Abstract
In the present work, we propose using the cumulative distribution functions derived from maximum entropy formalisms, utilizing thermodynamic entropy as a measure of damage to fit the low-cycle fatigue data of metals. The thermodynamic entropy is measured from hysteresis loops of cyclic tension–compression fatigue tests on aluminum 2024-T351. The plastic dissipation per cyclic reversal is estimated from Ramberg–Osgood constitutive model fits to the hysteresis loops and correlated to experimentally measured average damage per reversal. The developed damage models are shown to more accurately and consistently describe fatigue life than several alternative damage models, including the Weibull distribution function and the Coffin–Manson relation. The formalism is founded on treating the failure process as a consequence of the increase in the entropy of the material due to plastic deformation. This argument leads to using inelastic dissipation as the independent variable for predicting low-cycle fatigue damage, rather than the more commonly used plastic strain. The entropy of the microstructural state of the material is modeled by statistical cumulative distribution functions, following examples in recent literature. We demonstrate the utility of a broader class of maximum entropy statistical distributions, including the truncated exponential and the truncated normal distribution. Not only are these functions demonstrated to have the necessary qualitative features to model damage, but they are also shown to capture the random nature of damage processes with greater fidelity.
Highlights
The wrought aluminum alloy 2024-T351 is an important light structural metal commonly used in aerospace and other weight-critical applications [1]
We demonstrate the approach using low-cycle fatigue experimental data for aluminum 2024-T351 material, and generalize the application of the maximum entropy principle using a broader class of statistical distributions, including the truncated exponential and the truncated normal distribution
While information entropy is only proportional to thermodynamic entropy in certain circumstances, Jaynes argues that choosing the probability density function that maximizes the Shannon entropy subject to various constraints is appropriate to any situation where a reference probability distribution is needed
Summary
The wrought aluminum alloy 2024-T351 is an important light structural metal commonly used in aerospace and other weight-critical applications [1]. Khonsari and co-workers [10,11] demonstrated that the thermodynamic entropy generated during a low-cycle fatigue test can serve as a measure of degradation They proposed that the thermodynamic entropy is a constant when the material reaches its fracture point, independent of Entropy 2019, 21, x FOR PEER REVIEW geometry, load, and frequency. Jaynesthat [13], where generated a low-cycle fatigue test canapproach serve as a measure of degradation They of proposed the information theory concept of entropy waswhen applied to the energy levels of apoint, thermodynamic the thermodynamic entropy is a constant the material reaches its fracture independent system, of geometry, load, and frequency. We demonstrate the approach using low-cycle fatigue experimental data for aluminum 2024-T351 material, and generalize the application of the maximum entropy principle using a broader class of statistical distributions, including the truncated exponential and the truncated normal distribution. We begin first with a brief review of the maximum entropy principle
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