Thermodynamics of Fatigue: Degradation-Entropy Generation Methodology for System and Process Characterization and Failure Analysis

Abstract

Formulated is a new instantaneous fatigue model and predictor based on ab initio irreversible thermodynamics. The method combines the first and second laws of thermodynamics with the Helmholtz free energy, then applies the result to the degradation-entropy generation theorem to relate a desired fatigue measure—stress, strain, cycles or time to failure—to the loads, materials and environmental conditions (including temperature and heat) via the irreversible entropies generated by the dissipative processes that degrade the fatigued material. The formulations are then verified with fatigue data from the literature, for a steel shaft under bending and torsion. A near 100% agreement between the fatigue model and measurements is achieved. The model also introduces new material and design parameters to characterize fatigue.

Thermodynamics of Manufacturing Processes—The Workpiece and the Machinery

“…Note that highly dissipative processes such as friction can generate significant heat, which if not transferred out via cooling, results in a substantial value of S m/c dT m/c , a measure of the interfacial thermal fluctuations. Further breakdown of this term is given in Section 4 and references [18][19][20]. Total entropy generation in both the workpiece and the machinery, from Equations 7and 12,…”

“…The Helmholtz relation-Equation (6) and the subsequent version for the machinery-introduced "-SdT", the portion of the free energy dissipated and accumulated internally by a loaded component, which includes effects of plastic work, chemical reaction heat generation, and sometimes heat from an external source [18][19][20]. Temperature change dT is driven by the system entropy content S. Without an entropy measurement device, S is often neglected in thermodynamic formulations characterizing real systems, justified by setting dT = 0, which in turn requires experiments to be isothermal for validation, and significant temperature correction for application to real-world operation.…”

“…> 0 is the generalized isothermal loadability [18], obtained via the application of Callen's technique [15] = −Xκ T , a system/material property. ∂µ ∂T is the reaction potential-temperature gradient, also obtained for batteries, with µ = V, by Osara et al via the Gibbs-Duhem formulation [20].…”

“…• Wp ≥ ∆Gp and S'p ≥ 0 for a product-forming or energy-adding process; and • as Wp → ∆Gp, S'p → 0 and ∆T → 0, limit of which is the reversible transformation, i.e., Wp = ∆Gp, S'p = 0 and ∆T = 0. For manufacturing processes that deform the workpiece (elastically and plastically), δWp = σdε where is the volume, σ is stress, and ε is strain [18,21]; dAp = σ'fd(σ'f/E), a constant, where σ'f is the fatigue strength coefficient and E is Young's modulus. Similarly, δWp for other processes can be expressed in terms of process-defining variables or characterized using the specific process energy as done in [22,23] for cutting and grinding processes and accompanying dAp specified in similar parameters as done above for battery charging and material deformation.…”

Residual fatigue life prediction based on a novel damage accumulation model considering loading history

“…The irreversible thermodynamics theory, combined with the continuum damage mechanics, provided an acceptable life prediction with clear physical meaning. Subsequently, numerous scholars [48][49][50][51][52][53][54][55] developed the entropy-based models for fatigue life prediction. Wang and Yao 49 proposed a novel entropy increment model based on the framework of continuum damage mechanics, which was validated by eight groups of experiments.…”