*Article* **A Constitutive Relation Based on the Johnson–Cook Model for Ti-22Al-23Nb-2(Mo, Zr) Alloy at Elevated Temperature**

**Yanju Wang 1, Duo Zhou 2, Yi Zhou 1, Aixue Sha 1, Huaxing Cheng <sup>2</sup> and Yabin Yan 2,\***


**Abstract:** Although several schemes have been proposed to modify the classical Johnson–Cook (J-C) model, the effect of temperature on the flow stress of materials at different temperatures has not been clarified. In the current study, to investigate the deformation behavior of Ti-22Al-23Nb-2(Mo, Zr) alloy at different temperatures, uniaxial tension experiments were performed at both room (RT, 28 ◦C) and elevated temperatures, and a modified J-C model was developed to describe the temperature-dependent plastic flow. In tensile experiments, Ti2AlNb-based alloy showed a continuous work hardening until reaching the ultimate strength at RT, while an apparent drop appeared in the flow stress after the peak stress at elevated temperature. Moreover, the experimental peak stress significantly depends on the testing temperature. To correctly describe the different variations of flow stresses at different temperatures, a parameter, S, which represents the softening behavior of flow stress, is integrated into the classical J-C model. In addition, the applicability and validity of the proposed J-C model were verified by calibration with experimental curves of different temperatures. On the other hand, the fractography of post-test specimens was examined to interrupt the increased fracture brittleness of Ti2AlNb-based alloy at elevated temperatures. The proposed constitutive relation based on the J-C model is applicable to predict the deformation behavior of other Ti2AlNb-based alloys at different temperatures.

**Keywords:** Ti2AlNb alloy; mechanical properties; constitutive relation; Johnson–Cook model
