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Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires

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} div.type-section h2 { font-size: 20px; line-height: 26px; font-weight: 300; } div.type-section h3 { margin-left: 15px; margin-bottom: 0px; font-weight: 300; } .journal-tabs .tab-title.active a { } </style> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/slick.css?f38b2db10e01b157?1732286508"> <meta name="title" content="Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires"> <meta name="description" content="Pearlitic steel rods are subjected to cold-drawing processes to produce pearlitic steel wires with true strains ranging from 0.81 to 2.18. Tensile tests are utilized to attain mechanical properties of cold-drawn pearlitic steel wires. TEM and XRD investigations were performed on the microstructure of the cold-drawn steel wires. With an increasing cold-drawn strain, both the interlamellar spacing and cementite lamellae thickness decrease, while the dislocation density significantly increases. The drawn wire has a tensile strength of 2170 MPa when the true stain reaches 2.18. Deformation-induced cementite dissolution occurs during cold-drawing progress, which releases many C atoms. The findings indicate that the supersaturation of C is heterogeneously distributed in the ferrite matrix. The ordered distribution of the released C in ferrite phases creates short-range order (SRO). SRO clusters and disordered Cottrell atmospheres contribute to solution strengthening, which, together with dislocation strengthening and interlamellar boundary strengthening, form an effective strengthening mechanism in cold-drawn pearlitic steel wires. Our work provides new insights into carbon redistribution and the mechanism of solution strengthening within ferrous phases." > <link rel="image_src" href="https://pub.mdpi-res.com/img/journals/crystals-logo.png?a2c22e8538083c0b" > <meta name="dc.title" content="Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires"> <meta name="dc.creator" content="Gang Zhao"> <meta name="dc.creator" content="Jianyu Jiao"> <meta name="dc.creator" content="Yan Wu"> <meta name="dc.creator" content="Fengmei Bai"> <meta name="dc.creator" content="Hongwei Zhou"> <meta name="dc.creator" content="Jun Xue"> <meta name="dc.creator" content="Yixuan Zhu"> <meta name="dc.creator" content="Guangwen Zheng"> <meta name="dc.type" content="Article"> <meta name="dc.source" content="Crystals 2024, Vol. 14, Page 977"> <meta name="dc.date" content="2024-11-13"> <meta name ="dc.identifier" content="10.3390/cryst14110977"> <meta name="dc.publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="dc.rights" content="http://creativecommons.org/licenses/by/3.0/"> <meta name="dc.format" content="application/pdf" > <meta name="dc.language" content="en" > <meta name="dc.description" content="Pearlitic steel rods are subjected to cold-drawing processes to produce pearlitic steel wires with true strains ranging from 0.81 to 2.18. Tensile tests are utilized to attain mechanical properties of cold-drawn pearlitic steel wires. TEM and XRD investigations were performed on the microstructure of the cold-drawn steel wires. With an increasing cold-drawn strain, both the interlamellar spacing and cementite lamellae thickness decrease, while the dislocation density significantly increases. The drawn wire has a tensile strength of 2170 MPa when the true stain reaches 2.18. Deformation-induced cementite dissolution occurs during cold-drawing progress, which releases many C atoms. The findings indicate that the supersaturation of C is heterogeneously distributed in the ferrite matrix. The ordered distribution of the released C in ferrite phases creates short-range order (SRO). SRO clusters and disordered Cottrell atmospheres contribute to solution strengthening, which, together with dislocation strengthening and interlamellar boundary strengthening, form an effective strengthening mechanism in cold-drawn pearlitic steel wires. Our work provides new insights into carbon redistribution and the mechanism of solution strengthening within ferrous phases." > <meta name="dc.subject" content="metals and alloys" > <meta name="dc.subject" content="pearlitic steel wires" > <meta name="dc.subject" content="short–range order" > <meta name="dc.subject" content="solution strengthening" > <meta name="dc.subject" content="Cottrell atmospheres" > <meta name ="prism.issn" content="2073-4352"> <meta name ="prism.publicationName" content="Crystals"> <meta name ="prism.publicationDate" content="2024-11-13"> <meta name ="prism.volume" content="14"> <meta name ="prism.number" content="11"> <meta name ="prism.section" content="Article" > <meta name ="prism.startingPage" content="977" > <meta name="citation_issn" content="2073-4352"> <meta name="citation_journal_title" content="Crystals"> <meta name="citation_publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="citation_title" content="Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires"> <meta name="citation_publication_date" content="2024/11"> <meta name="citation_online_date" content="2024/11/13"> <meta name="citation_volume" content="14"> <meta name="citation_issue" content="11"> <meta name="citation_firstpage" content="977"> <meta name="citation_author" content="Zhao, Gang"> <meta name="citation_author" content="Jiao, Jianyu"> <meta name="citation_author" content="Wu, Yan"> <meta name="citation_author" content="Bai, Fengmei"> <meta name="citation_author" content="Zhou, Hongwei"> <meta name="citation_author" content="Xue, Jun"> <meta name="citation_author" content="Zhu, Yixuan"> <meta name="citation_author" content="Zheng, Guangwen"> <meta name="citation_doi" content="10.3390/cryst14110977"> <meta name="citation_id" content="mdpi-cryst14110977"> <meta name="citation_abstract_html_url" content="https://www.mdpi.com/2073-4352/14/11/977"> <meta name="citation_pdf_url" content="https://www.mdpi.com/2073-4352/14/11/977/pdf?version=1731487044"> <link rel="alternate" type="application/pdf" title="PDF Full-Text" href="https://www.mdpi.com/2073-4352/14/11/977/pdf?version=1731487044"> <meta name="fulltext_pdf" content="https://www.mdpi.com/2073-4352/14/11/977/pdf?version=1731487044"> <meta name="citation_fulltext_html_url" content="https://www.mdpi.com/2073-4352/14/11/977/htm"> <link rel="alternate" type="text/html" title="HTML Full-Text" href="https://www.mdpi.com/2073-4352/14/11/977/htm"> <meta name="fulltext_html" content="https://www.mdpi.com/2073-4352/14/11/977/htm"> <link rel="alternate" type="text/xml" title="XML Full-Text" href="https://www.mdpi.com/2073-4352/14/11/977/xml"> <meta name="fulltext_xml" content="https://www.mdpi.com/2073-4352/14/11/977/xml"> <meta name="citation_xml_url" content="https://www.mdpi.com/2073-4352/14/11/977/xml"> <meta name="twitter:card" content="summary" /> <meta name="twitter:site" content="@MDPIOpenAccess" /> <meta name="twitter:image" content="https://pub.mdpi-res.com/img/journals/crystals-logo-social.png?a2c22e8538083c0b" /> <meta property="fb:app_id" content="131189377574"/> <meta property="og:site_name" content="MDPI"/> <meta property="og:type" content="article"/> <meta property="og:url" content="https://www.mdpi.com/2073-4352/14/11/977" /> <meta property="og:title" content="Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires" /> <meta property="og:description" content="Pearlitic steel rods are subjected to cold-drawing processes to produce pearlitic steel wires with true strains ranging from 0.81 to 2.18. Tensile tests are utilized to attain mechanical properties of cold-drawn pearlitic steel wires. TEM and XRD investigations were performed on the microstructure of the cold-drawn steel wires. With an increasing cold-drawn strain, both the interlamellar spacing and cementite lamellae thickness decrease, while the dislocation density significantly increases. The drawn wire has a tensile strength of 2170 MPa when the true stain reaches 2.18. Deformation-induced cementite dissolution occurs during cold-drawing progress, which releases many C atoms. The findings indicate that the supersaturation of C is heterogeneously distributed in the ferrite matrix. The ordered distribution of the released C in ferrite phases creates short-range order (SRO). SRO clusters and disordered Cottrell atmospheres contribute to solution strengthening, which, together with dislocation strengthening and interlamellar boundary strengthening, form an effective strengthening mechanism in cold-drawn pearlitic steel wires. Our work provides new insights into carbon redistribution and the mechanism of solution strengthening within ferrous phases." /> <meta property="og:image" content="https://pub.mdpi-res.com/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g001-550.jpg?1731487113" /> <link rel="alternate" type="application/rss+xml" title="MDPI Publishing - Latest articles" href="https://www.mdpi.com/rss"> <meta name="google-site-verification" content="PxTlsg7z2S00aHroktQd57fxygEjMiNHydKn3txhvwY"> <meta name="facebook-domain-verification" content="mcoq8dtq6sb2hf7z29j8w515jjoof7" /> <script id="Cookiebot" data-cfasync="false" src="https://consent.cookiebot.com/uc.js" data-cbid="51491ddd-fe7a-4425-ab39-69c78c55829f" type="text/javascript" async></script> <!--[if lt IE 9]> <script>var browserIe8 = true;</script> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/ie8foundationfix.css?50273beac949cbf0?1732286508"> <script src="//html5shiv.googlecode.com/svn/trunk/html5.js"></script> <script src="//cdnjs.cloudflare.com/ajax/libs/html5shiv/3.6.2/html5shiv.js"></script> <script src="//s3.amazonaws.com/nwapi/nwmatcher/nwmatcher-1.2.5-min.js"></script> <script src="//html5base.googlecode.com/svn-history/r38/trunk/js/selectivizr-1.0.3b.js"></script> <script src="//cdnjs.cloudflare.com/ajax/libs/respond.js/1.1.0/respond.min.js"></script> <script src="https://pub.mdpi-res.com/assets/js/ie8/ie8patch.js?9e1d3c689a0471df?1732286508"></script> <script src="https://pub.mdpi-res.com/assets/js/ie8/rem.min.js?94b62787dcd6d2f2?1732286508"></script> <![endif]--> <script type="text/plain" data-cookieconsent="statistics"> (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); 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href="https://scholar.google.com/scholar?q=Gang%20Zhao" class="button button--color-inversed" target="_blank" rels="noopener noreferrer"> Google Scholar </a></div></div><sup> 1</sup>, </span><span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop13391189' data-options='is_hover:true, hover_timeout:5000'> Jianyu Jiao</div><div id="profile-card-drop13391189" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Jianyu Jiao</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a 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href="https://scholar.google.com/scholar?q=Yan%20Wu" class="button button--color-inversed" target="_blank" rels="noopener noreferrer"> Google Scholar </a></div></div><sup> 2</sup>, </span><span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop13391191' data-options='is_hover:true, hover_timeout:5000'> Fengmei Bai</div><div id="profile-card-drop13391191" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Fengmei Bai</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a 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class='profile-card-drop' data-dropdown='profile-card-drop13391195' data-options='is_hover:true, hover_timeout:5000'> Guangwen Zheng</div><div id="profile-card-drop13391195" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Guangwen Zheng</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a href="https://sciprofiles.com/profile/author/YysvVUkyL2E1c29kZWpzQ2Z1eGQ4UT09?utm_source=mdpi.com&amp;utm_medium=website&amp;utm_campaign=avatar_name" class="button button--color-inversed" target="_blank"> SciProfiles </a><a href="https://scilit.net/scholars?q=Guangwen%20Zheng" class="button 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243002, China</div> </div> <div class="affiliation "> <div class="affiliation-item"><sup>3</sup></div> <div class="affiliation-name ">School of Materials Science and Technology, Anhui University of Technology, Maanshan 243002, China</div> </div> <div class="affiliation"> <div class="affiliation-item"><sup>*</sup></div> <div class="affiliation-name ">Authors to whom correspondence should be addressed. </div> </div> </div> </div> <div class="bib-identity" style="margin-bottom: 10px;"> <em>Crystals</em> <b>2024</b>, <em>14</em>(11), 977; <a href="https://doi.org/10.3390/cryst14110977">https://doi.org/10.3390/cryst14110977</a> </div> <div class="pubhistory" style="font-weight: bold; padding-bottom: 10px;"> <span style="display: inline-block">Submission received: 16 October 2024</span> / <span style="display: inline-block">Revised: 7 November 2024</span> / <span style="display: inline-block">Accepted: 11 November 2024</span> / <span style="display: inline-block">Published: 13 November 2024</span> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/crystals/special_issues/WR1I18BK4K ">Microstructure and Properties of Metals and Alloys</a>)<br/> </div> <div class="highlight-box1"> <div class="download"> <a class="button button--color-inversed button--drop-down" data-dropdown="drop-download-1519728" aria-controls="drop-supplementary-1519728" aria-expanded="false"> Download <i class="material-icons">keyboard_arrow_down</i> </a> <div id="drop-download-1519728" class="f-dropdown label__btn__dropdown label__btn__dropdown--button" data-dropdown-content aria-hidden="true" tabindex="-1"> <a class="UD_ArticlePDF" href="/2073-4352/14/11/977/pdf?version=1731487044" data-name="Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires" data-journal="crystals">Download PDF</a> <br/> <a id="js-pdf-with-cover-access-captcha" href="#" data-target="/2073-4352/14/11/977/pdf-with-cover" class="accessCaptcha">Download PDF with Cover</a> <br/> <a id="js-xml-access-captcha" href="#" data-target="/2073-4352/14/11/977/xml" class="accessCaptcha">Download XML</a> <br/> <a href="/2073-4352/14/11/977/epub" id="epub_link">Download Epub</a> <br/> </div> <div class="js-browse-figures" style="display: inline-block;"> <a href="#" class="button button--color-inversed margin-bottom-10 openpopupgallery UI_BrowseArticleFigures" data-target='article-popup' data-counterslink = "https://www.mdpi.com/2073-4352/14/11/977/browse" >Browse Figures</a> </div> <div id="article-popup" class="popupgallery" style="display: inline; line-height: 200%"> <a href="https://pub.mdpi-res.com/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g001.png?1731487112" title=" <strong>Figure 1</strong><br/> &lt;p&gt;(&lt;b&gt;a&lt;/b&gt;) Schematic of the tensile specimens; (&lt;b&gt;b&lt;/b&gt;) tensile stress–strain curves of wires with the different true stains; (&lt;b&gt;c&lt;/b&gt;) tensile strength, yield strength and elongation vs drawn strains.&lt;/p&gt; "> </a> <a href="https://pub.mdpi-res.com/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g002.png?1731487115" title=" <strong>Figure 2</strong><br/> &lt;p&gt;TEM images of wires in solution treatment before cold-drawing: (&lt;b&gt;a&lt;/b&gt;) pearlitic in different colonies; (&lt;b&gt;b&lt;/b&gt;,&lt;b&gt;c&lt;/b&gt;) bright field (BF) and dark field (DF) images of complete lamellar; (&lt;b&gt;d&lt;/b&gt;,&lt;b&gt;e&lt;/b&gt;) BF and DF images of broken θ–Fe&lt;sub&gt;3&lt;/sub&gt;C; (&lt;b&gt;f&lt;/b&gt;) a SADP of lamellar in (&lt;b&gt;b&lt;/b&gt;).&lt;/p&gt; "> </a> <a href="https://pub.mdpi-res.com/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g003.png?1731487118" title=" <strong>Figure 3</strong><br/> &lt;p&gt;TEM images and corresponding EDS mapping of wires before and after cold-drawing: (&lt;b&gt;a&lt;/b&gt;,&lt;b&gt;b&lt;/b&gt;) ε = 0; (&lt;b&gt;c&lt;/b&gt;,&lt;b&gt;d&lt;/b&gt;) ε = 2.18.&lt;/p&gt; "> </a> <a href="https://pub.mdpi-res.com/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g004.png?1731487121" title=" <strong>Figure 4</strong><br/> &lt;p&gt;TEM images of pearlitic structures: (&lt;b&gt;a&lt;/b&gt;) wire rod; (&lt;b&gt;b&lt;/b&gt;) ε = 0.81; (&lt;b&gt;c&lt;/b&gt;) ε = 2.18; (&lt;b&gt;a1&lt;/b&gt;,&lt;b&gt;b1&lt;/b&gt;,&lt;b&gt;c1&lt;/b&gt;) BF images; (&lt;b&gt;a2&lt;/b&gt;,&lt;b&gt;b2&lt;/b&gt;,&lt;b&gt;c2&lt;/b&gt;) the corresponding DF images; (&lt;b&gt;a3&lt;/b&gt;,&lt;b&gt;b3&lt;/b&gt;,&lt;b&gt;c3&lt;/b&gt;) dislocation configurations in α–Fe; (&lt;b&gt;a4&lt;/b&gt;,&lt;b&gt;b4&lt;/b&gt;,&lt;b&gt;c4&lt;/b&gt;) SADP of the areas marked by circles in (&lt;b&gt;a3&lt;/b&gt;,&lt;b&gt;b3&lt;/b&gt;,&lt;b&gt;c3&lt;/b&gt;).&lt;/p&gt; "> </a> <a href="https://pub.mdpi-res.com/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g005.png?1731487123" title=" <strong>Figure 5</strong><br/> &lt;p&gt;Spacing of cold-drawn steel wire lamellae under different strains:(&lt;b&gt;a&lt;/b&gt;) interlamellar spacing (ILS); (&lt;b&gt;b&lt;/b&gt;) cementite lamellar thickness (CLT).&lt;/p&gt; "> </a> <a href="https://pub.mdpi-res.com/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g006.png?1731487124" title=" <strong>Figure 6</strong><br/> &lt;p&gt;XRD patterns of cold-drawn wires.&lt;/p&gt; "> </a> <a href="https://pub.mdpi-res.com/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g007.png?1731487125" title=" <strong>Figure 7</strong><br/> &lt;p&gt;The dislocation density (&lt;span class=&quot;html-italic&quot;&gt;ρ&lt;/span&gt;) of the cold-drawn wires: (&lt;b&gt;a&lt;/b&gt;) linear fitting plots for the diffraction patterns of the wires in &lt;a href=&quot;#crystals-14-00977-f006&quot; class=&quot;html-fig&quot;&gt;Figure 6&lt;/a&gt;: (&lt;b&gt;b&lt;/b&gt;) &lt;span class=&quot;html-italic&quot;&gt;ρ&lt;/span&gt; as the function of ε.&lt;/p&gt; "> </a> <a href="https://pub.mdpi-res.com/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g008.png?1731487125" title=" <strong>Figure 8</strong><br/> &lt;p&gt;The calculated and experimental strengthening of cold-drawn pearlitic steel wires.&lt;/p&gt; "> </a> <a href="https://pub.mdpi-res.com/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g009.png?1731487127" title=" <strong>Figure 9</strong><br/> &lt;p&gt;HRTEM images of α–Fe/θ–Fe&lt;sub&gt;3&lt;/sub&gt;C interfaces at: (&lt;b&gt;a&lt;/b&gt;) ε = 0, (&lt;b&gt;b&lt;/b&gt;) ε = 2.18. (&lt;b&gt;a2&lt;/b&gt;,&lt;b&gt;b2&lt;/b&gt;) The FFT patterns of α–Fe and θ–Fe&lt;sub&gt;3&lt;/sub&gt;C phases in (&lt;b&gt;a1&lt;/b&gt;,&lt;b&gt;b1&lt;/b&gt;), respectively; (&lt;b&gt;a3&lt;/b&gt;,&lt;b&gt;b3&lt;/b&gt;) magnified view of the yellow box areas in (&lt;b&gt;a1&lt;/b&gt;,&lt;b&gt;b1&lt;/b&gt;); and (&lt;b&gt;a4&lt;/b&gt;,&lt;b&gt;b4&lt;/b&gt;) the corresponding strain maps along the [100]&lt;sub&gt;α-Fe&lt;/sub&gt; axis calculated by Strain++ software V1.8 for HRTEM images in (&lt;b&gt;a3&lt;/b&gt;,&lt;b&gt;b3&lt;/b&gt;).&lt;/p&gt; "> </a> </div> <a class="button button--color-inversed" href="/2073-4352/14/11/977/notes">Versions&nbsp;Notes</a> </div> </div> <div class="responsive-moving-container small hidden" data-id="article-counters" style="margin-top: 15px;"></div> <div class="html-dynamic"> <section> <div class="art-abstract art-abstract-new in-tab hypothesis_container"> <p> <div><section class="html-abstract" id="html-abstract"> <h2 id="html-abstract-title">Abstract</h2><b>:</b> <div class="html-p">Pearlitic steel rods are subjected to cold-drawing processes to produce pearlitic steel wires with true strains ranging from 0.81 to 2.18. Tensile tests are utilized to attain mechanical properties of cold-drawn pearlitic steel wires. TEM and XRD investigations were performed on the microstructure of the cold-drawn steel wires. With an increasing cold-drawn strain, both the interlamellar spacing and cementite lamellae thickness decrease, while the dislocation density significantly increases. The drawn wire has a tensile strength of 2170 MPa when the true stain reaches 2.18. Deformation-induced cementite dissolution occurs during cold-drawing progress, which releases many C atoms. The findings indicate that the supersaturation of C is heterogeneously distributed in the ferrite matrix. The ordered distribution of the released C in ferrite phases creates short-range order (SRO). SRO clusters and disordered Cottrell atmospheres contribute to solution strengthening, which, together with dislocation strengthening and interlamellar boundary strengthening, form an effective strengthening mechanism in cold-drawn pearlitic steel wires. Our work provides new insights into carbon redistribution and the mechanism of solution strengthening within ferrous phases.</div> </section> <div id="html-keywords"> <div class="html-gwd-group"><div id="html-keywords-title">Keywords: </div><a href="/search?q=metals+and+alloys">metals and alloys</a>; <a href="/search?q=pearlitic+steel+wires">pearlitic steel wires</a>; <a href="/search?q=short%E2%80%93range+order">short&ndash;range order</a>; <a href="/search?q=solution+strengthening">solution strengthening</a>; <a href="/search?q=Cottrell+atmospheres">Cottrell atmospheres</a></div> <div> </div> </div> </div> </p> </div> </section> </div> <div class="hypothesis_container"> <ul class="menu html-nav" data-prev-node="#html-quick-links-title"> </ul> <div class="html-body"> <section id='sec1-crystals-14-00977' type='intro'><h2 data-nested='1'> 1. Introduction</h2><div class='html-p'>Cold-drawing technology is the main process used to produce high-strength pearlitic steel wires [<a href="#B1-crystals-14-00977" class="html-bibr">1</a>,<a href="#B2-crystals-14-00977" class="html-bibr">2</a>]. Pearlitic lamellar structures consist of alternating phases of ferrite (α–Fe) and cementite (θ–Fe<sub>3</sub>C). Drawn wires are subject to three distinct strengthening methods, including dislocation strengthening, fine-grain strengthening, and solution strengthening. There are reliable models quantifying both dislocation strengthening and fine-grain strengthening [<a href="#B2-crystals-14-00977" class="html-bibr">2</a>,<a href="#B3-crystals-14-00977" class="html-bibr">3</a>,<a href="#B4-crystals-14-00977" class="html-bibr">4</a>]. However, the calculated results by several models are distant from the experimental ones [<a href="#B5-crystals-14-00977" class="html-bibr">5</a>,<a href="#B6-crystals-14-00977" class="html-bibr">6</a>]. It remains challenging to develop an accurate model of solution strengthening due to ongoing controversy about the mechanism of solution strengthening.</div><div class='html-p'>The solution strengthening can be attributed to deformation-induced θ–Fe<sub>3</sub>C dissolution, which releases C atoms into α–Fe [<a href="#B7-crystals-14-00977" class="html-bibr">7</a>,<a href="#B8-crystals-14-00977" class="html-bibr">8</a>,<a href="#B9-crystals-14-00977" class="html-bibr">9</a>]. Several mechanisms have been proposed to explain the θ–Fe<sub>3</sub>C dissolution due to plastic deformation: (i) the binding enthalpy between carbon atoms and dislocations in α–Fe surpassing the solution enthalpy of θ–Fe<sub>3</sub>C [<a href="#B10-crystals-14-00977" class="html-bibr">10</a>]; (ii) the thinning of θ–Fe<sub>3</sub>C lamellae during drawing causing the destabilization of θ–Fe<sub>3</sub>C due to an increase in its free energy [<a href="#B11-crystals-14-00977" class="html-bibr">11</a>]; (iii) the diffusion of carbon atoms from θ–Fe<sub>3</sub>C to the excessive vacancies formed in α–Fe during cold-drawing [<a href="#B12-crystals-14-00977" class="html-bibr">12</a>,<a href="#B13-crystals-14-00977" class="html-bibr">13</a>]. Most researchers agree with the solution strengthening from the interaction between dislocations and carbon atoms released from θ–Fe<sub>3</sub>C dissolution diffusing into α–Fe phase. Dislocations are locked down by the so-called carbon Cottrell atmospheres [<a href="#B12-crystals-14-00977" class="html-bibr">12</a>,<a href="#B14-crystals-14-00977" class="html-bibr">14</a>]. Others propose that a lot of deformation-induced vacancy clusters are believed to play important roles in hardening the wires, known as defect hardening or strengthening [<a href="#B12-crystals-14-00977" class="html-bibr">12</a>,<a href="#B13-crystals-14-00977" class="html-bibr">13</a>]. Since vacancies are always associated with carbon, they will not contribute additionally to solid solution hardening [<a href="#B5-crystals-14-00977" class="html-bibr">5</a>]. Beside strengthening due to Cottrell atmospheres, solid solution strengthening or hardening originates from the redistribution of carbon [<a href="#B6-crystals-14-00977" class="html-bibr">6</a>], which are also obstacles pinning movable dislocations [<a href="#B15-crystals-14-00977" class="html-bibr">15</a>].</div><div class='html-p'>Carbon solubility in α–Fe exhibits a positive correlation with cold-drawn strain [<a href="#B16-crystals-14-00977" class="html-bibr">16</a>]. This relationship can be revealed through the measurement of thermoelectric power, resistivity, and internal friction [<a href="#B16-crystals-14-00977" class="html-bibr">16</a>]. Atom probe tomography (APT) studies have demonstrated the existence of carbon Cottrell atmospheres that are linked to dislocations [<a href="#B14-crystals-14-00977" class="html-bibr">14</a>,<a href="#B17-crystals-14-00977" class="html-bibr">17</a>]. In the present work, we are not going to propose a new model for solution strengthening. We deeply focus on solution strengthening mechanism. The transmission electron microscope (TEM) analysis reveals the presence of SRO structures in α–Fe, which is caused by the ordered distribution of carbon. This feature also validates the occurrence of deformation-induced θ–Fe<sub>3</sub>C during cold-drawing. Both SRO clusters and Cottrell atmospheres are responsible for solution strengthening. This finding provides new insights into carbon redistribution and the mechanism of solution strengthening within ferrous phases.</div></section><section id='sec2-crystals-14-00977' type=''><h2 data-nested='1'> 2. Materials and Methods</h2><div class='html-p'>The specimen employed in the present investigation is a pearlitic steel wire with the following composition: Fe–0.82C–0.50Mn–0.22Si–0.03Cr in wt.%. The wire rods, initially 7.81 mm in diameter, were patented at 580 °C. The drawing process involved multi-pass drawing with 10 dies. The diameter of the 10 dies decreased continuously. The wire rods underwent cold-drawing processes, resulting in wires with diameters of 5.20 mm, 3.82 mm, and 2.61 mm, at the corresponding true strains (ε) of 0.81, 1.43, and 2.18, respectively, where ε is defined by 2ln(d<sub>0</sub>/d<sub>i</sub>) (d<sub>0</sub> is an initial diameter of wire rods and d<sub>i</sub> is a diameter of a cold-drawn wire). The wire rods are presented as ε = 0.</div><div class='html-p'>The tensile testing was measured at room temperature via a universal materials testing machine (CMT 4503, Shenzhen Xinsansi Testing Co., Ltd., Shenzhen, China) at a strain rate of 3 × 10<sup>−3</sup>/s. <a href="#crystals-14-00977-f001" class="html-fig">Figure 1</a>a presents the geometry utilized for tensile testing. The length of the wire between the jigs for the tests was 50 times its diameter. For each testing condition, three identical samples were evaluated to determine the mean tensile strength, yielding strength and uniform elongation. The microstructure observations were conducted using a Talos F200X TEM (Thermo Fisher Scientific Inc., Waltham, MA, USA) at an accelerated voltage of 200 kV. For TEM observations, thin foils with a thickness of 40 μm were prepared by mechanical polishing and then thinning by ion milling. At the same time, Argon ions were used to remove surface contaminants such as carbon atoms of TEM foils. A Talos F200X TEM was equipped with an Energy Dispersive Spectrometer (EDS) probe with a mapping spatial resolution of 1 nm. X–ray analysis was performed using an Ultima IV diffractometer (Japan Rigaku Corporation, Japan). Before X–ray analysis, the specimens were electrochemically polished to remove deformed zones on the surfaces. The X–ray diffraction (XRD) analysis was performed with Cu K radiation (wavelength, λ = 0.1542 nm). The scanning rate of X–ray testing was 0.5°/min, with a step size of 0.02°.</div></section><section id='sec3-crystals-14-00977' type='results'><h2 data-nested='1'> 3. Results</h2><section id='sec3dot1-crystals-14-00977' type=''><h4 class='html-italic' data-nested='2'> 3.1. Tensile Properties</h4><div class='html-p'><a href="#crystals-14-00977-f001" class="html-fig">Figure 1</a>b shows the engineering stress–strain curves of the cold-drawn pearlitic wires as a function of ε ranging from 0 to 2.18. None of the specimens showed a distinct yield point, and hardening was observed up to the ultimate tensile stress. The tensile strength of pearlitic steel rods (ε = 0) was found to be about 1401 MPa. With the increase of the drawn strain, the tensile strength, yield strength (<span class='html-italic'>σ</span><sub>0.2</sub>) and elongation of the wires gradually increased, as shown in <a href="#crystals-14-00977-f001" class="html-fig">Figure 1</a>c. As the ε increased to 2.18, the tensile strength was about 2170 MPa.</div></section><section id='sec3dot2-crystals-14-00977' type=''><h4 class='html-italic' data-nested='2'> 3.2. TEM Observation</h4><div class='html-p'><a href="#crystals-14-00977-f002" class="html-fig">Figure 2</a> depicts TEM images of wires before cold-drawing. Some lamellae are complete in <a href="#crystals-14-00977-f002" class="html-fig">Figure 2</a>a–c, while some θ–Fe<sub>3</sub>C is broken in <a href="#crystals-14-00977-f002" class="html-fig">Figure 2</a>d,e. <a href="#crystals-14-00977-f002" class="html-fig">Figure 2</a>f displays a selected area electron diffraction pattern (SADP) of lamellar indicated by a circle in <a href="#crystals-14-00977-f002" class="html-fig">Figure 2</a>b. It is deduced from the SADP that two phases have a crystallographic orientation relationship (OR): [101]<sub>θ-Fe3C</sub>//[101]<sub>α-Fe</sub> and (010)<sub>θ-Fe3C</sub>//(111)<sub>α-Fe</sub>, which is the Isaichev OR, consistent with other reports [<a href="#B8-crystals-14-00977" class="html-bibr">8</a>,<a href="#B18-crystals-14-00977" class="html-bibr">18</a>]. The orthorhombic crystal structure of θ–Fe<sub>3</sub>C possesses the space group Pbnm, with dimensions a = 0.451 nm, b = 0.508 nm, and c = 0.675 nm [<a href="#B18-crystals-14-00977" class="html-bibr">18</a>].</div><div class='html-p'><a href="#crystals-14-00977-f003" class="html-fig">Figure 3</a> is EDS mapping of pearlitic lamellae at ε = 0 and ε = 2.18. Before the TEM test, the sample was cleaned by an Argon ion beam to eliminate the influence of surface carbon contamination. At ε = 0, the lamellae interfaces are clearly visible and the C enrichment in θ–Fe<sub>3</sub>C is significant; at ε = 2.18, the θ–Fe<sub>3</sub>C lamellae are complete in morphology and the interface is clear, but the C enrichment in θ–Fe<sub>3</sub>C decreases, indicating that under cold-drawing, θ–Fe<sub>3</sub>C is dissolved and the released C atoms diffuse into α–Fe.</div><div class='html-p'>The TEM images of pearlitic wires with varying ε are shown in <a href="#crystals-14-00977-f004" class="html-fig">Figure 4</a>. <a href="#crystals-14-00977-f004" class="html-fig">Figure 4</a>(a1,a2) depicts the BF and DF images of α–Fe and θ–Fe<sub>3</sub>C, respectively. <a href="#crystals-14-00977-f004" class="html-fig">Figure 4</a>(a4) displays a SADP of the region indicated by a circle in <a href="#crystals-14-00977-f004" class="html-fig">Figure 4</a>(a3). The presence of superlattice {001} spots remarked by arrows in a [100]<sub>α-Fe</sub> zone axis implies that ordered structures are formed in α–Fe. Several studies indicate that the ordered carbon configuration in α–Fe [<a href="#B19-crystals-14-00977" class="html-bibr">19</a>,<a href="#B20-crystals-14-00977" class="html-bibr">20</a>] and austenitic steels [<a href="#B21-crystals-14-00977" class="html-bibr">21</a>] can lead to SRO formations. In the SRO B2–NiAl phase, the superlattice reflections are also observed at {001} spots in an SADP along the [100]<sub>α-Fe</sub> axis [<a href="#B22-crystals-14-00977" class="html-bibr">22</a>]. There are a lot of references about SRO in FCC and BCC alloys/phases validated by additional spots in SADP [<a href="#B22-crystals-14-00977" class="html-bibr">22</a>,<a href="#B23-crystals-14-00977" class="html-bibr">23</a>]. In <a href="#crystals-14-00977-f004" class="html-fig">Figure 4</a>(a4–c4), the diffraction spots of θ–Fe<sub>3</sub>C with low crystallographic index almost disappear along the [100]<sub>α-Fe</sub> zone axis.</div><div class='html-p'>At ε = 0.81, the lamellae exhibited kinking in <a href="#crystals-14-00977-f004" class="html-fig">Figure 4</a>(b1) and a partial disappearance, as indicated by an arrow in <a href="#crystals-14-00977-f004" class="html-fig">Figure 4</a>(b3). Plastic deformation produces numerous dislocations. The majority of dislocations are distributed throughout α–Fe lamellae, and the two extremities of the dislocation line are situated in the α–Fe/θ–Fe<sub>3</sub>C boundaries [<a href="#B2-crystals-14-00977" class="html-bibr">2</a>]. The dislocation groups in α–Fe were pinned by the boundaries. Superlattice spots of α-Fe {001} planes at ε = 0.81 suggest SRO formations.</div><div class='html-p'>Although the strain has reached 2.18, the SRO structure remains stable. The α–Fe/θ–Fe<sub>3</sub>C interface is not clearly visible in <a href="#crystals-14-00977-f004" class="html-fig">Figure 4</a>(c1,c2). As ε increases, there is a notable reduction in the length of dislocation lines, accompanied by a corresponding increase in dislocation intensity. Multiple θ–Fe<sub>3</sub>C lamellae undergo dissolution, as indicated by the arrows in <a href="#crystals-14-00977-f004" class="html-fig">Figure 4</a>(c3). The dislocation configuration bears resemblance to the structure depicted in <a href="#crystals-14-00977-f004" class="html-fig">Figure 4</a>(b3).</div><div class='html-p'><a href="#crystals-14-00977-f005" class="html-fig">Figure 5</a> displays interlamellar spacing (ILS) and cementite layers thickness (CLT) as a function of ε. This trend is also found in other references [<a href="#B1-crystals-14-00977" class="html-bibr">1</a>,<a href="#B9-crystals-14-00977" class="html-bibr">9</a>,<a href="#B24-crystals-14-00977" class="html-bibr">24</a>]. ILS and CLT can be calculated according to the relationship [<a href="#B25-crystals-14-00977" class="html-bibr">25</a>]:<div class='html-disp-formula-info' id=''> <div class='f'> 𝑟<sub>𝜀</sub> = 𝑟<sub>0</sub><span class='html-italic'>exp</span>(−𝜀/2) </div> <div class='l'> <label >(1)</label> </div> </div> where <span class='html-italic'>r</span><sub>0</sub> and <span class='html-italic'>r<sub>ε</sub></span> are the original dimensions of lamellar and the ones after cold-drawing with <span class='html-italic'>ε</span>. Calculated results of ILS and CLT are also illustrated in <a href="#crystals-14-00977-f005" class="html-fig">Figure 5</a>. Measurements of both ILS and CLT are close to the calculated results.</div></section><section id='sec3dot3-crystals-14-00977' type=''><h4 class='html-italic' data-nested='2'> 3.3. XRD Analysis</h4><div class='html-p'><a href="#crystals-14-00977-f006" class="html-fig">Figure 6</a> shows XRD patterns of cold-drawn wires with the different ε. The α–Fe diffraction peaks of the (110), (200), (211), (220), and (310) planes can be identified according to bcc crystal patterns. But the α–Fe diffraction peaks show broadening, which is resulting from a refinement of pearlitic lamellae and an increase in dislocation density during the cold-drawing process [<a href="#B26-crystals-14-00977" class="html-bibr">26</a>]. At ε = 0, diffraction peaks from θ–Fe<sub>3</sub>C can be observed, while these peaks almost disappear with the increase of ε. Deformation-induced θ–Fe<sub>3</sub>C dissolution and θ–Fe<sub>3</sub>C amorphization may be responsible for the disappearance of θ–Fe<sub>3</sub>C diffraction peaks [<a href="#B7-crystals-14-00977" class="html-bibr">7</a>,<a href="#B26-crystals-14-00977" class="html-bibr">26</a>].</div><div class='html-p'>Generally, the XRD peak widening is related to dislocation density, which can be determined using the following Williamson–Hall equations [<a href="#B27-crystals-14-00977" class="html-bibr">27</a>]:<div class='html-disp-formula-info' id='FD1-crystals-14-00977'> <div class='f'> <math display='block'><semantics> <mrow> <mi>β</mi> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msub> <mi>θ</mi> <mrow> <mi>h</mi> <mi>k</mi> <mi>l</mi> </mrow> </msub> </mrow> <mi>λ</mi> </mfrac> </mstyle> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mi>D</mi> </mfrac> </mstyle> <mo>+</mo> <mn>2</mn> <mi>e</mi> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <msub> <mi>θ</mi> <mrow> <mi>h</mi> <mi>k</mi> <mi>l</mi> </mrow> </msub> </mrow> <mi>λ</mi> </mfrac> </mstyle> </mrow> </semantics></math> </div> <div class='l'> <label >(2)</label> </div> </div> where <span class='html-italic'>β</span>, <span class='html-italic'>θ<sub>hkl</sub></span>, <span class='html-italic'>λ</span>, <span class='html-italic'>e</span> and <span class='html-italic'>D</span>, are the half-height width of the diffraction peaks (hkl), the diffraction angle at the selected peak position, X–ray wavelength (0.1542 nm), the effective mean microstrain, and the average grain size, respectively. In Formula (2), the broadening of the diffraction peak caused by the grain size becomes significantly pronounced only when the grain size is less than 100 nm. In <a href="#crystals-14-00977-f002" class="html-fig">Figure 2</a>a, the size of the pearlitic clusters/grains is several micrometers, indicating that 1/<span class='html-italic'>D</span> is relatively small and can be ignored here. Therefore, the linear fitting diagram of <math display='inline'><semantics> <mrow> <mi>β</mi> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msub> <mi>θ</mi> <mrow> <mi>h</mi> <mi>k</mi> <mi>l</mi> </mrow> </msub> </mrow> <mi>λ</mi> </mfrac> </mstyle> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <msub> <mi>θ</mi> <mrow> <mi>h</mi> <mi>k</mi> <mi>l</mi> </mrow> </msub> </mrow> <mi>λ</mi> </mfrac> </mstyle> </mrow> </semantics></math> for different α–Fe diffraction peaks of (110), (200), (211), and (220) can generate the slope of 2<span class='html-italic'>e</span>. The linear fitting plots for the wires with the different ε are shown in <a href="#crystals-14-00977-f007" class="html-fig">Figure 7</a>a.</div><div class='html-p'>The dislocation density, <span class='html-italic'>ρ</span>, is then calculated using the following Equation [<a href="#B3-crystals-14-00977" class="html-bibr">3</a>]:<div class='html-disp-formula-info' id='FD2-crystals-14-00977'> <div class='f'> <math display='block'><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>14.4</mn> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msup> <mi>e</mi> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mstyle> </mrow> </semantics></math> </div> <div class='l'> <label >(3)</label> </div> </div> where <span class='html-italic'>ρ</span>, <span class='html-italic'>e</span> and <span class='html-italic'>b</span> are the dislocation density, the effective mean microstrain, and the Burgers vector (0.246 nm), respectively. Substituting <span class='html-italic'>e</span> into Equation (3) to obtain <span class='html-italic'>ρ</span>, <a href="#crystals-14-00977-f007" class="html-fig">Figure 7</a>b illustrates the dislocation density increase with ε. At ε = 0.81, the dislocation density slowly increases, while it significantly increases when ε rises from 0.81 to 2.18. Dislocation densities at ε = 0 and ε = 2.18 are 6.2 × 10<sup>14</sup> and 6.8 × 10<sup>15</sup> m<sup>−2</sup>, respectively, which are in the same order of magnitude as the values measured by XRD [<a href="#B13-crystals-14-00977" class="html-bibr">13</a>], TEM [<a href="#B2-crystals-14-00977" class="html-bibr">2</a>], and transmission Kikuchi diffraction (TKD) methods [<a href="#B4-crystals-14-00977" class="html-bibr">4</a>].</div></section></section><section id='sec4-crystals-14-00977' type='discussion'><h2 data-nested='1'> 4. Discussion</h2><section id='sec4dot1-crystals-14-00977' type=''><h4 class='html-italic' data-nested='2'> 4.1. Strengthening Mechanism</h4><div class='html-p'>There are three strengthening mechanisms in cold-drawn pearlitic steel wires: (i) boundary strengthening (σ<sub>b</sub>), (ii) dislocation strengthening (σ<span class='html-italic'><sub>ρ</sub></span>), and (iii) solution strengthening (σ<sub>ss</sub>). The flow stress or yield stress (σ<sub>0.2</sub>) of cold-drawn pearlitic wires during tensile is described by [<a href="#B2-crystals-14-00977" class="html-bibr">2</a>]:<div class='html-disp-formula-info' id=''> <div class='f'> σ<sub>0.2</sub> = σ<sub>0</sub> + σ<sub>b</sub> + σ<span class='html-italic'><sub>ρ</sub></span> + σ<sub>SS</sub> </div> <div class='l'> <label >(4)</label> </div> </div></div><div class='html-p'>Boundary strengthening results from nanoscale θ–Fe<sub>3</sub>C lamellae, which act as obstacles to dislocation glide between α–Fe lamellae. It can be estimated via the Hall–Petch relationship, as follows [<a href="#B2-crystals-14-00977" class="html-bibr">2</a>]:<div class='html-disp-formula-info' id=''> <div class='f'> σ<sub>b</sub> = σ<sub>0</sub> + <span class='html-italic'>k</span>(<span class='html-italic'>d</span>)<sup>−0.5</sup> </div> <div class='l'> <label >(5)</label> </div> </div> where σ<sub>0</sub> is the friction stress of pure α–Fe, and σ<sub>0</sub> is taken as 60 MPa. <span class='html-italic'>k</span> is the slope of the Hall–Petch equation, and <span class='html-italic'>k</span> = 0.31 MPamm<sup>−0.5</sup> in the present work, which is reported from measurements over a wide strain range [<a href="#B28-crystals-14-00977" class="html-bibr">28</a>]. <span class='html-italic'>d</span> is the width of the α–Fe lamellae, as shown in <a href="#crystals-14-00977-f005" class="html-fig">Figure 5</a>.</div><div class='html-p'>Dislocation strengthening is associated with the interactions of dislocations. The increase in flow stress is given by [<a href="#B5-crystals-14-00977" class="html-bibr">5</a>,<a href="#B28-crystals-14-00977" class="html-bibr">28</a>]:<div class='html-disp-formula-info' id=''> <div class='f'> σ<span class='html-italic'><sub>ρ</sub></span> = αMG<span class='html-italic'>bρ</span><sup>0.5</sup> </div> <div class='l'> <label >(6)</label> </div> </div> where α is a constant of 0.24; M is the orientation factor, about 1.84 for the strong &lt;110&gt; of Fe [<a href="#B28-crystals-14-00977" class="html-bibr">28</a>]; G is the shear modulus (77.5 GPa [<a href="#B2-crystals-14-00977" class="html-bibr">2</a>]); <span class='html-italic'>b</span> is the Burgers vector, 0.248 nm for α–Fe; and <span class='html-italic'>ρ</span> is the dislocation density, which is based on XRD patterns, as show in <a href="#crystals-14-00977-f007" class="html-fig">Figure 7</a>b. The calculated σ<sub>b</sub> and σ<span class='html-italic'><sub>ρ</sub></span> based on Equations (5) and (6), respectively, together with the measurements of yield stress are shown in <a href="#crystals-14-00977-f008" class="html-fig">Figure 8</a>. Both σ<sub>b</sub> and σ<span class='html-italic'><sub>ρ</sub></span> increase with ε. σ<sub>b</sub> is much higher than σ<span class='html-italic'><sub>ρ</sub></span> at all strains, which means that boundary strengthening is prominent in cold-drawn pearlitic steel wires. This feature is consistent with other results [<a href="#B25-crystals-14-00977" class="html-bibr">25</a>]. The combination of σ<sub>b</sub> and σ<span class='html-italic'><sub>ρ</sub></span> is a little lower than experimental results at different ε. This trend indicates that there is a solution strengthening mechanism beside boundary strengthening and dislocation strengthening in the cold-drawn pearlitic steel wires.</div></section><section id='sec4dot2-crystals-14-00977' type=''><h4 class='html-italic' data-nested='2'> 4.2. Cottrell Atmosphere Strengthening</h4><div class='html-p'><a href="#crystals-14-00977-f007" class="html-fig">Figure 7</a>b based on XRD patterns reveals the dislocation density of the entire steel wire, while the distribution of dislocation density in α–Fe and θ–Fe<sub>3</sub>C phase remains ambiguous. Geometric phase analysis (GPA) is a method for mapping the strain field from high-resolution TEM (HRTEM) micrographs. The strain mapping calculated by the GPA method is related to the lattice dislocations, which can directly show the dislocation density distribution [<a href="#B29-crystals-14-00977" class="html-bibr">29</a>].</div><div class='html-p'><a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a> displays HRTEM images of α–Fe/θ–Fe<sub>3</sub>C lamellae. Prior to drawing, θ–Fe<sub>3</sub>C θ–Fe<sub>3</sub>C displays a platelet-like morphology in the wires, as depicted in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(a1). Fast Fourier Transform (FFT) patterns imply that both phases exhibit single crystalline at ε = 0. The HRTEM image in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(a3), obtained by magnifying the yellow square in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(a1), demonstrates an Isaichev OR between α–Fe and θ–Fe<sub>3</sub>C phases. <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(b1) displays bending θ–Fe<sub>3</sub>C lamellae at ε = 2.18, with blurred interphase boundaries. The thickness of θ–Fe<sub>3</sub>C lamellae in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(b1) decreases as ε increases. The FFT patterns of the α–Fe phase and θ–Fe<sub>3</sub>C in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(b2) are similar to those in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(a2).</div><div class='html-p'>The strain mapping using GPA method is shown in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(a4,b4) and only the strain component xx is depicted. Prior to drawing, strain concentrations are mostly observed at the α–Fe/θ–Fe<sub>3</sub>C interface in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(a4). Additionally, the strain is uniformly distributed throughout α–Fe. This observation suggests that the dislocation densities are low prior to the cold-drawing process. When ε reaches 2.18, there are noticeable strain concentrations within α–Fe and at the interphase boundaries, as shown in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(b4). The dislocation densities rapidly increase due to plastic deformation of both phases caused by cold-drawing, as shown in <a href="#crystals-14-00977-f007" class="html-fig">Figure 7</a>b. The distribution of strain inside the α–Fe phase exhibits non-uniformity, with certain regions experiencing higher levels of strain compared to others.</div><div class='html-p'>Significant strain concentrations suggests that a large number of dislocations are formed in the regions surrounding the interphase boundaries during cold-drawing at ε = 2.81, in comparison to that before drawing. The diffusion of C atoms in a solid solution into the dislocation cores is facilitated by the strong interaction between C and dislocations [<a href="#B10-crystals-14-00977" class="html-bibr">10</a>]. Dislocations are locked down by so-called Cottrell atmospheres, as described in reference [<a href="#B12-crystals-14-00977" class="html-bibr">12</a>,<a href="#B14-crystals-14-00977" class="html-bibr">14</a>]. Cottrell atmospheres segregated into dislocations have been proven by APT studies [<a href="#B14-crystals-14-00977" class="html-bibr">14</a>,<a href="#B17-crystals-14-00977" class="html-bibr">17</a>]. Disordered Cottrell atmospheres are considered in the solution strengthening contributions in cold-drawn pearlitic steel wires. In martensitic steels [<a href="#B20-crystals-14-00977" class="html-bibr">20</a>] and low carbon steels [<a href="#B30-crystals-14-00977" class="html-bibr">30</a>], Cottrell atmosphere strengthening is also investigated.</div></section><section id='sec4dot3-crystals-14-00977' type=''><h4 class='html-italic' data-nested='2'> 4.3. SRO Cluster Strengthening</h4><div class='html-p'>Solution-treated steel wires have low dislocation density, as shown in <a href="#crystals-14-00977-f007" class="html-fig">Figure 7</a>b and <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(a4), as well as very low vacancy concentration. At the same time, carbon concentration is much lower in α–Fe than in θ–Fe<sub>3</sub>C, which is also verified by APT [<a href="#B6-crystals-14-00977" class="html-bibr">6</a>]. Therefore, Cottrell atmosphere strengthening is weaker than that in cold-drawn conditions. SRO clusters are observed in cold-drawn pearlitic steel wires before and after the different strains. It is generally believed that the formation of SRO is related to interstitial atoms, such as C, boron (N), nitrogen (N), and hydrogen (H) [<a href="#B31-crystals-14-00977" class="html-bibr">31</a>,<a href="#B32-crystals-14-00977" class="html-bibr">32</a>]. Kim et al. [<a href="#B23-crystals-14-00977" class="html-bibr">23</a>] report the influence of C addition on the mechanical properties of high–Mn TRIP steels and find that C can be used to manipulate plastic instability and SRO clusters. In Fe–40Ni–15Cr–0.25 N (wt.%) austenitic stainless steel, Grujicic et al. [<a href="#B33-crystals-14-00977" class="html-bibr">33</a>] determined that N strongly tends to occupy interstitial sites with high concentrations of Cr atoms, which results in the formation of SRO clusters. In B-doped high-entropy alloys (HEA), it is found that soluble B increases the stress/strain field at the recrystallized HEA grain structure, leading to the generation of SRO in those deformation structures under loading [<a href="#B34-crystals-14-00977" class="html-bibr">34</a>]. Lu et al. [<a href="#B35-crystals-14-00977" class="html-bibr">35</a>] also find that SRO is a result of ordered interstitial complexes in the BCC HEAs doped with either 2.0 at %O or N, (Ta<sub>0.5</sub>Nb<sub>0.5</sub>HfZrTi)<sub>98</sub>O<sub>2</sub> and (Ta<sub>0.5</sub>Nb<sub>0.5</sub>HfZrTi)<sub>98</sub>N<sub>2</sub>.</div><div class='html-p'>The octahedral position pertaining to C interstitial atoms can result in SRO in the pearlitic steels and other BCC alloys. There may be other C configurations or clusters that are responsible for SRO. Numerous studies suggest that the formation of SRO in high-Mn steel originates from Mn–C clusters [<a href="#B36-crystals-14-00977" class="html-bibr">36</a>]. Kim et al. [<a href="#B23-crystals-14-00977" class="html-bibr">23</a>] suggest that an SRO structure is caused by the short-range clustering (SRC) of carbon vacancies (CV), which is referred to as CV SRO. CV pairs can be more easily formed by a short-range C ordering than Mn–C clusters. In austenitic steels, the mechanism of interstitial–interstitial (i–i) atom pair re-orientation is responsible for SRO, rather than re-orientation of interstitial–substitutional (i–s) atoms and interstitial atom–vacancy (i–v) pairs re-orientation [<a href="#B37-crystals-14-00977" class="html-bibr">37</a>]. In our work, there are few accounts of substitutional Mn and Cr elements in the pearlitic steel with the composition of Fe–0.82C–0.50Mn–0.22Si–0.03Cr in wt.%, and C is the dominant interstitial atom. Consequently, i–s pairs are not the factor for SRO. Dislocation density and vacancies are much lower in solution-treated conditions. Therefore, the C ordered arrangement results in SRO clusters. Deformation-induced vacancies are easily formed in cold-drawn conditions, meaning that SRO could be related with CV-ordered clusters in the pearlitic steels.</div><div class='html-p'>The dislocation density increases with ε, as presented in <a href="#crystals-14-00977-f007" class="html-fig">Figure 7</a>b. If only the carbon atoms in α–Fe phases diffuse into dislocations to form disordered Cottrell atmospheres, the initial SRO structure will be quickly broken down by cold-drawing. Nevertheless, SRO constructions continue to maintain their prevalence at ε = 2.18. This finding suggests that there exists a sufficient quantity of carbon resources that can diffuse into both the ordered sites and dislocation cores. Only deformation-induced θ–Fe<sub>3</sub>C dissolution can yield a large number of C atoms. The dislocations are predominantly distributed within the α–Fe lamellae, as depicted in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(a3–c3). The interphase borders pin both ends of the dislocation lines during the cold-drawing, causing the accumulation of dislocations along the boundaries (<a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(b4)). Based on the results of EDS mapping in <a href="#crystals-14-00977-f003" class="html-fig">Figure 3</a>, XRD patterns in <a href="#crystals-14-00977-f006" class="html-fig">Figure 6</a>, GPA analysis in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>, and other findings [<a href="#B8-crystals-14-00977" class="html-bibr">8</a>], the strong interaction between dislocations and θ–Fe<sub>3</sub>C leads to the dissolution and amorphization of θ–Fe<sub>3</sub>C. A robust carbon-dislocation interaction in α–Fe enhances the solution of carbon atoms in α–Fe [<a href="#B16-crystals-14-00977" class="html-bibr">16</a>,<a href="#B38-crystals-14-00977" class="html-bibr">38</a>]. It is advantageous for the production of both SRO clusters and disordered Cottrell atmospheres when carbon is present in a solid solution in α–Fe phase. SRO clusters in the present study further verify the transfer of carbon atoms from dissolved θ–Fe<sub>3</sub>C to the α–Fe phase, as well as the carbon supersaturation of the α–Fe phase in the cold-drawn wires.</div><div class='html-p'>Dislocation density is much higher in cold-drawn conditions than in solution treatment while the dislocation density distribution is locally non-uniform, as show in <a href="#crystals-14-00977-f009" class="html-fig">Figure 9</a>(b4). The disordered Cottrell atmospheres and SRO clusters are both generated in cold-drawn pearlitic steel wires. This feature indicates that the C amount corresponding to a high supersaturation is heterogeneously distributed in the α–Fe matrix.</div><div class='html-p'>The strengthening of SRO clusters has been proved in HEAs [<a href="#B35-crystals-14-00977" class="html-bibr">35</a>,<a href="#B39-crystals-14-00977" class="html-bibr">39</a>,<a href="#B40-crystals-14-00977" class="html-bibr">40</a>], low-carbon steel [<a href="#B30-crystals-14-00977" class="html-bibr">30</a>], and austenitic stainless steels [<a href="#B31-crystals-14-00977" class="html-bibr">31</a>,<a href="#B41-crystals-14-00977" class="html-bibr">41</a>,<a href="#B42-crystals-14-00977" class="html-bibr">42</a>]. It can be concluded that this strengthening mechanism also plays a role in drawn steel wires. Consequently, solution strengthening in the present work can be ascribed to both disordered Cottrell atmospheres and SRO clusters. This finding may be useful for proposing a new model of solution strengthening.</div></section></section><section id='sec5-crystals-14-00977' type='conclusions'><h2 data-nested='1'> 5. Conclusions</h2><dl class='html-order'><dt id=''>(1)</dt><dd><div class='html-p'>With increasing cold-drawn strains, both the interlamellar spacing and cementite lamellae thickness decreases, while dislocation densities significantly increase. The drawn wire has a tensile strength of 2170 MPa when the true stain reaches 2.18. Both disordered Cottrell atmospheres and SRO clusters are formed in cold-drawn pearlitic steel wires. SRO clusters and disordered Cottrell atmospheres contribute to solution strengthening which, together with dislocation strengthening and interlamellar boundary strengthening, form an effective strengthening mechanism in cold-drawn pearlitic steel wires.</div></dd><dt id=''>(2)</dt><dd><div class='html-p'>Deformation-induced cementite dissolution occurs during cold-drawing progress, which release many C atoms. Both the supersaturation of C and the dislocation density are heterogeneously distributed in the α–Fe matrix. The strong binding between C atoms and dislocation leads to the creation of disordered Cottrell atmospheres.</div></dd><dt id=''>(3)</dt><dd><div class='html-p'>SRO clusters are formed both before and after the heavy cold-drawing in pearlitic steel wires. The ordered distribution of the released C from cementite dissolution within ferrite phases creates short-range order (SRO). SRO clusters are formed both before and after the heavy cold-drawing in pearlitic steel wires, which validates the occurrence of deformation-induced θ–Fe<sub>3</sub>C dissolution. The ordered distribution of C released by θ–Fe<sub>3</sub>C dissolution in α–Fe phases generates SRO clusters.</div></dd></dl></section> </div> <div class="html-back"> <section class='html-notes'><h2 >Author Contributions</h2><div class='html-p'>Conceptualization, G.Z. (Gang Zhao), J.J., F.B. and H.Z.; methodology, G.Z. (Gang Zhao), J.J., F.B. and H.Z.; validation, G.Z. (Gang Zhao), J.J., Y.W. and H.Z.; formal analysis, G.Z. (Gang Zhao), J.J., Y.W., J.X. and Y.Z.; investigation, G.Z. (Gang Zhao), J.J., F.B., H.Z., J.X. and Y.Z.; data curation, G.Z. (Gang Zhao), J.J., Y.W., F.B., H.Z., J.X. and Y.Z.; writing—original draft preparation, G.Z. (Gang Zhao), F.B. and H.Z.; writing—review and editing, G.Z. (Gang Zhao), F.B., H.Z. and G.Z. (Guangwen Zheng); project administration, F.B., H.Z. and G.Z. (Guangwen Zheng); funding acquisition, F.B. and H.Z. All authors have read and agreed to the published version of the manuscript.</div></section><section class='html-notes'><h2>Funding</h2><div class='html-p'>This research was funded by Natural Science Foundation of China, grant number 52174359, and Natural Science Foundation of Anhui, grant numbers 2022AH050325 and 2022AH050327, Domestic Visit and Training Project of Young Backbone Teachers in Anhui Province, grant number JNFX2024012, and Overseas Visit and Training Project of Young Backbone Teachers in Anhui Province, grant number JWFX2023012.</div></section><section class='html-notes'><h2 >Data Availability Statement</h2><div class='html-p'>The original contributions presented in the study are included in this article, further inquiries can be made available by the corresponding author.</div></section><section class='html-notes'><h2 >Conflicts of Interest</h2><div class='html-p'>The authors declare no conflicts of interest.</div></section><section id='html-references_list'><h2>References</h2><ol class='html-xx'><li id='B1-crystals-14-00977' class='html-x' data-content='1.'>Wei, D.; Wang, L.; Hu, X.; Fang, F. 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data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g001.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g001.png" alt="Crystals 14 00977 g001" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g001-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f001"></a> </div> </div> <div class="html-fig_description"> <b>Figure 1.</b> (<b>a</b>) Schematic of the tensile specimens; (<b>b</b>) tensile stress–strain curves of wires with the different true stains; (<b>c</b>) tensile strength, yield strength and elongation vs drawn strains. <!-- <p><a class="html-figpopup" href="#fig_body_display_crystals-14-00977-f001"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_crystals-14-00977-f001"> <div class="html-caption"> <b>Figure 1.</b> (<b>a</b>) Schematic of the tensile specimens; (<b>b</b>) tensile stress–strain curves of wires with the different true stains; (<b>c</b>) tensile strength, yield strength and elongation vs drawn strains.</div> <div class="html-img"><img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g001.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g001.png" alt="Crystals 14 00977 g001" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g001.png" /></div> </div> <div class="html-fig-wrap" id="crystals-14-00977-f002"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f002"> <img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g002.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g002.png" alt="Crystals 14 00977 g002" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g002-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f002"></a> </div> </div> <div class="html-fig_description"> <b>Figure 2.</b> TEM images of wires in solution treatment before cold-drawing: (<b>a</b>) pearlitic in different colonies; (<b>b</b>,<b>c</b>) bright field (BF) and dark field (DF) images of complete lamellar; (<b>d</b>,<b>e</b>) BF and DF images of broken θ–Fe<sub>3</sub>C; (<b>f</b>) a SADP of lamellar in (<b>b</b>). <!-- <p><a class="html-figpopup" href="#fig_body_display_crystals-14-00977-f002"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_crystals-14-00977-f002"> <div class="html-caption"> <b>Figure 2.</b> TEM images of wires in solution treatment before cold-drawing: (<b>a</b>) pearlitic in different colonies; (<b>b</b>,<b>c</b>) bright field (BF) and dark field (DF) images of complete lamellar; (<b>d</b>,<b>e</b>) BF and DF images of broken θ–Fe<sub>3</sub>C; (<b>f</b>) a SADP of lamellar in (<b>b</b>).</div> <div class="html-img"><img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g002.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g002.png" alt="Crystals 14 00977 g002" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g002.png" /></div> </div> <div class="html-fig-wrap" id="crystals-14-00977-f003"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f003"> <img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g003.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g003.png" alt="Crystals 14 00977 g003" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g003-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f003"></a> </div> </div> <div class="html-fig_description"> <b>Figure 3.</b> TEM images and corresponding EDS mapping of wires before and after cold-drawing: (<b>a</b>,<b>b</b>) ε = 0; (<b>c</b>,<b>d</b>) ε = 2.18. <!-- <p><a class="html-figpopup" href="#fig_body_display_crystals-14-00977-f003"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_crystals-14-00977-f003"> <div class="html-caption"> <b>Figure 3.</b> TEM images and corresponding EDS mapping of wires before and after cold-drawing: (<b>a</b>,<b>b</b>) ε = 0; (<b>c</b>,<b>d</b>) ε = 2.18.</div> <div class="html-img"><img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g003.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g003.png" alt="Crystals 14 00977 g003" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g003.png" /></div> </div> <div class="html-fig-wrap" id="crystals-14-00977-f004"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f004"> <img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g004.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g004.png" alt="Crystals 14 00977 g004" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g004-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f004"></a> </div> </div> <div class="html-fig_description"> <b>Figure 4.</b> TEM images of pearlitic structures: (<b>a</b>) wire rod; (<b>b</b>) ε = 0.81; (<b>c</b>) ε = 2.18; (<b>a1</b>,<b>b1</b>,<b>c1</b>) BF images; (<b>a2</b>,<b>b2</b>,<b>c2</b>) the corresponding DF images; (<b>a3</b>,<b>b3</b>,<b>c3</b>) dislocation configurations in α–Fe; (<b>a4</b>,<b>b4</b>,<b>c4</b>) SADP of the areas marked by circles in (<b>a3</b>,<b>b3</b>,<b>c3</b>). <!-- <p><a class="html-figpopup" href="#fig_body_display_crystals-14-00977-f004"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_crystals-14-00977-f004"> <div class="html-caption"> <b>Figure 4.</b> TEM images of pearlitic structures: (<b>a</b>) wire rod; (<b>b</b>) ε = 0.81; (<b>c</b>) ε = 2.18; (<b>a1</b>,<b>b1</b>,<b>c1</b>) BF images; (<b>a2</b>,<b>b2</b>,<b>c2</b>) the corresponding DF images; (<b>a3</b>,<b>b3</b>,<b>c3</b>) dislocation configurations in α–Fe; (<b>a4</b>,<b>b4</b>,<b>c4</b>) SADP of the areas marked by circles in (<b>a3</b>,<b>b3</b>,<b>c3</b>).</div> <div class="html-img"><img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g004.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g004.png" alt="Crystals 14 00977 g004" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g004.png" /></div> </div> <div class="html-fig-wrap" id="crystals-14-00977-f005"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f005"> <img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g005.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g005.png" alt="Crystals 14 00977 g005" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g005-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f005"></a> </div> </div> <div class="html-fig_description"> <b>Figure 5.</b> Spacing of cold-drawn steel wire lamellae under different strains:(<b>a</b>) interlamellar spacing (ILS); (<b>b</b>) cementite lamellar thickness (CLT). <!-- <p><a class="html-figpopup" href="#fig_body_display_crystals-14-00977-f005"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_crystals-14-00977-f005"> <div class="html-caption"> <b>Figure 5.</b> Spacing of cold-drawn steel wire lamellae under different strains:(<b>a</b>) interlamellar spacing (ILS); (<b>b</b>) cementite lamellar thickness (CLT).</div> <div class="html-img"><img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g005.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g005.png" alt="Crystals 14 00977 g005" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g005.png" /></div> </div> <div class="html-fig-wrap" id="crystals-14-00977-f006"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f006"> <img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g006.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g006.png" alt="Crystals 14 00977 g006" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g006-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f006"></a> </div> </div> <div class="html-fig_description"> <b>Figure 6.</b> XRD patterns of cold-drawn wires. <!-- <p><a class="html-figpopup" href="#fig_body_display_crystals-14-00977-f006"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_crystals-14-00977-f006"> <div class="html-caption"> <b>Figure 6.</b> XRD patterns of cold-drawn wires.</div> <div class="html-img"><img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g006.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g006.png" alt="Crystals 14 00977 g006" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g006.png" /></div> </div> <div class="html-fig-wrap" id="crystals-14-00977-f007"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f007"> <img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g007.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g007.png" alt="Crystals 14 00977 g007" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g007-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f007"></a> </div> </div> <div class="html-fig_description"> <b>Figure 7.</b> The dislocation density (<span class='html-italic'>ρ</span>) of the cold-drawn wires: (<b>a</b>) linear fitting plots for the diffraction patterns of the wires in <a href="#crystals-14-00977-f006" class="html-fig">Figure 6</a>: (<b>b</b>) <span class='html-italic'>ρ</span> as the function of ε. <!-- <p><a class="html-figpopup" href="#fig_body_display_crystals-14-00977-f007"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_crystals-14-00977-f007"> <div class="html-caption"> <b>Figure 7.</b> The dislocation density (<span class='html-italic'>ρ</span>) of the cold-drawn wires: (<b>a</b>) linear fitting plots for the diffraction patterns of the wires in <a href="#crystals-14-00977-f006" class="html-fig">Figure 6</a>: (<b>b</b>) <span class='html-italic'>ρ</span> as the function of ε.</div> <div class="html-img"><img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g007.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g007.png" alt="Crystals 14 00977 g007" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g007.png" /></div> </div> <div class="html-fig-wrap" id="crystals-14-00977-f008"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f008"> <img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g008.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g008.png" alt="Crystals 14 00977 g008" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g008-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f008"></a> </div> </div> <div class="html-fig_description"> <b>Figure 8.</b> The calculated and experimental strengthening of cold-drawn pearlitic steel wires. <!-- <p><a class="html-figpopup" href="#fig_body_display_crystals-14-00977-f008"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_crystals-14-00977-f008"> <div class="html-caption"> <b>Figure 8.</b> The calculated and experimental strengthening of cold-drawn pearlitic steel wires.</div> <div class="html-img"><img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g008.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g008.png" alt="Crystals 14 00977 g008" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g008.png" /></div> </div> <div class="html-fig-wrap" id="crystals-14-00977-f009"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f009"> <img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g009.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g009.png" alt="Crystals 14 00977 g009" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g009-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2073-4352/14/11/977/display" href="#fig_body_display_crystals-14-00977-f009"></a> </div> </div> <div class="html-fig_description"> <b>Figure 9.</b> HRTEM images of α–Fe/θ–Fe<sub>3</sub>C interfaces at: (<b>a</b>) ε = 0, (<b>b</b>) ε = 2.18. (<b>a2</b>,<b>b2</b>) The FFT patterns of α–Fe and θ–Fe<sub>3</sub>C phases in (<b>a1</b>,<b>b1</b>), respectively; (<b>a3</b>,<b>b3</b>) magnified view of the yellow box areas in (<b>a1</b>,<b>b1</b>); and (<b>a4</b>,<b>b4</b>) the corresponding strain maps along the [100]<sub>α-Fe</sub> axis calculated by Strain++ software V1.8 for HRTEM images in (<b>a3</b>,<b>b3</b>). <!-- <p><a class="html-figpopup" href="#fig_body_display_crystals-14-00977-f009"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_crystals-14-00977-f009"> <div class="html-caption"> <b>Figure 9.</b> HRTEM images of α–Fe/θ–Fe<sub>3</sub>C interfaces at: (<b>a</b>) ε = 0, (<b>b</b>) ε = 2.18. (<b>a2</b>,<b>b2</b>) The FFT patterns of α–Fe and θ–Fe<sub>3</sub>C phases in (<b>a1</b>,<b>b1</b>), respectively; (<b>a3</b>,<b>b3</b>) magnified view of the yellow box areas in (<b>a1</b>,<b>b1</b>); and (<b>a4</b>,<b>b4</b>) the corresponding strain maps along the [100]<sub>α-Fe</sub> axis calculated by Strain++ software V1.8 for HRTEM images in (<b>a3</b>,<b>b3</b>).</div> <div class="html-img"><img data-large="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g009.png" data-original="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g009.png" alt="Crystals 14 00977 g009" data-lsrc="/crystals/crystals-14-00977/article_deploy/html/images/crystals-14-00977-g009.png" /></div> </div> </section><section class='html-fn_group'><table><tr id=''><td></td><td><div class='html-p'><b>Disclaimer/Publisher’s Note:</b> The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). 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margin-top: 15px;"> <div><b>MDPI and ACS Style</b></div> <p> Zhao, G.; Jiao, J.; Wu, Y.; Bai, F.; Zhou, H.; Xue, J.; Zhu, Y.; Zheng, G. Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires. <em>Crystals</em> <b>2024</b>, <em>14</em>, 977. https://doi.org/10.3390/cryst14110977 </p> <div style="display: block"> <b>AMA Style</b><br> <p> Zhao G, Jiao J, Wu Y, Bai F, Zhou H, Xue J, Zhu Y, Zheng G. Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires. <em>Crystals</em>. 2024; 14(11):977. https://doi.org/10.3390/cryst14110977 </p> <b>Chicago/Turabian Style</b><br> <p> Zhao, Gang, Jianyu Jiao, Yan Wu, Fengmei Bai, Hongwei Zhou, Jun Xue, Yixuan Zhu, and Guangwen Zheng. 2024. "Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires" <em>Crystals</em> 14, no. 11: 977. https://doi.org/10.3390/cryst14110977 </p> <b>APA Style</b><br> <p> Zhao, G., Jiao, J., Wu, Y., Bai, F., Zhou, H., Xue, J., Zhu, Y., & Zheng, G. (2024). Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires. <em>Crystals</em>, <em>14</em>(11), 977. https://doi.org/10.3390/cryst14110977 </p> </div> </div> <div class="info-box no-margin"> Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. 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Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires. <em>Crystals</em> <b>2024</b>, <em>14</em>, 977. https://doi.org/10.3390/cryst14110977 </p> <div style="display: block"> <b>AMA Style</b><br> <p> Zhao G, Jiao J, Wu Y, Bai F, Zhou H, Xue J, Zhu Y, Zheng G. Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires. <em>Crystals</em>. 2024; 14(11):977. https://doi.org/10.3390/cryst14110977 </p> <b>Chicago/Turabian Style</b><br> <p> Zhao, Gang, Jianyu Jiao, Yan Wu, Fengmei Bai, Hongwei Zhou, Jun Xue, Yixuan Zhu, and Guangwen Zheng. 2024. "Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires" <em>Crystals</em> 14, no. 11: 977. https://doi.org/10.3390/cryst14110977 </p> <b>APA Style</b><br> <p> Zhao, G., Jiao, J., Wu, Y., Bai, F., Zhou, H., Xue, J., Zhu, Y., & Zheng, G. (2024). Solution Strengthening and Short-Range Order in Cold-Drawn Pearlitic Steel Wires. <em>Crystals</em>, <em>14</em>(11), 977. https://doi.org/10.3390/cryst14110977 </p> </div> </div> <div class="info-box no-margin"> Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. 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