Structures are subjected to a number of individual loads. These loads vary in amplitude and phase, resulting in multiaxial loading and fatigue. The fatigue analysis technique presented here is based on available models for multiaxial cyclic plasticity, notch correction, critical plane and rainflow counting, and damage estimation. Integration of these models with elastic finite-element analysis (FEA) is discussed, and an example of the fatigue design process from FEA to life prediction is presented.

Understanding the damaging nature of a multiaxial load history is difficult because it is not obvious how these loads combine to produce fatigue damage at a critical location. When joined with the aforementioned computational techniques, use of current visualization hardware and software tools can provide a designer or test engineer considerable insight into the damaging nature of a multiaxial load history. Visualization examples are presented to illustrate the capability and utility of this approach and show the potential options for visual output.

PostScript version of the article

A step-by-step process for multiaxial fatigue life prediction is outlined. The approach is built from existing models and methods, modified to fit into integrated software. The process begins with an elastic finite element analysis to determine geometry factors, continues with stress-strain calculation via notch correction/plasticity, and finishes with critical plane damage estimation to assess fatigue lives. The use of FEA and notch correction/plasticity to calculate local stress-strain behavior is discussed and critical plane methods are reviewed. As an example of the complete process, the integrated method is used to generate life predictions for the SAE notched shaft from a sample load history.

PostScript version of the article

A cyclic plasticity model is developed which can predict both proportional and nonproportional loading for multiaxial stresses and strains. The method developed herein is based on classical incremental plasticity theory and adopts a multiple surface hardening rule first proposed by \mroz~\cite{Mroz67} in 1967. Development of the plasticity model is aimed toward efficient computer implementation and usability. The model is suitable for fatigue life predictions using the strain-life approach and can be used to calculate stresses for a critical-plane damage estimator. The model is tested for a variety of proportional and nonproportional strain histories. Results are compared to the experimental thin-walled tube results of Bannantine~\cite{Bannantine89}. The model exactly predicts stabilized proportional behavior and predicts stresses within $30\%$ of actual for most nonproportional histories. It is in qualitative agreement with results from all loading cases. The proposed software implementation of model compares favorably to more conventional implementations. The model uses adaptive integration methods and reworked governing equations to achieve substantial time savings. A typical 20,000 point strain history can be processed in less than 3 minutes on 486DX 66MHz DOS compatible machine.

PostScript version of the thesis

The strain-based approach to fatigue life prediction usually relies on the conventional strain-life equation which correlates the elastic and plastic strain to the life. The correlation is based on separate log-linear curve fits of the elastic and plastic components of the strain data versus the life. It is well known, however, that these linear relationships may be valid only within a specific interval of stress or strain. When material behavior approaches elastic-perfectly plastic for instance, it is not uncommon for the test data to deviate from linearity at both very high and very low strains. For such materials a separate fit of each curve is likely to give material constants significantly inconsistent with the fit of the cyclic stress strain curve, especially if a good local fit over a restricted interval is obtained. In this work, some of the errors that arise as a result of this inconsistency are described, and recommended methods are developed for treating these errors. Numerical concerns are also addressed, and sample results are included.

PostScript version of the article

Back to Tim's World