A phase-field method coupled with CALPHAD for the simulation of ordered -carbide precipitates in both disordered and phases in low density steel

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• 作者：Aireza Rahnama ; ^{a.rahnama@warwick.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; ^{alirezarahnama@ymail.com" class="auth_mail" title="E-mail the corresponding author} ; Richard Dashwood ; Seetharaman Sridhar
• 关键词：00-01 ; 99-00
• 刊名：Computational Materials Science
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：126
• 期：Complete
• 页码：152-159
• 全文大小：1044 K

文摘

In order to simulate multi-component diffusion controlled precipitation of ordered phases in low density steels using the phase-field method, the Gibbs free energy of the mmlsi90" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si90.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=81130730ad6372873f763409b8cfa4db" title="Click to view the MathML source">γ,αmathContainer hidden">mathCode"><math altimg="si90.gif" overflow="scroll"><mrow><mi>γmi><mtext>,mtext><mi>αmi>mrow>math> and mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si1.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=28e6ec706a0f2f0321bf707a1a723806" title="Click to view the MathML source">κmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mrow><mi>κmi>mrow>math> phases in the quaternary Fe-Mn-Al-C system was linked to the CALPHAD method using a three-sublattice model which is based on the accumulation of considerable thermodynamic data in multi-component systems and the assurance of continuous variation of the interface area. This model includes the coherent precipitation of mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si1.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=28e6ec706a0f2f0321bf707a1a723806" title="Click to view the MathML source">κmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mrow><mi>κmi>mrow>math> phase from a disordered FCC mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si2.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=bb27d9dc4a1e543a398efb4cfe505856" title="Click to view the MathML source">γmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><mrow><mi>γmi>mrow>math> phase and semi-coherent precipitation of the same mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si1.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=28e6ec706a0f2f0321bf707a1a723806" title="Click to view the MathML source">κmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mrow><mi>κmi>mrow>math> phase from a disordered BCC mmlsi3" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si3.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=d444ce8e7abbff49bdb50d1c21966436" title="Click to view the MathML source">αmathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll"><mrow><mi>αmi>mrow>math> structure. The microstructure evolution of mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si1.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=28e6ec706a0f2f0321bf707a1a723806" title="Click to view the MathML source">κmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mrow><mi>κmi>mrow>math>-carbide was simulated with three-dimensional phase-field model. The simulation was first performed for a single particle in both mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si2.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=bb27d9dc4a1e543a398efb4cfe505856" title="Click to view the MathML source">γmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><mrow><mi>γmi>mrow>math> and mmlsi3" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si3.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=d444ce8e7abbff49bdb50d1c21966436" title="Click to view the MathML source">αmathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll"><mrow><mi>αmi>mrow>math> phases to investigate the evolution of interfacial and elastic strain energy during the precipitation process. The simulation results show that mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si1.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=28e6ec706a0f2f0321bf707a1a723806" title="Click to view the MathML source">κmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mrow><mi>κmi>mrow>math> has a cuboidal morphology in mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si2.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=bb27d9dc4a1e543a398efb4cfe505856" title="Click to view the MathML source">γmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><mrow><mi>γmi>mrow>math> and elongated plate-like morphology in mmlsi3" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si3.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=d444ce8e7abbff49bdb50d1c21966436" title="Click to view the MathML source">αmathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll"><mrow><mi>αmi>mrow>math> which is in agreement with the morphologies reported in the literature. The multi-particle simulations were also performed for the precipitation of mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si1.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=28e6ec706a0f2f0321bf707a1a723806" title="Click to view the MathML source">κmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mrow><mi>κmi>mrow>math> phase from both disordered mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si2.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=bb27d9dc4a1e543a398efb4cfe505856" title="Click to view the MathML source">γmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><mrow><mi>γmi>mrow>math> and mmlsi3" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si3.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=d444ce8e7abbff49bdb50d1c21966436" title="Click to view the MathML source">αmathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll"><mrow><mi>αmi>mrow>math>. The results also demonstrate that the size of mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si1.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=28e6ec706a0f2f0321bf707a1a723806" title="Click to view the MathML source">κmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mrow><mi>κmi>mrow>math> precipitates in mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si2.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=bb27d9dc4a1e543a398efb4cfe505856" title="Click to view the MathML source">γmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><mrow><mi>γmi>mrow>math> is remarkably smaller than that in mmlsi3" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0927025616304566&_mathId=si3.gif&_user=111111111&_pii=S0927025616304566&_rdoc=1&_issn=09270256&md5=d444ce8e7abbff49bdb50d1c21966436" title="Click to view the MathML source">αmathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll"><mrow><mi>αmi>mrow>math> phase.