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Abstract Stress triaxiality is a parameter that expresses the stress state and can be used as a variable to characterize the plasticity and fracture damage model of materials. It plays an important role in structural strength and failure analysis. The round bar tensile test with notch can be used to calibrate the parameters in the plastic and damage models. However, there are two different formulas in the literatures to calculate the triaxiality of the minimum cross-sectional axis of notched round bar under tensile load, which were proposed by internationally renowned scholars Bridgman and Wierzbicki, respectively. Their differences often cause confusion in application. Through refined finite element numerical analysis, this article attempts to clarify the validity and applicability of the two formulas. The results show that the Bridgman formula is more accurate only in elastic stage and in the specific a /R range, and the Bao-Wierzbicki formula is in good agreement with the experimental data and results of simulation, which can be used to calculate the arithmetic mean value of the triaxiality during the whole tensile process. Based on further analysis, a new revised stress triaxiality formula in the plastic stage under elastic perfectly-plastic condition is proposed, and the notch geometry and strain strengthening effect are further discussed. It is pointed out that different notch proportions will affect the neck stress field. The smaller the notch ratio is, the closer the stress triaxiality value in the elastic stage is to 1/3, When the notch ratio is too small, it will also affect the changes of stress triaxiality throughout the entire tensile process; The strain strengthening effect will change the trend of stress triaxiality during the stretching process, and the increase in strengthening modulus will lead to a decrease in the peak value of the plastic stage. The higher the strengthening modulus, the faster the decrease of stress triaxiality after entering the plastic stage.
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Received: 27 June 2023
Published: 11 April 2024
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2024, Vol. 45 
