WATMUS: Wavelet Transformation-Induced Multi-time Scaling for Accelerating Fatigue Simulations at Multiple Spatial Scales

Abstract

This paper establishes the wavelet transformation induced multi-time scaling (WATMUS) method as an enabler for modeling fatigue crack nucleation at microstructural and structural scales of polycrystalline metals. The WATMUS method derives its efficiency from (i) transformation of time-scale integration into cycle-scale integration for marching forward in time, and (ii) adaptive cycle-stepping in the integration process. The integration of the WATMUS method with crystal plasticity finite element models for micromechanical modeling, and the parametrically homogenized constitutive models (PHCM)-based FE solvers for macroscopic modeling provides a unique spatiotemporal multiscale platform for simulating large number of cycles (~ 104–106) to fatigue nucleation. Time-scale acceleration is highly relevant when material microstructure plays a significant role, such as with dwell loading. The model is tested for cyclic and dwell loadings at multiple spatial scales of a Ti alloy Ti7AL, viz. the μm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu \\mathrm{m}$$\\end{document} scale of the microstructure, the mm–cm scale of laboratory specimen, and structural scale of turbine blades. Numerical results demonstrate the ability of WATMUS-accelerated FE solvers in accurately solving fatigue problems across multiple scales of the material.