In global oil and gas exploration, downhole equipment is exposed to increasingly extreme conditions—including higher temperatures, greater pressures, and more aggressive corrosive environments—as wells are drilled to greater depths. Consequently, nickel-based corrosion-resistant alloys for deeper downhole applications demand not only exceptional corrosion resistance but also substantially enhanced mechanical strength to withstand the intensified operational demands. This study established a precipitation strengthening parameter-oriented design strategy for aging hardened nickel-based corrosion-resistant alloys by integrating thermodynamic calculations and genetic algorithm (GA) optimization. Based on precipitated phase strengthening mechanisms, a precipitation strengthening parameter (PSP) mathematical model <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$PSP={({f}_{v}/r)}^{1/2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <mi>S</mi> <mi>P</mi> <mo>=</mo> <msup> <mrow> <mo stretchy="false">(</mo> <msub> <mi>f</mi> <mi>v</mi> </msub> <mo stretchy="false">/</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> was constructed. Fitting and verification showed a strong correlation between the precipitation strengthening parameter and yield strength (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$R{p}_{0.2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>p</mi> <mrow> <mn>0.2</mn> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation>) (R2 = 0.85, Pearson correlation coefficient r = 0.86), deriving the quantitative formula: <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$R{p}_{0.2}=0.16PSP - 260.18.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>p</mi> <mrow> <mn>0.2</mn> </mrow> </msub> <mo>=</mo> <mn>0.16</mn> <mi>P</mi> <mi>S</mi> <mi>P</mi> <mo>-</mo> <mn>260.18</mn> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> Via the TC-Python interface, Thermo-Calc calculated the volume fractions and precipitation driving forces of γ′ (Ni3(Al, Ti)) and γ″(Ni3Nb) phases under different compositions, which were input into the model to predict yield strength. The volume fractions and critical nucleation radii of γ′ and γ″ phases were used to construct the precipitation strengthening parameter as the GA fitness function. Results showed GA efficiently explored the composition space. After 50 generations of evolution, the optimized alloy (GA1) exhibited yield strength (1446 MPa), while maintaining good ductility (15.7%). Experimental validation confirmed the method’s effectiveness, providing a novel approach for high-performance nickel-based corrosion-resistant alloy design for downhole applications.

A Precipitation Strengthening Parameter Driven Design Strategy for Aging Hardened Nickel-Based Corrosion-Resistant Alloys: Thermodynamics-Genetic Algorithm Integration

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发表日期：

2026年5月15日

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Yintian Gao,
Yong Lian,
Yingjie Sun,
Rongrong Chen,
Jin Zhang,
Yinghu Wang,
Qubo He,
Dadi Zhou,
Hengcan Yang

摘要

In global oil and gas exploration, downhole equipment is exposed to increasingly extreme conditions—including higher temperatures, greater pressures, and more aggressive corrosive environments—as wells are drilled to greater depths. Consequently, nickel-based corrosion-resistant alloys for deeper downhole applications demand not only exceptional corrosion resistance but also substantially enhanced mechanical strength to withstand the intensified operational demands. This study established a precipitation strengthening parameter-oriented design strategy for aging hardened nickel-based corrosion-resistant alloys by integrating thermodynamic calculations and genetic algorithm (GA) optimization. Based on precipitated phase strengthening mechanisms, a precipitation strengthening parameter (PSP) mathematical model $PSP={({f}_{v}/r)}^{1/2}$ $P S P = {(f_{v} / r)}^{1 / 2}$ was constructed. Fitting and verification showed a strong correlation between the precipitation strengthening parameter and yield strength ( $R{p}_{0.2}$ $R p_{0.2}$ ) (R² = 0.85, Pearson correlation coefficient r = 0.86), deriving the quantitative formula: $R{p}_{0.2}=0.16PSP - 260.18.$ $R p_{0.2} = 0.16 P S P - 260.18 .$ Via the TC-Python interface, Thermo-Calc calculated the volume fractions and precipitation driving forces of γ′ (Ni₃(Al, Ti)) and γ″(Ni₃Nb) phases under different compositions, which were input into the model to predict yield strength. The volume fractions and critical nucleation radii of γ′ and γ″ phases were used to construct the precipitation strengthening parameter as the GA fitness function. Results showed GA efficiently explored the composition space. After 50 generations of evolution, the optimized alloy (GA1) exhibited yield strength (1446 MPa), while maintaining good ductility (15.7%). Experimental validation confirmed the method’s effectiveness, providing a novel approach for high-performance nickel-based corrosion-resistant alloy design for downhole applications.