PSI - Issue 68

Wenqi Liu et al. / Procedia Structural Integrity 68 (2025) 458–464 L. Wenqi et al. / Structural Integrity Procedia 00 (2025) 000–000

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Subsequent displacement data would be corrected by the previous data recorded by the extensometer. Hence, the drop parts of the stress curves at 5% strain levels were caused by the removal of the extensometer, which did not affect the subsequent analysis of tensile properties. The photos of fractured specimens are shown in Fig. 2.

Fig. 1. Uniaxial tensile tests of Ti65 alloy. (a) Engineering stress–engineering strain curves; (b) Flow curves.

Fig. 2. Fractured specimens’ photos of Ti65 alloy.

3. Models 3.1. Johnson–cook model Johnson–Cook equation is normally applied to describe the strain-hardening behavior of metals and alloys under varying temperatures and loading rates. (1) Here, σ is the equivalent flow stress, ɛ is the equivalent plastic strain, ̇ is the testing strain rate, ̇ ! is the reference strain rate, T is the testing temperature, T 0 is the reference temperature, T m is the melting temperature, A is the nominal yield strength, B and n are the strain hardening coefficients, C is the strain rate hardening coefficient, and m is the thermal softening coefficient. All coefficients A , B , n , C , and m should be calibrated based on experimental data. Using the flow curve at room temperature (RT, 25 °C) and quasi-static (QS, 10 -5 s -1 ) loading condition as a reference, the Johnson–Cook equation is converted to the Ludwik format. Its logarithmic form could be used to calibrate the strain hardening related parameters by fitting the experimental flow curve, as shown in Fig.3 a. The fitting quality is compared in Fig.3 b. Furthermore, the strain rate coefficient C could be calibrated by fitting the flow stresses at various strain rates and RT. The flow stresses at the true plastic strain of 0.01 under evaluated strain rates were normalized with its value under QS loading (Fig. 3 c). Then the parameter C was calibrated according to the logarithmic strain rate effect equation (Fig. 3 d). Like the strain rate parameter calibration process, the temperate-related parameter m was calibrated using the flow curves at elevated temperatures under QS loading. The temperature influence normally ( ) ! " " # " $ %! $ ! " " # A B " " ! " ! ! # $ # % &$ % ' & ( ) = + + ' ( * +) * + ' ( ) , - , - . / . /