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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mater.</journal-id>
<journal-title>Frontiers in Materials</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mater.</abbrev-journal-title>
<issn pub-type="epub">2296-8016</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1135407</article-id>
<article-id pub-id-type="doi">10.3389/fmats.2023.1135407</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Materials</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Why do cracks occur in the weld joint of Ti-22Al-25Nb alloy during post-weld heat treatment?</article-title>
<alt-title alt-title-type="left-running-head">Shao et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fmats.2023.1135407">10.3389/fmats.2023.1135407</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Shao</surname>
<given-names>Ling</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Xinyu</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Chen</surname>
<given-names>Yingwei</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Zhu</surname>
<given-names>Liu</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/884341/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Wu</surname>
<given-names>Sujun</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Liu</surname>
<given-names>Qijie</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Li</surname>
<given-names>Weiwei</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Xue</surname>
<given-names>Na</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Tu</surname>
<given-names>Zhibiao</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Tianle</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1675018/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Jitang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Dai</surname>
<given-names>Sheng</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Shi</surname>
<given-names>Xinxing</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Chen</surname>
<given-names>Mengliang</given-names>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Zhejiang Provincial Key Laboratory for Cutting Tools</institution>, <institution>Taizhou University</institution>, <addr-line>Taizhou</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Taizhou Key Laboratory of Medical Devices and Advanced Materials</institution>, <institution>Research Institute of Zhejiang University-Taizhou</institution>, <addr-line>Taizhou</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Taizhou Clean Carbon Technology Company Limited</institution>, <addr-line>Taizhou</addr-line>, <country>China</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>School of Materials Science and Engineering</institution>, <institution>Beihang University</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff5">
<sup>5</sup>
<institution>School of Materials Science and Engineering</institution>, <institution>Zhejiang Sci-Tech University</institution>, <addr-line>Hangzhou</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1146630/overview">Xiangchen Meng</ext-link>, Harbin Institute of Technology, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/871773/overview">Wenbin Zhou</ext-link>, University of Dundee, United Kingdom</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2176510/overview">Pengkang Zhao</ext-link>, Xi&#x2019;an University of Technology, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Liu Zhu, <email>zhuliu@tzc.edu.cn</email>; Sujun Wu, <email>wusj@buaa.edu.cn</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Structural Materials, a section of the journal Frontiers in Materials</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>07</day>
<month>03</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>10</volume>
<elocation-id>1135407</elocation-id>
<history>
<date date-type="received">
<day>31</day>
<month>12</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>20</day>
<month>02</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Shao, Zhang, Chen, Zhu, Wu, Liu, Li, Xue, Tu, Wang, Zhang, Dai, Shi and Chen.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Shao, Zhang, Chen, Zhu, Wu, Liu, Li, Xue, Tu, Wang, Zhang, Dai, Shi and Chen</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Ultrasonic pulse frequency tungsten inert gas welding technology was adopted to join Ti-22Al-25Nb alloy. There were some cracks in the Ti-22Al-25Nb alloy weld joint after post-weld heat treatment. The hardness and Young&#x2019;s modulus of &#x3b1;<sub>2</sub>, O, and <italic>&#x3b2;</italic>/B2 phases in Ti-22Al-25Nb alloy were examined with an <italic>in situ</italic> nanoindentation technique. The phase transition stresses of three different phases in the weld joint of Ti-22Al-25Nb alloy were analyzed to explain why cracks occur in the weld joint of Ti-22Al-25Nb alloy during post-weld heat treatment. The results show that mean hardness is highest for the &#x3b1;<sub>2</sub> phase, second-highest for the O phase, and lowest for the <italic>&#x3b2;</italic>/B2 phase; the mean Young&#x2019;s modulus has the same trend in Ti-22Al-25Nb alloy. Phase transition stress results in cracks in the weld joint of Ti-22Al-25Nb alloy during post-weld heat treatment. By improving post-weld heat treatment, the ultimate strength of the Ti-22Al-25Nb alloy weld joints reaches 750&#xa0;MPa, which is 72.5% that of the base material.</p>
</abstract>
<kwd-group>
<kwd>Ti-22Al-25Nb alloy</kwd>
<kwd>weld joint</kwd>
<kwd>post-weld heat treatment</kwd>
<kwd>
<italic>in situ</italic> nanoindentation</kwd>
<kwd>phase transition stress</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Ti<sub>2</sub>AlNb-based alloys, known as orthorhombic alloys, have drawn much attention for having great potential in advanced automotive and aerospace applications due to their high specific strength and stiffness, excellent oxidation and creep resistance at elevated temperatures, good room temperature toughness and workability, as well as low density (<xref ref-type="bibr" rid="B35">Zhang et al., 2021a</xref>; <xref ref-type="bibr" rid="B9">Han et al., 2022</xref>; <xref ref-type="bibr" rid="B15">Li et al., 2022</xref>; <xref ref-type="bibr" rid="B38">Zhang et al., 2022</xref>). As a second generation of Ti<sub>2</sub>AlNb-based alloys, Ti-22Al-25Nb (at%) alloy exhibits high strength and large elongation to failure at both room and elevated temperatures and thus attracts interest in scientific circles (<xref ref-type="bibr" rid="B31">Yang et al., 2019</xref>; <xref ref-type="bibr" rid="B41">Zhou et al., 2019</xref>). In some cases, Ti-22Al-25Nb alloy, like any structural material, must be welded to fabricate components with complex geometries. The joining of Ti-22Al-25Nb alloy has been conducted using various welding technologies, such as diffusion bonding welding (<xref ref-type="bibr" rid="B42">Zou et al., 2009</xref>; <xref ref-type="bibr" rid="B6">Chu et al., 2017</xref>), electron beam welding (<xref ref-type="bibr" rid="B3">Chen et al., 2016</xref>; <xref ref-type="bibr" rid="B14">Li et al., 2017</xref>), laser beam welding (<xref ref-type="bibr" rid="B34">Zhang et al., 2021b</xref>; <xref ref-type="bibr" rid="B36">Zhang et al., 2021c</xref>), and friction welding (<xref ref-type="bibr" rid="B4">Chen et al., 2018</xref>; <xref ref-type="bibr" rid="B39">Zhao et al., 2020</xref>). The main shortcomings of these Ti-22Al-25Nb alloy welding methods are their high cost and limited versatility.</p>
<p>In a previous study (<xref ref-type="bibr" rid="B25">Shao et al., 2018a</xref>), we adopted ultrasonic pulse frequency tungsten inert gas (TIG) welding technology to join Ti-22Al-25Nb alloy, due to its advantages of versatile workpiece shape requirements, low cost, and simplicity. Post-weld heat treatment (PWHT) is widely used to relieve the residual stresses caused by welding (<xref ref-type="bibr" rid="B27">Somashekara et al., 2016</xref>) and can stabilize the structure and properties of the joints (<xref ref-type="bibr" rid="B21">Panov et al., 2022</xref>). Ti-22Al-25Nb alloy, which primarily consists of a two-phase <italic>&#x3b2;</italic>/B2 &#x2b; O microstructure, has the optimum combination of strength, creep, and fracture toughness properties (<xref ref-type="bibr" rid="B37">Zhang et al., 2021d</xref>). In order to completely remove the residual stress and to have a similar strength as the base material, PWHT was carried out on the weld joint Ti-22Al-25Nb alloy at the temperature range of the <italic>&#x3b2;</italic>/B2 &#x2b; O two-phase region. However, cracks were found in the weld joint of Ti-22Al-25Nb alloy after PWHT.</p>
<p>Nanoindentation has become an increasingly popular technique for determining the properties of various materials (metals, composites, polymers, coatings, films, <italic>etc.</italic>) (<xref ref-type="bibr" rid="B17">Ma et al., 2020</xref>; <xref ref-type="bibr" rid="B23">Rominiyi and Mashinini, 2023</xref>). The technique has been used for extracting residual stress field (<xref ref-type="bibr" rid="B40">Zhou et al., 2015</xref>), investigating the phase transformation process (<xref ref-type="bibr" rid="B29">Wang et al., 2017</xref>), and examining the hardness and Young&#x2019;s modulus (<xref ref-type="bibr" rid="B11">Jin et al., 2023</xref>). In particular, the <italic>in situ</italic> nanoindentation technique is conducted using a scanning electron microscope (SEM), which can visualize the behavior of the material in real-time (<xref ref-type="bibr" rid="B12">Juri et al., 2021</xref>). In this study, an <italic>in situ</italic> nanoindentation technique was used to examine the hardness and Young&#x2019;s modulus of three different phases in the Ti-22Al-25Nb alloy. Load&#x2013;displacement (<italic>P</italic>-<italic>h</italic>) curves were converted to indentation stress&#x2013;strain (<italic>&#x3c3;</italic>-<italic>&#x3b5;</italic>) curves in order to analyze the phase transition stresses of the three different phases in the weld joints of Ti-22Al-25Nb alloy and to better explain why cracks occur in the weld joint of Ti-22Al-25Nb alloy during PWHT.</p>
</sec>
<sec sec-type="materials|methods" id="s2">
<title>2 Materials and methods</title>
<p>A Ti-22Al-25Nb alloy butt joint with a high ultimate strength was obtained by ultrasonic pulse frequency TIG welding technology under welding parameters of 50&#xa0;KHz pulse frequency, 125&#xa0;mm&#xa0;min<sup>-1</sup> welding speed, 80 A peak current, 35 A base current, 13&#xa0;L&#xa0;min<sup>-1</sup> argon gas flow, a welding wire of 1.5&#xa0;mm diameter, and a welding torch polarity of electrode-positive direct current. A schematic illustration of the experimental setup is shown in <xref ref-type="fig" rid="F1">Figure 1A</xref> and the weld seam appearance of the butt joint is presented in <xref ref-type="fig" rid="F1">Figure 1B</xref>. At the location indicated by the rectangular box in <xref ref-type="fig" rid="F1">Figure 1B</xref>, the specimen was cut along the cross-section by wire cutting used for PWHT. Microstructural features of the cross-section of the weld joint observed using an optical microscope (OM) are given in <xref ref-type="fig" rid="F1">Figure 1C</xref> and exhibit three different zones: fusion zone (FZ), heat-affected zone (HAZ), and base material (BM). The weld joints of Ti-22Al-25Nb alloy after welding were heat treated in an STF1200 tube furnace under argon atmosphere, followed by heating (10&#xb0;C&#xa0;s<sup>-1</sup> heating rate) to 800&#xb0;C, 850&#xb0;C, and 900&#xb0;C, in that order, including a 2-h hold at each temperature, and then cooling to room temperature by decreasing the furnace temperature (<xref ref-type="bibr" rid="B16">Liu, 2013</xref>). <xref ref-type="table" rid="T1">Table 1</xref> shows that the ultimate strength of weld joints is higher before PWHT than after PWHT.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Welding of Ti-22Al-25Nb alloy: <bold>(A)</bold> schematic illustration of the experimental setup; <bold>(B)</bold> weld seam appearance of the weld joint of Ti-22Al-25Nb alloy; <bold>(C)</bold> weld joint includes three different zones: fusion zone (FZ), heat-affected zone (HAZ), and base material (BM).</p>
</caption>
<graphic xlink:href="fmats-10-1135407-g001.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Ultimate strength of the weld joints of Ti-22Al-25Nb alloy before and after post-weld heat treatment.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Temperature of post-weld heat treatment (&#xb0;C)</th>
<th align="center">Ultimate strength (MPa)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">0</td>
<td align="center">906 &#xb1; 15</td>
</tr>
<tr>
<td align="center">800</td>
<td align="center">204 &#xb1; 18</td>
</tr>
<tr>
<td align="center">850</td>
<td align="center">277 &#xb1; 12</td>
</tr>
<tr>
<td align="center">900</td>
<td align="center">388 &#xb1; 14</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Optical microscopy for metallurgical examination of the weld joints was performed on a Keyence VHX-500F digital optical microscope, after the specimens were cut perpendicular to the welding direction of the joint using electro-discharge machining (EDM). The cross-sections of the specimens were polished for microstructural characterization. The samples were ground with wet abrasive paper and mechanically polished using a velvet cloth to obtain mirror-polished sections and then etched in a solution containing 2&#xa0;mL HF, 2&#xa0;mL HNO<sub>3</sub>, and 80&#xa0;mL ultrapure water to reveal the microstructure. The cross-sections of the weld joints before and after PWHT are shown in <xref ref-type="fig" rid="F2">Figure 2</xref>. Cracks in the weld joint can be clearly seen after PWHT. We seek to answer the question: why do these cracks occur in the weld joint of Ti-22Al-25Nb alloy during PWHT?</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Macromorphology of the weld joints of Ti-22Al-25Nb alloy: <bold>(A)</bold> before post-weld heat treatment and <bold>(B)</bold> after post-weld heat treatment. <bold>(C)</bold> Magnification of the area indicated by the rectangular box in <bold>(B)</bold>.</p>
</caption>
<graphic xlink:href="fmats-10-1135407-g002.tif"/>
</fig>
<p>The phase constituents of the Ti-22Al-25Nb alloy plate were investigated by X-ray diffraction (XRD, Bruker D8 Avance) using Cu&#x2013;K&#x3b1; radiation at a diffraction angle of 2<italic>&#x3b8;</italic> from 10 to 90&#xb0; with a step width of 0.02&#xb0; and a scan speed of 3&#xb0; min<sup>-1</sup>. The microstructure of the Ti-22Al-25Nb alloy plate was characterized by scanning electron microscopy using a Hitachi SU8230 cold-field emission (CFE) microscope. An extremely smooth surface of the observed sample was obtained by grinding with 2,500-grit paper and polishing to a 0.05-&#x3bc;m surface. <italic>In situ</italic> nanoindentation tests were performed to determine the elastic and plastic properties of phases at room temperature using a Hysitron Triboindenter with a Berkovich tip. Load-controlled indentations were made using a constant loading rate of 100&#xa0;&#x3bc;N&#xa0;s<sup>-1</sup> up to maximum load of 500&#xa0;&#x3bc;N and then equilibrated at 500&#xa0;&#x3bc;N for 2&#xa0;s before unloading.</p>
</sec>
<sec sec-type="results|discussion" id="s3">
<title>3 Results and discussion</title>
<p>To answer the question &#x201c;why do cracks occur in the weld joint of Ti-22Al-25Nb alloy during PWHT?&#x201d;, a Ti-22Al-25Nb alloy plate consisting of <italic>&#x3b2;</italic>/B2 matrix, equiaxed &#x3b1;<sub>2</sub> particle, and lath-shaped O phase (<xref ref-type="fig" rid="F3">Figure 3</xref>) was adopted. The phase constituents of the Ti-22Al-25Nb alloy plate were examined by XRD (<xref ref-type="fig" rid="F3">Figure 3A</xref>). The microstructure of the Ti-22Al-25Nb alloy plate (<xref ref-type="fig" rid="F3">Figures 3B,C</xref>) was observed with an SEM. The dark phase corresponds to the &#x3b1;<sub>2</sub> phase, the gray phase corresponds to the O phase, and the lightest phase is the <italic>&#x3b2;</italic>/B2 phase. The phases in the weld joint of Ti-22Al-25Nb alloy before PWHT contained &#x3b1;<sub>2</sub> (D0<sub>19</sub> structure based on Ti<sub>3</sub>Al), O (Cmcm system based on Ti<sub>2</sub>AlNb), and either &#x3b2; (disordered structure, the allotrope of titanium) or B2 (ordered structure) (<xref ref-type="bibr" rid="B26">Shao et al., 2018b</xref>; <xref ref-type="bibr" rid="B33">Zavodov et al., 2021</xref>), as shown in <xref ref-type="fig" rid="F4">Figure 4</xref>.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>X-ray diffraction pattern <bold>(A)</bold> and microstructure <bold>(B)</bold> and <bold>(C)</bold> of Ti-22Al-25Nb alloy. Dark phase corresponds to &#x3b1;<sub>2</sub> phase, gray phase corresponds to O phase, and lightest phase is &#x3b2;/B2 phase.</p>
</caption>
<graphic xlink:href="fmats-10-1135407-g003.tif"/>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>X-ray diffraction patterns of different zones in the weld joint of Ti-22Al-25Nb alloy before post-weld heat treatment: <bold>(A)</bold> fusion zone (FZ), <bold>(B)</bold> heat-affected zone (HAZ).</p>
</caption>
<graphic xlink:href="fmats-10-1135407-g004.tif"/>
</fig>
<p>The lattice parameters of the body-centered cubic <italic>&#x3b2;</italic>/B2 phase were a &#x3d; b &#x3d; c &#x3d; 0.328 nm, &#x3b1; &#x3d; &#x3b2; &#x3d; &#x3b3; &#x3d; 90&#xb0;, and V &#x3d; 0.03516&#xa0;nm<sup>3</sup> (from PDF Card No. 01&#x2013;077&#x2013;3482). The lattice parameters of the hexagonal close-packed &#x3b1;<sub>2</sub> phase were a &#x3d; b &#x3d; 0.576 nm, c &#x3d; 0.466 nm, &#x3b1; &#x3d; &#x3b2; &#x3d; 90&#xb0;, &#x3b3; &#x3d; 120&#xb0;, and V &#x3d; 0.13420&#xa0;nm<sup>3</sup> (from PDF Card No. 01&#x2013;074&#x2013;4579 (<xref ref-type="bibr" rid="B19">Novoselova et al., 2004</xref>)). The lattice parameters of the orthorhombic O phase were a &#x3d; 0.609 nm, b &#x3d; 0.957 nm, c &#x3d; 0.467 nm, &#x3b1; &#x3d; &#x3b2; &#x3d; &#x3b3; &#x3d; 90&#xb0;, and V &#x3d; 0.27193&#xa0;nm<sup>3</sup> (from PDF Card No. 01&#x2013;072&#x2013;8492 (<xref ref-type="bibr" rid="B18">Mozer et al., 1990</xref>; <xref ref-type="bibr" rid="B30">Wei et al., 2017</xref>)). The densities of <italic>&#x3b2;</italic>/B2, &#x3b1;<sub>2</sub>, and O phases were calculated as density &#x3d; (mass of atoms in the unit cell)/(volume of unit cell) (<xref ref-type="bibr" rid="B13">Kasap, 2001</xref>), as shown in <xref ref-type="table" rid="T2">Table 2</xref>. The densities of the three different phases in the weld joint of Ti-22Al-25Nb alloy follow the order O phase &#x3e; &#x3b2;/B2 phase &#x3e; &#x3b1;<sub>2</sub> phase. Therefore, it can be concluded that the volumes of the three different phases follow the order &#x3b1;<sub>2</sub> phase &#x3e; &#x3b2;/B2 phase &#x3e; O phase. The <italic>B</italic>/<italic>G</italic> ratio of the bulk modulus to the shear modulus is an index of ductility; the larger the ratio, the higher the ductility (<xref ref-type="bibr" rid="B28">Tanaka et al., 1996</xref>). The <italic>B</italic>/<italic>G</italic> ratio of the three different phases in the weld joint of Ti-22Al-25Nb alloy (<xref ref-type="table" rid="T2">Table 2</xref>) shows that the ductility of the <italic>&#x3b2;</italic>/B2 phase is the highest, &#x3b1;<sub>2</sub> phase second, and O phase lowest.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Density (<italic>&#x3c1;</italic>) and elastic constants such as bulk modulus (<italic>B</italic>), shear modulus (<italic>G</italic>), <italic>B</italic>/<italic>G</italic> ratio, and Poisson&#x2019;s ratio (<italic>&#x3c5;</italic>) for <italic>&#x3b2;</italic>/B2, &#x3b1;<sub>2</sub>, and O phases (<xref ref-type="bibr" rid="B22">Pathak and Singh, 2015</xref>).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Phase</th>
<th align="center">
<italic>&#x3c1;</italic> (g cm<sup>-3</sup>)</th>
<th align="center">
<italic>B</italic> (GPa)</th>
<th align="center">
<italic>G</italic> (GPa)</th>
<th align="center">
<italic>B/G</italic>
</th>
<th align="center">
<italic>&#x3c5;</italic>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">&#x3b2;/B2</td>
<td align="char" char=".">4.5215</td>
<td align="char" char=".">112</td>
<td align="char" char=".">45</td>
<td align="char" char=".">2.500</td>
<td align="char" char=".">0.3236</td>
</tr>
<tr>
<td align="center">&#x3b1;<sub>2</sub> (Ti<sub>3</sub>Al)</td>
<td align="char" char=".">0.7036</td>
<td align="char" char=".">111</td>
<td align="char" char=".">47</td>
<td align="char" char=".">2.364</td>
<td align="char" char=".">0.3146</td>
</tr>
<tr>
<td align="center">O (Ti<sub>2</sub>AlNb)</td>
<td align="char" char=".">6.5836</td>
<td align="char" char=".">100</td>
<td align="char" char=".">51</td>
<td align="char" char=".">1.938</td>
<td align="char" char=".">0.2798</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Cai et al. (<xref ref-type="bibr" rid="B1">2016</xref>) reported that the hardness of the <italic>&#x3b2;</italic>/B2 phase (6.11&#xa0;GPa) was higher than that of the O phase (3.85&#xa0;GPa) in Ti<sub>2</sub>AlNb alloy. However, Yang et al. (<xref ref-type="bibr" rid="B32">2012</xref>) proposed that the hardness of the O phase (6.6&#xa0;GPa) was higher than that of the <italic>&#x3b2;</italic>/B2 phase (4.75&#xa0;GPa) in Ti<sub>2</sub>AlNb alloy. In this study, <italic>in situ</italic> nanoindentation technology was adopted to examine the hardness of the three different phases in Ti-22Al-25Nb alloy. <xref ref-type="fig" rid="F5">Figure 5A</xref> shows the loading contact between the Berkovich tip and &#x3b1;<sub>2</sub> phase. The continuous stiffness measurement (CSM) method was used for all the nanoindentation experiments (<xref ref-type="bibr" rid="B7">Datye et al., 2016</xref>; <xref ref-type="bibr" rid="B24">Shao et al., 2017</xref>). <italic>E</italic>
<sub>s</sub> (<italic>E</italic> is the Young&#x2019;s modulus and the subscript <italic>s</italic> refers to the different phases) can be given by the following equation (<xref ref-type="bibr" rid="B20">Oliver and Pharr, 1992</xref>; <xref ref-type="bibr" rid="B5">Choudhury and Ladani, 2014</xref>):<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.000872</mml:mn>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c5;</mml:mi>
<mml:mi>s</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where <italic>&#x3c5;</italic> is the Poisson&#x2019;s ratio and the subscript <italic>s</italic> refers to the different phases<italic>.</italic> The <italic>&#x3c5;</italic> of the three different phases in Ti-22Al-25Nb alloy is presented in <xref ref-type="table" rid="T2">Table 2</xref>. <italic>E</italic>
<sub>
<italic>r</italic>
</sub> is the reduced modulus estimated from the unloading part of the <italic>P</italic>-<italic>h</italic> curve as (<xref ref-type="bibr" rid="B20">Oliver and Pharr, 1992</xref>)<disp-formula id="e2">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msqrt>
<mml:mi>&#x3c0;</mml:mi>
</mml:msqrt>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mfrac>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msqrt>
<mml:mi>A</mml:mi>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where <italic>S</italic> is the unloading stiffness, taken as the slope of the curve at the beginning of unloading and <italic>A</italic> is the projected contact area. Phase hardness (<italic>H</italic>) is given using the expression for an indentation,<disp-formula id="e3">
<mml:math id="m3">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>P</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:math>,<label>(3)</label>
</disp-formula>
</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>
<italic>In situ</italic> nanoindentation test of the three different phases in Ti-22Al-25Nb alloy. <bold>(A)</bold> Image was extracted from an SEM video recorded during the indentation test; <bold>(B)</bold> mean hardness and mean Young&#x2019;s modulus of the three different phases; <bold>(C)</bold> their typical load&#x2013;displacement (<italic>P</italic>-<italic>h</italic>) curves; and <bold>(D)</bold> their indentation stress&#x2013;strain (<italic>&#x3c3;</italic>-<italic>&#x3b5;</italic>) curves.</p>
</caption>
<graphic xlink:href="fmats-10-1135407-g005.tif"/>
</fig>
<p>where <italic>P</italic> is the applied load. The mean hardness and mean Young&#x2019;s modulus of the three different phases in Ti-22Al-25Nb alloy measured by the <italic>in situ</italic> nanoindentation method are shown in <xref ref-type="fig" rid="F5">Figure 5B</xref>, which shows that the mean hardness is highest in the &#x3b1;<sub>2</sub> phase, second-highest in the O phase, and lowest in the <italic>&#x3b2;</italic>/B2 phase, and that the mean Young&#x2019;s modulus has the same trend. In general, phases with lower hardness and Young&#x2019;s modulus present a higher capability of plastic deformation (<xref ref-type="bibr" rid="B1">Cai et al., 2016</xref>). The typical <italic>P</italic>-<italic>h</italic> curves for the &#x3b1;<sub>2</sub>, O, and <italic>&#x3b2;</italic>/B2 phases are presented in <xref ref-type="fig" rid="F5">Figure 5C</xref> and show elastic&#x2013;plastic material responses. The differences in hardness of the materials are evident from the large differences in peak depth (<xref ref-type="bibr" rid="B2">Chen et al., 2009</xref>). As can be seen in <xref ref-type="fig" rid="F5">Figure 5C</xref>, the &#x3b1;<sub>2</sub> phase recovers 60.12&#xa0;nm of the 81.76&#xa0;nm indentation depth, corresponding to an elastic recovery of 21.64&#xa0;nm; the elastic recovery is 23.70&#xa0;nm for the O phase and 19.67&#xa0;nm for the <italic>&#x3b2;</italic>/B2 phase. The <italic>P</italic>-<italic>h</italic> curves were converted to indentation <italic>&#x3c3;</italic>-<italic>&#x3b5;</italic> curves, as shown in <xref ref-type="fig" rid="F5">Figure 5D</xref>. The indentation stress is determined by the equation <italic>&#x3c3;</italic> &#x3d; <italic>P</italic>/<italic>A</italic>. The indentation strain is obtained by formulas established by <xref ref-type="bibr" rid="B10">Hochstetter et al. (2003</xref>):<disp-formula id="e4">
<mml:math id="m4">
<mml:mrow>
<mml:mi>&#x3b5;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.081</mml:mn>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>log</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>X</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1.2</mml:mn>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>1.2</mml:mn>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>tan</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b8;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1.2</mml:mn>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>1.2</mml:mn>
<mml:mi>X</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>tan</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b8;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
<disp-formula id="e5">
<mml:math id="m5">
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mfrac>
<mml:mrow>
<mml:mn>1.2</mml:mn>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.51921</mml:mn>
</mml:mrow>
<mml:mn>0.32598</mml:mn>
</mml:mfrac>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>where <italic>h</italic>
<sub>r</sub> is the plastic depth, <italic>h</italic>
<sub>1</sub> (&#x3d; 5&#xa0;nm) is the tip defect for a well-manufactured Berkovich diamond (<xref ref-type="bibr" rid="B8">Hochstetter et al., 1999</xref>), <italic>X</italic> is the plasticity index, <italic>h</italic>
<sub>t</sub> is the total depth, and <italic>&#x3b8;</italic> (&#x3d; 70.3&#xb0;) is the half tip of a perfect cone.</p>
<p>Strain resulting from phase transition can be obtained from the corresponding stress resulting from phase transition by <italic>&#x3c3;</italic>-<italic>&#x3b5;</italic> curves in <xref ref-type="fig" rid="F5">Figure 5D</xref>. During PWHT (at 800&#xb0;C, 850&#xb0;C, and 900&#xb0;C) in the <italic>&#x3b2;</italic>/B2 &#x2b; O two-phase region, the <italic>&#x3b2;</italic>/B2 phase with a body-centered cubic structure transformed to O phase with an orthorhombic structure, and the volume decreased because the density of the O phase is larger than that of the <italic>&#x3b2;</italic>/B2 phase (<xref ref-type="table" rid="T2">Table 2</xref>). This results in the O phase suffering tensile stress, while the <italic>&#x3b2;</italic>/B2 phase suffers compressive stress. Supposing that one-quarter of the <italic>&#x3b2;</italic>/B2 phase transforms to O phase, it will produce 7.9% phase transition strain, a corresponding compressive stress of 0.59&#xa0;MPa for the <italic>&#x3b2;</italic>/B2 phase, and a corresponding tensile stress of 0.63&#xa0;MPa for the O phase. Therefore, it can be concluded that the cracks result from phase transition stresses in the weld joint of Ti-22Al-25Nb alloy during PWHT.</p>
<p>The PWHT conditions of the weld joint of Ti-22Al-25Nb alloy must be improved to avoid cracks resulting from phase transition stresses. The cleaned weld joint of Ti-22Al-25Nb alloy after welding was heated to 980&#xb0;C (5&#xb0;C&#xa0;s<sup>-1</sup> heating rate) for 2&#xa0;h in a tube furnace under argon atmosphere and then cooled to 850&#xb0;C for 3&#xa0;h, followed by cooling to room temperature by decreasing the furnace temperature. Tensile tests were performed for weld joints of Ti-22Al-25Nb alloy subjected to improved PWHT. The ultimate strength of the weld joints of Ti-22Al-25Nb alloy after improved PWHT can be up to 750&#xa0;MPa, which is close to that of the weld joints of Ti-22Al-25Nb alloy before PWHT and is 72.5% that of the base material (1,035&#xa0;MPa). This improved PWHT procedure is simple, convenient, and highly efficient. It can effectively avoid reducing the ultimate strength of weld joints subjected to a traditional ordinary annealing process.</p>
</sec>
<sec sec-type="conclusion" id="s4">
<title>4 Conclusion</title>
<p>To explain why cracks occurred in the weld joint of Ti-22Al-25Nb alloy during the PWHT process, the phase transition stresses of three different phases in Ti-22Al-25Nb alloy were analyzed with <italic>in situ</italic> nanoindentation technology and several formulas. The main conclusions that can be drawn are as follows.<list list-type="simple">
<list-item>
<p>(1) The densities of the three different phases in the weld joint of Ti-22Al-25Nb alloy follow the order O phase &#x3e; &#x3b2;/B2 phase &#x3e; &#x3b1;<sub>2</sub> phase, while the volumes of the three different phases follow the opposite order.</p>
</list-item>
<list-item>
<p>(2) In the weld joint of Ti-22Al-25Nb alloy, the mean hardness is highest in the &#x3b1;<sub>2</sub> phase, second highest in the O phase, and lowest in the <italic>&#x3b2;</italic>/B2 phase, and the mean Young&#x2019;s modulus has the same trend.</p>
</list-item>
<list-item>
<p>(3) The cracks resulted from phase transition stresses in the weld joint of Ti-22Al-25Nb alloy during PWHT.</p>
</list-item>
<list-item>
<p>(4) The ultimate strength of the weld joints of Ti-22Al-25Nb alloy after improved PWHT can be up to 750&#xa0;MPa, which is close to that of the weld joints of Ti-22Al-25Nb alloy before PWHT and is 72.5% that of the base material (1,035&#xa0;MPa).</p>
</list-item>
</list>
</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s5">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material; further inquiries can be directed to the corresponding authors.</p>
</sec>
<sec id="s6">
<title>Author contributions</title>
<p>LS analyzed the experimental data and wrote the manuscript. LZ and SW provided the idea of the manuscript and gave the main suggestions. Other people helped with the experiments.</p>
</sec>
<sec id="s7">
<title>Funding</title>
<p>The authors would like to acknowledge the National Natural Science Foundation of China (No. 52201187), the General Scientific Research Project of Zhejiang Provincial Education Department (No. Y202249336), the Zhejiang Public Welfare Technology Application Research Project (No. LGC20E010003), and the Science and Technology Plan Project of Taizhou (Nos. 22gya18, 21gya23, 2002gy06).</p>
</sec>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of interest</title>
<p>Authors LS, LZ, WL, NX, ZT, JZ, and SD are employed by Taizhou Clean Carbon Technology Company Limited.</p>
<p>The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s9">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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