Wavelet based dual time scale method for the analysis of cyclic deformation of polycrystalline materials

Microstructure based mechanistic calculations coupled with a physically motivated crack initiation criterion provide an accurate methodology to study the effect of fatigue loading leading to damage in polycrystalline materials. Two important components of such an approach would be an accurate constitutive model for the polycrystalline material, that takes into account its microstructural characteristics and an accelerated time integration scheme for the accommodation of large number of cycles to failure observed in the experiments that would otherwise be computationally very expensive to simulate using conventional FEM with a single time scale.;Rate dependent crystal plasticity models provide an effective constitutive law to simulate the mechanical response of polycrystalline alloys taking into account into their microstructural features such as grain orientations, misorientations and morphology. The development of a crystal plasticity based model to study the behavior of two phase alpha/beta polycrystalline Ti-6242 alloys is discussed. The model homogenizes the response of the primary alpha and the transformed beta phases and incorporates accurate phase volume fractions, orientation, misorientation and micro texture distributions.;In addition to a detailed constitutive model an efficient computational scheme is also required to integrate over the large number of cycles required for crack initiation while studying fatigue failure. Some of the commonly used approaches to accelerated time integration such as extrapolation and asymptotic expansion based methods suffer from various limitations. In the case of extrapolation based methods it is their inability to evolve microstructural variables consistently and the extrapolation error which can be substantial as the number of cycles become large. The asymptotic expansion based approaches have limitations under reversible loading conditions due to the large oscillations that arise in the plastic variables, violating the assumptions on the order of contribution of the various terms in the asymptotic series.;A dual-time scaling algorithm is therefore proposed using wavelet induced decomposition for accelerated integration of the evolution equations during cyclic loading. The algorithm decouples the governing equations into two sets of problems corresponding to two different time scales. One is a long time scale (low frequency) problem characterizing a slow varying solution across cycles, while the other is a short time scale (high frequency) problem for the remaining fast varying oscillatory portion. This is accomplished through the wavelet decomposition of the primary displacement variable whose coefficients form the input to the coarse cycle scale evolution equations for the crystal plasticity state variables. A modified finite element framework for the solution of the wavelet coefficients along with an adaptive coefficient and time step selection criterion is also introduced.;The methodology is demonstrated in the case of a simplified 1-D viscoplastic model as well as a representative 3-D polycrystalline microstructure under both reversible and non-reversible loading conditions. It is observed that the method significantly reduces the computational time with minimal impact on the accuracy and does not suffer the from the drawbacks of asymptotic based methods during non-negligible plastic oscillations.