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Metals
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Studies on Fatigue Behavior of Engineering Material and Structures
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Studies on Fatigue Behavior of Engineering Material and Structures

A special issue of Metals (ISSN 2075-4701). This special issue belongs to the section "Metal Failure Analysis".

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 10532

Special Issue Editors

Dr. Fang Wang

E-Mail Website
Guest Editor
College of Engineering Science and Technology, Shanghai Ocean University, No.999, Hucheng Huan Road, Shanghai 201306, China
Interests: submersible structures; fatigue of ships and marine structures; ultimate strength of ships and marine structures
Special Issues, Collections and Topics in MDPI journals
Dr. Yu Wu

E-Mail Website
Guest Editor
College of Engineering, Shanghai Ocean University, Shanghai, China
Interests: offshore engineering equipment design; performance analysis; structural damage detection technology; intelligent integrated inspection technology; intelligent sensor technology; intelligent equipment condition monitoring; fault diagnosis technology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Structural fatigue is a failure mode of particular concern in the engineering field. Fatigue behavior is affected by many factors, such as material, structure, environment, load, and so on. With the continuous application of new materials in engineering and the improvement of requirements for structural safety and reliability, fatigue theory, simulation/testing methods, and their application in engineering structure design are currently under development. The goal of this Special Issue is to give an exhaustive overview of new trends in the particular field by inviting researchers and engineers to contribute a series of articles, including reviews and original research. Theoretical, experimental, and computational studies on (but not limited to) the following topics are encouraged for this Special Issue:

  • Fatigue behavior of engineering materials;
  • Effect of microstructure and defects on fatigue behavior;
  • Fatigue failure mechanism;
  • New theories of fatigue models;
  • Crack initiation, growth, and final fracture;
  • Fatigue testing of engineering structures;
  • Fatigue resistance related to design and manufacturing;
  • Modeling of fatigue and fracture process;
  • Fatigue design and guidelines of engineering structures.

Prof. Dr. Fang Wang
Dr. Yu Wu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Metals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (5 papers)

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Research

13 pages, 10691 KiB  
Article
Creep of High-Strength Steel Coated with Plasma Sprayed Self-Fluxing Alloy
by Denison A. Moraes, Gisele F. C. Almeida, Antonio A. Couto, Marcos Massi, Felipe R. Caliari and Carlos R. C. Lima
Metals 2023, 13(4), 763; https://doi.org/10.3390/met13040763 - 14 Apr 2023
Cited by 2 | Viewed by 1784
Abstract
This article compares the creep testing behavior of AISI 4340 high-strength steel in the as-received and coated conditions. The coating material used was a NiCrBSi self-fluxing alloy. The microstructural characterization was carried out using optical and scanning electron microscopy. The creep tests were [...] Read more.
This article compares the creep testing behavior of AISI 4340 high-strength steel in the as-received and coated conditions. The coating material used was a NiCrBSi self-fluxing alloy. The microstructural characterization was carried out using optical and scanning electron microscopy. The creep tests were conducted at a temperature of 550 °C and with loads of 200, 250, and 300 MPa. The microstructure analysis of the deposited layer revealed some inclusions, very low porosity, and good adhesion to the substrate. The results of the creep tests indicated a decrease in the time to rupture under loads of 250 and 300 MPa for the coated steel. At a load of 200 MPa, the coated steel presented longer times to rupture and higher yield strength, demonstrating an improvement over the uncoated steel under these test condition. The fracture surface inspection showed a failure by a ductile fracture in both samples, with and without coating. Full article
(This article belongs to the Special Issue Studies on Fatigue Behavior of Engineering Material and Structures)
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Figure 1

Figure 1
<p>Creep test sample according to ASTM E139-11 (dimensions in mm).</p> Full article ">Figure 2
<p>Samples for creep testing (<b>a</b>) as received and (<b>b</b>) coated.</p> Full article ">Figure 3
<p>Optical microscopy image of the cross-section of the coating.</p> Full article ">Figure 4
<p>Optical image of AISI 4340 microstructure as received.</p> Full article ">Figure 5
<p>SEM image of the microstructure of AISI 4340 steel after coating process.</p> Full article ">Figure 6
<p>Creep curves at 550 °C/200 MPa.</p> Full article ">Figure 7
<p>Creep curves at 550 °C/250 MPa.</p> Full article ">Figure 8
<p>Creep curves at 550 °C/300 MPa.</p> Full article ">Figure 9
<p>Images of the fracture surface of the uncoated specimen at 550 °C with the stress of (<b>a</b>) 200 MPa, (<b>b</b>) 250 MPa, and (<b>c</b>) 300 MPa.</p> Full article ">Figure 10
<p>The fracture surface of the coated sample at 550 °C and 200 MPa: (<b>a</b>) full section, (<b>b</b>) enlargement of the upper right side, (<b>c</b>) detail of the partial coating detachment, (<b>d</b>) detail of the adhered coating.</p> Full article ">Figure 11
<p>The fracture surface of the coated sample at 550 °C and 250 MPa: (<b>a</b>) full section, (<b>b</b>) enlargement of the upper right side, (<b>c</b>) detail of the partial coating detachment, (<b>d</b>) detail of the full adhered coating.</p> Full article ">Figure 12
<p>The fracture the surface of the coated sample at 550 °C and 300 MPa: (<b>a</b>) full section with completely detached coating, (<b>b</b>) enlargement of the left side, (<b>c</b>) detail of the coating characteristic microstructure.</p> Full article ">Figure 13
<p>Optical longitudinal cross section images of the coated sample at 550 °C and 300 MPa showing the adhesion of the coating to the substrate and some fractures of the coating at (<b>a</b>) left side, (<b>b</b>) center-left, (<b>c</b>) center-right, (<b>d</b>) right side.</p> Full article ">Figure 14
<p>Cross sectional longitudinal optical images of the tested sample with the oxide layer formed on the substrate.</p> Full article ">
13 pages, 5382 KiB  
Article
Three-Dimension Crack Propagation Behavior of Conical-Cylindrical Shell
by Yongmei Zhu, Jiahao Yang and Hongzhang Pan
Metals 2023, 13(4), 698; https://doi.org/10.3390/met13040698 - 3 Apr 2023
Cited by 3 | Viewed by 1869
Abstract
The conical-cylindrical shell is prone to stress concentration in the convex cone position under the action of deep-sea pressures. This results in unidirectional or bidirectional positive tensile stresses on the surfaces of the shell. The conical-cylindrical shell is a large, welded structure. Welding [...] Read more.
The conical-cylindrical shell is prone to stress concentration in the convex cone position under the action of deep-sea pressures. This results in unidirectional or bidirectional positive tensile stresses on the surfaces of the shell. The conical-cylindrical shell is a large, welded structure. Welding residual stress was generated at the cone-column joint position, resulting in high-stress concentration at this location. Under both the residual stress of welding and seawater pressure, cracks easily form and propagate on the shell weld toe, leading to fatigue damage and even structural failure. In this paper, based on the seawater’s alternating load and the residual stress of welding, the three-dimensional crack propagation process was studied for the submarine conical-cylindrical shell. The effects of crack depth and shape ratio on crack propagation trend and fatigue life were analyzed. The results can provide references for predicting the crack propagation trend, assessing the remaining life and evaluating the structural safety of the submarine conical-cylindrical shell. Full article
(This article belongs to the Special Issue Studies on Fatigue Behavior of Engineering Material and Structures)
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Figure 1

Figure 1
<p>Submarine pressure hull.</p> Full article ">Figure 2
<p>Conical-cylindrical shell model. (<b>a</b>) Geometric model (<b>b</b>) Numerical model.</p> Full article ">Figure 3
<p>The distribution of residual stresses.</p> Full article ">Figure 4
<p>(<b>a</b>,<b>b</b>) Schematic diagram of equivalent thickness.</p> Full article ">Figure 5
<p>New crack front after fitting.</p> Full article ">Figure 6
<p>The location of the crack in the model.</p> Full article ">Figure 7
<p>The maximum value of different cracks, <span class="html-italic">K</span><sub>I</sub>.</p> Full article ">Figure 8
<p>Variation of shape ratio during crack propagation.</p> Full article ">Figure 9
<p>Change of crack surface during crack propagation.</p> Full article ">Figure 10
<p>The <span class="html-italic">a</span>-<span class="html-italic">N</span> curve of the conical-cylindrical shell.</p> Full article ">Figure 11
<p>Variation of shape ratio during crack propagation.</p> Full article ">Figure 12
<p>Change of crack surface during crack propagation.</p> Full article ">Figure 13
<p>The <span class="html-italic">a</span>-<span class="html-italic">N</span> curve of conical-cylindrical shell.</p> Full article ">
12 pages, 5588 KiB  
Article
Fatigue Limit Improvement and Rendering Surface Defects Harmless by Shot Peening for Carburized Steel
by Toshiya Tsuji, Masashi Fujino and Koji Takahashi
Metals 2023, 13(1), 42; https://doi.org/10.3390/met13010042 - 23 Dec 2022
Cited by 6 | Viewed by 2068
Abstract
Remanufacturing has become popular as a system for reducing CO2 emissions caused by the life cycle of products. Therefore, producing more components via remanufacturing is important. Shot peening can be used to render surface defects harmless owing to the compressive residual stress [...] Read more.
Remanufacturing has become popular as a system for reducing CO2 emissions caused by the life cycle of products. Therefore, producing more components via remanufacturing is important. Shot peening can be used to render surface defects harmless owing to the compressive residual stress effects. This study investigated the effects of shot peening as a means of remanufacturing gears. In this study, carburized steel specimens containing artificial defects were used to investigate the effects of shot peening on the fatigue strength; the defect size was rendered harmless by shot peening. Shot peening was conducted after inducing semicircular slits with depths of a = 0.15, 0.20, and 0.30 mm. Subsequently, plane bending fatigue tests were carried out. A maximum compressive residual stress of 1400 MPa was induced after shot peening. The fatigue limit of the smooth specimen increased by approximately 31% after shot peening. A semicircular slit of at least 0.20 mm deep could be rendered harmless by shot peening (SP). The defect size reduced by SP was evaluated on the basis of fracture mechanics. The estimated results are consistent with the experimental results. On the basis of the results, the feasibility of shot peening as a remanufacturing method for gears is discussed. Full article
(This article belongs to the Special Issue Studies on Fatigue Behavior of Engineering Material and Structures)
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Figure 1

Figure 1
<p>Shape and dimensions of the specimen (mm).</p> Full article ">Figure 2
<p>Flow chart of the specimen manufacturing process.</p> Full article ">Figure 3
<p>Microstructure after vacuum carburizing quenching and tempering near the surface.</p> Full article ">Figure 4
<p>Shapes and dimensions of the artificial defect.</p> Full article ">Figure 5
<p>Distribution of Vickers hardness.</p> Full article ">Figure 6
<p>Distribution of residual stress.</p> Full article ">Figure 7
<p>Fatigue test results. (<b>a</b>) Smooth, (<b>b</b>) Slit depth <span class="html-italic">a</span> = 0.15 mm, (<b>c</b>) Slit depth <span class="html-italic">a</span> = 0.20 mm, (<b>d</b>) Slit depth <span class="html-italic">a</span> = 0.30 mm.</p> Full article ">Figure 7 Cont.
<p>Fatigue test results. (<b>a</b>) Smooth, (<b>b</b>) Slit depth <span class="html-italic">a</span> = 0.15 mm, (<b>c</b>) Slit depth <span class="html-italic">a</span> = 0.20 mm, (<b>d</b>) Slit depth <span class="html-italic">a</span> = 0.30 mm.</p> Full article ">Figure 8
<p>Fracture surface observation results of smooth specimens.</p> Full article ">Figure 9
<p>Fracture surface observation results of slit specimens.</p> Full article ">Figure 10
<p>Relationship between stress amplitude and slit depth.</p> Full article ">Figure 11
<p>Relationship between stress intensity factor range and depth from the surface.</p> Full article ">Figure 12
<p>Flowchart of remanufacturing process with shot peening.</p> Full article ">
16 pages, 7709 KiB  
Article
Residual Stress Properties of the Welded Thick Underwater Spherical Pressure Hull Based on Finite Element Analysis
by Fang Wang, Pinpin Kong, Zhongzhou Sun, Jinfei Zhang, Fengluo Chen, Yu Wu and Yongmei Wang
Metals 2022, 12(11), 1958; https://doi.org/10.3390/met12111958 - 16 Nov 2022
Cited by 4 | Viewed by 2072
Abstract
Residual stress inevitably occurs at the weld in the process of manufacturing thick pressure hulls for manned submersibles, which affects the bearing capacity of the hull. In this study, an electron-beam-welded 32 mm-thick Ti-6Al-4V plate specimen is first tested, then the measured data [...] Read more.
Residual stress inevitably occurs at the weld in the process of manufacturing thick pressure hulls for manned submersibles, which affects the bearing capacity of the hull. In this study, an electron-beam-welded 32 mm-thick Ti-6Al-4V plate specimen is first tested, then the measured data of residual stress distribution is applied to validate the accuracy of the simulation method. Accordingly, three-dimensional numerical analysis on the equator welding by electron beam method of a 32 mm-thick Ti-6Al-4V spherical pressure hull is conducted to obtain the variation tendency of residual stress during the welding process. The results indicate that both compressive and tensile stresses exist along the weld path on the outer surface of the hull comparing to total tensile stresses on the inner surface. The maximum tensile stress that occurs on the inner surface approximates to 850 MPa, which is almost equivalent to the yield stress of the material. Based on the acceptance criterion that the peak value of residual stress due to weld technique is restricted to be less than 40% of the material yield strength in room temperature, post-weld heat treatment must be performed. Simulation on post-weld heat treatment for optimizing process parameters can be done by taking the results of welding simulation in the present study as input. Full article
(This article belongs to the Special Issue Studies on Fatigue Behavior of Engineering Material and Structures)
►▼ Show Figures

Figure 1

Figure 1
<p>Manned cabin of 10,000 m-class submersible made in China: (<b>a</b>) actual photograph, (<b>b</b>) structure of the spherical pressure hull of the manned cabin with outside frame for heat treatment, and (<b>c</b>) distribution of welding on spherical pressure hull of the manned cabin.</p> Full article ">Figure 2
<p>Electron beam welding of 32 mm-thick Ti-6Al-4V plate.</p> Full article ">Figure 3
<p>Measured data of longitudinal residual stress along vertical weld path.</p> Full article ">Figure 4
<p>Residual stress simulation flowchart.</p> Full article ">Figure 5
<p>Conical heat source model.</p> Full article ">Figure 6
<p>Meshing of the finite element model.</p> Full article ">Figure 7
<p>Shape of the weld pool compared to the experimental result.</p> Full article ">Figure 8
<p>Temperature field distributions (<b>a</b>) on the weld surface when <span class="html-italic">t</span> = 6 s, (<b>b</b>) in the direction perpendicular to the weld when <span class="html-italic">t</span> = 6 s, and (<b>c</b>) on the weld surface when <span class="html-italic">t</span> = 10 s.</p> Full article ">Figure 9
<p>Thermal cycle curve of typical node on the path vertical to the weld.</p> Full article ">Figure 10
<p>Comparison between simulation and test results of longitudinal residual stress along vertical weld path.</p> Full article ">Figure 11
<p>Meshing of the spherical pressure hull model.</p> Full article ">Figure 12
<p>Coordinate system for equator welding simulation.</p> Full article ">Figure 13
<p>Trajectory of heat source centre.</p> Full article ">Figure 14
<p>Conversion of coordinate systems.</p> Full article ">Figure 15
<p>Temperature fields of (<b>a</b>) weld section when <span class="html-italic">t</span> = 4 s, (<b>b</b>) weld section when <span class="html-italic">t</span> = 12 s, (<b>c</b>) spherical pressure hull when <span class="html-italic">t</span> = 4 s, and (<b>d</b>) spherical pressure hull when <span class="html-italic">t</span> = 12 s.</p> Full article ">Figure 16
<p>Enlarged temperature field of the spherical pressure hull when <span class="html-italic">t</span> = 12 s.</p> Full article ">Figure 17
<p>Longitudinal residual stress along the vertical weld path on the outer surface of the spherical pressure hull.</p> Full article ">Figure 18
<p>Transverse residual stress along the vertical weld path on the outer surface of the spherical pressure hull.</p> Full article ">Figure 19
<p>Residual stress along the weld on the outer surface of the spherical pressure hull.</p> Full article ">Figure 20
<p>Longitudinal residual stress along the vertical weld path on the inner surface of the spherical pressure hull.</p> Full article ">Figure 21
<p>Transverse residual stress along the vertical weld path on the inner surface of the spherical pressure hull.</p> Full article ">Figure 22
<p>Residual stress along the weld on inner surface of the spherical pressure hull.</p> Full article ">
19 pages, 7974 KiB  
Article
Effect of Constraint and Crack Contact Closure on Fatigue Crack Mechanical Behavior of Specimen under Negative Loading Ratio by Finite Element Method
by Xinting Miao, Haisheng Hong, Xinyi Hong, Jian Peng and Fengfeng Bie
Metals 2022, 12(11), 1858; https://doi.org/10.3390/met12111858 - 31 Oct 2022
Cited by 3 | Viewed by 1683
Abstract
Mechanical behaviors at fatigue crack tips of cracked specimens under negative loading ratios are studied in detail by the finite element method in this paper. Three factors induced by specimen type and loading type on fatigue crack field are discussed, including constraint, compressive [...] Read more.
Mechanical behaviors at fatigue crack tips of cracked specimens under negative loading ratios are studied in detail by the finite element method in this paper. Three factors induced by specimen type and loading type on fatigue crack field are discussed, including constraint, compressive loading effect (CL effect) and crack contact closure. For mode I crack under negative loading ratios, the effects of the CL effect and crack contact closure on plastic strain accumulations are dominant, with the constraint effect being minor. The constraint effect has effects on the monotonous plastic zone, while the CL effect and contact closure both have effects on the reversed plastic zone (RPZ) and residual tensile plastic zone (RTPZ). That is, the higher the constraint, the smaller the size of the monotonous plastic zone; the greater the CL effect, or the smaller the contact degree, the larger the size of RPZ and RTPZ. For mode II crack, there is only CL effect on the crack tip field without the effect of constraint and contact closure, so plastic strain accumulation at the mode II crack tip is much greater than that at the mode I crack tip when they are under the same loading level. Full article
(This article belongs to the Special Issue Studies on Fatigue Behavior of Engineering Material and Structures)
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Figure 1

Figure 1
<p>Sketch map of specimen and loading: (<b>a</b>) K1 specimen, (<b>b</b>) K3 specimen, (<b>c</b>) fatigue loading.</p> Full article ">Figure 2
<p>Finite element model: (<b>a</b>) mode I crack, (<b>b</b>) I-II mixed mode crack, (<b>c</b>) mesh detail.</p> Full article ">Figure 3
<p>Researches of contact between crack surfaces: (<b>a</b>) effect of <span class="html-italic">R</span> on COD for K3-N, (<b>b</b>) effect of <span class="html-italic">R</span> on COD for K1-S, (<b>c</b>) effect of mesh size on COD (<span class="html-italic">R</span> = −1), (<b>d</b>) effect of mesh size on EPS (<span class="html-italic">R</span> = −1).</p> Full article ">Figure 3 Cont.
<p>Researches of contact between crack surfaces: (<b>a</b>) effect of <span class="html-italic">R</span> on COD for K3-N, (<b>b</b>) effect of <span class="html-italic">R</span> on COD for K1-S, (<b>c</b>) effect of mesh size on COD (<span class="html-italic">R</span> = −1), (<b>d</b>) effect of mesh size on EPS (<span class="html-italic">R</span> = −1).</p> Full article ">Figure 4
<p>Research of contact stress: (<b>a</b>) effect of loading ratio, (<b>b</b>) effect of specimen type.</p> Full article ">Figure 5
<p>Stress distribution under tensile loading: (<b>a</b>) <span class="html-italic">σ</span><sub>xx</sub>; (<b>b</b>) <span class="html-italic">σ</span><sub>yy</sub>.</p> Full article ">Figure 6
<p>Normal stresses <span class="html-italic">σ</span><sub>yy</sub> with <span class="html-italic">d</span>: (<b>a</b>) effect of specimen type, (<b>b</b>) effect of loading ratio.</p> Full article ">Figure 7
<p>Regulations of contact coefficients <span class="html-italic">C</span>: (<b>a</b>) effect of loading ratio <span class="html-italic">R</span>, (<b>b</b>) effect of specimen type.</p> Full article ">Figure 8
<p>Circumferential distribution of EPS: (<b>a</b>) effect of loading ratio <span class="html-italic">R</span>, (<b>b</b>) effect of specimen type.</p> Full article ">Figure 9
<p>Effect of loading ratio on strain field: (<b>a</b>) <span class="html-italic">E</span><sub>yy</sub> with loading history for K3-N, (<b>b</b>) EPS with loading history for K3-N.</p> Full article ">Figure 10
<p>Effect of specimen type on EPS distribution: (<b>a</b>) <span class="html-italic">R</span> = 0, (<b>b</b>) <span class="html-italic">R</span> = −1.</p> Full article ">Figure 11
<p>Effect of loading ratio <span class="html-italic">R</span> on Mises stress distribution: (<b>a</b>) Peak loading point, (<b>b</b>) Valley loading point.</p> Full article ">Figure 12
<p>Normal stress distribution of: (<b>a</b>) K3-N, <span class="html-italic">R</span> = 0; (<b>b</b>) K3-N, <span class="html-italic">R</span> = −1; (<b>c</b>) K3-N, <span class="html-italic">R</span> = −2; (<b>d</b>) K1-S, <span class="html-italic">R</span> = 0; (<b>e</b>) K1-S, <span class="html-italic">R</span> = −1; (<b>f</b>) K1-S, <span class="html-italic">R</span> = −2.</p> Full article ">Figure 12 Cont.
<p>Normal stress distribution of: (<b>a</b>) K3-N, <span class="html-italic">R</span> = 0; (<b>b</b>) K3-N, <span class="html-italic">R</span> = −1; (<b>c</b>) K3-N, <span class="html-italic">R</span> = −2; (<b>d</b>) K1-S, <span class="html-italic">R</span> = 0; (<b>e</b>) K1-S, <span class="html-italic">R</span> = −1; (<b>f</b>) K1-S, <span class="html-italic">R</span> = −2.</p> Full article ">Figure 13
<p>Diagram of various plastic zones of the crack tip [<a href="#B18-metals-12-01858" class="html-bibr">18</a>,<a href="#B21-metals-12-01858" class="html-bibr">21</a>].</p> Full article ">Figure 14
<p>Relationships of plastic zones: (<b>a</b>) Monotonous plastic zone; (<b>b</b>) Reversed plastic zone; (<b>c</b>) Residual tensile plastic zone; (<b>d</b>) Results in the paper [<a href="#B18-metals-12-01858" class="html-bibr">18</a>].</p> Full article ">Figure 15
<p>Hysteresis loop: (<b>a</b>) effect of loading ratio <span class="html-italic">R</span>; (<b>b</b>) effect of specimen type.</p> Full article ">Figure 16
<p>Elastic and Plastic strain energy: (<b>a</b>) effect of <span class="html-italic">R</span> on elastic strain energy; (<b>b</b>) effect of <span class="html-italic">R</span> on plastic strain energy; (<b>c</b>) effect of specimen type on elastic strain energy; (<b>d</b>) effect of specimen type on plastic strain energy.</p> Full article ">Figure 17
<p>EPS field with loading history: (<b>a</b>) <span class="html-italic">β</span> = 0°, (<b>b</b>) <span class="html-italic">β</span> = 60°.</p> Full article ">Figure 18
<p>Circumferential EPS field: (<b>a</b>) <span class="html-italic">β</span> = 0°, (<b>b</b>) <span class="html-italic">β</span> = 60°.</p> Full article ">
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