Data-Driven Modeling of Multiaxial Fatigue of Structures in Frequency Domain

Abstract

Multiaxial fatigue failure can be a major concern in the design and evaluation of structures subjected to multiple time-varying loads or excitations. Multiaxial fatigue analysis can be carried out in both time and frequency domains. Time domain analyses are applied to a concerned stress or strain time history which are obtained through expensive numerical simulations or experiments. On the other hand, frequency domain fatigue analyses are applied to the stress or strain spectrum, which are obtained through transfer functions and load spectrums. Compared to frequency domain analyses, time domain analyses are computationally expensive and highly time-consuming. Thus, there has been increased interest in developing robust frequency domain fatigue evaluation. The existing frequency domain methods for multiaxial fatigue analysis capture the underlying mechanism implicitly or through certain postulated effective stress parameters. None of them are based on a consistent cycle counting method which becomes more challenging when non-proportional multiaxial variable amplitude loading conditions are present. Most recent developments in addressing both multiaxial fatigue cycle counting and a consistent fatigue damage parameter definition include the two variations of Path Dependent Maximum Range Cycle Counting (PDMR) namely path length based PDMR (PDMRPL) and moment of load path based PDMR (PDMRMLP). The fundamental aim of this doctoral work is to develop a multiaxial fatigue evaluation methodology in frequency domain that can tackle non-proportionality or capture the underlying fatigue damage mechanisms explicitly based on PDMR methods. This is done through the following three major steps. The first step towards realizing the primary goal is to first affirm the validity and applicability of PDMRPL and PDMRMLP for random multiaxial loadings. The PDMRPL and PDMRMLP methods are extensively studied and analyzed using multiaxial synchronous and asynchronous experimental data across four different materials (aluminum alloy, non-alloy steels and austenite steel). Parametric analysis is carried out to provide key insights into the non-proportionality damage that occur across different amplitude ratios and frequency ratios of loading. As a second step towards achieving the frequency domain formulation, a transfer function based PDMRMLP is developed. The developed approach is studied through multiple numerical test cases conducted on a fillet welded doubling plate component. Previously developed transfer function based PDMRPL is also studied and analyzed to understand its capabilities and limitations. The major finding from the analysis was that for highly non-proportional load paths, transfer function based frequency domain PDMRPL provided un-conservative estimations compared to time domain PDMRPL. Based on the limitations of the transfer function based approaches, a data-driven approach was then adopted to fulfill the primary objectives of this dissertation. A robust methodology is developed for building customized data-driven models. The methodology consists of three stages: exploratory study, data generation, and model development. Essentially, neural network models are built on simulated data in a dimensionally reduced parameter space to model two primary multiaxial fatigue parameters (i.e. damage per cycle and number of PDMR cycles). The developed models are able to tackle non-proportionality explicitly and are independent of bandwidth or origin of the spectrum. Through the case example of a doubling plate structure, the proposed methodology is implemented and studied. Additionally, the developed models are also tested on a rectangular beam structure to articulate their generality. The models are applied for both proportional and non-proportional cases. The performance and capabilities of the models are articulated through the test cases.