Crystal plasticity modeling of a titanium alloy under thermo-mechanical fatigue

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Abstract

A crystal plasticity model is developed to understand the fatigue behavior of Ti-6Al-4V under in-phase (IP) and out-of-phase (OP) thermo-mechanical loading. A systematic calibration and validation strategy using experimental data of isothermal monotonic and fatigue is developed to parameterize the model. Subsequently, crystal plasticity finite element method simulations under IP and OP thermo-mechanical fatigue loads are performed. A comparison of the stress range and hysteresis with cycles, between the IP and OP cases, shows that the proposed model is able to capture their differences appropriately. The stress distribution in the microstructure also clearly explains the larger life under IP as compared to OP as observed in experiments.

Introduction

Titanium alloys, primarily due to their higher specific strength, are routinely used as “compressor disc material” for gas-turbine engines [1]. In order to further increase the payload capacity, designers prefer to use blisk or bling instead of disc that results in significant temperature gradient near the rim region, thus demanding the characterization of Ti-alloys under thermo-mechanical fatigue (TMF) [2], [3]. TMF involves simultaneous variation of strain/stress and temperature, and therefore, needs sophisticated test modules to conduct such experiments. In-phase (IP) and Out-of-Phase (OP) TMF behaviour of one of the work-horse materials of aero-engine industry, Ti-6Al-4V, have been reported in [3]. The study shows that this alloy exhibits lower fatigue life under OP as compared to IP-TMF loading. The present work aims to understand this difference using mechanistic models within the framework of Crystal Plasticity (CP) modeling. The effect of anisotropic thermal stress and plastic deformation of the α-phase is considered in the CP model to explain this behavior.

CP models facilitate the incorporation of grain level mechanisms and their interactions to derive microstructure dependent engineering scale properties. In the realm of isothermal fatigue in Ti-alloys, a wide range of literature on CP modeling is available [4], [5], [6]. In contrast the literature on TMF of Ti-alloys are scarce. Of interest is the CP Finite Element Method (CPFEM) analysis under TMF performed in [7] to understand the role of thermal stress on crack nucleation on basal plane of Ti-6Al and Ti-6242. However, one of the major drawback of the model in [7] is the absence of cyclic softening that is typical of Ti-alloy.

In this work, a physically motivated CPFEM model incorporating cyclic softening for Ti-alloys is proposed. The model parameters are calibrated and validated using isothermal tensile and low-cycle fatigue data of Ti-6Al-4V. The calibrated model is then utilized to perform low-cycle TMF simulations under IP and OP conditions. Comparison of the simulated responses between the IP and OP TMF conditions is performed to understand the differences, both in the homogeneous and microstructural behavior, which can explain the significantly lower life under OP TMF. The development of a dedicated model along with a systematic parameterization and validation approach, to understand the TMF behavior of Ti-alloys doesn’t exist in the literature and is the novelty of this work.

Section snippets

Crystal plasticity constitutive model

A rate-dependent CP model is developed to capture the deformation behavior of α Ti-alloy under thermo-mechanical loading. In the model it is assumed that the deformation of a crystal occurs by elastic stretching and rotation, thermal expansion/contraction, and plastic slip on different slip systems. Thus, a multiplicative split of the deformation gradient is performed into elastic, thermal expansion and plastic components, and, is given byF̲̲=F̲̲eF̲̲θF̲̲pwhere F̲̲e, F̲̲θ and F̲̲p are the

Calibration of the model parameters and sensitivity analysis

The model parameters are calibrated utilizing experimentally available data under isothermal uniaxial tensile and fatigue loading. For tensile loading, the stress-strain curves of Ti-6Al-4V at 323 and 623 K from [10] are utilized. For low cycle fatigue, the data of Ti-6Al-4V under completely reversed strain cycling with maximum strains (ϵmax) of 1%, 1.2% and 1.4%, and temperatures of 373 and 673 K from [3] are utilized. A two dimensional microstructure considering 100 grains with random Euler

Simulation of thermo-mechanical fatigue

CPFEM simulations are performed for IP and OP TMF loading to investigate the effect of phase difference between temperature and strain cycles on hysteresis loop, cyclic mean stress and localization. The aforementioned 100 grain microstructure as well as a two-dimensional Voronoi tessellated microstructure with random Euler angles is used for this purpose. For the temperature cycle, the minimum and maximum temperatures are taken as 373 K and 673K, respectively. For the mechanical cycle, a fully

Summary

In the present study, a crystal plasticity model has been developed that considers thermal stress, kinematic (back stress) and isotropic (threshold stress) hardening, and temperature dependent drag stress. The model has been calibrated using data from isothermal tensile and low cycle fatigue experiments at different temperatures. Subsequently, CPFEM simulations have been performed on two dimensional one-grain-one-element and Voronoi tessellated microstructures under IP and OP low-cycle TMF

Declaration of Competing Interest

The authors declare that they do not have any financial or nonfinancial conflict of interests.

Acknowledgment

I gratefully acknowledge funding from the Aeronautical Research and Development Board India (ARDB) - DRDO India for supporting this research.

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