# Crystal Plasticity Finite Element Modeling on High Temperature Low Cycle Fatigue of Ti2 AlNb Alloy
## 1 Introduction  
Ductile metals fail within about \(10^{4}\) life cycles under periodic plastic loading; this phenomenon is often called the low cycle fatigue (LCF) [1; 2]. Aeroengine components are subjected to periodic variations of centrifugal forces and high temperature environments during operation, and the repeated action of high temperature alternating stress results in stress or strain concentration, and then causes local micro plastic deformation. The local micro-plastic deformation causes microcracks to form and spread further in the weak region of the alloy, causing the component to fail in the form of LCF [3]. TiAl-based alloys have received more and more attention because of their excellent high temperature properties and low density [4; 5; 6]. In the early of 21 st century, many researchers found that adding Nb to TiAl alloys improved high temperature properties and creep resistance, thus, research on TiAlNb alloys has increased in recent years. As an important lightweight alloy, Ti2 AlNb alloy is an intermetallic compound. Its long-range ordered super-lattice structure has the effect of weakening dislocation diffusion and high temperature diffusion, which gives the alloy the advantages of high strength, creep resistance, fracture toughness and oxidation resistance [6; 7]. Therefore, it is important to study the high temperature LCF of Ti2 AlNb alloy by experiments and simulations. At present, many experimental studies have been conducted on high temperature LCF of TiAlNb alloy, and the fatigue behavior, fatigue life influencing factors, damage evolution and many other aspects have been analyzed. [PERSON] et al. [8] found that the lamellar O phase of TiAlNb alloy exhibited super fatigue resistance, and fatigue crack growth was characterized mainly by crystallographic cracking. [PERSON] et al. [9] studied the LCF of TiAlNb alloy at 650 \({}^{\circ}\)C and \(\pm 0.4\)-\(\pm 1.2\)% strain amplitude and determined that the primary \(\alpha_{2}\)-phase and \(\alpha_{2}/\beta\) boundaries are important initiation positions for fatigue cracks, and that the lamellar O-phase plays a role in preventing fatigue crack propagation and causes the direction of the microcracks to deviate. [PERSON] et al. [10; 11] found thathigh temperature LCF will lead to strain-induced phase transformations and dynamic recrystallization. The large difference in lattice strain between different phases results in crack nucleated at and propagated along the phase boundary, which are detrimental to the fatigue life of the TiAlNb alloy. [PERSON] et al. [12] studied the LCF of TiAlNb alloy at 750 \({}^{\circ}\)C, and significant cyclic hardening characteristic was observed for 2%Nb alloy, but cyclic hardening was not observed for 7% Nb alloy, as the higher Nb content increased the stacking fault energy. Fatigue experiment results are lengthy, so establishing models to simulate the LCF process can improve efficiency. At present, the common modeling methods for LCF are macroscopical constitutive models, such as the Chaboche model, and microscopical models, such as the CPFEM. Macroscopic constitutive models can accurately simulate the stress-strain response of materials, and the few parameters defined in models make them convenient to use. [PERSON] et al. [13] constructed a high-temperature viscoplastic cyclic deformation model of 9 Cr-1 Mo steel based on the Chaboche model to accurately simulate the cyclic elastic-plastic deformation and stress relaxation of the material at 500-600 \({}^{\circ}\)C. [PERSON] et al. [14] studied the fatigue of shape memory alloys and proposed a three-dimensional constitutive model to describe the fatigue behavior with a continuum damage perspective. Based on the macroscopic behavior of fatigue crack growth, [PERSON] [15] established a physical model and constitutive equations to describe the stress life (S-N) fatigue behavior of materials. [PERSON] et al. [16] established a finite element (FE) model with the Chaboche model and ductile damage criterion to simulate the LCF behavior of H11 steel.