# Crystal Plasticity Finite Element Modeling on High Temperature Low Cycle Fatigue of Ti2 AlNb Alloy
## 1 Introduction
According to the above research, macroscopic constitutive models based on the Chaboche model can effectively describe the stress-strain response of metal cyclic deformation. However, the macroscopic constitutive method cannot obtain the microstructure of the material during the LCF, and it is difficult to analyze the fatigue mechanism and damage evolution. Therefore, establishing a micro-level model has become a key task. Among many micro-level models, crystal plastic mechanics is a continuum mechanics method based on crystal dislocation slip theory which can analyze the macroscopic mechanical behavior of materials from the underlying microstructure information. Therefore, many researchers use the crystal plastic method to study the fatigue behavior of materials at grain level. [PERSON] et al. [17] established a CPFEM to investigate the effects of the microstructure features (grain orientation, grain boundary, and intermetallic compound) on the Sn-rich solder joint fatigue behaviors at \(-\)20\(\sim\)400 \({}^{\circ}\)C. [PERSON] [18] proposed a method to establish polycrystalline CPFEM based on the EBSD measurement of the microstructure and obtained the accumulated plastic strain and slip system diagram. Combined with SEM, EBSD and crystal plastic simulation results, the fatigue deformation mechanism of HEA was comprehensively clarified. [PERSON] et al. [19] predicted the crack nucleation life of coarser crystal (CG) nickel superalloy RR1000 by using CPFEM combined with the critical local storage criterion. [PERSON] et al. [20] established a crystal plasticity finite element model to study the effects of microstructure as well as thermal and mechanical loading conditions on fatigue crack nucleation of Ti alloys. [PERSON] et al. [21] investigated the role of beta phase on room temperature cold dwell fatigue of dual-phase titanium alloys and established a strain gradient crystal plasticity model. The presence of the alpha-beta phase was predicted to increase dwell fatigue resistance compared to a pure alpha phase microstructure. However, the CPFEM of Ti2 AlNb alloy high temperature LCF has not been reported on; therefore, it is urgent to establish a CPFEM that can simulate the LCF of Ti2 AlNb alloy. In this paper, a CPFEM was established to conduct the macroscopic stress-strain response and stress and strain distribution at grain level. Firstly, the LCF true stress-strain curves at 650 \({}^{\circ}\)C and total strain ranges of 1.2%, 1.3%, 1.4% and 1.6% were obtained. The finite element model of Ti\({}_{2}\)AlNb alloy LCF was established by using the Chaboche constitutive model. Then, the CPFEM of O and \(\beta\) phases Ti\({}_{2}\)AlNb alloy LCF was established, the macroscopic stress-strain responses were obtained and then compared with the results of the experiments and Chaboche model. By analyzing the stress distribution and strain distribution of \(\beta\) and O phase, it was found that the phase boundary is the most important position of stress concentration, and that the main reason for stress concentration is the inconsistent deformation of grains resulting from the different deformation abilities of the O and \(\beta\) phases.