Dual-time scale crystal plasticity FE model for cyclic deformation of Ti alloys

Abstract

A dual-time scale finite element model is developed in this paper for simulating cyclic deformation in a Titanium alloy Ti-6242. The material is characterized by crystal plasticity constitutive relations. Modeling cyclic deformation using conventional time integration algorithms in a single time scale can be prohibitive for crystal plasticity computations. Typically 3D crystal plasticity based fatigue simulations found in the literature are in the range of 100 cycles. Results are subsequently extrapolated to thousands of cycles, which can lead to considerable error in fatigue predictions. However, the dual-time scale model enables simulations up to a significantly high number of cycles to reach local states of damage initiation leading to fatigue crack growth. This formulation decomposes the governing equations into two sets of problems, corresponding to a coarse time scale (low frequency) cycle-averaged problem and a fine time scale (high frequency) oscillatory problem. A statistically equivalent 3D polycrystalline model of Ti-6242 is simulated by the crystal plasticity finite element model to study the evolution of local stresses and strains in the microstructure with cyclic loading. The comparison with the single time scale reference solution shows excellent accuracy while the efficiency gained through time-scale compression can be enormous.

Computational Methods for Microstructure-Property Relationships

“…The main idea of the asymptotic methods and its application in (Manchiraju et al 2007(Manchiraju et al ,2008 can be understood through the 1-D viscoplastic problem introduced in Sect. 3.1.1.…”

“…It is desirable to conduct simulations for a high number of cycles, so as to reach local states of damage nucleation and growth in the microstructure. A few methods of multi-time scaling Yu and Fish 2002;Manchiraju et al 2007Manchiraju et al , 2008 have been introduced to avert these challenges. The time scales range from the loading frequency dependent scale of each cycle to the material dependent scale of relaxation times or the overall life of the component.…”

Wavelet transformation based multi-time scaling method for crystal plasticity FE simulations under cyclic loading

“…To avoid two-way coupling, Ghosh et al [37,48] have developed a decoupled set of crystal plasticity based governing equations. The problems are characterized by a cycle-averaged, low frequency behavior and a short time scale (high frequency) problem for the remaining oscillatory portion.…”

“…The main idea of the asymptotic methods and its application in [37,48] can be understood through the 1-D viscoplastic problem introduced in Section 3.1. All state variables, e.g.…”

“…This result ensures that the stress oscillator can be obtained at every material point by simulating a single cycle. The approach used in [37,48] makes use of this property and assumes a coarse scale evolution equation for the average plastic strain of the form:…”