Mechanism-based flow stress model for Ti-6Al-4V applicable for simulation of additive manufacturing and machining

Abstract: Ti-6Al-4V has remarkable properties such as high specific mechanical properties (viz. stiffness, strength, toughness, fatigue resistance), corrosion resistance, biocompatibility etc. These properties make it attractive for applications in aerospace, chemical industry, energy production, surgical implants, etc. Many of these applications have to satisfy high requirements on mechanical properties, which are directly affected by the microstructure. Therefore, it is essential to understand as well as to model the microstructure evolution during manufacturing as well as in-service. Furthermore, this alloy has a narrow temperature and strain rate window of workability.This work was initiated as part of a project aimed at performing finite element simulations of a manufacturing process chain involving hot forming, welding, machining, additive manufacturing and heat treatment of Ti-6Al-4V components within the aerospace industry. Manufacturing process chain simulations can compute the cumulative effect of the various processes by following the material state through the whole chain and give a realistic prediction of the final component. Capacity to describe material behavior in a wide range of temperatures and strain rates is crucial for this task.A material model based on the dominant deformation mechanisms of the alloy is assumed to have a more extensive range of validity compared to an empirical relationship. Explicit dislocation dynamics based models are not practically feasible for manufacturing process simulation, and therefore the concept of dislocation density, (length of dislocations per unit volume) developed by (Kocks1966; Bergström, 1970) is followed here. This mean field approach provides a representation of the average behavior of a large number of dislocations, grains, etc. Conrad (1981) studied the influence of various factors like solutes, interstitials, strain, strain rate, temperature, etc., on the strength and ductility of titanium systems and proposed a binary additive relationship for its yield strength. The first component relates to long-range interactions and second short-range relates to lattice resistance for dislocation motion. For high strain rate deformation, this short-range term is extended to include the effects of a viscous drag given by phonon and electron drag (Lesuer et al. 2001).  Immobilisation of dislocation by pile-ups gives hardening and remobilization/annihilation by dislocation glide and climb gives restoration. Globularization is also considered to restore the material. The material model is calibrated using isothermal compression tests at a wide range of temperatures and strain rates. Compression tests performed using Gleeble thermo-mechanical simulator is used at low-strain rates and split-Hopkins pressure bar is used at high strain rates for calibration.During additive manufacturing depending on the temperature, heating/cooling rates, Ti-6Al-4V undergoes allotropic phase transformation. This transformation results in a variety of textures that can give different mechanical properties.  Based on the texture (Semiatin et al., 1999b; Seetharaman and Semiatin, 2002; Thomas et al., 2005) identified few microstructural features that are relevant to the mechanical properties. The three separate alpha phase fractions; Widmanstatten,  grain boundary, Martensite, and the beta-phase fraction are included in the current model. However, since the strengthening contributions of these individual alpha phases are not known, a linear rule of mixtures for the total alpha-beta composition is developed. This model is calibrated using continuous cooling tests performed by Malinov et al. 2001 with differential scanning calorimeter at varying cooling rates.  This mechanism-based model is formulated in such a way that it can be implemented in any standard finite element software. In the current work, this is implemented as subroutines within MSC Marc and used for simulation of hot-forming and additive manufacturing.