| Summary: | High-strength steel has been increasingly applied to engineering structures and inevitably faces fire risks. The equivalent stress-plastic strain (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mi>eq</mi></mrow></msub></mrow></semantics></math></inline-formula>− <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ε</mi><mrow><mi>eqp</mi></mrow></msub></mrow></semantics></math></inline-formula>) curves of steel at elevated temperatures are indispensable if a refined finite element model is used to investigate the response of steel members and structures under fire. If the tensile deformation of steel is considerable, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mi>eq</mi></mrow></msub></mrow></semantics></math></inline-formula>− <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ε</mi><mrow><mi>eqp</mi></mrow></msub></mrow></semantics></math></inline-formula> curves at elevated temperatures are required to consider the strain-hardening behavior during the post-necking phase. However, there is little research on the topic. Based on the engineering stress-strain curves of Q890 high-strength steel in a uniaxial tension experiment at elevated temperatures, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mi>eq</mi></mrow></msub><mo>−</mo><msub><mi>ε</mi><mrow><mi>eqp</mi></mrow></msub></mrow></semantics></math></inline-formula> curves before necking are determined using theoretical formulations. An inverse method based on finite element analysis is used to determine the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mi>eq</mi></mrow></msub></mrow></semantics></math></inline-formula>− <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ε</mi><mrow><mi>eqp</mi></mrow></msub></mrow></semantics></math></inline-formula> curves during the post-necking phase. The characteristics of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mi>eq</mi></mrow></msub></mrow></semantics></math></inline-formula>−<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ε</mi><mrow><mi>eqp</mi></mrow></msub></mrow></semantics></math></inline-formula> curves, including the full-range strain hardening behavior at different temperatures, are discussed. An equivalent stress-plastic strain model of Q890 steel at elevated temperature is proposed, which is consistent with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mi>eq</mi></mrow></msub><mo>−</mo><msub><mi>ε</mi><mrow><mi>eqp</mi></mrow></msub></mrow></semantics></math></inline-formula> curves. The constitutive model is further verified by comparing the finite element analysis and test results.
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