The deformation behavior of austenitic stainless steels (ASSs) is strongly influenced by the transformation of austenite into martensite during loading. While most existing models of deformation-induced martensite primarily consider strain and temperature, they often neglect the influence of microstructural variables such as prior austenite grain size. In the present study, a quantitative relationship incorporating grain size and applied strain was developed to predict and optimize deformation-induced martensite formation in 304 stainless steel (SS 304). A face-centered central composite design (FCCD) based on the response surface methodology (RSM) was adopted to systematically evaluate the influence of grain size (10–30 µm) and relative strain (40–80%) on the martensite transformation. The volume fraction of martensite (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">${{\varvec{f}}}_{{\boldsymbol{\alpha }}^{\boldsymbol{^{\prime}}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow> <mi mathvariant="bold-italic">f</mi> </mrow> <mmultiscripts> <mrow> <mrow> <mi mathvariant="bold-italic">α</mi> </mrow> </mrow> <mrow /> <mrow> <mmultiscripts> <mrow /> <mrow /> <mo mathvariant="bold">′</mo> </mmultiscripts> </mrow> </mmultiscripts> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>) was quantified using X-ray diffraction and correlated with grain size and relative strain,while microstructural evolution during deformation was examined using scanning electron microscopy to understand the deformation mechanisms. A quadratic regression model was subsequently formulated and evaluated through analysis of variance, goodness of fit, and residual diagnostics, showing excellent agreement with experimental results (R2 = 0.9905). The results reveal that grain size exhibits a nonlinear, non-monotonic effect, indicating an optimal transformation window. Optimization predicted an optimum condition of 18 µm grain size and 50% strain, yielding <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$f_{{\alpha^{\prime}}} \approx 0.22$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>f</mi> <msup> <mi>α</mi> <mo>′</mo> </msup> </msub> <mo>≈</mo> <mn>0.22</mn> </mrow> </math></EquationSource> </InlineEquation>. The corresponding 95% prediction interval was 0.17–0.26, within which the experimentally measured value 0.23 ± 0.01 lies, confirming the predictive accuracy of the developed model. Graphical Abstract

Response Surface Modeling of Deformation-Induced Martensite in 304 Stainless Steel

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发表日期：

2026年4月9日

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Ashish Jain,
Priya Tiwari,
Abhinav Varshney

摘要

The deformation behavior of austenitic stainless steels (ASSs) is strongly influenced by the transformation of austenite into martensite during loading. While most existing models of deformation-induced martensite primarily consider strain and temperature, they often neglect the influence of microstructural variables such as prior austenite grain size. In the present study, a quantitative relationship incorporating grain size and applied strain was developed to predict and optimize deformation-induced martensite formation in 304 stainless steel (SS 304). A face-centered central composite design (FCCD) based on the response surface methodology (RSM) was adopted to systematically evaluate the influence of grain size (10–30 µm) and relative strain (40–80%) on the martensite transformation. The volume fraction of martensite ( ${{\varvec{f}}}_{{\boldsymbol{\alpha }}^{\boldsymbol{^{\prime}}}}$ $f_{α^{^{'}}}$ ) was quantified using X-ray diffraction and correlated with grain size and relative strain,while microstructural evolution during deformation was examined using scanning electron microscopy to understand the deformation mechanisms. A quadratic regression model was subsequently formulated and evaluated through analysis of variance, goodness of fit, and residual diagnostics, showing excellent agreement with experimental results (R² = 0.9905). The results reveal that grain size exhibits a nonlinear, non-monotonic effect, indicating an optimal transformation window. Optimization predicted an optimum condition of 18 µm grain size and 50% strain, yielding $f_{{\alpha^{\prime}}} \approx 0.22$ $f_{α^{'}} \approx 0.22$ . The corresponding 95% prediction interval was 0.17–0.26, within which the experimentally measured value 0.23 ± 0.01 lies, confirming the predictive accuracy of the developed model.

Graphical Abstract