High cycle fatigue (HCF) is the dominant failure mechanism of many engineering components and structures. Traditional fatigue life prediction approaches such as safe life and damage tolerance depend on extensive fatigue tests to establish the characteristic data and lack the critical insight on the microstructural effects. It is also difficult to extend these empirical approaches to engineering parts of complicated geometry and subjected to complex loading conditions. With the rapid advancement in computing technologies in the past few decades, there is a strong interest in developing simulation-based fatigue life prediction approaches to handle the above-mentioned complex scenarios. The key challenges in developing such simulation approaches lie in the fact that the HCF failure mechanism involves multiple scales in both time and space, which need to be properly addressed.

In this work, we present a multiscale HCF simulation approach that integrates the extended space-time finite element method (XTFEM) and the self-consistent clustering analysis (SCA). The XTFEM is established based on the time-discontinuous Galerkin (TDG) approach and the key concepts introduced in GFEM/XFEM and the Partition of Unity Method. It has been extensively shown that the TDG-based space-time FEM is higher-order accurate, A-stable, and capable of capturing sharp gradients and discontinuities, which allows the employment of much larger time steps compared to the regular FEM. By augmenting the regular space-time shape functions with enrichment functions that represent problem physics, we further extended its predictive capability in handling multiple temporal scales for simulations of the HCF problem \[1\]. To address the challenge in capturing nonlinear material behaviour associated with material microstructures under the HCF loading condition, we established a microstructure-based HCF damage model based on the self-consistent clustering analysis (SCA) \[2-3\] and the Continuum Damage Mechanics (CDM). As a novel reduced-order method derived from machine learning, SCA enables direct modeling of complex material microstructures with much reduced computational cost. It starts with the offline/training stage that performs the high-fidelity representative volume element (RVE) analysis and establishes homogenized material clusters with similar mechanistic features using the data compression algorithms. Subsequently rapid online/predicting stage is performed in the concurrent multiscale simulation by solving the discretized Lippmann-Schwinger integral equation using a self-consistent scheme, in which each material cluster is governed by the local constitutive law. To capture the RVE damage evolution under HCF loading, a CDM-based fatigue damage model is further introduced to the online stage of SCA. Finally, HCF life prediction on Aluminum alloy plates joined by the self-piercing riveting process, which is widely employed in the automotive industry, is performed to demonstrate the capability of the proposed multiscale approach.

References:

\[1\]   R. Zhang, S. Naboulsi, T. Eason, and D. Qian. A high-performance multiscale space-time approach to high cycle fatigue simulation based on hybrid CPU/GPU computing. *Finite Elements in Analysis & Design*, 2019, 166: 103320.

\[2\]   Z. Liu, M.A. Bessa, and W.K. Liu. Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials. *Computer Methods in Applied Mechanics and Engineering*, 2016, 306: 319-341.

\[3\]   C. Yu, O.L. Kafka, and W.K. Liu. Self-consistent clustering analysis for multiscale modeling at finite strains. *Computer Methods in Applied Mechanics and Engineering*, 2019, 349: 339-359


A Multiscale Approach to High Cycle Fatigue Life Prediction Based on Extended Space-Time Finite Element Method and Self-Consistent Clustering Analysis

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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