MATHEMATICAL MODELLING AND PREDICTION ANALYSIS OF THE TENSILE STRENGTH OF DC01 SHEET STEEL BASED ON TESTING SPEED

Abstract

This paper presents a regression-based mathematical modelling approach for analysing and predicting the tensile behaviour of  DC01 sheet steel as a function of tensile testing speed. Experimental tensile tests were conducted at three different crosshead speeds (2, 5, and 10 mm/min), and the corresponding ultimate tensile strength (UTS) values were obtained from engineering stress–strain curves. Two specimens were tested at each speed level, and the mean values were used for regression analysis to ensure data consistency. A linear regression model was developed to describe the relationship between testing speed and tensile strength, showing a strong correlation between the variables with a coefficient of determination R² = 0.9968. In addition, a quadratic regression model was introduced to capture potential nonlinear behaviour and improve prediction capability. The developed models were further used for the prediction of tensile strength at intermediate testing speeds, demonstrating the applicability of regression-based approaches for estimating material behaviour beyond experimentally tested conditions. A response surface analysis was also performed, providing a graphical interpretation of the relationship between testing speed and tensile strength. The results indicate that tensile strength slightly increases with increasing testing speed, reflecting the strain rate sensitivity of the material. The proposed modelling approach enables efficient analysis and prediction of mechanical properties and can serve as a useful tool in material testing, optimisation, and engineering applications.