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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">732931</article-id>
<article-id pub-id-type="doi">10.3389/fmats.2021.732931</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>Effect of Acidizing Process on the Stress Corrosion Cracking of HP-13Cr Stainless Steel in the Ultra-depth Well Environment</article-title>
<alt-title alt-title-type="left-running-head">Qi et&#x20;al.</alt-title>
<alt-title alt-title-type="right-running-head">Acidizing on SCC of HP-13Cr</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Qi</surname>
<given-names>Wenlong</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhao</surname>
<given-names>Yang</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1366797/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Zhang</surname>
<given-names>Tao</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1033380/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Fuhui</given-names>
</name>
</contrib>
</contrib-group>
<aff>Shenyang National Laboratory for Materials Science, Northeastern University, <addr-line>Shenyang</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/649841/overview">Jianbo Sun</ext-link>, China University of Petroleum, 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/1396457/overview">Zhongyu Cui</ext-link>, Ocean University of China, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/831737/overview">Liang Wu</ext-link>, Chongqing University, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Tao Zhang, <email>zhangtao@mail.neu.edu.cn</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Environmental Degradation of Materials, a section of the journal Frontiers in Materials</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>15</day>
<month>09</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="collection">
<year>2021</year>
</pub-date>
<volume>8</volume>
<elocation-id>732931</elocation-id>
<history>
<date date-type="received">
<day>29</day>
<month>06</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>06</day>
<month>08</month>
<year>2021</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2021 Qi, Zhao, Zhang and Wang.</copyright-statement>
<copyright-year>2021</copyright-year>
<copyright-holder>Qi, Zhao, Zhang and Wang</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&#x20;terms.</p>
</license>
</permissions>
<abstract>
<p>The effect of acidizing process on the stress corrosion cracking of HP-13Cr stainless steel in the ultra-depth well environment was studied by the slow strain rate test, the electrochemical measurement, the microstructure observation, and the finite element modeling. The results indicated that the acidizing process significantly increased the stress corrosion cracking susceptibility of HP-13Cr stainless steel and induced the fracture mode to the brittle characteristic in the high temperature and CO<sub>2</sub> pressure environment. The stress corrosion cracking susceptibility also increased with the increase of temperature and CO<sub>2</sub> pressure. There were dense defects including pits and cracks in the fracture section from the transverse view. After the acidizing process, under tensile stress condition, the increasing roughness will cause the stress concentration and promote the local anodic dissolution, which induces the initiation of stress corrosion cracking.</p>
</abstract>
<kwd-group>
<kwd>key word: acidification</kwd>
<kwd>HP-13Cr stainless steel</kwd>
<kwd>stress corrosion cracking</kwd>
<kwd>roughness</kwd>
<kwd>anodic dissolution</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>For the abundant oil and gas reservoir, ultra-depth well exploitation was widely carried out in northwestern China. The well depth was more than 8,000&#xa0;m with carbonatite rocks and sandstone structures, which brings challenges to effective exploitation (<xref ref-type="bibr" rid="B4">Cui et&#x20;al., 2004</xref>; <xref ref-type="bibr" rid="B13">Lan et&#x20;al., 2015</xref>; <xref ref-type="bibr" rid="B28">Singh et&#x20;al., 2017</xref>; <xref ref-type="bibr" rid="B41">Zhao et&#x20;al., 2019a</xref>). On account of this, many methods such as hydraulic fracturing, steam-assisted gravity drainage, and acidizing are employed to enhance the property value by fast delivery of oil and gas fluid in a cost-effective manner. Among the above effective methods, acidizing has been recognized as the most accessible means to exploit the carbonate and sandstone reservoirs around the northwest of China (<xref ref-type="bibr" rid="B22">Mu and Zhao, 2010</xref>; <xref ref-type="bibr" rid="B41">Zhao et&#x20;al., 2019a</xref>). However, the injection of lived acid (LA) during the acidizing process will cause severe corrosion of tubing and further affect the corrosion behavior of tubing in the formation water (FW), which is ejected from the geothermal environment during the exploitation process. The corrosion protection techniques, such as coating, inhibitors, and developing novel materials, are not effective in such an aggressive environment (<xref ref-type="bibr" rid="B3">Cui et&#x20;al., 2021</xref>; <xref ref-type="bibr" rid="B17">Liu et&#x20;al., 2021</xref>; <xref ref-type="bibr" rid="B29">Song et&#x20;al., 2021</xref>). HP-13Cr stainless steel (SS), containing lower C and higher Ni and Mo than traditional 13Cr SS, was widely used as tubing material in the oil and gas industry because of its appropriate mechanical properties, excellent corrosion resistance, and cost-effectiveness. However, severe corrosion failures occurred after LA immersion.</p>
<p>The corrosion behavior of HP-13Cr SS during the acidizing process and in the FW has been investigated in recent years (<xref ref-type="bibr" rid="B21">Moreira et&#x20;al., 2004</xref>; <xref ref-type="bibr" rid="B22">Mu and Zhao, 2010</xref>; <xref ref-type="bibr" rid="B20">Marcus, 2011</xref>; <xref ref-type="bibr" rid="B26">Qi et&#x20;al., 2021</xref>; <xref ref-type="bibr" rid="B3">Cui et&#x20;al., 2021</xref>; <xref ref-type="bibr" rid="B17">Liu et&#x20;al., 2021</xref>; <xref ref-type="bibr" rid="B29">Song et&#x20;al., 2021</xref>). (<xref ref-type="bibr" rid="B38">Zhang et&#x20;al., 2020</xref>) built the Pourbaix diagram for HP-13Cr SS in the aggressive FW and researched the general corrosion rate and pitting (<xref ref-type="bibr" rid="B21">Moreira et&#x20;al., 2004</xref>; <xref ref-type="bibr" rid="B20">Marcus, 2011</xref>; <xref ref-type="bibr" rid="B43">Zhao et&#x20;al., 2018</xref>; <xref ref-type="bibr" rid="B15">Li et&#x20;al., 2019a</xref>; <xref ref-type="bibr" rid="B16">Li et&#x20;al., 2019b</xref>; <xref ref-type="bibr" rid="B42">Zhao et&#x20;al., 2019b</xref>; <xref ref-type="bibr" rid="B26">Qi et&#x20;al., 2021</xref>; <xref ref-type="bibr" rid="B3">Cui et&#x20;al., 2021</xref>; <xref ref-type="bibr" rid="B17">Liu et&#x20;al., 2021</xref>). The effect of LA composition and the surface roughness on the corrosion behavior of HP-13Cr SS was also studied (<xref ref-type="bibr" rid="B26">Qi et&#x20;al., 2021</xref>; <xref ref-type="bibr" rid="B44">Zhao et&#x20;al., 2020</xref>). While many ultra-depth well tubes fractured due to stress corrosion cracking (SCC), further research interests should be shifted to SCC in the HTHP environment (<xref ref-type="bibr" rid="B45">Zhu et&#x20;al., 2011</xref>; <xref ref-type="bibr" rid="B14">Lei et&#x20;al., 2015</xref>; <xref ref-type="bibr" rid="B39">Zhang et&#x20;al., 2019</xref>). The SCC susceptibility of HP-13Cr SS was up to 42% exposure at 150&#xb0;C and 1&#xa0;MPa CO<sub>2</sub> environment (<xref ref-type="bibr" rid="B36">Yue et&#x20;al., 2018</xref>).</p>
<p>SCC of tubing materials in the high temperature, high CO<sub>2</sub> pressure, and high salinity environments evolved from localized corrosion such as pitting, which may induce the stress concentration (<xref ref-type="bibr" rid="B12">Isaacs, 1988</xref>; <xref ref-type="bibr" rid="B6">Cui et&#x20;al., 2011</xref>; <xref ref-type="bibr" rid="B40">Zhao et&#x20;al., 2012</xref>; <xref ref-type="bibr" rid="B27">Ramamurthy and Atrens, 2013</xref>; <xref ref-type="bibr" rid="B33">Wang and Han, 2013</xref>; <xref ref-type="bibr" rid="B2">Calabrese et&#x20;al., 2015</xref>; <xref ref-type="bibr" rid="B19">Mai and Soghrati, 2017</xref>; <xref ref-type="bibr" rid="B34">Wang et&#x20;al., 2019</xref>). Considering the effect of stress on the electrochemical reaction, Gutman built a mechano-electrochemical model to describe the effect of elastic and plastic deformation on the anodic dissolution of metals (<xref ref-type="bibr" rid="B9">Gutman, 1998</xref>). The applied stress can shift the pitting potential of 304 SS to a more negative value in 1&#xa0;M HCl at room temperature (<xref ref-type="bibr" rid="B31">Suter et&#x20;al., 2001</xref>). Meanwhile, the stress and strain concentration at the pitting area changed with the pitting morphology, determined by corrosive environments (<xref ref-type="bibr" rid="B11">Horner et&#x20;al., 2011</xref>; <xref ref-type="bibr" rid="B30">Spencer et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B24">Parkins, 1996</xref>; <xref ref-type="bibr" rid="B25">Persaud et&#x20;al., 2019</xref>; <xref ref-type="bibr" rid="B18">Lu et&#x20;al., 2020</xref>). The LA immersion will result in many defects and larger roughness on the metal surface. It is not clear about the LA immersion on the SCC of HP-13Cr&#x20;SS.</p>
<p>The aim of this work is to reveal the effect of the acidizing process, especially the LA process, on the SCC susceptibility of HP-13Cr SS in FW and clarify the interaction of surface roughness, water chemistry, and stress concentration on SCC by slow strain rate test (SSRT) (<xref ref-type="bibr" rid="B10">Henthorne, 2016</xref>), electrochemical measurements, micromorphology observation, and numerical simulation.</p>
</sec>
<sec id="s2">
<title>Experimental</title>
<sec id="s2-1">
<title>Material and Solution</title>
<p>The material applied in this work is a commercial HP-13Cr SS, with a chemical composition (<italic>wt</italic>%) of Si 0.15, Mn 0.51, Cr 12.77, Mo 2.19, S 0.002, <italic>p</italic> 0.02, Cu 0.047, Ni 5.36, V 0.014, Al 0.037, and Fe balance. The yield strength is 700&#xa0;MPa and the elongation is 21.6%. A typical tempered martensitic structure was observed in <xref ref-type="fig" rid="F1">Figure&#x20;1</xref>. The dimension of the SSRT specimen was given in <xref ref-type="fig" rid="F2">Figure&#x20;2</xref>. Prior to the experiment, the gauge section of the specimens was ground to 2000 grit abrasive paper along the tensile direction, then degreased with ethanol, washed with distilled water, and dried by the flow of air. The chemical composition of LA and FW have been listed in our previous work (<xref ref-type="bibr" rid="B3">Cui et&#x20;al., 2021</xref>). Before the SSRT in FW, the specimen was immersed in LA for 6&#xa0;h.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>The microstructure of HP-13Cr SS.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g001.tif"/>
</fig>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Dimensions of the SSRT test specimen (unit, mm).</p>
</caption>
<graphic xlink:href="fmats-08-732931-g002.tif"/>
</fig>
</sec>
<sec id="s2-2">
<title>Slow Stain Rate Test</title>
<p>The slow stain rate test (SSRT) was carried out in the HTHP-SCC system at 95&#xb0;C/2.8&#xa0;MPa CO<sub>2</sub> and 120&#xb0;C/3.2&#xa0;MPa CO<sub>2</sub> FW conditions, with a strain rate of 10<sup>&#x2212;6 s&#x2212;1</sup>. Before SSRT, the specimen was immersed in LA for 6&#xa0;h at 95&#xb0;C/2.8&#xa0;MPa CO<sub>2</sub> and 120&#xb0;C/3.2&#xa0;MPa CO<sub>2</sub>. There was also a SSRT as a normal group conducted at room temperature (25&#xb0;C) and 0.1&#xa0;MPa N<sub>2</sub> atmosphere.</p>
<p>The SCC susceptibility of the HP-13Cr SS was evaluated by the elongation loss ratio (<italic>I</italic>
<sub>&#x3b4;</sub>) and reduction-in-area loss (<italic>I</italic>
<sub>&#x3c8;</sub>) according to the following <xref ref-type="disp-formula" rid="e1">Eqs 1</xref>, <xref ref-type="disp-formula" rid="e2">2</xref> (<xref ref-type="bibr" rid="B32">Tian et&#x20;al., 2018</xref>):<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>&#x3b4;</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b4;</mml:mi>
<mml:mtext>s</mml:mtext>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b4;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>100</mml:mn>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x0025;</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
<disp-formula id="e2">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>&#x3c8;</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c8;</mml:mi>
<mml:mtext>s</mml:mtext>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c8;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>100</mml:mn>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x0025;</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where <inline-formula id="inf1">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b4;</mml:mi>
<mml:mtext>s</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf2">
<mml:math id="m4">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>&#x3c8;</mml:mi>
<mml:mtext>s</mml:mtext>
</mml:msub>
<mml:mtext>&#xa0;and</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> <inline-formula id="inf3">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b4;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf4">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c8;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> were the elongation and reduction-in-area of the HP-13Cr SS in the FW and at room temperature (25&#xb0;C) and N<sub>2</sub> atmosphere, respectively.</p>
</sec>
<sec id="s2-3">
<title>Micromorphology Examination</title>
<p>The fracture surface of the HP-13Cr SS was cut off after removing the corrosion products based on ASTM standard G1-03 (<xref ref-type="bibr" rid="B1">ASTM, 2003</xref>). The fracture morphology viewed from the top and the transverse of the specimens was observed by SEM (Quanta 200&#xa0;F, U.S.). The cross-section morphology of HP-13Cr SS after LA immersion has also been observed by SEM (Quanta 200&#xa0;F,&#x20;U.S.).</p>
</sec>
<sec id="s2-4">
<title>Electrochemical Measurement</title>
<p>The potentiodynamic polarization measurements were carried out in FW using the high temperature and high pressure static electrochemical measurement autoclave at 95&#xb0;C/2.8&#xa0;MPa CO<sub>2</sub> and 120&#xb0;C/3.2&#xa0;MPa CO<sub>2</sub>, respectively (<xref ref-type="bibr" rid="B15">Li et&#x20;al., 2019a</xref>). The specimen was also immersed in LA for 6&#xa0;h before potentiodynamic polarization measurements.</p>
<p>The relationship between the electrode potential vs. standard hydrogen electrode (SHE) and the observed potential vs. the Ag/AgCl reference electrode is shown as <xref ref-type="disp-formula" rid="e3">Eq. 3</xref>,<disp-formula id="e3">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mtext>SHE</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mtext>obs</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.2866</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.001</mml:mn>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1.754</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3.03</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>9</mml:mn>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>3</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>where the <italic>E</italic>
<sub>SHE</sub> is the electrode potential vs. SHE, V; the <italic>E</italic>
<sub>obs</sub> is the observed potential vs. the Ag/AgCl reference electrode, V; <italic>T</italic> is the system temperature, K; and <italic>T</italic>
<sub>0</sub> is the room temperature (25&#xb0;C).</p>
<p>The potentiodynamic polarization curves swept from &#x2212;0.3&#xa0;V vs. open circuit potential (OCP) to 1.6&#xa0;V vs. SHE with a scanning rate of 0.167&#xa0;mV/s. To ensure reproducibility, identical experiments were repeated at least three&#x20;times.</p>
</sec>
<sec id="s2-5">
<title>Numerical Simulation</title>
<p>The profile of HP-13Cr SS (OS) and HP-13Cr SS after immersion tests was observed by Ultra-Depth 3D Microscope (Olympus ILS4100, Japan). The roughness of surface was evaluated as <italic>S</italic>
<sub>a</sub>, which is the average absolute deviation of the roughness in a small area. <italic>S</italic>
<sub>a</sub> (&#x3bc;m) was defined as <xref ref-type="disp-formula" rid="e4">Eq. 4</xref>,<disp-formula id="e4">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mtext>a</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
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<mml:munderover>
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</mml:mstyle>
<mml:mrow>
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<mml:mo>&#x2211;</mml:mo>
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<mml:mn>1</mml:mn>
</mml:mrow>
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</mml:munderover>
<mml:mrow>
<mml:mo>&#x7c;</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>Z</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>&#x7c;</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>where <italic>M</italic>, <italic>N</italic> is the collected data points from two perpendicular directions in the measurement area; and <inline-formula id="inf5">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>Z</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the distance from the mean area to the number <italic>i j</italic>&#x20;point.</p>
<p>The tensile stress was set as 350&#xa0;MPa (half of yield strength) by the finite element method (FEM) in <xref ref-type="fig" rid="F3">Figure&#x20;3</xref>. The profile of the surface applied in the FEM was captured from the actual data of the specimen surface after LA immersion at 120&#xb0;C/3.2&#xa0;MPa. The mesh near the surface has been refined.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Modeling and meshing of HP-13Cr SS surface after LA immersion.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g003.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>Result</title>
<sec id="s3-1">
<title>SCC Susceptibility of HP-13Cr SS After LA Immersion</title>
<p>The stress-strain curves of HP-13Cr SS during SSRT were shown in <xref ref-type="fig" rid="F4">Figure&#x20;4</xref>. Compared with the normal condition (25&#xb0;C/N<sub>2</sub>) and HP-13Cr SS without LA immersion, the curves of HP-13Cr SS drifted down dramatically and yielded at a low stress; meanwhile, the fracture occurred at a quite low strain. With the temperature and CO<sub>2</sub> pressure increasing from 95&#xb0;C/2.8MPa to 120&#xb0;C/3.2 MPa, the stress-strain curve further deteriorated.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Stress&#x2013;strain curves of HP-13Cr SS in the FW at 25&#xb0;C/N<sub>2</sub> atmosphere and at <bold>(A)</bold> 95&#xb0;C/2.8MPa CO<sub>2</sub> and <bold>(B)</bold> 120&#xb0;C/3.2 MPa CO<sub>2</sub> after LA immersion, respectively.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g004.tif"/>
</fig>
<p>The SCC susceptibility of HP-13Cr SS evaluated by <inline-formula id="inf6">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>&#x3b4;</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf7">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>&#x3c8;</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was demonstrated in <xref ref-type="fig" rid="F5">Figure&#x20;5</xref>. Compared to the mechanical property at normal conditions, with the temperature and CO<sub>2</sub> pressure increasing from 95&#xb0;C/2.8 MPa to 120&#xb0;C/3.2 MPa, <inline-formula id="inf8">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>&#x3b4;</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf9">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>&#x3c8;</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> increased from 18.8 to 22.2% and from 13.9 to 48.1% without LA immersion. While after an LA immersion, the <inline-formula id="inf10">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>&#x3b4;</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> increased to 55.5 and 60.3% and <inline-formula id="inf11">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
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</mml:mrow>
</mml:math>
</inline-formula> increased to 62.9 and 70.1% at 95&#xb0;C/2.8 MPa and 120&#xb0;C/3.2 MPa, respectively. The dramatic increase of SCC susceptibility indicated that the LA process promoted the SCC of HP-13C SS in the FW environment and with the temperature and CO<sub>2</sub> pressure increasing, the mechanical properties are more severely reduced.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>SCC susceptibility of HP-13Cr SS. <bold>(A)</bold> elongation loss and <bold>(B)</bold> area reduction&#x20;loss.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g005.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>Fracture Morphology</title>
<p>The fracture morphologies of HP-13Cr SS viewed from the top after SSRT at normal conditions were illustrated in <xref ref-type="fig" rid="F6">Figure&#x20;6</xref>. The remarkable necking phenomena and typical cup-and-cone fracture, evidencing a high ductility, were observed (<xref ref-type="fig" rid="F6">Figure&#x20;6A</xref>). There was a considerable amount of fine ductile dimples in corresponding high magnification figure (<xref ref-type="fig" rid="F6">Figure&#x20;6B</xref>), indicating ductile fracture characteristics.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Fracture morphologies of HP-13Cr SS viewed from the top after SSRT at 25&#xb0;C/N<sub>2</sub> atmosphere. <bold>(A)</bold> low magnification and <bold>(B)</bold> high magnification.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g006.tif"/>
</fig>
<p>The fracture morphologies HP-13Cr SS without LA immersion showed a certain brittle fracture feature, including reduced necking at low magnification (<xref ref-type="fig" rid="F7">Figures 7A,E</xref>) and reduced dimples and increased quasi-cleavage plane at high magnification (<xref ref-type="fig" rid="F7">Figures 7B,F</xref>) at 95&#xb0;C/2.8 MPa and 120&#xb0;C/3.2&#xa0;MPa FW. After LA immersion, most of the necking disappeared (<xref ref-type="fig" rid="F7">Figures 7C,G</xref>) and the micromorphology showed a characteristic of brittle fracture with an almost flat plane (<xref ref-type="fig" rid="F7">Figures&#x20;7D,H</xref>).</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Fracture morphologies of HP-13Cr SS viewed from the top after SSRT in FW at 95&#xb0;C/2.8 MPa CO<sub>2</sub> without LA immersion at <bold>(A)</bold> low magnification and <bold>(B)</bold> high magnification, after LA immersion at <bold>(C)</bold> low magnification and <bold>(D)</bold> high magnification and 120&#xb0;C/3.2 MPa CO<sub>2</sub> without LA immersion at <bold>(E)</bold> low magnification and <bold>(F)</bold> high magnification, after LA immersion <bold>(G)</bold> low magnification and <bold>(H)</bold> high magnification.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g007.tif"/>
</fig>
</sec>
<sec id="s3-3">
<title>Electrochemical Behavior of HP-13Cr SS After LA Immersion in FW</title>
<p>The potentiodynamic polarization curves of HP-13Cr SS after LA immersion in the FW at 95&#xb0;C/2.8&#xa0;MPa CO<sub>2</sub> and 120&#xb0;C/3.2&#xa0;MPa CO<sub>2</sub> were shown in <xref ref-type="fig" rid="F8">Figure&#x20;8</xref> and the fitting electrochemical parameters were listed in <xref ref-type="table" rid="T1">Table&#x20;1</xref> with the temperature and CO<sub>2</sub> pressure increasing from 95&#xb0;C/2.8 MPa to 120&#xb0;C/3.2 MPa, the corrosion potential (<italic>E</italic>
<sub>corr</sub>) slightly increased, and corrosion current (<italic>i</italic>
<sub>corr</sub>) doubled from 2.45&#x20;&#xb1; 0.25&#x2715;10<sup>&#x2212;4</sup> A/cm<sup>2</sup> to 4.14&#x20;&#xb1; 0.23&#x2715;10<sup>&#x2212;4</sup> A/cm<sup>2</sup>. Since the corrosion production film formed after LA immersion, no significant passivation occurred, especially at 120&#xb0;C/3.2&#xa0;MPa&#x20;FW.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Polarization curves of HP-13Cr SS after LA immersion in the FW at 95&#xb0;C/2.8MPa CO<sub>2</sub> and 120&#xb0;C/3.2 MPa CO<sub>2</sub>.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g008.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Fitting electrochemical parameter of the potentiodynamic polarization curves of HP-13Cr SS after LA immersion in the FW at 95&#xb0;C/2.8&#xa0;MPa CO<sub>2</sub> and 120&#xb0;C/3.2&#xa0;MPa CO<sub>2</sub>.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Temperature (<sup>o</sup>C)/CO<sub>2</sub> pressure (MPa)</th>
<th align="center">
<italic>E</italic>
<sub>corr</sub> (mV)</th>
<th align="center">
<italic>i</italic>
<sub>corr</sub> (&#x2715;10<sup>-4</sup> A/cm<sup>2</sup>)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">95/2.8</td>
<td align="char" char="plusmn">&#x2212;564.61&#x20;&#xb1; 5.4</td>
<td align="char" char="plusmn">2.45&#x20;&#xb1; 0.25</td>
</tr>
<tr>
<td align="left">120/3.2</td>
<td align="char" char="plusmn">&#x2212;529.23&#x20;&#xb1; 6.6</td>
<td align="char" char="plusmn">4.14&#x20;&#xb1; 0.23</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>Discussion</title>
<sec id="s4-1">
<title>The Initiation of SCC</title>
<p>The HP-13Cr SS in LA, as a quite low pH solution, will dissolve and fail to passivate (<xref ref-type="bibr" rid="B41">Zhao et&#x20;al., 2019a</xref>). During LA immersion, the instant of the very thin and efficient corrosion-resistant passivating film as in the normal condition, a loose and thickness up to dozens of microns corrosion production film deposited on the surface, as the cross-sectional morphology after LA immersion shown in <xref ref-type="fig" rid="F9">Figure&#x20;9</xref>. The corrosion production film was comprised of an outer layer rich in copper and comes from the inhibitors in LA solution and an FeCO<sub>3</sub> inner layer (<xref ref-type="bibr" rid="B26">Qi et&#x20;al., 2021</xref>; <xref ref-type="bibr" rid="B44">Zhao et&#x20;al., 2020</xref>). There were plenty of defects including cracking and partial holes. Under a tensile stress condition, the stress and strain will be concentrated in the defects to deteriorate the corrosion production film and the substrate metal under the film. Then, the pitting occurred as the origin of anodic dissolution cracking (<xref ref-type="bibr" rid="B44">Zhao et&#x20;al., 2020</xref>).</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Cross-sectional morphologies of HP-13Cr SS after LA immersion. <bold>(A)</bold> 95&#xb0;C/2.8 MPa and <bold>(B)</bold> 120&#xb0;C/3.2 MPa.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g009.tif"/>
</fig>
<p>The cracking and pitting can be observed from the fracture morphologies viewed from transverse in <xref ref-type="fig" rid="F10">Figure&#x20;10</xref>. At 95&#xb0;C/2.8&#xa0;MPa CO<sub>2</sub>, the cracking in the surface near the fracture area was dense and almost distributed perpendicular to the tensile direction. The cracking had a spindle shape and revealed a characteristic of anodic dissolution cracking. As the temperature and CO<sub>2</sub> pressure went up to 120&#xb0;C/3.2 MPa, the cracking was longer and had a larger opening, indicating the greater anodic dissolution and more stress and strain concentration occurred after higher temperature and higher CO<sub>2</sub> pressure FA immersion.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Fracture morphologies of HP-13Cr SS after LA immersion and SSRT in the FW viewed from the transverse at 95&#xb0;C/2.8MPa CO<sub>2</sub> <bold>(A)</bold> low magnification and <bold>(B)</bold> high magnification and 120&#xb0;C/3.2 MPa CO<sub>2</sub> <bold>(C)</bold> low magnification and <bold>(D)</bold> high magnification.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g010.tif"/>
</fig>
</sec>
<sec id="s4-2">
<title>The Interaction of Roughness, Water Chemistry, and Stress Concentration on the SCC</title>
<p>As a process of mechanical and electrochemical interaction, SCC was closely related to the water chemical environment. In the formation water, the equilibrium reactions during the CO<sub>2</sub> dissolution process and corresponding reaction equilibrium constants were listed as follows (Reaction <xref ref-type="disp-formula" rid="e5">Eqs 5</xref>&#x2013;<xref ref-type="disp-formula" rid="e9">9</xref>) (<xref ref-type="bibr" rid="B8">Garsany et&#x20;al., 2002</xref>; <xref ref-type="bibr" rid="B23">Nordsveen et&#x20;al., 2003</xref>; <xref ref-type="bibr" rid="B7">Duan and Li, 2008</xref>; <xref ref-type="bibr" rid="B37">Zhang and Cheng, 2009</xref>),<disp-formula id="e5">
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<mml:mtext>HCO</mml:mtext>
</mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>&#x2212;</mml:mo>
</mml:msubsup>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>ca</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>9</mml:mn>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msup>
<mml:mtext>H</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mtext>HCO</mml:mtext>
</mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>&#x2212;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mtext>H</mml:mtext>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mtext>CO</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mtext>aq</mml:mtext>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
<disp-formula id="e8">
<mml:math id="m19">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mtext>HCO</mml:mtext>
</mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>&#x2212;</mml:mo>
</mml:msubsup>
<mml:mo>&#x21cc;</mml:mo>
<mml:msup>
<mml:mtext>H</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mtext>CO</mml:mtext>
</mml:mrow>
<mml:mn>3</mml:mn>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2212;</mml:mo>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>bi</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msup>
<mml:mtext>H</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mtext>CO</mml:mtext>
</mml:mrow>
<mml:mn>3</mml:mn>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2212;</mml:mo>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mtext>HCO</mml:mtext>
</mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>&#x2212;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
<disp-formula id="e9">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mtext>H</mml:mtext>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:msub>
<mml:mtext>O</mml:mtext>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mtext>l</mml:mtext>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:msub>
<mml:mo>&#x21cc;</mml:mo>
<mml:msup>
<mml:mtext>H</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mtext>OH</mml:mtext>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
</mml:msup>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mtext>w</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msubsup>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>11</mml:mn>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msup>
<mml:mtext>H</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mtext>OH</mml:mtext>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>where <inline-formula id="inf12">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mtext>H</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf13">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>hyd</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf14">
<mml:math id="m23">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>ca</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf15">
<mml:math id="m24">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>bi</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf16">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mtext>w</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denote the mathematical description of reaction equilibriums, respectively. The fugacity coefficient (<italic>&#x3c6;</italic>) can be determined by the following <xref ref-type="disp-formula" rid="e10">Eq. 10</xref>:<disp-formula id="e10">
<mml:math id="m26">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>g</mml:mi>
<mml:mi>&#x3c6;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>0.0031</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1.4</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mtext>K</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>where <italic>p</italic> was the pressure bar and <italic>T</italic>
<sub>
<italic>k</italic>
</sub> was the temperature in degrees Kelvin. The temperature-pressure-ionic strength (<italic>I</italic>) dependence relationship for <inline-formula id="inf17">
<mml:math id="m27">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mtext>H</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf18">
<mml:math id="m28">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>hyd</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf19">
<mml:math id="m29">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>ca</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf20">
<mml:math id="m30">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>bi</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf21">
<mml:math id="m31">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mtext>w</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> were listed in <xref ref-type="table" rid="T2">Table&#x20;2</xref>, and <italic>I</italic> was calculated as follows:<disp-formula id="e11">
<mml:math id="m32">
<mml:mrow>
<mml:mi>I</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mn>2</mml:mn>
</mml:mfrac>
<mml:munder>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mtext>i</mml:mtext>
</mml:munder>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mtext>i</mml:mtext>
</mml:msub>
<mml:msubsup>
<mml:mi>z</mml:mi>
<mml:mtext>i</mml:mtext>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>where <inline-formula id="inf22">
<mml:math id="m33">
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mtext>i</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf23">
<mml:math id="m34">
<mml:mrow>
<mml:msub>
<mml:mi>z</mml:mi>
<mml:mtext>i</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> were the molar concentration and charge of species i, respectively. The mean ionic activity coefficients <inline-formula id="inf24">
<mml:math id="m35">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>9</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf25">
<mml:math id="m36">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf26">
<mml:math id="m37">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>11</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in the formation water were&#x20;0.662.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Formula of the reaction equilibrium constants.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Equilibrium constants</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">
<inline-formula id="inf27">
<mml:math id="m38">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mtext>H</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>14.46269</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mn>2.27</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>5.65</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi>T</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>8.06</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mi>T</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.075</mml:mn>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B7">Duan and Li, 2008</xref>; <xref ref-type="bibr" rid="B37">Zhang and Cheng, 2009</xref>)</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf28">
<mml:math id="m39">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>hyd</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2.58</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B7">Duan and Li, 2008</xref>; <xref ref-type="bibr" rid="B37">Zhang and Cheng, 2009</xref>)</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf29">
<mml:math id="m40">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>ca</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>387.6</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>6.41</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1.594</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi>T</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>3.52</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mi>T</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3.07</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi>P</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.4772</mml:mn>
<mml:msup>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mn>2</mml:mn>
</mml:mfrac>
</mml:mrow>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.1180</mml:mn>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B7">Duan and Li, 2008</xref>; <xref ref-type="bibr" rid="B37">Zhang and Cheng, 2009</xref>)</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf30">
<mml:math id="m41">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mtext>bi</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>10.61</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>4.97</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi>T</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>8.59</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mi>T</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>7.00</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi>P</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3.21</mml:mn>
<mml:msup>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mn>2</mml:mn>
</mml:mfrac>
</mml:mrow>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1.073</mml:mn>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B7">Duan and Li, 2008</xref>; <xref ref-type="bibr" rid="B37">Zhang and Cheng, 2009</xref>)</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf31">
<mml:math id="m42">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mtext>w</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>29.3868</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.0737549</mml:mn>
<mml:mi>T</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>7.47881</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mi>T</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B7">Duan and Li, 2008</xref>; <xref ref-type="bibr" rid="B37">Zhang and Cheng, 2009</xref>)</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In a solution without an externally induced electric field, the concentration of ions must satisfy the electroneutrality constraint. The species Na<sup>2&#x2b;</sup>, Ca<sup>2&#x2b;</sup>, Mg<sup>2&#x2b;</sup>, Cl<sup>&#x2212;</sup>, and SO<sub>4</sub>
<sup>2-</sup> dissociated completely in the formation water. Since the addition of NaHCO<sub>3</sub> to the formation water would affect the electroneutrality constraint, the charge relationship between ions can be expressed by <xref ref-type="disp-formula" rid="e12">Eq. 12</xref>:<disp-formula id="e12">
<mml:math id="m43">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mtext>Na</mml:mtext>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msup>
<mml:mtext>H</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mtext>OH</mml:mtext>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mtext>HCO</mml:mtext>
</mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>&#x2212;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mtext>CO</mml:mtext>
</mml:mrow>
<mml:mn>3</mml:mn>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2212;</mml:mo>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>where <inline-formula id="inf32">
<mml:math id="m44">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mtext>Na</mml:mtext>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was Na<sup>&#x2b;</sup> concentration of the artificial addition NaHCO<sub>3</sub> in the simulation formation water, and <inline-formula id="inf33">
<mml:math id="m45">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msup>
<mml:mtext>H</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf34">
<mml:math id="m46">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mtext>OH</mml:mtext>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf35">
<mml:math id="m47">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mtext>HCO</mml:mtext>
</mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>&#x2212;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf36">
<mml:math id="m48">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mtext>CO</mml:mtext>
</mml:mrow>
<mml:mn>3</mml:mn>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2212;</mml:mo>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> were the equilibrium concentrations of H<sup>&#x2b;</sup>, OH<sup>&#x2212;</sup>, HCO<sub>3</sub>
<sup>&#x2212;</sup>, and CO<sub>3</sub>
<sup>2-</sup>, respectively.</p>
<p>The pH values of FW were calculated as 3.52 and 3.62&#xa0;at 95&#xb0;C/2.8&#xa0;MPa CO<sub>2</sub> and 120&#xb0;C/3.2&#xa0;MPa CO<sub>2</sub>, respectively.</p>
<p>Surface roughness is of great importance to the chemical and mechanical states at the corrosion interface (<xref ref-type="bibr" rid="B35">Wang et&#x20;al., 2021</xref>). The surface roughness of HP-13Cr SS after FA immersion became larger and increased with the temperature and CO<sub>2</sub> pressure, as is shown in <xref ref-type="fig" rid="F11">Figure&#x20;11</xref>. At 95&#xb0;C/2.8&#xa0;MPa CO<sub>2</sub>, the roughness was 3.5&#xa0;&#x3bc;m (<xref ref-type="fig" rid="F11">Figure&#x20;11A</xref>), which is quite larger than the roughness of the polishing surface, without LA immersion, less than 0.1&#xa0;&#x3bc;m. In addition, the roughness increased to 7.8&#xa0;&#x3bc;m&#xa0;at 120&#xb0;C/3.2&#xa0;MPa (<xref ref-type="fig" rid="F11">Figure&#x20;11B</xref>). According to the FEM of rough and flat surfaces under 350&#xa0;MPa tensile stress condition, in <xref ref-type="fig" rid="F12">Figure&#x20;12</xref>, the stress (<xref ref-type="fig" rid="F12">Figure&#x20;12A</xref>), and the plastic strain (<xref ref-type="fig" rid="F12">Figure&#x20;12B</xref>) distribution at 120&#xb0;C/3.2&#xa0;MPa were obtained. There was obvious stress and strain concentration in the valley position of the rough surface.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>3D image and surface roughness of HP-13Cr SS after LA immersion. <bold>(A)</bold> 95&#xb0;C/2.8 MPa and <bold>(B)</bold> 120&#xb0;C/3.2 MPa.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g011.tif"/>
</fig>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>
<bold>(A)</bold> stress and <bold>(B)</bold> strain distribution of the surface after LA immersion at 120&#xb0;C/3.2 MPa.</p>
</caption>
<graphic xlink:href="fmats-08-732931-g012.tif"/>
</fig>
<p>Gutman proposed a kinetic equation for the mechanochemical effect of macroscopic stress on the anodic current <inline-formula id="inf37">
<mml:math id="m49">
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mtext>P</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of stressed metal (<xref ref-type="bibr" rid="B9">Gutman, 1998</xref>),<disp-formula id="e13">
<mml:math id="m50">
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mtext>P</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mtext>a</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mtext>&#x394;</mml:mtext>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>m</mml:mtext>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>where <inline-formula id="inf38">
<mml:math id="m51">
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mtext>a</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was the anodic current of stress-free metal, <inline-formula id="inf39">
<mml:math id="m52">
<mml:mrow>
<mml:mtext>&#x394;</mml:mtext>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> was the plastic strain, <inline-formula id="inf40">
<mml:math id="m53">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was the strain at onset of strain hardening, <inline-formula id="inf41">
<mml:math id="m54">
<mml:mi>P</mml:mi>
</mml:math>
</inline-formula> was the macroscopic stress, Pa, <inline-formula id="inf42">
<mml:math id="m55">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>m</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was molar volume, taken as 7.1&#xd7;10<sup>-6</sup>&#xa0;m<sup>3</sup>mol<sup>&#x2212;1</sup>, <italic>R</italic> was the gas constant, and <italic>T</italic> was the temperature,&#x20;K.</p>
<p>The anodic current in the area with maximum stress and strain concentration was calculated as 1.7&#x20;times than that at a flat surface at 120&#xb0;C/3.2&#xa0;MPa.</p>
<p>Therefore, the larger roughness caused by LA immersion promoted the local anodic dissolution and then the greater stress and strain concentration occurred. The further increase of stress and strain concentration will further promote the local anodic dissolution, which forms a mutually reinforcing cycle and results in severe SCC (<xref ref-type="bibr" rid="B5">Cui et&#x20;al., 2016</xref>). Moreover, with the temperature/CO<sub>2</sub> pressure increasing from 95&#xb0;C/2.8 MPa to 120&#xb0;C/3.2 MPa, the increase in roughness seemed more crucial to SCC than the pH reduction, and eventually, the more severe SCC occurred after higher temperature and CO<sub>2</sub> pressure LA immersion.</p>
</sec>
</sec>
<sec sec-type="conclusion" id="s5">
<title>Conclusion</title>
<p>
<list list-type="simple">
<list-item>
<p>1. The LA immersion in the acidification process obviously promoted the SCC susceptibility of HP-13Cr SS in&#x20;FW.</p>
</list-item>
<list-item>
<p>2. With the temperature/CO<sub>2</sub> pressure increasing from 95&#xb0;C/2.8 MPa to 120&#xb0;C/3.2 MPa, the surface roughness of HP-13Cr SS after LA immersion increased, resulting in the greater stress concentration and induced the SCC occurring easily.</p>
</list-item>
<list-item>
<p>3. After LA immersion, the interaction of surface roughness, water chemistry, and stress concentration mutually reinforced and deteriorated the SCC of HP-13Cr SS in&#x20;FW.</p>
</list-item>
</list>
</p>
</sec>
</body>
<back>
<sec id="s6">
<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 author.</p>
</sec>
<sec id="s7">
<title>Author Contributions</title>
<p>WQ: Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing&#x2014;original draft. YZ: Investigation, Validation, Visualization, Supervision, Writing&#x2014;reviewing and editing. TZ: Project administration, Conceptualization, Supervision, Funding, acquisition, Writing&#x2014;reviewing and editing. FW: Conceptualization, Supervision, Funding acquisition.</p>
</sec>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of Interest</title>
<p>The 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>
<ack>
<p>The authors express their gratitude to the National Key R&#x26;D Research (2017YFB0702203) and National Natural Science Foundation of China (No. 52001061 and No. U1460202) for the long-term support of the programs. The National Program for the Young Top-Notch Professionals and China Postdoctoral Science Foundation (No. 01270012810066) is also acknowledged.</p>
</ack>
<ref-list>
<title>References</title>
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<given-names>L.</given-names>
</name>
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<surname>Wang</surname>
<given-names>Z.</given-names>
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<surname>Hou</surname>
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<etal/>
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<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Cui</surname>
<given-names>Z. D.</given-names>
</name>
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