sub>3</sub> corresponding to a (012) cleavage plane and [100] as the propagation direction (view along [12<math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math>] where the gray region represents the frozen boundary and the colored (red and blue atoms) region is allowed to relax at every load step. Energy as a function of load <span class="html-italic">K</span> for crack tips centered at two consecutive bonds, states <span class="html-italic">A</span> and <span class="html-italic">B</span>, as illustrated in the insets, for (<b>b</b>) (012)[100] and (<b>c</b>) (110)[1 <math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math> <math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math>] crack. An enlarged view of the region near the critical load <math display="inline"><semantics> <msub> <mi>K</mi> <mi>c</mi> </msub> </semantics></math> is also shown in the inset. Atoms that comprise the crack tip are highlighted in light gray. ReaxFF-computed energies for state <span class="html-italic">A</span> are shown as black dots, while for state <span class="html-italic">B</span> are shown as red squares, with nearly a <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>∼</mo> <msup> <mi>K</mi> <mn>2</mn> </msup> </mrow> </semantics></math> behavior.</p>
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<p>(<b>a</b>) Blunt tip model for a (110)[1 <math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math> <math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math>] crack with passivated surfaces; the definition of the contour <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="normal">Γ</mi> <mo>*</mo> </msup> <mo>=</mo> <msubsup> <mo>⋃</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </msubsup> <msub> <mi mathvariant="normal">Γ</mi> <mi>i</mi> </msub> </mrow> </semantics></math>, used to compute the <span class="html-italic">J</span>-integral, is illustrated, with arrows indicating the direction of traversing. (<b>b</b>) Solvent-accessible surface profiles for sharp cracks (012) [100] and [110][1 <math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math> <math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math>], and a blunt (110)[1 <math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math> <math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math>] crack. A probe sphere with a diameter of 2.6 Å was used to represent a water molecule, where the corresponding Connolly surface is shown in the inset for a blunt (110)[1 <math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math> <math display="inline"><semantics> <mover accent="true"> <mn>1</mn> <mo stretchy="false">¯</mo> </mover> </semantics></math>] crack. (<b>c</b>) Computed <span class="html-italic">J</span>-integral for water-assisted cracking (red curve) compared with pure Al-O bond breaking (black curve).</p>
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<p>(<b>a</b>) Schematics of a crack blunted by atomic dissolution. (<b>b</b>) Zoomed view of the strained flat surface model used in the metadynamics simulations for the free energy of atom detachment from a (110) surface, with the reaction coordinate d indicated as the orthogonal distance of a surface atom to a plane determined by the position of three fixed atoms. (<b>c</b>) Time evolution of the coordination number of Fe with O atoms from the surface of oxide, <math display="inline"><semantics> <mrow> <mi>C</mi> <mi>N</mi> </mrow> </semantics></math>(Fe-Os), (at strains <math display="inline"><semantics> <mi>ε</mi> </semantics></math> = 0, 1, and 3%) keeping track of the bond-breaking events during the whole process. The free energy surfaces of metal atom dissolution for hematite (<b>d</b>) and corundum (<b>e</b>). Intermediate steps (ii)–(vi) are indicated on the free energy paths and are discussed in <a href="#materials-18-00538-f006" class="html-fig">Figure 6</a>a.</p>
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<p>(<b>a</b>) Free energy diagram of the dissolution process at <math display="inline"><semantics> <mi>ε</mi> </semantics></math> = 3% for both hematite and corundum. Reaction steps (i) and (vi) correspond to states where <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>−</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and 4, respectively, whereas intermediate ones are indicated in <a href="#materials-18-00538-f005" class="html-fig">Figure 5</a>d,e. (<b>b</b>) Energy change <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>E</mi> </mrow> </semantics></math> of static change of atom height d, where a geometry minimization is performed every step with the constraint of <span class="html-italic">z</span>-coordinate of the target atom. (<b>c</b>) The intermediate state where the bond below the target atom (here indicated by the coordination polyhedral) shows a small change in the curve in (<b>b</b>). (<b>d</b>) Lateral bond breaking presents a larger effect in the structural relaxation upon breaking, as observed by the deeper minima that arise from the increase in externally applied strain nearly parallel to such bond.</p>
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<p>(<b>a</b>) Angular dependence of the dissolution rate <span class="html-italic">v</span> near the tip determined from Equation (<a href="#FD8-materials-18-00538" class="html-disp-formula">8</a>), with parameters corresponding to the <math display="inline"><semantics> <mi>α</mi> </semantics></math>-Fe<sub>2</sub>O<sub>3</sub> (110) surface. Each curve corresponds to a different strain value (as labeled). The <span class="html-italic">v</span> values are normalized by stress-free corrosion of a flat surface, <math display="inline"><semantics> <msub> <mi>v</mi> <mn>0</mn> </msub> </semantics></math> (dashed line). The inset shows the tip geometry. Schematics of the crack tip blunting evolution are shown with steps consisting of (<b>b</b>) gross blunting, (<b>c</b>) enhanced tip blunting, and (<b>d</b>) gross sharpening.</p>
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14 pages, 12626 KiB  
Article
Study of the Intrinsic Factors Determining the Near-Threshold Fatigue Crack Propagation Behavior of a High-Strength Titanium Alloy
by Huan Wang, Yongqing Zhao, Ping Guo, Fei Qiang, Lei Zhang, Zhongli Qiao and Shewei Xin
Metals 2025, 15(1), 84; https://doi.org/10.3390/met15010084 - 17 Jan 2025
Viewed by 485
Abstract
The resistance to near-threshold fatigue crack growth and its correlation with the microstructure of the Ti-5Al-3Mo-3V-2Zr-2Cr-1Nb-1Fe alloy were investigated. K-decreasing fatigue crack propagation rate tests were conducted on compact tension samples (ASTM standard) with a stress ratio R of 0.1 and a [...] Read more.
The resistance to near-threshold fatigue crack growth and its correlation with the microstructure of the Ti-5Al-3Mo-3V-2Zr-2Cr-1Nb-1Fe alloy were investigated. K-decreasing fatigue crack propagation rate tests were conducted on compact tension samples (ASTM standard) with a stress ratio R of 0.1 and a frequency of 15 HZ in a laboratory atmosphere. At a similar strength level of 1200 MPa, the sample with a fine basket-weave microstructure (F-BW) displayed the slowest near-threshold fatigue crack propagation rate compared with the samples with equiaxed (EM) and basket-weave (BW) microstructures. The fatigue threshold value (ΔKth) was 4.4 MPa·m1/2 for F-BW, 3.6 for BW, and 3.2 for EM. The fracture surfaces and crack profiles were observed by scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) to elucidate the mechanism of fatigue crack propagation in the near-threshold regime. The results revealed that the near-threshold crack growth in the three samples was primarily transgranular. The crack always propagated parallel to the crystal plane, with a high Schmid factor. In addition, the near-threshold fatigue crack growth behavior was synergistically affected by the crack tip plastic zone and crack bifurcation. The increased fatigue crack propagation resistance in F-BW was attributed to the better stress/strain compatibility and greater number of interface obstacles in the crack tip plastic zone. Full article
(This article belongs to the Special Issue Structure and Mechanical Properties of Titanium Alloys)
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<p>Microstructures after forging and heat treatment of the Ti-5321 alloy. (<b>a</b>) Processing schematic; (<b>b</b>) EM; (<b>c</b>) BW; (<b>d</b>) F-BW.</p>
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<p>The tensile properties of Ti-5321 alloy with EM, BW, and F-BW samples [<a href="#B15-metals-15-00084" class="html-bibr">15</a>].</p>
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<p>The size of fatigue samples used in this study (unit: mm).</p>
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<p>FCP rate curves of Ti-5321 alloy (<b>a</b>) and the ultimate tensile strength and <span class="html-italic">ΔK<sub>th</sub></span> for several typical titanium alloys (<b>b</b>) [<a href="#B8-metals-15-00084" class="html-bibr">8</a>,<a href="#B9-metals-15-00084" class="html-bibr">9</a>,<a href="#B20-metals-15-00084" class="html-bibr">20</a>,<a href="#B21-metals-15-00084" class="html-bibr">21</a>].</p>
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<p>Fracture surfaces and roughness analysis of the <span class="html-italic">da/dN</span> samples with EM (<b>a1</b>–<b>a3</b>), BW (<b>b1</b>–<b>b3</b>), and F-BW (<b>c1</b>–<b>c3</b>) in the near-threshold regime.</p>
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<p>SEM fractographs showing crack growth in the EM sample: (<b>a</b>) crack path at low magnification; (<b>b</b>) crack path at high magnification in rectangle (<b>b</b>) of (<b>a</b>); (<b>c</b>) crack path at high magnification in rectangle (<b>c</b>) of (<b>b</b>); (<b>d</b>) crack path at high magnification in rectangle (<b>d</b>) of (<b>a</b>).</p>
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<p>SEM fractographs showing crack growth in the BW sample: (<b>a</b>) crack path at low magnification; (<b>b</b>–<b>d</b>) crack path at high magnification.</p>
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<p>SEM fractographs showing crack growth in the F-BW sample: (<b>a</b>) crack path at low magnification; (<b>b</b>–<b>d</b>) crack path at high magnification.</p>
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<p>The load–unload hysteresis loop and back stress of EM, BW, and F-BW samples. (<b>a</b>) Schematic hysteresis loop; (<b>b</b>) hysteresis loops of Ti-5321 alloy with EM, BW, and F-BW; (<b>c</b>) back stress of EM, BW, and F-BW samples at tensile true strains of 0.5%, 1.5%, and 2.5%.</p>
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<p>SEM image and EBSD orientation maps containing crack paths in the BW sample: (<b>a</b>) SEM image in the vicinity of the crack path; (<b>b</b>) EBSD orientation maps in the vicinity of the crack path; (<b>c</b>) reconstructed map of crack propagation; (<b>d</b>) misorientation distribution map.</p>
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<p>SEM image and EBSD orientation maps containing crack paths in the F-BW sample: (<b>a</b>) SEM image in the vicinity of the crack path; (<b>b</b>) EBSD orientation maps in the vicinity of the crack path; (<b>c</b>) reconstructed map of crack propagation; (<b>d</b>) misorientation distribution map of the α plates in <a href="#metals-15-00084-f010" class="html-fig">Figure 10</a>c.</p>
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14 pages, 6487 KiB  
Article
Application of Surface-Cracking Process to Improve Impact Toughness of High-Strength BCC Steel at Low Temperatures
by Minha Park, Gang Ho Lee, Byoungkoo Kim, Sanghoon Noh, Jong Bae Jeon, Changwoo Lee and Byung Jun Kim
Crystals 2025, 15(1), 69; https://doi.org/10.3390/cryst15010069 - 12 Jan 2025
Viewed by 624
Abstract
At very low temperatures, typically ductile materials, especially body-centered cubic (BCC) steels, often exhibit an abrupt transition to brittle fracture, significantly limiting their applicability in cryogenic and low-temperature environments. This challenge arises from the inherent properties of BCC steels, where ductility is drastically [...] Read more.
At very low temperatures, typically ductile materials, especially body-centered cubic (BCC) steels, often exhibit an abrupt transition to brittle fracture, significantly limiting their applicability in cryogenic and low-temperature environments. This challenge arises from the inherent properties of BCC steels, where ductility is drastically reduced, leading to unexpected failures under mechanical stress. Despite the advantages of high-strength BCC steels, including cost-effectiveness and mechanical robustness, their susceptibility to brittle fracture restricts their use in demanding low-temperature applications. To address this limitation, we developed an innovative surface-cracking process to enhance the impact toughness of BCC steels. The introduction of controlled surface cracks redistributes stress and energy dissipation mechanisms, improving the toughness of high-strength BCC steels at cryogenic temperatures. Microscopic observations and finite element analyses reveal that these surface cracks not only dissipate crack formation energy but also alter stress triaxiality at crack tips. This causes the stress state to transition toward a plane stress condition, effectively mitigating stress concentrations typically observed in plane strain states. By reducing localized stress severity and promoting uniform energy distribution, the surface cracks encourage failure mechanisms favoring ductile behavior over brittle fracture. Full article
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<p>Schematic design of the Charpy impact test specimen with surface-cracking (5 L, 10 L) used in this study.</p>
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<p>Microstructure of X80 steels obtained from OM (<b>a</b>,<b>b</b>) and SEM (<b>c</b>,<b>d</b>) at different magnifications.</p>
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<p>The absorbed energy as a function of the test temperature curves, load–displacement graphs, and P<sub>max</sub> obtained from the instrumented Charpy impact test from room temperature to very low temperatures: (<b>a</b>) absorbed energy, (<b>b</b>) load–displacement graphs, and (<b>c</b>) maximum load (P<sub>max</sub>) from the Charpy impact test.</p>
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<p>The ratio of crack initiation energy (E<sub>i</sub>) to crack propagation energy (E<sub>p</sub>) of high-strength steels from room temperature to very low temperatures: (<b>a</b>) the standard specimen (0 L); (<b>b</b>) the surface-cracked specimen with 5 lines (5 L) and (<b>c</b>) 10 lines (10 L).</p>
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<p>The fracture surface of X80 steels with the surface-cracking process applied around the notch and center of the impact-fractured specimen at various temperatures: (<b>a</b>–<b>c</b>) 20 °C, (<b>d</b>–<b>f</b>) −80 °C, and (<b>g</b>–<b>i</b>) −140 °C.</p>
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<p>Schematic diagram (5 L) of the 1/4 FE model for CVN impact testing at room temperature of high-strength steel in this study: (<b>a</b>) front view and (<b>b</b>) side view.</p>
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<p>Finite element analysis results for deformation (top view) and triaxiality distribution (cross-section view) according to changing displacement (8 mm, 14 mm, 20 mm) for the Charpy impact specimens caused by surface cracks: (<b>a</b>) 0 L, (<b>b</b>) 5 L, and (<b>c</b>) 10 L sample and (<b>d</b>) average triaxiality.</p>
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22 pages, 4547 KiB  
Article
Investigation of the Sensitivity of Acoustic Emission to the Differentiation Between Mode I, II, and III Fracture in Bulk Polymer Materials
by Ali Shivaie Kojouri, Dimitrios G. Aggelis, Javane Karami, Akash Sharma, Wim Van Paepegem, Danny Van Hemelrijck and Kalliopi-Artemi Kalteremidou
Polymers 2025, 17(1), 125; https://doi.org/10.3390/polym17010125 - 6 Jan 2025
Viewed by 687
Abstract
There is very limited research in the literature investigating the way acoustic emission signals change when polymer materials are undergoing different fracture modes. This study investigates the capability of acoustic emission to recognize the fracture mode through acoustic emission parameter analysis, and can [...] Read more.
There is very limited research in the literature investigating the way acoustic emission signals change when polymer materials are undergoing different fracture modes. This study investigates the capability of acoustic emission to recognize the fracture mode through acoustic emission parameter analysis, and can be considered the first-ever study which examines the impact of different loading conditions, i.e., fracture mode I, mode II, and mode III, on the acoustic emission parameters in polymer materials. To accomplish this, prism-like pre-cracked polymer specimens were tested under the three different fracture modes. Acoustic emission parameters appeared sensitive to the different loading conditions of the pre-cracked specimens, indicating that acoustic emission can be used to distinguish the three fracture modes in polymer materials. Both frequency and time parameters reflect changes in the stress states at the crack tip. The duration and rise time of the waveforms were found to be the most sensitive acoustic emission parameters for identifying the fracture mode, while the average frequency variation can be employed to differentiate between in-plane and out-of-plane fracture modes. In order to interpret the experimental results in relation to wave mechanics, numerical wave propagation simulations for longitudinal and shear excitations were performed to simulate tensile and shear fracture modes and the corresponding emitted waves. An interesting correlation between the experimental and numerical results exists, showcasing acoustic emission’s potential for fracture identification. Full article
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<p>Schematic of different fracture modes acting at the crack front, from left to right: mode I or in-plane opening, mode II or in-plane shear, and mode III or out-of-plane shear.</p>
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<p>Pre-cracked prism-shaped specimens manufactured using Sika power<sup>®</sup>-830 (Sika Technology AG, Zürich, Switzerland) for the fracture tests.</p>
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<p>Schematic of specimens, location of the supports and sensors, and experimental setups for (<b>a</b>) mode I, (<b>b</b>) mode II, and (<b>c</b>) mode III fracture tests.</p>
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<p>Typical AE burst signal and AE parameters [<a href="#B47-polymers-17-00125" class="html-bibr">47</a>].</p>
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<p>Geometry, crack, wave source, and sensors of the numerical model in the Wave 2000 software.</p>
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<p>Gaussian sine pulse waveforms: (<b>a</b>) Case A, one cycle, (<b>b</b>) Case B, three cycles, and (<b>c</b>) Case C, five cycles.</p>
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<p>Load and number of AE hits and events versus displacement for (<b>a</b>) mode I, (<b>b</b>) mode II, (<b>c</b>) mode III tests.</p>
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<p>Manual AE source localization based on pencil lead breaks (distance between two sensors is 35 mm).</p>
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<p>AE event localization for the (<b>a</b>) mode I, (<b>b</b>) mode II, and (<b>c</b>) mode III fracture tests.</p>
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<p>AE event parameters versus fracture mode: (<b>a</b>) duration, (<b>b</b>) rise time, (<b>c</b>) average frequency, and (<b>d</b>) peak frequency.</p>
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<p>AE hit parameters versus fracture mode: (<b>a</b>) duration and (<b>b</b>) rise time.</p>
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<p>Wave propagation in the pre-cracked specimen for longitudinal and shear excitations: (<b>a</b>,<b>b</b>) development of the elastic wave after excitation, (<b>c</b>,<b>d</b>) arrival of the longitudinal wave to the sensors, and (<b>e</b>,<b>f</b>) arrival of the shear wave to the sensors.</p>
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<p>Simulated acoustic wave signals as received by the sensor for (<b>a</b>) one-cycle, (<b>b</b>) three-cycle, and (<b>c</b>) five-cycle excitation (threshold is shown by two horizontal dash lines).</p>
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15 pages, 11357 KiB  
Article
Catastrophic Failure Analysis of a Wind Turbine Gearbox by the Finite Element Method and Fracture Analysis
by Jairo Aparecido Martins and Estaner Claro Romão
Designs 2025, 9(1), 4; https://doi.org/10.3390/designs9010004 - 5 Jan 2025
Viewed by 619
Abstract
The wind turbine gearbox, used as a multiplier, is one of the main components directly related to a wind turbine’s efficiency and lifespan. Therefore, strict control of the gearbox and its manufacturing processes and even minor improvements in this component strongly and positively [...] Read more.
The wind turbine gearbox, used as a multiplier, is one of the main components directly related to a wind turbine’s efficiency and lifespan. Therefore, strict control of the gearbox and its manufacturing processes and even minor improvements in this component strongly and positively impact energy production/generation over time. Since only some papers in the literature analyze the mechanical aspect of wind turbines, focusing on some parts in depth, this paper fills the gap by offering an analysis of the gearbox component under the highest amount of stress, namely relating to the sun shaft, as well as a more holistic analysis of the main gear drives, its components, and the lubrification system. Thus, this work diagnoses the fracture mechanics of a 1600 kW gearbox to identify the main reason for the fracture and how the chain of events took place, leading to catastrophic failure. The diagnoses involved numerical simulation (finite element analysis—FEA) and further analysis of the lubrication system, bearings, planetary stage gears, helical stage gears, and the high-speed shaft. In conclusion, although the numerical simulation showed high contact stresses on the sun shaft teeth, the region with the unexpectedly nucleated crack was the tip of the tooth. The most likely factors that led to premature failure were the missed lubrication for the planetary bearings, a lack of cleanliness in regard to the raw materials of the gears (voids found), and problems with the sun shaft heat treatment. With the sun gear’s shaft, planet bearings, and planet gears broken into pieces, those small and large pieces dropped into the oil, between the gears, and into the tooth ring, causing the premature and catastrophic gearbox failure. Full article
(This article belongs to the Special Issue Design and Analysis of Offshore Wind Turbines)
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<p>Gearbox dimensions (mm)—weight {160,000 NJ].</p>
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<p>Schematic of a wind turbine gearbox.</p>
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<p>Sun shaft—first stage planet (dimensions in mm).</p>
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<p>Maximum von Mises stress (MPa).</p>
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<p>Profile of von Mises stress localized on the tooth.</p>
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<p>Profile of von Mises stress localized at ½ length in the tooth.</p>
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<p>First principal stress on tooth.</p>
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<p>Third principal stress on tooth.</p>
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<p>Distribution of von Mises stress along the sun shaft.</p>
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<p>The lubrication system (<b>left</b>) foams into the oil (<b>mid</b>), and the coupling spider is slatted (<b>right</b>).</p>
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<p>High-speed shaft teeth.</p>
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<p>Low-speed gear.</p>
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<p>View of the HSS and Intermediate helical gear engagement.</p>
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<p>Intermediate shaft.</p>
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<p>View of the planet gear bearing.</p>
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<p>Sun shaft—upper arrow shows crack propagation/lower arrow shows core separation.</p>
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<p>Sun shaft—arrows show material separation.</p>
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<p>Sun shaft.</p>
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<p>Planet gears.</p>
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<p>Ring gear.</p>
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<p>Ring gear teeth. Two different regions close to the bottom of the tooth ring. Position when assembled.</p>
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<p>Ring gear teeth. Two different regions at the bottom of the tooth ring. Position when assembled.</p>
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16 pages, 6662 KiB  
Article
Study on the Influence of Notched Empty Hole Parameters on Directional Fracture Blasting Effect
by Xiantang Zhang, Rongyan Ma, Yong Yang, Tonghua Fu, Yubing Tian, Haibo Yan, Deqing Wang, Xiangtuan Jiao and Hongmin Zhou
Buildings 2024, 14(12), 4077; https://doi.org/10.3390/buildings14124077 - 22 Dec 2024
Viewed by 615
Abstract
Placing empty holes between charging holes is widely used in blasting engineering to achieve directional fracture blasting. Studies have shown that the presence of a notch along the empty hole wall enhances stress concentration and supports improved control over crack propagation. The notch [...] Read more.
Placing empty holes between charging holes is widely used in blasting engineering to achieve directional fracture blasting. Studies have shown that the presence of a notch along the empty hole wall enhances stress concentration and supports improved control over crack propagation. The notch angle and length are the two main parameters influencing the impact of notch holes. Therefore, in this study, we used numerical simulations to investigate how varying notch angles and lengths influence the directional fracture blasting effect. The findings suggest that, among the different types of holes used in directional fracture rock blasting, notched empty holes have the most significant guiding effect, followed by empty holes, while the absence of empty holes yields the least effective results. In the directional fracture blasting of a notched empty hole, stress concentration occurs at the notch tip following the explosion. This alters the stress field distribution around the empty hole, which shifts from a compressive to a tangential tensile state. Additionally, this concentration of stress causes the explosion energy to be focused on that location, resulting in a directional fracture blasting effect. In blasting construction, selecting the appropriate notch hole parameters is necessary to achieve optimal effects and reduce damage to surrounding rocks. Based on the notch parameters assessed in this study, the optimal effect of directional fracture blasting is achieved when the notch angle is 30°. Full article
(This article belongs to the Special Issue The Damage and Fracture Analysis in Rocks and Concretes)
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<p>Schematic diagram of stress concentration effect of empty hole.</p>
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<p>Schematic diagram of the numerical calculation model.</p>
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<p>A comparative analysis of the simulation results and the test results. (<b>a</b>) Single-hole experiment results [<a href="#B40-buildings-14-04077" class="html-bibr">40</a>]; (<b>b</b>) simulation result of single-hole; (<b>c</b>) notched empty hole test results [<a href="#B41-buildings-14-04077" class="html-bibr">41</a>]; (<b>d</b>) simulation result of notched empty hole.</p>
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<p>A comparative analysis of the simulation results and the test results. (<b>a</b>) Single-hole experiment results [<a href="#B40-buildings-14-04077" class="html-bibr">40</a>]; (<b>b</b>) simulation result of single-hole; (<b>c</b>) notched empty hole test results [<a href="#B41-buildings-14-04077" class="html-bibr">41</a>]; (<b>d</b>) simulation result of notched empty hole.</p>
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<p>The evolution of crack propagation during double-hole blasting. (<b>a</b>) No empty hole; (<b>b</b>) common empty holes; (<b>c</b>) notched empty hole.</p>
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<p>Simulation results under different operating conditions. (<b>a</b>) Conditions A1–D1; (<b>b</b>) Conditions A2–D2; (<b>c</b>) Conditions A3–D3.</p>
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<p>Main crack propagation process diagram. (<b>a</b>–<b>c</b>) Condition B2; (<b>d</b>–<b>f</b>) Condition C2.</p>
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<p>Stress wave propagation diagram. (<b>a</b>,<b>b</b>) Condition B2; (<b>c</b>,<b>d</b>) Condition C2.</p>
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<p>Stress wave propagation diagram. (<b>a</b>,<b>b</b>) Condition B2; (<b>c</b>,<b>d</b>) Condition C2.</p>
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<p>Wing-shaped crack propagation diagram. (<b>a</b>–<b>c</b>) Condition C1; (<b>d</b>–<b>f</b>) Condition D1.</p>
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<p>Stress wave propagation diagram. (<b>a</b>) Condition C1; (<b>b</b>) Condition D1.</p>
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<p>The layout of the measuring point.</p>
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<p>Peak effective stress variation diagram of different notch lengths. (<b>a</b>) <span class="html-italic">l</span> = 2.5 mm; (<b>b</b>) <span class="html-italic">l</span> = 5 mm; (<b>c</b>) <span class="html-italic">l</span> = 7.5 mm.</p>
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<p>The stress change diagram under different working conditions.</p>
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<p>Distribution range of rock with different damage degrees. (<b>a</b>) <span class="html-italic">D</span> &gt; 0.3; (<b>b</b>) <span class="html-italic">D</span> &gt; 0.4; (<b>c</b>) <span class="html-italic">D</span> &gt; 0.5.</p>
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<p>The rock damage area diagram under different working conditions.</p>
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22 pages, 16060 KiB  
Article
Study on the Dynamic Fracture Properties of Defective Basalt Fiber Concrete Materials Under a Freeze–Thaw Environment
by Guangzhao Pei, Dingjun Xiao, Miaomiao Zhang, Jiajie Jiang, Jiping Xie, Xiongzi Li and Junbo Guo
Materials 2024, 17(24), 6275; https://doi.org/10.3390/ma17246275 - 22 Dec 2024
Viewed by 567
Abstract
This study examines the crack resistance of basalt-fiber-reinforced concrete (BFRC) materials subjected to freeze–thaw cycles (FTCs). We utilized a φ50 mm Split Hopkinson Pressure Bar (SHPB) apparatus alongside numerical simulations to carry out impact compression tests at a velocity of 5 m/s on [...] Read more.
This study examines the crack resistance of basalt-fiber-reinforced concrete (BFRC) materials subjected to freeze–thaw cycles (FTCs). We utilized a φ50 mm Split Hopkinson Pressure Bar (SHPB) apparatus alongside numerical simulations to carry out impact compression tests at a velocity of 5 m/s on BFRC specimens that experienced 0, 10, 20, and 30 FTCs. Additionally, we investigated the effects of basalt fiber (BF) orientation position and length on stress intensity factors. The results reveal that with an increasing number of FTCs, the dynamic crack propagation speed of BFRC with a prefabricated crack inclined at 0° rises from 311.84 m/s to 449.92 m/s, while its pure I fracture toughness decreases from 0.6266 MPa·m0.5 to 0.4902 MPa·m0.5. For BFRC specimens with a prefabricated crack inclination of 15°, the dynamic crack propagation speed increases from 305.81 m/s to 490.02 m/s, accompanied by a reduction in mode I fracture toughness from 0.3901 MPa·m0.5 to 0.2867 MPa·m0.5 and mode II fracture toughness from 0.6266 MPa·m0.5 to 0.4902 MPa·m0.5. In the case of a prefabricated crack inclination of 28.89°, the dynamic crack propagation speed rises from 436.10 m/s to 494.28 m/s, while its pure mode II fracture toughness decreases from 1.1427 MPa·m0.5 to 0.7797 MPa·m0.5. Numerical simulations indicate that fibers positioned ahead of the crack tip—especially those that are longer, located closer to the crack tip, and oriented more perpendicularly—significantly reduce the mode I stress intensity factor. However, these fibers have a minimal impact on reducing the mode II stress intensity factor. The study qualitatively and quantitatively analyzes the crack resistance of basalt-fiber-reinforced concrete in relation to freeze–thaw cycles and the fibers ahead of the crack tip, offering insights into the fiber reinforcement effects within the concrete matrix. Full article
(This article belongs to the Special Issue Advances in Natural Rocks and Their Composite Materials)
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<p>Test setup and flow chart.</p>
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<p>The crack tip position and crack propagation speed of the specimen when the inclination angle of the precast crack is 0.</p>
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<p>The crack tip position and crack propagation speed of the specimen when the precast crack inclination angle is 15.</p>
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<p>The crack tip position and crack propagation speed of the specimen when the precast crack inclination angle is 28.89.</p>
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<p>The crack tip position and crack propagation speed of the specimen when the precast crack inclination angle is 28.89.</p>
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<p>Crack propagation path.</p>
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<p>Relationship between dynamic crack growth rate and FTC.</p>
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<p>SEM images of basalt fiber concrete with different freeze–thaw times.</p>
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<p>Numerical verification of Chen problem.</p>
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<p>Time history curve of stress intensity factor <span class="html-italic">K</span><sub>I</sub> when the inclination angle of the precast crack is 0.</p>
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<p>Time history curve of stress intensity factor <span class="html-italic">K</span><sub>I</sub> when the inclination angle of the precast crack is 15.</p>
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<p>Time history curve of stress intensity factor <span class="html-italic">K</span><sub>I</sub> when the inclination angle of the precast crack is 15.</p>
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<p>Time history curve of stress intensity factor <span class="html-italic">K</span><sub>II</sub> when the inclination angle of the precast crack is 15.</p>
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<p>Time history curve of stress intensity factor <span class="html-italic">K</span><sub>II</sub> when the inclination angle of the precast crack is 28.89.</p>
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<p>Fracture toughness of the Brazilian disc specimen with a straight crack platform in a dynamic fracture test center calculated by an experimental–numerical analysis method.</p>
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<p>Fiber distribution before crack tip.</p>
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<p>Stress intensity factors of concrete with different fiber lengths (<b>a</b>) <span class="html-italic">K</span><sub>I</sub> with a 0 inclination angle of precast crack; (<b>b</b>) <span class="html-italic">K</span><sub>II</sub> with a 28.89 inclination angle of precast crack; (<b>c</b>) <span class="html-italic">K</span><sub>I</sub> with a 15 inclination angle of precast crack; (<b>d</b>) <span class="html-italic">K</span><sub>II</sub> with a 15 inclination angle of precast crack.</p>
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<p>Force nephogram of fiber influence: (<b>a</b>) pure I stress nephogram; (<b>b</b>) pure II stress nephogram; (<b>c</b>) force nephogram of pure I fiber; (<b>d</b>) force nephogram of pure II fiber.</p>
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<p>Stress intensity factors of concrete under different fiber angles (<b>a</b>) <span class="html-italic">K</span><sub>I</sub> with a 0 inclination angle of precast crack; (<b>b</b>) <span class="html-italic">K</span><sub>II</sub> with a 28.89 inclination angle of precast crack; (<b>c</b>) <span class="html-italic">K</span><sub>I</sub> with a 15 inclination angle of precast crack; (<b>d</b>) <span class="html-italic">K</span><sub>II</sub> with a 15 inclination angle of precast crack.</p>
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<p>Force nephogram influenced by fiber angle: (<b>a</b>) pure I 0-degree fiber stress nephogram; (<b>b</b>) pure I 40-degree fiber stress nephogram; (<b>c</b>) pure II 0-degree fiber stress nephogram; (<b>d</b>) pure II 40-degree fiber stress nephogram.</p>
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<p>Stress intensity factors of concrete under different fiber positions: (<b>a</b>) <span class="html-italic">K</span><sub>I</sub> with a 0 inclination angle of the precast crack; (<b>b</b>) <span class="html-italic">K</span><sub>II</sub> with a 28.89 inclination angle of the precast crack; (<b>c</b>) <span class="html-italic">K</span><sub>I</sub> with a 15 inclination angle of the precast crack; (<b>d</b>) <span class="html-italic">K</span><sub>II</sub> with 15 inclination angle of the precast crack.</p>
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<p>Fiber position affects the force nephogram: (<b>a</b>) force nephogram of pure I short-distance fiber; (<b>b</b>) force nephogram of pure I long-distance fiber; (<b>c</b>) force nephogram of pure II short-distance fiber; (<b>d</b>) force nephogram of pure II long-distance fiber.</p>
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17 pages, 2640 KiB  
Article
An Expanded Wing Crack Model for Fracture and Mechanical Behavior of Sandstone Under Triaxial Compression
by Esraa Alomari, Kam Ng and Lokendra Khatri
Materials 2024, 17(23), 5973; https://doi.org/10.3390/ma17235973 - 6 Dec 2024
Viewed by 610
Abstract
A new model is developed to predict the mechanical behavior of brittle sandstone under triaxial compression. The proposed model aims to determine the normalized critical crack length (Lcr), through which the failure strength (σf) of sandstone [...] Read more.
A new model is developed to predict the mechanical behavior of brittle sandstone under triaxial compression. The proposed model aims to determine the normalized critical crack length (Lcr), through which the failure strength (σf) of sandstone can be estimated based on fracture mechanics applied to secondary cracks emanating from pre-existing flaws, while considering the interaction of neighboring cracks. In this study, the wing crack model developed by Ashby and Hallam (1986) was adopted to account for the total stress intensity at the crack tip (KI) as the summation of the stress intensity due to crack initiation and crack interaction. The proposed model is developed by first deriving the Lcr and then setting the crack length equal to the Lcr. Next, the total stress intensity is set equal to the rock fracture toughness in the original equation of KI, resulting in an estimate of the σf. Finally, to evaluate the performance of the proposed model on predicting σf, theoretical results are compared with laboratory data obtained on sandstone formations collected from Wyoming and the published literature. Moreover, the σf predicted by our proposed model is compared with those predicted from other failure criteria from the literature. The comparison shows that the proposed model better predicts the rock failure strength under triaxial compression, based on the lowest RMSE and MAD values of 36.95 and 30.93, respectively. Full article
(This article belongs to the Special Issue Advances in Rock and Mineral Materials)
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<p>(<b>a</b>) Triaxial testing system at the University of Wyoming, and (<b>b</b>) Tested specimen.</p>
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<p>Axial, radial, and volumetric strain curves for Arikaree sandstone.</p>
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<p>Measured strength versus predicted for (<b>a</b>) our proposed model, (<b>b</b>) HB criterion, (<b>c</b>) Griffith criterion, (<b>d</b>) Renshaw and Schulson criterion, and (<b>e</b>) Wiebols and Cook criterion.</p>
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<p>Measured to predicted strength ratio versus confining pressure [<a href="#B37-materials-17-05973" class="html-bibr">37</a>,<a href="#B38-materials-17-05973" class="html-bibr">38</a>,<a href="#B39-materials-17-05973" class="html-bibr">39</a>].</p>
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<p>Microcracks emanating from pre-existing flaws.</p>
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<p>Relationship between the failure strength and normalized critical crack length.</p>
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<p>Relationship between the normalized critical crack length and stress ratio under constant damage levels.</p>
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19 pages, 4996 KiB  
Article
Experimental Study on the Size Effect of Compression-Shear Fracture Characteristics of Rock-like Materials Containing Open Cracks
by Zixuan Li, Shiyuan Huang, Chuan Lv, Cheng Liao, Xudong Li and Hongbo Du
Materials 2024, 17(23), 5941; https://doi.org/10.3390/ma17235941 - 4 Dec 2024
Viewed by 583
Abstract
Understanding fracture mechanics in rock-like materials under compression-shear condition is critical for predicting failure mechanisms in various engineering applications, such as mining and civil infrastructure. This study conducted uniaxial compression tests on cubic gypsum specimens of varying sizes (side lengths of 75 mm, [...] Read more.
Understanding fracture mechanics in rock-like materials under compression-shear condition is critical for predicting failure mechanisms in various engineering applications, such as mining and civil infrastructure. This study conducted uniaxial compression tests on cubic gypsum specimens of varying sizes (side lengths of 75 mm, 100 mm, 125 mm, and 150 mm) and crack inclination angles (ranging from 0° to 90°) to assess the size effect on fracture behavior. The effects of specimen size and crack inclination on fracture characteristics, including strength, failure mode, and crack initiation angle, were analyzed based on the maximum tangential stress (MTS) criterion and the generalized maximum tangential stress (GMTS) criterion, with relative critical size (α) and relative openness (η). Results indicate that the crack initiation angle increases with crack inclination, while compressive strength decreases significantly with increasing specimen size. For example, at a 30° crack inclination, the peak compressive strength of 75 mm specimens was 2.53 MPa, whereas that of 150 mm specimens decreased to 1.05 MPa. Crack type and failure mode were found to be primarily influenced by crack inclination rather than specimen size. The experimental crack initiation angle aligned with the theoretical crack initiation angle at inclinations below 50° but diverged at higher inclinations. A linear relationship was established between rc and specimen size (L) under compression-shear stress, expressed as rc=0.01772L+3.54648; larger specimens exhibited increased tangential stress at the crack tip, leading to earlier macroscopic crack formation, while rc decreased as specimen size increased. These results underscore the significant influence of size on fracture behavior in quasi-brittle materials under compression-shear stress, providing essential insights for predicting material failure in rock-like structures. Full article
(This article belongs to the Topic Sustainable Building Materials)
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<p>Gypsum specimen preparation device and prepared specimens: (<b>a</b>) the assembled device for preparing gypsum specimens with open cracks; (<b>b</b>) gypsum specimens of different sizes and open cracks.</p>
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<p>Specimen loading and failure patterns: (<b>a</b>) the condition of the specimen during the initial loading stage; (<b>b</b>) the condition of the specimen at final failure.</p>
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<p>Stress state of the open crack on the upper surface.</p>
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<p>Stress fields at crack tip.</p>
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<p>Stress–strain curves of open crack specimens.</p>
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<p>Stress–strain curves of open crack specimens.</p>
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<p>Crack inclusion and uniaxial compressive strength curves of gypsum specimens of different sizes.</p>
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<p>Typical failure characteristics of open crack specimens: (<b>a</b>) when <span class="html-italic">β</span> = 50°, with specimen sizes ranging from 75 mm to 150 mm; (<b>b</b>) when <span class="html-italic">L</span> = 75 mm, with <span class="html-italic">β</span> ranging from 0° to 90°.</p>
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<p>Influence of <span class="html-italic">β</span> on <span class="html-italic">θ</span> in gypsum specimens of different sizes.</p>
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<p>GMTS tension crack initiation angle prediction curves and average test data for gypsum specimens with different <span class="html-italic">η</span> values.</p>
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<p>The relationship between <span class="html-italic">α</span> and <math display="inline"><semantics> <mrow> <msub> <mrow> <msub> <mrow> <mo>(</mo> <mi>σ</mi> </mrow> <mrow> <mi mathvariant="sans-serif">θ</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math>/<span class="html-italic">σ</span> with different <span class="html-italic">β</span>.</p>
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<p></p>
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16 pages, 17582 KiB  
Article
An In Situ Study of Short Crack Initiation and Propagation During Fatigue Testing of a Hot Isostatically Pressed Al-7%Si-0.5%Mg (A357-T6) Alloy Specimen
by Toni Bogdanoff and Murat Tiryakioğlu
Materials 2024, 17(23), 5928; https://doi.org/10.3390/ma17235928 - 4 Dec 2024
Viewed by 784
Abstract
A hot isostatically pressed specimen of the A357 alloy in T6 condition has been tested for fatigue performance in situ. During testing, multiple small cracks were observed during the first cycle, both in proximity to and far from the stress concentration. These cracks [...] Read more.
A hot isostatically pressed specimen of the A357 alloy in T6 condition has been tested for fatigue performance in situ. During testing, multiple small cracks were observed during the first cycle, both in proximity to and far from the stress concentration. These cracks have competed to form a propagating crack, forming multiple crack paths initially. Once the propagating crack has been established, it has chosen paths from multiple cracks that have opened around the tip to grow further. All small cracks observed to open have been attributed to bifilms, i.e., liquid metal damage. It is imperative to develop processes that minimize liquid metal damage to enhance the fatigue performance of aluminum alloy castings. Full article
(This article belongs to the Special Issue Fatigue Crack Growth in Metallic Materials (Volume II))
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<p>(<b>a</b>) Dimensions of the CT sample in mm [<a href="#B17-materials-17-05928" class="html-bibr">17</a>]; (<b>b</b>) miniature stage for in situ cyclic tests [<a href="#B17-materials-17-05928" class="html-bibr">17</a>]; (<b>c</b>) FOV of the A357 sample.</p>
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<p>Microstructure of the A357 specimen. The arrow indicates a Fe-bearing intermetallic particle.</p>
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<p>The specimen after the 1st cycle showed multiple cracks in the specimen and no crack connected to the stress concentrator.</p>
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<p>Cracks on the surface of the specimen after N = 16. Note that Cracks 3 and 6 in <a href="#materials-17-05928-f002" class="html-fig">Figure 2</a> have now merged.</p>
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<p>Cracks on the surface of the specimen after N = 100.</p>
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<p>Cracks on the surface of the specimen after N = 143. Cracks 3, 6 and 8 in <a href="#materials-17-05928-f002" class="html-fig">Figure 2</a> have coalesced.</p>
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<p>Cracks on the surface of the specimen after N = 215. Two side branches in the main crack and two new cracks ahead of the crack tip have become visible.</p>
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<p>Cracks on the surface of the specimen after N = 254. Multiple cracks around the crack tip are readily visible.</p>
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<p>The crack and its tip at N = 300. Multiple cracks are opening around the crack tip.</p>
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<p>The crack and its tip at N = 310. Multiple cracks are opening up in front as well as on the right and left of the crack tip.</p>
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<p>The crack and its tip just before the final fracture at N = 362. The crack tip has split into three branches.</p>
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<p>The crack after the final fracture.</p>
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<p>The details of the area within the box are in <a href="#materials-17-05928-f011" class="html-fig">Figure 11</a>. The small cracks seem to have taken place in the matrix as well.</p>
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<p>Cracked Fe-bearing particles were found on the fracture surface.</p>
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<p>EDS maps for (<b>a</b>) Fe, (<b>b</b>) Si and (<b>c</b>) Mg in the same area as in <a href="#materials-17-05928-f014" class="html-fig">Figure 14</a>.</p>
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<p>A feature on the fracture surface away from the notch.</p>
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<p>EDS map showing where Fe atoms are densely located.</p>
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<p>EDS point analysis of an area that opened during crack propagation.</p>
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20 pages, 10274 KiB  
Article
High-Cycle Fatigue Fracture Behavior and Stress Prediction of Ni-Based Single-Crystal Superalloy with Film Cooling Hole Drilled Using Femtosecond Laser
by Zhen Li, Yuanming Xu, Xinling Liu, Changkui Liu and Chunhu Tao
Metals 2024, 14(12), 1354; https://doi.org/10.3390/met14121354 - 27 Nov 2024
Viewed by 671
Abstract
A high-temperature, high-cycle fatigue test was conducted on a nickel-based single-crystal superalloy with a pore structure. Optical and scanning electron microscopy were utilized to examine the crack propagation paths and fatigue fracture surfaces at the macro and micro scales. The analysis of crack [...] Read more.
A high-temperature, high-cycle fatigue test was conducted on a nickel-based single-crystal superalloy with a pore structure. Optical and scanning electron microscopy were utilized to examine the crack propagation paths and fatigue fracture surfaces at the macro and micro scales. The analysis of crack initiation and propagation related to the pore structure facilitated the development of a crack shape factor reflecting these distinct fracture behaviors. Predictions about the high-cycle fatigue stress experienced by the specimen were made, accompanied by an error analysis, providing critical insights for precise stress calculations and structural optimization in engine blade design. The results reveal that high-cycle fatigue cracks originate from corner cracks at pore edges, with the initial propagation displaying smooth crystallographic plane features. Subsequent stages show clear fatigue arc patterns in the propagation zones. The fracture surface exhibits the significant layering of oxide layers, primarily composed of NiO, with traces of CoO displaying columnar growth. AL2O3 is predominantly found at the interfaces between the matrix and oxide layers. Short and straight dislocations near the oxide layers and within the matrix suggest that dislocation multiplication and planar slip dominate the slip mechanisms in this alloy. The orientation of the fracture surface is mainly perpendicular to the load direction, with minor inclined facets in localized areas. Correlations were established between the plastic zone dimensions at the crack tips and the corresponding fatigue stresses. Without grain boundaries in single-crystal alloys, these dimensions are easily derived as parameters for fatigue stress analysis. The selected crack shape factor, “elliptical corner crack at pore edges”, captures the initiation and propagation traits relevant to porous structures. Subsequent calculations, accounting for the impact of oxide layers on stress assessments, indicated an error ratio ranging from 1.00 to 1.21 compared to nominal stress values. Full article
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<p>Microstructural characteristics of enhanced phase (γ′-Ni<sub>3</sub>Al) morphology.</p>
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<p>(<b>a</b>) Structural morphology of pore walls in aerogel; (<b>b</b>) morphological characteristics of pore edge structure.</p>
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<p>(<b>a</b>) Geometrical dimensions of high-cycle fatigue specimens (all dimensions are in mm); (<b>b</b>) schematic diagram of the vibration excitation system; (<b>c</b>) monitoring position (red dot) and strain gauge position (yellow square) of the laser displacement sensor.</p>
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<p>High-cycle fatigue life of specimens with perforations compared to those without perforations (specimens marked in yellow for stress prediction analysis).</p>
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<p>(<b>a</b>) Microstructural characteristics of cross-section of M9; (<b>b</b>) Microstructural characteristics of cross-section of M1; (<b>c</b>) Microstructural characteristics of cross-section of M4.</p>
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<p>(<b>a</b>) Microstructural characteristics of the cross-section of M9; (<b>b</b>) Microstructural characteristics of the cross-section of M1; (<b>c</b>) Microstructural characteristics of the cross-section of M4.</p>
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<p>(<b>a</b>) Analysis of the morphologies of oxidized particles (The yellow box shows the EDS analysis area); (<b>b</b>) Euler angle results of oxidized particles (Different colors represent different grain orientations).</p>
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<p>(<b>a</b>) Back to bottom plot of HAADF elemental analysis; (<b>b</b>) Elemental distribution map.</p>
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<p>Characteristics of dislocation morphology.</p>
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<p>Schematic representation of the plastic deformation zone at the crack tip.</p>
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<p>Schematic representation of the EBSD sample preparation procedure.</p>
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<p>Results and data analysis of the KAM experiment.</p>
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<p>(<b>a</b>) Schematic representation of the elliptical corner crack model; (<b>b</b>) crack extension direction versus θ angle definition plot; (<b>c</b>) the cross-section of a high-cycle simulation specimen.</p>
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<p>Meshing and convergence study of M4 specimens.</p>
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<p>Finite element analysis of stress distribution at the chip placement interface of the M4 specimen (red marked positions).</p>
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<p>Stress along the crack propagation path for the M4 specimen.</p>
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