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<journal-id journal-id-type="publisher-id">Front. Mater.</journal-id>
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<journal-title>Frontiers in Materials</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mater.</abbrev-journal-title>
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<issn pub-type="epub">2296-8016</issn>
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<article-id pub-id-type="publisher-id">1609564</article-id>
<article-id pub-id-type="doi">10.3389/fmats.2025.1609564</article-id>
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<subj-group subj-group-type="heading">
<subject>Original Research</subject>
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<title-group>
<article-title>Pre-qualification of additively manufactured 316L stainless steel using small punch and uniaxial creep testing</article-title>
<alt-title alt-title-type="left-running-head">Simonovski 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.2025.1609564">10.3389/fmats.2025.1609564</ext-link>
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<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Simonovski</surname>
<given-names>I.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<xref ref-type="corresp" rid="c001">&#x2a;</xref>
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<surname>Nilsson</surname>
<given-names>K.-F.</given-names>
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<name>
<surname>Holmstr&#xf6;m</surname>
<given-names>S.</given-names>
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<sup>2</sup>
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<name>
<surname>Kus</surname>
<given-names>M.</given-names>
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<surname>Garc&#xed;a-Junceda</surname>
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<sup>1</sup>
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<aff id="aff1">
<label>1</label>
<institution>European Commission DG-JRC, JRC Directorate G &#x2013; Nuclear Safety and Security G.I.4 Reactor Safety and Components</institution>, <city>Petten</city>, <country country="NL">Netherlands</country>
</aff>
<aff id="aff2">
<label>2</label>
<institution>SCK CEN, Belgian Nuclear Research Centre, NET &#x2013; Nuclear Energy Technology, FMA - Fuel Materials</institution>, <city>Mol</city>, <country country="BE">Belgium</country>
</aff>
<author-notes>
<corresp id="c001">
<label>&#x2a;</label>Correspondence: I. Simonovski, <email xlink:href="Igor.Simonovski@ec.europa.eu">Igor.Simonovski@ec.europa.eu</email>
</corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2025-11-24">
<day>24</day>
<month>11</month>
<year>2025</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2025</year>
</pub-date>
<volume>12</volume>
<elocation-id>1609564</elocation-id>
<history>
<date date-type="received">
<day>10</day>
<month>04</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>26</day>
<month>08</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>15</day>
<month>09</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Simonovski, Nilsson, Holmstr&#xf6;m, Kus and Garc&#xed;a-Junceda.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Simonovski, Nilsson, Holmstr&#xf6;m, Kus and Garc&#xed;a-Junceda</copyright-holder>
<license>
<ali:license_ref start_date="2025-11-24">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. 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.</license-p>
</license>
</permissions>
<abstract>
<p>Additive manufacturing represents a cutting-edge technology that offers significant reductions in both manufacturing time and cost. However, any new technology or material must go through a qualification process before it can be used in the nuclear industry. This article reports on a pre-qualification process of 316L stainless steel manufactured using the laser powder bed fusion (LPBF) additive manufacturing process. The study compares LPBF 316L, aged, and non-aged materials from two different manufacturers. A small punch creep test campaign at 650 &#xb0;C was performed at different loads. These tests are particularly advantageous because they require only a small amount of material, making them ideal when material availability is limited. Additionally, standard uniaxial creep tests were performed at the same temperature for comparative reference. A good correlation for the time to rupture&#x2013;equivalent stress between the two test types was observed, with the equivalent stress calculated using the Small Punch Test EN 10371:2021 standard. A significant finding is that the small punch creep deflection rate curves for LPBF-manufactured 316L exhibit multiple minima, unlike the single minimum observed in forged 316L. This is believed to result from micro-cracking and has important implications for determining the equivalent stress creep properties, which are based on the single minimum value in the EN 10371:2021 standard. The multiple minima finding suggests that the approach used to determine equivalent stress and strain rate in small punch creep tests in the EN 10371:2021 standard must be re-evaluated to accommodate this complexity.</p>
</abstract>
<kwd-group>
<kwd>additive manufacturing</kwd>
<kwd>316L stainless steel</kwd>
<kwd>small punch</kwd>
<kwd>uniaxial creep testing</kwd>
<kwd>laser powder bed fusion</kwd>
<kwd>LPBF</kwd>
<kwd>small punch creep</kwd>
<kwd>uniaxial creep</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declare that financial support was received for the research and/or publication of this article. This project has received funding from the European research and training programme 2014&#x2013;2018 under grant agreement No. 945313 (NUCOBAM project).</funding-statement>
</funding-group>
<counts>
<fig-count count="21"/>
<table-count count="6"/>
<equation-count count="3"/>
<ref-count count="15"/>
<page-count count="17"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>section-in-acceptance</meta-name>
<meta-value>Environmental Degradation of Materials</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<label>1</label>
<title>Introduction</title>
<p>Additive manufacturing (AM) represents a cutting-edge technology that potentially offers significant reductions in both manufacturing time and cost. Due to completely different principles of manufacturing, both the AM feed stock material and build process must be qualified, especially for application in the nuclear industry. The Procedure for the Acquisition of New Material Data (PTAN) of the RCC-MRx code for design and construction rules (<xref ref-type="bibr" rid="B1">AFCEN, 2017</xref>) and <xref ref-type="sec" rid="s3">Section 3</xref>, Division 5 of ASME Boiler and Pressure Vessel Code (BPVC) (<xref ref-type="bibr" rid="B3">ASME, 2013</xref>) are two examples of procedures for the qualification of new materials. The qualification process includes defining a material property file, which, among others, includes physical and material properties from a wide range of tests and laboratories to establish material confidence limits in view of variation of properties. These can be due to material taken from a thick or thin plate, heat-to-heat variability, different cooling rates from AM melt, and later reheating by following passes of the heat source, etc.</p>
<p>The EU-funded research project NUclear COmponents Based on Additive Manufacturing (NUCOBAM) recently ended (2020&#x2013;2024) (<xref ref-type="bibr" rid="B13">NUCOBAM, 2024</xref>). It examined the qualification of AM 316L stainless steel to demonstrate the compatibility of AM 316L in a light water reactor (LWR)-irradiated environment (<xref ref-type="bibr" rid="B10">Konstantinovi&#x107; et al., 2025</xref>). A more comprehensive program is currently being considered in ASME (<xref ref-type="bibr" rid="B12">Messner, 2023</xref>). In this work, laser powder bed fusion (LPBF) was used because no excessive ferrite phase builds up during rapid cooling.</p>
<p>The nuclear community (scientists, reactor designs, and regulators) is currently debating whether traditional material qualification tests, which assume that material properties derived from standard tests reduce uncertainty through extensive testing, are sufficient or if component-level tests are necessary (<xref ref-type="bibr" rid="B12">Messner, 2023</xref>; <xref ref-type="bibr" rid="B15">Torres and Gordon, 2021</xref>; <xref ref-type="bibr" rid="B11">Lal&#xe9; and Viguier, 2024</xref>; <xref ref-type="bibr" rid="B2">ASM Handbook, 2017</xref>). In NUCOBAM, the process involved qualification of 316L feedstock powder first, followed by qualification of the AM build process and platforms, and qualification of the AM build material through a number of mechanical tests. Finally, a valve body and debris filter were manufactured for component testing. In this work, we focus on the recently standardized (EN, ASME, and RCC-MRx) small punch test (<xref ref-type="bibr" rid="B6">CEN EN, 2024</xref>; <xref ref-type="bibr" rid="B4">ASTM, 2024</xref>; <xref ref-type="bibr" rid="B14">RCC-MRx, 2022</xref>). This test uses small disks for test pieces (8 mm diameter, 0.5 &#xb1; 0.005 mm thickness), which is a crucial advantage when only a small amount of test material is available (<xref ref-type="fig" rid="F1">Figure 1</xref>). Specifically, the small punch creep (SPC) tests were carried out to estimate creep properties, followed by validating these properties by performing a small number of standard uniaxial creep (UC) tests.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Uniaxial creep test piece (green) in relation to the small punch test piece given in two orientations (red and grey). The LPBF build direction is the Z-axis.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g001.tif">
<alt-text content-type="machine-generated">Uniaxial creep test piece (green) in relation to the small punch test piece given in two orientations (red and grey). The LPBF build direction is the Z-axis.</alt-text>
</graphic>
</fig>
<p>The article is structured as follows. We first describe the feedstock material, followed by a description of the methods used. Next, we discuss the specificities of the analysis of the SPC test results of AM 316L material and the transferability of these results to UC. Conclusions are given at the end.</p>
</sec>
<sec sec-type="materials" id="s2">
<label>2</label>
<title>Materials</title>
<p>A 316L stainless steel feedstock powder was used to manufacture bars for material tests using the laser powder bed fusion (LPBF) additive manufacturing process in accordance with the ASTM F3184 (<xref ref-type="bibr" rid="B5">ASTM F3184-16 Standard Specification for Additive Manufacturing Stainless Steel Alloy, 2024</xref>). The basis for the feedstock powder chemical composition requirements was taken from ASTM F3184, with additional requirements imposed for the weight % of N, O, Cu, Co, Ta, B, and Cu. The chemical composition of the feedstock powder is comparable to the 316L(N) forged plate but lower in the C (0.02 vs. 0.024) and Mn (0.8 vs 1.794) content and higher in Si (1 vs. 0.689). <xref ref-type="table" rid="T1">Table 1</xref> provides the chemical composition, while the measured particle size distribution is given in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Chemical composition of powder feedstock 316L stainless steel.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Material</th>
<th colspan="14" align="center">% Weight</th>
</tr>
<tr>
<th align="left">C</th>
<th align="left">Mn</th>
<th align="left">P</th>
<th align="left">S</th>
<th align="left">Si</th>
<th align="left">Ni</th>
<th align="left">Cr</th>
<th align="left">Mo</th>
<th align="left">N</th>
<th align="left">O</th>
<th align="left">Cu</th>
<th align="left">Co</th>
<th align="left">Ta</th>
<th align="left">B</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">ASTM F3184-316L</td>
<td align="left">0.03</td>
<td align="left">2</td>
<td align="left">0.045</td>
<td align="left">0.03</td>
<td align="left">1</td>
<td align="left">10&#x2013;14</td>
<td align="left">16&#x2013;18</td>
<td align="left">2&#x2013;3</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left">31L(N) forged plate</td>
<td align="left">0.024</td>
<td align="left">1.794</td>
<td align="left">0.0171</td>
<td align="left">0.0083</td>
<td align="left">0.689</td>
<td align="left">12.061</td>
<td align="left">17.669</td>
<td align="left">2.416</td>
<td align="left">0.065</td>
<td align="left"/>
<td align="left"/>
<td align="left">0.028</td>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left">Used powder</td>
<td align="left">0.02</td>
<td align="left">0.8</td>
<td align="left">0.01</td>
<td align="left">0.004</td>
<td align="left">1</td>
<td align="left">12.6</td>
<td align="left">17.8</td>
<td align="left">2.3</td>
<td align="left">0.09</td>
<td align="left">0.02</td>
<td align="left">&#x3c;0.1</td>
<td align="left">0.03</td>
<td align="left">&#x3c;0.02</td>
<td align="left">&#x3c;0.001</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Measured size properties of powder feedstock 316L stainless steel.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">D10</th>
<th align="left">D50</th>
<th align="left">D90</th>
<th align="left">Volume &#x3c;10 &#xb5;m</th>
<th align="left">Volume &#x3c;14.5 &#xb5;m</th>
<th align="left">Apparent density</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">20.1 &#xb5;m</td>
<td align="left">31.0 &#xb5;m</td>
<td align="left">47.2 &#xb5;m</td>
<td align="left">0%</td>
<td align="left">1.68%</td>
<td align="left">4.43 g/cm<sup>3</sup>
</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The powder feedstock was then used to manufacture bars on a build platform (<xref ref-type="fig" rid="F2">Figure 2</xref>). In this article, we use bars manufactured using a Renishaw AM250 single laser machine at the Advanced Manufacturing Centre (AMRC), University of Sheffield, and Commissariat &#xe0; l&#x27;&#xe9;nergie atomique et aux &#xe9;nergies alternatives (CEA), using an SLM Solutions SLM280HL single laser, both using argon as an inert gas. The bars used in this work are in the as-built z-direction, protruding out of the build platform, as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Build platforms: AMRC (left) and CEA (right).</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g002.tif">
<alt-text content-type="machine-generated">Two images display arrays of metal blocks, each labeled and arranged in varying heights. The left image, labeled &#x22;A5&#x22;, features both cylindrical and rectangular blocks on a metallic base. The right image, labeled &#x22;C1&#x22;, shows a denser cluster of irregularly shaped metal blocks on a wooden surface.</alt-text>
</graphic>
</fig>
<p>A heat treatment consisting of soaking at 1,066 &#xb1; 14 &#xb0;C with a holding time of 1 h 15 min &#xb1;15 min was applied to the AMRC build platform, while for the CEA, the bars were cut from the build platform prior to application of the same thermal treatment. The holding time counter initiated when a lower temperature limit, 1052 &#xb0;C &#x3d; 1066 &#xb0;C&#x2013;14 &#xb0;C, was attained. An argon atmosphere was used, with the prescribed heating rate of 4 &#xb0;C/min and a cooling rate of at least 10 &#xb0;C/min. We refer to this heat treatment as HT2 to distinguish it from other heat treatments applied within NUCOBAM.</p>
<p>In addition to HT2, some bars were aged for 10,000 h at 450 &#xb0;C. The following combinations of materials were used in the current article: a) AMRC, HT2; b) AMRC, HT2 aged; and c) CEA, HT2, aged. To simplify labeling, these will be referred to as AMRC NA (not aged), AMRC Aged, and CEA Aged. These materials were then used to manufacture all small punch and uniaxial creep test pieces.</p>
<p>Four bars from the internal AMRC qualification process were used for three UC tests (at initial stress of 250 MPa, 270 MPa, and 290 MPa) due to an insufficient amount of originally shipped material. The heat treatment of these bars was performed at the JRC, following the same HT2 procedure.</p>
</sec>
<sec sec-type="methods" id="s3">
<label>3</label>
<title>Methods</title>
<sec id="s3-1">
<label>3.1</label>
<title>Small punch creep tests</title>
<p>A two-stage approach was taken for estimating creep properties. In the first stage, a small punch creep (SPC) test campaign was performed at 650 &#xb0;C. The SPC test involves pressing a 2.5-mm-diameter punch (a high precision silicon nitride Si<sub>3</sub>N<sub>4</sub> bearing ball) into a test piece at a constant force (<xref ref-type="fig" rid="F3">Figure 3</xref>). The test piece is a disk with a diameter of 8 mm and a thickness of 0.5 &#xb1; 0.005 mm. The test piece is clamped between the upper and lower dies. The lower die has a 4-mm-diameter receiving hole with a 0.2 mm/45&#xb0; chamfer. The deflection of the test piece is measured from below the test piece with a ceramic rod touching the test piece and extending to a linear variable differential transformer (LVDT) gauge. The LVDT has a negligible spring counter force. The result of an SPC test is a deflection versus time curve, resulting in a given time to rupture, t<sub>r</sub>.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Illustration of the small punch test.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g003.tif">
<alt-text content-type="machine-generated">Diagram showing a sequence of a punching process with components labeled. The first image highlights a red miniature disk placed on a lower die. The second shows the upper die and punch rod aligned above the miniature disk. The third displays the completed punch with the rod fully inserted, compressing the disk.</alt-text>
</graphic>
</fig>
<p>Small punch creep (SPC) tests were done at 650 &#xb0;C with the test piece in an argon environment to prevent test piece corrosion. Force levels from 240 N to 500 N were used by the application of dead weights. The test matrix is given in <xref ref-type="table" rid="T3">Table 3</xref>. This test matrix was then used to estimate the equivalent load conditions of uniaxial creep tests as described below.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>SPC test matrix at 650 &#xb0;C.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Material</th>
<th colspan="8" align="center">Force [N]</th>
</tr>
<tr>
<th align="left">240</th>
<th align="left">260</th>
<th align="left">300</th>
<th align="left">320</th>
<th align="left">350</th>
<th align="left">400</th>
<th align="left">450</th>
<th align="left">500</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">AMRC NA</td>
<td align="left">2x</td>
<td align="left">2x</td>
<td align="left">2x<xref ref-type="table-fn" rid="Tfn1">
<sup>a</sup>
</xref>
</td>
<td align="left">2x</td>
<td align="left">2x</td>
<td align="left">2x</td>
<td align="left">2x</td>
<td align="left">6x</td>
</tr>
<tr>
<td align="left">AMRC Aged</td>
<td align="left">2x</td>
<td align="left">2x<xref ref-type="table-fn" rid="Tfn2">
<sup>b</sup>
</xref>
</td>
<td align="left">2x</td>
<td align="left"/>
<td align="left"/>
<td align="left">2x</td>
<td align="left"/>
<td align="left">2x</td>
</tr>
<tr>
<td align="left">CEA Aged</td>
<td align="left">2x</td>
<td align="left">2x</td>
<td align="left">2x</td>
<td align="left"/>
<td align="left"/>
<td align="left">2x</td>
<td align="left"/>
<td align="left">2x</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="Tfn1">
<label>
<sup>a</sup>
</label>
<p>One test was discarded because data acquisition only started 66,720 s after the application of the dead weights.</p>
</fn>
<fn id="Tfn2">
<label>
<sup>b</sup>
</label>
<p>One test was discarded due to cooling lines impeding the dead weights, resulting in significantly decreased force load.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>From the SPC deflection versus time curve, one can estimate the equivalent initial stress, <inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, to apply to a UC test (at the same temperature) that results in the same rupture time. The informative Annex G in EN 10371:2021 standard (<xref ref-type="bibr" rid="B6">CEN EN, 2024</xref>) provides <xref ref-type="disp-formula" rid="e1">Equation 1</xref> for estimating <inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. We distinguish here between <inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, calculated using <xref ref-type="disp-formula" rid="e1">Equation 1</xref> from the SPC test, and <inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, which is the initial stress applied to the uniaxial creep test.<disp-formula id="e1">
<mml:math id="m5">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1.916</mml:mn>
<mml:mo>&#xb7;</mml:mo>
<mml:msubsup>
<mml:mi>u</mml:mi>
<mml:mi mathvariant="italic">min</mml:mi>
<mml:mn>0.6579</mml:mn>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="&#x7c;">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="normal">N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>MPa</mml:mtext>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<p>In <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, <italic>F</italic> stands for the force applied in the SPC test, and <inline-formula id="inf5">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mi mathvariant="italic">min</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> stands for the deflection in the SPC test where the minimum deflection rate, <inline-formula id="inf6">
<mml:math id="m7">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>u</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula>, is obtained.</p>
<sec id="s3-1-1">
<label>3.1.1</label>
<title>Estimation of equivalent stress <inline-formula id="inf7">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</title>
<p>Accurate deflection measurements and estimation of deflection rate are essential for calculating equivalent stress, <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, and creep assessment in general. Temperature control precision, susceptibility of the laboratory environment to external vibrations, and systematic noise are only a few of the influencing parameters. A typical recorded deflection during an SPC test in our laboratory is given in <xref ref-type="fig" rid="F4">Figure 4</xref>. A sampling rate of 1 Hz is used to capture the initial load application. Because our data acquisition software can only sample at a constant rate, a 1 Hz sampling rate is maintained for the duration of the test.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>A typical deflection in an SPC test. Insert: zoom in on the measured deflection (noise).</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g004.tif">
<alt-text content-type="machine-generated">Graph showing deflection in millimeters over time in hours. The curve starts steep, then gradually increases with a sharp rise near the end. An inset graph zooms into the deflection between zero point nine and zero point nine five millimeters from six to eight hours, showing detailed fluctuations.</alt-text>
</graphic>
</fig>
<p>The deflection signal contains approximately &#xb1;1 to &#xb1;2 &#xb5;m noise (<xref ref-type="fig" rid="F4">Figure 4</xref> insert). It is well known that differentiating a signal increases the noise. It is clear that such a signal cannot be used for evaluating equivalent stress, <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, where the deflection at a minimum deflection rate must be identified.</p>
<p>We tackle the issue by first down sampling the deflection signal to 2<sup>14</sup> &#x3d; 16,384 points using a linear interpolation. This significantly reduces the number of points for processing the signal, decreasing computational time for noise filtering and calculation of deflection rate. A large number of points can result in a prohibitively large amount of required memory. A larger number of points can be used for longer experiments. In the second step, we deal with the noise. One way is to split the signal into segments and calculate the linear regression line for each segment. We investigated the impact of 50, 100, 200, and 300 segments. Using 200 segments was determined to be the optimal number in terms of minimizing noise while still retaining sufficient local detail (important for, e.g., determining the crack initiation). The deflection rate is then the inclination of the regression line. This decreases noise in the calculated deflection rate, but significant local peaks remain; see the black solid line in <xref ref-type="fig" rid="F5">Figure 5</xref>. If a Whittaker noise filter (<xref ref-type="bibr" rid="B7">Eilers, 2003</xref>) is applied prior to calculating the regression lines, the noise in the calculated deflection rate improves further. However, there are still a number of local variations; see the red solid line in <xref ref-type="fig" rid="F5">Figure 5</xref>. We also tried several methods for calculating a derivative, available in the Python &#x201c;derivative&#x201d; library. The best performing method was using a &#x201c;spline&#x201d; derivative; see the solid green line in <xref ref-type="fig" rid="F5">Figure 5</xref>. The combination of a Whittaker noise filter and the spline derivative method consistently resulted in very good noise removal, preservation of significant local variations in the deflection curve (see the red circle), and few artificial peaks in the calculated deflection rate. This combination is therefore used in all further results in this article.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Deflection rate calculation methods.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g005.tif">
<alt-text content-type="machine-generated">Graph showing deflection and deflection rates over time in hours. The lines represent deflection original, Whittaker filter, and deflection rates with original, segments, and spline methods. A red circle highlights a section. Deflection is measured in millimeters and deflection rate in millimeters per hour.</alt-text>
</graphic>
</fig>
</sec>
</sec>
<sec id="s3-2">
<label>3.2</label>
<title>Uniaxial creep tests</title>
<p>In the second stage, reference uniaxial creep tests were performed at 650 &#xb0;C. The equivalent stress <inline-formula id="inf8">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was estimated from SPC tests, using <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, and then initial (uniaxial) stress levels between 150 MPa and 290 MPa were selected (<xref ref-type="table" rid="T4">Table 4</xref>).</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>UC test matrix at 650 &#xb0;C.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Material</th>
<th colspan="7" align="center">Initial stress <italic>&#x3c3;</italic>
<sub>
<italic>init</italic>
</sub> [MPa]</th>
</tr>
<tr>
<th align="left">150</th>
<th align="left">170</th>
<th align="left">190</th>
<th align="left">210</th>
<th align="left">250</th>
<th align="left">270</th>
<th align="left">290</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">AMRC NA</td>
<td align="left">1x</td>
<td align="left">1x</td>
<td align="left">1x</td>
<td align="left">1x</td>
<td align="left">1x</td>
<td align="left">1x</td>
<td align="left">1x</td>
</tr>
<tr>
<td align="left">AMRC Aged</td>
<td align="left">1x</td>
<td align="left">1x</td>
<td align="left">1x</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left">CEA Aged</td>
<td align="left">1x</td>
<td align="left">1x</td>
<td align="left">1x</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec sec-type="results|discussion" id="s4">
<label>4</label>
<title>Results and discussion</title>
<p>
<xref ref-type="fig" rid="F6">Figure 6</xref> shows the SPC initial deflections, u<sub>0</sub>, defined as a deflection 5 s after the application of the full force load. These deflections are the result of an elastic&#x2013;plastic response of a test piece. Because the calculation of the equivalent stress <inline-formula id="inf9">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, depends strongly on the deflection, it is important to accurately capture these deflections. The initial deflections follow a linear trend relative to the load, with some scatter even within the same material. AMRC NA tests were performed first and have the largest scatter. Lessons learned in applying the test procedure reduced the scatter later on during AMRC Aged and CEA Aged tests. All the test pieces conformed to the very strict EN 10371:2021 thickness tolerances (0.5 &#xb1; 0.005 mm), and both the test piece temperature and the force load were strictly controlled. Some scatter in results within the same material is probably due to differences in the microstructure of test pieces. Because LPBF is used, the test pieces are basically welds, and local variations in material properties can be expected. Furthermore, surface roughness of the test pieces and the silicon nitride Si3N4 bearing ball, resulting in different friction effects between the tests, could be a contributing factor. The minor influencing factor could be the small variations in the silicon nitride Si<sub>3</sub>N<sub>4</sub> bearing ball diameter (grade 5, &#xb1;0.0013 mm diameter tolerance) and load application rate, which we are not able to strictly control on our test machines.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Measured initial elastic&#x2013;plastic deflection u<sub>0</sub>.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g006.tif">
<alt-text content-type="machine-generated">Scatter plot showing initial deflection \(u_0\) in millimeters vs. force in Newtons. Black stars represent AMRC NA, red circles for AMRC Aged, and blue triangles also for AMRC Aged. Deflection ranges from 0.2 to 0.6 millimeters, and force ranges from 250 to 500 Newtons.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F7">Figures 7</xref>&#x2013;<xref ref-type="fig" rid="F14">14</xref> show measured deflections during SPC tests at load rates from 500 N to 240 N (<xref ref-type="bibr" rid="B9">Jorge and Myriam, 2025</xref>). The symbols indicate the time at which the minimum deflection rate was estimated, using the procedure described above. In general, the aged material exhibits shorter creep life. In addition, the minimum deflection rate occurs earlier for the aged material; see <xref ref-type="table" rid="T5">Table 5</xref>. The exception is the AMRC NA FK-13 test at 260 N, where the minimum deflection rate occurs earlier than in both CEA Aged tests (GB-08, GB-09). In general, the CEA Aged creep lives are somewhat shorter than AMRC Aged lives at loads from 500 N to 300 N. At 260 N and 240 N loads, there is no significant difference between the two.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Measured deflection and calculated deflection rates at the 500 N load level.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g007.tif">
<alt-text content-type="machine-generated">Graph showing deflection versus time for various materials tested at 650 degrees Celsius with a force of 500 Newtons. The solid lines represent deflection in millimeters, and the dashed lines represent deflection rate in micrometers per hour. Each material type is color-coded, and a legend indicates specific material codes. Deflection increases over time, with varying rates for different materials.</alt-text>
</graphic>
</fig>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Measured deflection and calculated deflection rates at the 450 N load level.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g008.tif">
<alt-text content-type="machine-generated">Graph showing deflection versus time for two conditions labeled FI-22 and FI-23 at 650&#xB0;C and 450N. Deflection is plotted on the left Y-axis and deflection rate on the right Y-axis. Solid lines represent deflection, and dashed lines represent deflection rate. FI-23 exhibits higher initial deflection, then stabilizes and increases again after 15 hours. FI-22 shows a lower initial deflection and more gradual increase.</alt-text>
</graphic>
</fig>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Measured deflection and calculated deflection rates at the 400 N load level.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g009.tif">
<alt-text content-type="machine-generated">Graph showing deflection versus time for various materials at 650&#xB0;C and 400N. Solid lines represent deflection in millimeters, and dashed lines show deflection rate in micrometers per hour. Different colored lines represent specific materials, such as FI-09 AMRC NA and GB-04 CEA Aged, with key points marked by stars.</alt-text>
</graphic>
</fig>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Measured deflection and calculated deflection rates at the 350 N load level.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g010.tif">
<alt-text content-type="machine-generated">Line graph showing deflection and deflection rates over time at 650 degrees Celsius and 350 Newtons. Two primary lines represent FI-26 and FI-27 AMRC NA data, with corresponding deflection rate lines. Deflection increases gradually over 60 hours, with FI-26 deflecting more than FI-27. The plot uses a dual-axis to display deflection in millimeters and deflection rate in micrometers per hour.</alt-text>
</graphic>
</fig>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Measured deflection and calculated deflection rates at the 320 N load level.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g011.tif">
<alt-text content-type="machine-generated">Graph comparing deflection and deflection rate over time for two test pieces, FK-07 and FK-08, under SPC 650&#xB0;C, 320N conditions. Solid lines represent deflection (FK-07 in blue, FK-08 in orange) in millimeters, while dashed lines show deflection rate in micrometers per hour. FK-07 exhibits higher deflection and deflection rate than FK-08, especially noticeable after 80 hours. Stars mark significant points on the curves.</alt-text>
</graphic>
</fig>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Measured deflection and calculated deflection rates at the 300 N load level.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g012.tif">
<alt-text content-type="machine-generated">Graph showing deflection and deflection rate over time for different materials tested at 650 degrees Celsius and 300 Newtons. Solid lines represent deflection in millimeters, while dashed lines indicate deflection rate in micrometers per hour. Legends distinguish various material samples coded FI-12, FV-02, FV-03, GB-06, and GB-07. Time is in hours.</alt-text>
</graphic>
</fig>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Measured deflection and calculated deflection rates at the 260 N load level.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g013.tif">
<alt-text content-type="machine-generated">Graph showing deflection versus time for various materials at 650 degrees Celsius and 260 Newtons. Solid lines represent deflection while dashed lines indicate deflection rates. Test pieces include FK-13, FK-14, FV-14, GB-08, and GB-09 in 'AMRC NA' and 'CEA Aged' conditions. Deflection increases with time, showing varying trends for each material.</alt-text>
</graphic>
</fig>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>Measured deflection and calculated deflection rates at the 240 N load level.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g014.tif">
<alt-text content-type="machine-generated">Graph showing deflection versus time with curves labeled FK-09, FK-10, FV-08, FV-09, GB-12, and GB-13. Solid lines represent deflection, while dashed lines indicate deflection rates. The x-axis represents time in hours, and the y-axis represents deflection in millimeters. Annotations indicate tests at 650&#xB0;C with a 240N load.</alt-text>
</graphic>
</fig>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>SPC test results.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="right">Test piece</th>
<th align="right">Material</th>
<th align="right">Test Machine</th>
<th align="right">Force [N]</th>
<th align="right">u<sub>0</sub> [mm]</th>
<th align="right">&#x3c3;<sub>eq</sub> [MPa]</th>
<th align="right">t<sub>r</sub> [h]</th>
<th align="right">t<sub>&#x16f; min</sub> [h]</th>
<th align="right">
<inline-formula id="inf110">
<mml:math id="m111">
<mml:mrow>
<mml:msub>
<mml:mover accent="true">
<mml:mi>u</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
<mml:mi mathvariant="italic">min</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> [&#x3bc;m/h]</th>
<th align="right">u<sub>at &#x16f; min</sub> [mm]</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="right">FI-16</td>
<td align="right">AMRC NA</td>
<td align="right">SP-00</td>
<td rowspan="10" align="right">500.0</td>
<td align="right">0.66</td>
<td align="right">274.70</td>
<td align="right">15.01</td>
<td align="right">7.52</td>
<td align="right">11.62</td>
<td align="right">0.92</td>
</tr>
<tr>
<td align="right">FI-17</td>
<td align="right">AMRC NA</td>
<td align="right">SP-01</td>
<td align="right">0.67</td>
<td align="right">274.38</td>
<td align="right">10.46</td>
<td align="right">5.26</td>
<td align="right">17.05</td>
<td align="right">0.93</td>
</tr>
<tr>
<td align="right">FI-28</td>
<td align="right">AMRC NA</td>
<td align="right">SP-00</td>
<td align="right">0.63</td>
<td align="right">282.66</td>
<td align="right">10.27</td>
<td align="right">5.24</td>
<td align="right">16.66</td>
<td align="right">0.89</td>
</tr>
<tr>
<td align="right">FI-29</td>
<td align="right">AMRC NA</td>
<td align="right">SP-01</td>
<td align="right">0.60</td>
<td align="right">298.10</td>
<td align="right">11.25</td>
<td align="right">5.30</td>
<td align="right">15.47</td>
<td align="right">0.82</td>
</tr>
<tr>
<td align="right">FK-04</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-00</td>
<td align="right">0.65</td>
<td align="right">286.63</td>
<td align="right">13.65</td>
<td align="right">5.72</td>
<td align="right">14.26</td>
<td align="right">0.87</td>
</tr>
<tr>
<td align="right">FK-05</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-01</td>
<td align="right">0.66</td>
<td align="right">286.64</td>
<td align="right">12.75</td>
<td align="right">4.92</td>
<td align="right">12.79</td>
<td align="right">0.87</td>
</tr>
<tr>
<td align="right">FV-06</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-00</td>
<td align="right">0.63</td>
<td align="right">287.18</td>
<td align="right">9.35</td>
<td align="right">4.70</td>
<td align="right">20.62</td>
<td align="right">0.86</td>
</tr>
<tr>
<td align="right">FV-07</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-01</td>
<td align="right">0.65</td>
<td align="right">291.75</td>
<td align="right">9.05</td>
<td align="right">3.40</td>
<td align="right">22.49</td>
<td align="right">0.84</td>
</tr>
<tr>
<td align="right">GB-02</td>
<td align="right">CEA Aged</td>
<td align="right">SP-00</td>
<td align="right">0.62</td>
<td align="right">292.81</td>
<td align="right">6.39</td>
<td align="right">3.13</td>
<td align="right">27.45</td>
<td align="right">0.84</td>
</tr>
<tr>
<td align="right">GB-03</td>
<td align="right">CEA Aged</td>
<td align="right">SP-01</td>
<td align="right">0.63</td>
<td align="right">297.30</td>
<td align="right">9.88</td>
<td align="right">2.80</td>
<td align="right">22.68</td>
<td align="right">0.82</td>
</tr>
<tr>
<td align="right">FI-22</td>
<td align="right">AMRC NA</td>
<td align="right">SP-00</td>
<td rowspan="2" align="right">450.0</td>
<td align="right">0.54</td>
<td align="right">272.31</td>
<td align="right">22.00</td>
<td align="right">8.62</td>
<td align="right">10.12</td>
<td align="right">0.80</td>
</tr>
<tr>
<td align="right">FI-23</td>
<td align="right">AMRC NA</td>
<td align="right">SP-01</td>
<td align="right">0.58</td>
<td align="right">270.25</td>
<td align="right">19.64</td>
<td align="right">6.56</td>
<td align="right">8.79</td>
<td align="right">0.81</td>
</tr>
<tr>
<td align="right">FI-09</td>
<td align="right">AMRC NA</td>
<td align="right">SP-01</td>
<td rowspan="6" align="right">400.0</td>
<td align="right">0.53</td>
<td align="right">251.31</td>
<td align="right">33.66</td>
<td align="right">7.23</td>
<td align="right">7.00</td>
<td align="right">0.75</td>
</tr>
<tr>
<td align="right">FI-10</td>
<td align="right">AMRC NA</td>
<td align="right">SP-00</td>
<td align="right">0.49</td>
<td align="right">262.23</td>
<td align="right">31.31</td>
<td align="right">8.33</td>
<td align="right">9.17</td>
<td align="right">0.71</td>
</tr>
<tr>
<td align="right">FV-04</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-00</td>
<td align="right">0.49</td>
<td align="right">258.71</td>
<td align="right">23.61</td>
<td align="right">6.79</td>
<td align="right">11.04</td>
<td align="right">0.72</td>
</tr>
<tr>
<td align="right">FV-05</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-01</td>
<td align="right">0.44</td>
<td align="right">271.24</td>
<td align="right">27.09</td>
<td align="right">7.83</td>
<td align="right">9.63</td>
<td align="right">0.67</td>
</tr>
<tr>
<td align="right">GB-04</td>
<td align="right">CEA Aged</td>
<td align="right">SP-00</td>
<td align="right">0.45</td>
<td align="right">272.33</td>
<td align="right">22.32</td>
<td align="right">4.89</td>
<td align="right">15.87</td>
<td align="right">0.67</td>
</tr>
<tr>
<td align="right">GB-05</td>
<td align="right">CEA Aged</td>
<td align="right">SP-01</td>
<td align="right">0.46</td>
<td align="right">278.96</td>
<td align="right">19.05</td>
<td align="right">3.81</td>
<td align="right">15.44</td>
<td align="right">0.64</td>
</tr>
<tr>
<td align="right">FI-26</td>
<td align="right">AMRC NA</td>
<td align="right">SP-00</td>
<td rowspan="2" align="right">350.0</td>
<td align="right">0.39</td>
<td align="right">197.55</td>
<td align="right">59.55</td>
<td align="right">32.90</td>
<td align="right">7.60</td>
<td align="right">0.89</td>
</tr>
<tr>
<td align="right">FI-27</td>
<td align="right">AMRC NA</td>
<td align="right">SP-01</td>
<td align="right">0.32</td>
<td align="right">287.02</td>
<td align="right">57.97</td>
<td align="right">9.66</td>
<td align="right">7.32</td>
<td align="right">0.50</td>
</tr>
<tr>
<td align="right">FK-07</td>
<td align="right">AMRC NA</td>
<td align="right">SP-00</td>
<td rowspan="2" align="right">320.0</td>
<td align="right">0.33</td>
<td align="right">188.11</td>
<td align="right">86.08</td>
<td align="right">49.90</td>
<td align="right">5.60</td>
<td align="right">0.83</td>
</tr>
<tr>
<td align="right">FK-08</td>
<td align="right">AMRC NA</td>
<td align="right">SP-01</td>
<td align="right">0.35</td>
<td align="right">185.76</td>
<td align="right">121.18</td>
<td align="right">72.66</td>
<td align="right">3.34</td>
<td align="right">0.85</td>
</tr>
<tr>
<td align="right">FI-12</td>
<td align="right">AMRC NA</td>
<td align="right">SP-00</td>
<td align="left"/>
<td align="right">0.39</td>
<td align="right">175.32</td>
<td align="right">182.60</td>
<td align="right">92.77</td>
<td align="right">2.27</td>
<td align="right">0.84</td>
</tr>
<tr>
<td align="right">FV-02</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-00</td>
<td align="left"/>
<td align="right">0.30</td>
<td align="right">184.87</td>
<td align="right">103.79</td>
<td align="right">56.81</td>
<td align="right">4.91</td>
<td align="right">0.78</td>
</tr>
<tr>
<td align="right">FV-03</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-01</td>
<td align="right">300</td>
<td align="right">0.32</td>
<td align="right">178.92</td>
<td align="right">111.56</td>
<td align="right">60.95</td>
<td align="right">3.97</td>
<td align="right">0.82</td>
</tr>
<tr>
<td align="right">GB-06</td>
<td align="right">CEA Aged</td>
<td align="right">SP-00</td>
<td align="left"/>
<td align="right">0.29</td>
<td align="right">173.87</td>
<td align="right">87.21</td>
<td align="right">62.62</td>
<td align="right">4.89</td>
<td align="right">0.85</td>
</tr>
<tr>
<td align="right">GB-07</td>
<td align="right">CEA Aged</td>
<td align="right">SP-01</td>
<td align="left"/>
<td align="right">0.28</td>
<td align="right">188.74</td>
<td align="right">94.12</td>
<td align="right">59.94</td>
<td align="right">3.35</td>
<td align="right">0.75</td>
</tr>
<tr>
<td align="right">FK-13</td>
<td align="right">AMRC NA</td>
<td align="right">SP-00</td>
<td rowspan="5" align="right">260.0</td>
<td align="right">0.31</td>
<td align="right">149.79</td>
<td align="right">298.45</td>
<td align="right">142.48</td>
<td align="right">1.93</td>
<td align="right">0.86</td>
</tr>
<tr>
<td align="right">FK-14</td>
<td align="right">AMRC NA</td>
<td align="right">SP-01</td>
<td align="right">0.22</td>
<td align="right">148.36</td>
<td align="right">520.45</td>
<td align="right">312.25</td>
<td align="right">0.62</td>
<td align="right">0.87</td>
</tr>
<tr>
<td align="right">FV-14</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-01</td>
<td align="right">0.27</td>
<td align="right">157.74</td>
<td align="right">214.45</td>
<td align="right">104.72</td>
<td align="right">2.18</td>
<td align="right">0.80</td>
</tr>
<tr>
<td align="right">GB-08</td>
<td align="right">CEA Aged</td>
<td align="right">SP-00</td>
<td align="right">0.17</td>
<td align="right">159.12</td>
<td align="right">262.58</td>
<td align="right">173.48</td>
<td align="right">1.56</td>
<td align="right">0.79</td>
</tr>
<tr>
<td align="right">GB-09</td>
<td align="right">CEA Aged</td>
<td align="right">SP-01</td>
<td align="right">0.20</td>
<td align="right">165.87</td>
<td align="right">260.93</td>
<td align="right">174.16</td>
<td align="right">1.50</td>
<td align="right">0.74</td>
</tr>
<tr>
<td align="right">FK-09</td>
<td align="right">AMRC NA</td>
<td align="right">SP-00</td>
<td rowspan="6" align="right">240.0</td>
<td align="right">0.14</td>
<td align="right">135.32</td>
<td align="right">958.48</td>
<td align="right">600.55</td>
<td align="right">0.36</td>
<td align="right">0.89</td>
</tr>
<tr>
<td align="right">FK-10</td>
<td align="right">AMRC NA</td>
<td align="right">SP-01</td>
<td align="right">0.19</td>
<td align="right">135.10</td>
<td align="right">848.35</td>
<td align="right">596.43</td>
<td align="right">0.38</td>
<td align="right">0.89</td>
</tr>
<tr>
<td align="right">FV-08</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-00</td>
<td align="right">0.16</td>
<td align="right">145.44</td>
<td align="right">459.93</td>
<td align="right">282.37</td>
<td align="right">1.03</td>
<td align="right">0.80</td>
</tr>
<tr>
<td align="right">FV-09</td>
<td align="right">AMRC Aged</td>
<td align="right">SP-00</td>
<td align="right">0.15</td>
<td align="right">148.48</td>
<td align="right">385.29</td>
<td align="right">195.38</td>
<td align="right">1.49</td>
<td align="right">0.77</td>
</tr>
<tr>
<td align="right">GB-12</td>
<td align="right">CEA Aged</td>
<td align="right">SP-01</td>
<td align="right">0.18</td>
<td align="right">159.14</td>
<td align="right">390.88</td>
<td align="right">215.25</td>
<td align="right">1.09</td>
<td align="right">0.70</td>
</tr>
<tr>
<td align="right">GB-13</td>
<td align="right">CEA Aged</td>
<td align="right">SP-00</td>
<td align="right">0.27</td>
<td align="right">125.38</td>
<td align="right">413.38</td>
<td align="right">268.40</td>
<td align="right">1.09</td>
<td align="right">1.00</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In <xref ref-type="fig" rid="F9">Figure 9</xref>, we can see that all the deflection rate curves at 400 N force load exhibit two minima, with the first one having a significantly lower deflection rate than the second one. The two minima are even more apparent at decreased force load, 350 N, but are now almost evenly matched in terms of deflection rate. Calculation of the equivalent initial stress <inline-formula id="inf10">
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</inline-formula>, <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, according to the EN 10371:2021, depends on the identification of the minimum deflection rate. However, the standard assumes that only one minimum deflection rate is observed. At 350 N, it is unclear if we should select the first or the second minimum, especially because they are evenly matched in terms of deflection rate, and the estimation of the deflection rate itself is subject to the approach for dealing with the noise in the measured deflection signal and the derivative calculation method.</p>
<p>Another question that emerges is what causes the first minimum. In this work, we conjecture that a significant crack develops and manifests in the first minimum. It is well known that the region of maximal stress/strain in small punch tests continuously moves radially outwards during the test. We therefore conjecture that if the material is ductile enough, the crack that results in the first minimum in the deflection rate curve arrests as the zone of maximal stress/strain redistributes radially outwards. At a certain point, a second crack initializes and starts to propagate, resulting in the second minimum, shortly before the rupture of the test piece. At the 240 N load, one can see a significant local increase in the deflection at approximately 0.9 mm for the FK-10 AMRC NA and FV-08 AMRC tests (the orange and green curves in <xref ref-type="fig" rid="F14">Figure 14</xref>). We assume these sudden deflection increases are due to a final/secondary crack initialization. To evaluate these conjectures, we performed an interrupted SPC test with AMRC NA material. Because no more test pieces conformant with the strict 0.5 &#xb1; 0.005 mm requirement of the EN 10371:2021 were available, we used a test piece with a thickness of 0.4661 mm, labeled FI-07. The EN 10371:2021 standard provides a formula for estimating the ultimate tensile stress, <inline-formula id="inf11">
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</p>
<p>Based on the SPC tests at 350 N, we decided to interrupt the SPC test for the first time 12 h after application of the force load of 326 N. We defined the interruption as stopping the furnace heating by setting the target furnace temperature to 22 &#xb0;C, triggering the cool down. During the cool-down, the force load remained at 326 N. Following the cool-down, we removed the dead weights, removed the test piece from the test machine, and performed a scanning electron microscope (SEM) analysis of the test piece. Two crack fronts are visible, as shown in <xref ref-type="fig" rid="F15">Figures 15</xref>, <xref ref-type="fig" rid="F16">16</xref>. The first crack front with a diameter of 1.28 mm is fully developed after 12 h. The second front, with a diameter of 1.46 mm, has only started developing.</p>
<fig id="F15" position="float">
<label>FIGURE 15</label>
<caption>
<p>SPC interrupted test, FI-07 test piece, 326 N load level. Crack fronts 12 h after the start of the SPC test.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g015.tif">
<alt-text content-type="machine-generated">Close-up of a circular object with concentric rings and visible cracks in the center. The surface has a rough texture with scattered small debris. A scale in the bottom right shows &#x22;2 mm&#x22; for reference.</alt-text>
</graphic>
</fig>
<fig id="F16" position="float">
<label>FIGURE 16</label>
<caption>
<p>SPC interrupted test, FI-07 test piece, 326 N load level. Crack fronts 12 h (top) and 28 h 48 min (bottom) after the start of the SPC test.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g016.tif">
<alt-text content-type="machine-generated">Close-up of two circular indentations on a surface. The top image shows an intact circle with a diameter marked as 1.28 millimeters in red and 1.46 millimeters in yellow. The bottom image shows a fractured circle with similar markings in red and yellow, indicating the break pattern radiating from the center. Both images include scale bars for reference.</alt-text>
</graphic>
</fig>
<p>Next, we put the FI-07 test piece back into the test machine, added the same dead weights to reapply a 326 N force load, and heated the test piece back to 650 &#xb0;C. After reaching the target temperature, we waited for 16 h and 48 min (cumulative time 12 h &#x2b; 16 h &#x2b; 48 min) and then initiated the second interruption, using the same procedure as for the first interruption. A second SEM analysis was performed (see the lower part of <xref ref-type="fig" rid="F16">Figure 16</xref>). The analysis showed the arrest of the first crack front and full development of the second, much larger crack front that only started forming after the first interruption. We did not continue the SPC tests beyond this point, 16 h and 48 min (cumulative time 12 h &#x2b; 16 h &#x2b; 48 min). The deflection versus time curve and the calculated deflection rates indeed show two minima (<xref ref-type="fig" rid="F17">Figure 17</xref>), although these minima are less pronounced than the ones at 350 N (<xref ref-type="fig" rid="F10">Figure 10</xref>). Nevertheless, this confirms our conjecture that cracks formed during the SPC test. More interrupted tests are required to confirm that crack initiation results in a local minimum in the deflection rate.</p>
<fig id="F17" position="float">
<label>FIGURE 17</label>
<caption>
<p>Interrupted AMRC NA test. Deflection was measured and deflection rates were calculated at the 326 N load level.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g017.tif">
<alt-text content-type="machine-generated">Graph showing deflection and deflection rate over time for an interrupted test. The red line represents deflection up to stop 1, with a local minimum marked by a red star around 10 hours. The blue line shows deflection after stop 1, with a local minimum indicated by a blue star near 20 hours. Deflection is on the left y-axis in millimeters, deflection rate on the right y-axis in micrometers per hour, with time on the x-axis in hours.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F18">Figure 18</xref> shows the time to rupture versus the applied force for the SPC test data for the three materials and the regression lines. This confirms again that the aged materials have consistently reduced creep life compared to the non-aged material.</p>
<fig id="F18" position="float">
<label>FIGURE 18</label>
<caption>
<p>SPC: measured time to rupture versus force.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g018.tif">
<alt-text content-type="machine-generated">Graph showing the relation between force (N) and time to rupture (hours) with several trendlines and data points. Data symbols represent different samples: stars for SPC: AMRC NA, circles for SPC: AMRC Aged, and triangles for SPC: CEA Aged. Trendlines are provided for each dataset and a combined materials trend. A mathematical formula and R-squared value are displayed for reference, indicating the fit quality of the trendlines.</alt-text>
</graphic>
</fig>
<p>Nuclear design codes, and in particular evaluation of material properties, are primarily based on standard uniaxial tests. Uniaxial tests were conducted to assess the SPC test data and to assess the transferability. To this end, we calculated the equivalent stress <inline-formula id="inf17">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
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</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, for all the SPC tests, and compared <inline-formula id="inf18">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
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<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> versus rupture time to the applied initial stress of UC tests <inline-formula id="inf19">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
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<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> versus rupture time, <xref ref-type="fig" rid="F19">Figure 19</xref>. One UC test was performed for each material at 150 MPa, 170 MPa, and 190 MPa initial stress <inline-formula id="inf20">
<mml:math id="m23">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mrow>
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<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. For the AMRC NA, we also performed UC tests at 210 MPa, 250 MPa, 270 MPa, and 290 MPa initial stress <inline-formula id="inf21">
<mml:math id="m24">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. <xref ref-type="table" rid="T6">Table 6</xref> gives an overview of the UC test results.</p>
<fig id="F19" position="float">
<label>FIGURE 19</label>
<caption>
<p>SPC and UC: measured time to rupture versus <inline-formula id="inf22">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="disp-formula" rid="e1">Equation 1</xref>), <inline-formula id="inf23">
<mml:math id="m26">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g019.tif">
<alt-text content-type="machine-generated">A graph displays the relationship between stress (\( \sigma_{eq}, \sigma_{init} \) in MPa) and time to rupture (\( t_r \) in hours). Data points are represented by different symbols: stars, circles, and triangles, which are also color-coded. Two trendlines are shown: a dashed line for UC and a solid line for SPC. The graph includes two equations with \( R^2 \) values of 0.9261 and 0.9938. The legend explains the symbols used for different conditions, including AMRC NA, AMRC Aged, and CEA Aged for both SPC and UC.</alt-text>
</graphic>
</fig>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>UC test results.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="right">Test piece</th>
<th align="right">Material</th>
<th align="right">Test Machine</th>
<th align="right">&#x3c3;<sub>init</sub> [MPa]</th>
<th align="right">t<sub>r</sub> [h]</th>
<th align="right">
<inline-formula id="inf131">
<mml:math id="m132">
<mml:mrow>
<mml:msub>
<mml:mover accent="true">
<mml:mi>&#x3b5;</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
<mml:mi mathvariant="italic">min</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>[%/h]</th>
<th align="right">
<inline-formula id="inf132">
<mml:math id="m133">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:msub>
<mml:mover accent="true">
<mml:mi>&#x3b5;</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
<mml:mi mathvariant="italic">min</mml:mi>
</mml:msub>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> [h]</th>
<th align="right">
<inline-formula id="inf133">
<mml:math id="m134">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:msub>
<mml:mover accent="true">
<mml:mi>&#x3b5;</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
<mml:mi mathvariant="italic">min</mml:mi>
</mml:msub>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> [%]</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="right">FA-01</td>
<td align="right">AMRC NA</td>
<td align="right">RIG04</td>
<td rowspan="3" align="right">150.0</td>
<td align="right">1292.32</td>
<td align="right">0.00</td>
<td align="right">0.00</td>
<td align="right">0.75</td>
</tr>
<tr>
<td align="right">GA-01</td>
<td align="right">AMRC Aged</td>
<td align="right">RIG04</td>
<td align="right">1235.54</td>
<td align="right">0.00</td>
<td align="right">0.00</td>
<td align="right">0.23</td>
</tr>
<tr>
<td align="right">GC-01</td>
<td align="right">CEA Aged</td>
<td align="right">RIG10</td>
<td align="right">1160.73</td>
<td align="right">0.00</td>
<td align="right">0.00</td>
<td align="right">0.39</td>
</tr>
<tr>
<td align="right">FA-02</td>
<td align="right">AMRC NA</td>
<td align="right">RIG10</td>
<td rowspan="3" align="right">170.0</td>
<td align="right">485.19</td>
<td align="right">0.01</td>
<td align="right">16.08</td>
<td align="right">0.35</td>
</tr>
<tr>
<td align="right">FZ-01</td>
<td align="right">AMRC Aged</td>
<td align="right">RIG10</td>
<td align="right">408.70</td>
<td align="right">0.01</td>
<td align="right">0.00</td>
<td align="right">0.16</td>
</tr>
<tr>
<td align="right">GB-01</td>
<td align="right">CEA Aged</td>
<td align="right">RIG10</td>
<td align="right">442.15</td>
<td align="right">-0.00</td>
<td align="right">0.00</td>
<td align="right">0.25</td>
</tr>
<tr>
<td align="right">FA-03</td>
<td align="right">AMRC NA</td>
<td align="right">RIG08</td>
<td rowspan="3" align="right">190.0</td>
<td align="right">226.33</td>
<td align="right">0.00</td>
<td align="right">0.00</td>
<td align="right">0.15</td>
</tr>
<tr>
<td align="right">FV-01</td>
<td align="right">AMRC Aged</td>
<td align="right">RIG04</td>
<td align="right">212.48</td>
<td align="right">0.02</td>
<td align="right">0.00</td>
<td align="right">0.24</td>
</tr>
<tr>
<td align="right">GD-01</td>
<td align="right">CEA Aged</td>
<td align="right">RIG05</td>
<td align="right">219.31</td>
<td align="right">0.01</td>
<td align="right">0.00</td>
<td align="right">0.00</td>
</tr>
<tr>
<td align="right">FA-04</td>
<td align="right">AMRC NA</td>
<td align="right">RIG08</td>
<td align="right">210.0</td>
<td align="right">79.01</td>
<td align="right">0.06</td>
<td align="right">16.51</td>
<td align="right">1.11</td>
</tr>
<tr>
<td align="right">IC-02</td>
<td align="right">AMRC NA</td>
<td align="right">RIG05</td>
<td align="right">250.0</td>
<td align="right">19.80</td>
<td align="right">0.59</td>
<td align="right">5.17</td>
<td align="right">4.98</td>
</tr>
<tr>
<td align="right">IB-03</td>
<td align="right">AMRC NA</td>
<td align="right">RIG10</td>
<td align="right">270.0</td>
<td align="right">9.43</td>
<td align="right">1.76</td>
<td align="right">2.70</td>
<td align="right">7.91</td>
</tr>
<tr>
<td align="right">IB-02</td>
<td align="right">AMRC NA</td>
<td align="right">RIG08</td>
<td align="right">290.0</td>
<td align="right">3.71</td>
<td align="right">5.65</td>
<td align="right">0.23</td>
<td align="right">4.59</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>We can observe that UC tests for the three materials overlap perfectly and are distributed along the regression line with an R<sup>2</sup> &#x3d; 0.9938, <xref ref-type="fig" rid="F19">Figure 19</xref>. In contrast to SPC tests, there is practically no difference between the three materials in UC tests. Furthermore, the scatter in the UC results between three different materials is much smaller than in the SPC results. We can also see that the transferability of SPC results to UC, by evaluating <inline-formula id="inf24">
<mml:math id="m27">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from the SPC tests, is relatively good. <xref ref-type="disp-formula" rid="e1">Equation 1</xref> from the EN 10371:2021 standard works quite well. One can therefore estimate the equivalent UC initial stress load condition from the SCP tests. However, the evaluated <inline-formula id="inf25">
<mml:math id="m28">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> slightly overestimates the stress below t<sub>r</sub> &#x3d; 50 h and underpredicts it above that value due to different slopes of the SPC and UC trendlines.</p>
<p>Several explanations are possible for the SPC trendline having a different slope than the UC trendline. First, <xref ref-type="disp-formula" rid="e1">Equation 1</xref> is based on one minimum in the SPC deflection rate, whereas here, we can have two minima, as shown in <xref ref-type="fig" rid="F10">Figure 10</xref>. In this work, we always select the one with the lowest deflection rate value to use in <xref ref-type="disp-formula" rid="e1">Equation 1</xref>. However, as shown in <xref ref-type="fig" rid="F15">Figures 15</xref>&#x2013;<xref ref-type="fig" rid="F17">17</xref>, the first minimum is probably the one where the initial crack has already formed. If the second minimum is used, the measured deflection is not solely due to creep but is significantly affected by the crack propagation. Second, the orientation of the SPC test pieces in relation to the uniaxial test piece is the one shown in red in <xref ref-type="fig" rid="F1">Figure 1</xref>. This was driven by the limited amount of material, as more disc slices for SPC test pieces can be extracted from a bar in the red orientation than in the gray SPC orientation. In the SPC test, most of the stress acts in the radial direction of the SPC test piece. With the red SPC test piece orientation, the red SPC test piece has stress perpendicular to the stress in the uniaxial test piece. We are therefore testing a different material direction in the SPC tests. In fact, we should have used the gray SPC test piece orientation, but as mentioned, this was not possible due to the limited amount of available material. The SPC test piece orientation in relation to the test build can have a significant impact on the time to rupture in LPBF. For Inconel 718, <xref ref-type="bibr" rid="B16">Zhang et al. (2025)</xref> report significantly shorter rupture times for the SPC test piece in the build direction (red color in <xref ref-type="fig" rid="F1">Figure 1</xref>) compared to the one perpendicular to the build direction (gray color in <xref ref-type="fig" rid="F1">Figure 1</xref>). In this case, only aged heat treatment was applied. However, when they applied the solution and aged heat treatments, the differences in rupture times decreased significantly. This behavior is at least in part driven by a different microstructure (<xref ref-type="bibr" rid="B16">Zhang et al., 2025</xref>) of the two directions. Third, and probably the most important, <xref ref-type="disp-formula" rid="e1">Equation 1</xref> has been developed based on 97 UC tests and 159 SPC tests with both new and service-exposed materials, mainly low-alloy steels and 9Cr steels, such as 14MoV63, X20CrMoV121, P91, P92, Eurofer97, and stainless steel 316L (<xref ref-type="bibr" rid="B6">CEN EN, 2024</xref>). However, this data set had a large share of P92 steel. <xref ref-type="disp-formula" rid="e1">Equation 1</xref> coefficients 1.916 and 0.6579 are probably not the best for AM 316L material.</p>
<sec id="s4-1">
<label>4.1</label>
<title>Microstructural analysis</title>
<p>The fracture surfaces of AMRC NA, AMRC Aged, and CEA Aged UC test pieces, at a load level of <inline-formula id="inf26">
<mml:math id="m29">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
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<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
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</mml:math>
</inline-formula> &#x3d; 150 MPa, were analyzed by scanning electron microscope (SEM). <xref ref-type="fig" rid="F20">Figures 20</xref>, <xref ref-type="fig" rid="F21">21</xref> show similar patterns obtained for both the AMRC NA and CEA Aged test pieces, respectively. The surfaces are not flat and exhibit a mixed ductile-brittle fracture. For the same test piece, one of the fracture surfaces exhibits cavities while the other shows slight spherical extrusions, roughly 50 &#xb5;m in diameter. The parallel patterns observed in the structure are likely due to the laser scanning paths followed, related to scanning speed and hatch spacing. The fracture surface morphologies suggest that the overlapping regions of two laser tracks generate more ductile thin areas where some dimples can be distinguished. On the other hand, the cavities and elevation exhibit a more brittle aspect, with some cleavage features.</p>
<fig id="F20" position="float">
<label>FIGURE 20</label>
<caption>
<p>SEM picture of both UC fracture surfaces in the XY orientation. AMRC NA, test piece FA-01, <inline-formula id="inf27">
<mml:math id="m30">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
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<mml:mi>n</mml:mi>
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<mml:mi>t</mml:mi>
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</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 150 MPa.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g020.tif">
<alt-text content-type="machine-generated">Four scanning electron microscope (SEM) images show the porous surface morphology of materials. The top images, at 200x and 1000x magnification, reveal rough textures with varying pore sizes. The bottom images, at similar magnifications, highlight detailed surface structures and interconnected cavities, emphasizing the material's complex, irregular patterns and porosity.</alt-text>
</graphic>
</fig>
<fig id="F21" position="float">
<label>FIGURE 21</label>
<caption>
<p>SEM picture of both UC fracture surfaces in XY orientation. CEA Aged, test piece GC-01, <inline-formula id="inf28">
<mml:math id="m31">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
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<mml:mi>t</mml:mi>
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</mml:math>
</inline-formula> &#x3d; 150 MPa.</p>
</caption>
<graphic xlink:href="fmats-12-1609564-g021.tif">
<alt-text content-type="machine-generated">Four-panel microscopic images display porous structures with varying magnification levels. Each panel shows detailed textures and cavities, suggesting a material with significant porosity, ideal for scientific analysis of surface morphology.</alt-text>
</graphic>
</fig>
</sec>
</sec>
<sec sec-type="conclusion" id="s5">
<label>5</label>
<title>Conclusion</title>
<p>In this article, we provide a significant set of small punch creep (SPC) and uniaxial creep (UC) data of additively manufactured (AM) 316L stainless steel at 650 &#xb0;C. We show that SPC tests of this material result in double minima for deflection rates at relatively short rupture times (tens of hours). For a specific case, we show that these two minima are related to crack initiation and propagation. The measured SPC deflection is then not only due to the creep of the test piece but also due to its cracking. This could potentially be an issue for SPC testing of non-ductile materials. Further work is necessary to confirm additionally that the multiple crack initiations in SPC tests result in multiple deflection rate minima, to determine which minimum should be used for estimating <inline-formula id="inf29">
<mml:math id="m32">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and/or whether a completely different method should be used. We demonstrate the transferability of SPC results to UC results by calculating that the <inline-formula id="inf30">
<mml:math id="m33">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
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<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> works quite well for the AM 316L in this work. However, the <inline-formula id="inf31">
<mml:math id="m34">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> underestimates the stress for the shorter rupture times and overestimates the stress for longer rupture times. This is probably due to the EN 10371:2021 standard assuming a single minimum in the SPC deflection rate, while we show here that two minima can occur. It is clear, however, that the EN 10371:2021 standard must be re-evaluated to accommodate this complexity.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: NUCOBAM SPC, 650C catalogue, <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.5290/76">https://doi.org/10.5290/76</ext-link>, NUCOBAM UC, 650C catalogue, <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.5290/77">https://doi.org/10.5290/77</ext-link>.</p>
</sec>
<sec sec-type="author-contributions" id="s7">
<title>Author contributions</title>
<p>IS: Conceptualization, Data curation, Formal Analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing &#x2013; original draft, Writing &#x2013; review and editing. KN: Formal Analysis, Methodology, Writing &#x2013; original draft, Writing &#x2013; review and editing. SH: Conceptualization, Methodology, Writing &#x2013; review and editing. MK: Investigation, Writing &#x2013; review and editing. AG-J: Investigation, Writing &#x2013; review and editing.</p>
</sec>
<sec sec-type="COI-statement" id="s9">
<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="ai-statement" id="s10">
<title>Generative AI statement</title>
<p>The author(s) declare that no Generative AI was used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p>
</sec>
<sec sec-type="disclaimer" id="s11">
<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>
<fn-group>
<fn fn-type="custom" custom-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2750145/overview">Petr Dym&#xe1;&#x10d;ek</ext-link>, Institute of Physics of Materials (ASCR), Czechia</p>
</fn>
<fn fn-type="custom" custom-type="reviewed-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2750403/overview">Shin-ichi Komazaki</ext-link>, Kagoshima University, Japan</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3038711/overview">Juhani Rantala</ext-link>, VTT Technical Research Centre of Finland Ltd, Finland</p>
</fn>
</fn-group>
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