scholarly journals Measures of Entropy to Characterize Fatigue Damage in Metallic Materials

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 804 ◽  
Author(s):  
Huisung Yun ◽  
Mohammad Modarres
Keyword(s):  
Statistical Mechanics ◽  
Fatigue Damage ◽  
Fatigue Failure ◽  
Probabilistic Models ◽  
Failure Process ◽  
Second Law Of Thermodynamics ◽  
Boltzmann Constant ◽  
Metallic Materials ◽  
Thermodynamic Entropy ◽  
Macro Scale

This paper presents the entropic damage indicators for metallic material fatigue processes obtained from three associated energy dissipation sources. Since its inception, reliability engineering has employed statistical and probabilistic models to assess the reliability and integrity of components and systems. To supplement the traditional techniques, an empirically-based approach, called physics of failure (PoF), has recently become popular. The prerequisite for a PoF analysis is an understanding of the mechanics of the failure process. Entropy, the measure of disorder and uncertainty, introduced from the second law of thermodynamics, has emerged as a fundamental and promising metric to characterize all mechanistic degradation phenomena and their interactions. Entropy has already been used as a fundamental and scale-independent metric to predict damage and failure. In this paper, three entropic-based metrics are examined and demonstrated for application to fatigue damage. We collected experimental data on energy dissipations associated with fatigue damage, in the forms of mechanical, thermal, and acoustic emission (AE) energies, and estimated and correlated the corresponding entropy generations with the observed fatigue damages in metallic materials. Three entropic theorems—thermodynamics, information, and statistical mechanics—support approaches used to estimate the entropic-based fatigue damage. Classical thermodynamic entropy provided a reasonably constant level of entropic endurance to fatigue failure. Jeffreys divergence in statistical mechanics and AE information entropy also correlated well with fatigue damage. Finally, an extension of the relationship between thermodynamic entropy and Jeffreys divergence from molecular-scale to macro-scale applications in fatigue failure resulted in an empirically-based pseudo-Boltzmann constant equivalent to the Boltzmann constant.

The Analogical Turn (1884–1887)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Boltzmann Equation ◽  
Statistical Mechanics ◽  
Mechanical System ◽  
Thermal Equilibrium ◽  
Special Kind ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Equipartition Theorem ◽  
Royal Road ◽  
H Theorem

This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.

Supradegeneracy and the Second Law of Thermodynamics

2020 ◽  
Vol 45 (2) ◽  
pp. 121-132
Author(s):  
Daniel P. Sheehan
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Population Inversion ◽  
Laboratory Experiments ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Boltzmann Factor ◽  
Energy Currents ◽  
Non Equilibrium

AbstractCanonical statistical mechanics hinges on two quantities, i. e., state degeneracy and the Boltzmann factor, the latter of which usually dominates thermodynamic behaviors. A recently identified phenomenon (supradegeneracy) reverses this order of dominance and predicts effects for equilibrium that are normally associated with non-equilibrium, including population inversion and steady-state particle and energy currents. This study examines two thermodynamic paradoxes that arise from supradegeneracy and proposes laboratory experiments by which they might be resolved.

Evolution of the universe from the perspective of entropy and information

2021 ◽  
pp. 2150111
Author(s):  
Fei-Quan Tu ◽  
Bin Sun ◽  
Meng Wan ◽  
Qi-Hong Huang
Keyword(s):  
Information Entropy ◽  
Second Law Of Thermodynamics ◽  
Boltzmann Entropy ◽  
Evolution Of The Universe ◽  
Thermodynamic Entropy ◽  
Entire Universe ◽  
Low Entropy ◽  
The Relationship ◽  
The Universe ◽  
Entropy Of The Universe

Entropy is a key concept widely used in physics and other fields. At the same time, the meaning of entropy with different names and the relationship among them are confusing. In this paper, we discuss the relationship among the Clausius entropy, Boltzmann entropy and information entropy and further show that the three kinds of entropy are equivalent to each other to some extent. Moreover, we point out that the evolution of the universe is a process of entropy increment and life originates from the original low entropy of the universe. Finally, we discuss the evolution of the entire universe composed of the cosmological horizon and the space surrounded by it and interpret the entropy as a measure of information of all microstates corresponding to a certain macrostate. Under this explanation, the thermodynamic entropy and information entropy are unified and we can conclude that the sum of the entropy of horizon and the entropy of matter in the space surrounded by the horizon does not decrease with time if the second law of thermodynamics holds for the entire universe.

A Study on the Main Parameters That Affects the Reliability of Fatigue Failure in a Marine Drilling Riser

2021 ◽  
Author(s):  
Bruno Luiz Barbosa das Chagas ◽  
Celso Kazuyuki Morooka
Keyword(s):  
Fatigue Damage ◽  
Fatigue Failure ◽  
Petroleum Reservoirs ◽  
Offshore Drilling ◽  
Deepwater Drilling ◽  
Sea Bottom ◽  
Reliability Method ◽  
Drilling Operations ◽  
Maritime Operations ◽  
Sea Currents

Abstract Advances in subsea exploration in the oceans to discover new petroleum reservoirs and sometimes different kind of minerals at the seabed in ultra deepwater, continuously introduce new challenges in offshore drilling operations. This motivates the development of increasingly safe maritime operations. In offshore petroleum, a marine drilling riser is the pipe that connects a wellhead at the sea bottom to a drillship at the sea surface, as an access to the wellbore. It serves as a guide for the drilling column with the drill bit and conductor to carry cuttings of rock coming from the wellbore drilling and its construction. Drilling riser is constantly exposed to adversity from the environment, such as waves, sea currents and platform motions induced by waves. These elements of the environment are prevailing factors that can cause a riser failure during deepwater drilling operations with undesirable consequences for the environment. In the present work, key parameters that influence the probability of fatigue failure in a marine drilling riser are identified, and a parametric evaluation with those parameters are carried out. Dynamic behavior of a riser is previously calculated and fatigue damage is estimated. Afterwards, the First Order Reliability Method (FORM) is applied to determine the probability of fatigue failure on the riser. Fundamentals of the procedure are described, and results are illustrated through the analysis for a typical riser in deepwater drilling operation. Parametric evaluations are done observing points considered as critical along the riser length, and looking to the sensitivity of key parameters in the process. For this study, the SN curve from API guidelines is applied and accumulated fatigue damage is estimated from simulations of the stress time series and applying the Palmgren-Miner’s rule. Finally, the influence of each parameter in the reliability of fatigue failure is verified and discussions given.

Probabilistic Fatigue Assessment of a Mooring Line Based on Station-Keeping Trials in Ice

2021 ◽  
Author(s):  
Chana Sinsabvarodom ◽  
Bernt J. Leira ◽  
Wei Chai ◽  
Arvid Naess
Keyword(s):  
Fatigue Damage ◽  
Probabilistic Models ◽  
Full Scale ◽  
Mooring Line ◽  
Stress Range ◽  
Station Keeping ◽  
Probability Models ◽  
Line System ◽  
Fatigue Assessment ◽  
Rainflow Counting

Abstract The intention of this work is to perform a probabilistic fatigue assessment of a mooring line due to loads associated with the station-keeping of a ship in ice. In March 2017, the company Equinor (Statoil) conducted full-scale tests by means of station-keeping trials (SKT) in drifting ice in the Bay of Bothnia. The vessel Magne Viking was employed in order to represent a supply vessel equipped with a mooring line system, and the realtime loading during the full-scale measurement was recorded. The second vessel Tor Viking was serving as an ice breaker in order to maintain the physical ice management activities with different ice-breaking schemes, i.e. square updrift pattern, round circle pattern, circular updrift pattern and linear updrift pattern. The fatigue degradation corresponding to these different patterns were investigated. The peaks and valleys of the mooring tension are determined using the min peak prominence method. For the purpose of probabilistic fatigue assessment, the Rainflow-counting algorithm is applied to estimate the mooring stress range. Fatigue assessment based both on Rainflow counting and fitted probabilistic models were performed. For the latter, the stress range distributions from the observed data of mooring loads are fitted to various probability models in order to estimate the fatigue damage. It is found that the stress ranges represented by application of the Weibull distribution for the probabilistic fatigue approach provides results of the fatigue damage most similar to the Rainflow counting approach. Among the different scenarios of Ice management schemes, the circular updrift pattern provides the lowest magnitude of the fatigue degradation.

A Mathematical Model for Internal Friction and Local Fatigue Damage Based on Populations of Yielding Microelements

1987 ◽  
Vol 109 (2) ◽  
pp. 201-206 ◽  
Author(s):  
P. W. Whaley
Keyword(s):  
Mathematical Model ◽  
Internal Friction ◽  
Fatigue Damage ◽  
Strain Energy ◽  
Crack Nucleation ◽  
Second Law Of Thermodynamics ◽  
Microplastic Deformation ◽  
Irreversible Processes ◽  
Amplitude Dependence ◽  
Microplastic Strain

A mathematical model for internal friction and fatigue damage based on populations of yielding microelements is described. Using two parameters, the model accounts for amplitude dependence of material damping. For low excitation levels the Zener theory of thermoelasticity is reproduced. The significance of this new damping model is that fatigue damage due to local accumulations of microplastic deformation is quantified. The entropy production is defined by expressing the second law of thermodynamics for irreversible processes as an equality, and quantifying local accumulations of microplastic strain energy as the source of irreversibility. A critical entropy threshold is defined in terms of the local microplastic strain energy density of local failure. The hypothesis is offered that local fatigue damage leading to crack nucleation occurs by exceeding the critical entropy threshold.

scholarly journals Examining the Interaction of Force and Repetition on Musculoskeletal Disorder Risk

2012 ◽  
Vol 55 (1) ◽  
pp. 108-124 ◽  
Author(s):  
Sean Gallagher ◽  
John R. Heberger
Keyword(s):  
Fatigue Failure ◽  
Musculoskeletal Disorder ◽  
Failure Process ◽  
Epidemiological Studies ◽  
Laboratory Studies ◽  
Musculoskeletal Tissues ◽  
Relationship Of ◽  
The Relationship ◽  
Risk Fatigue ◽  
Increases In Risk

Objective: Our aims were (a) to perform a systematic literature review of epidemiological studies that examined the interaction of force and repetition with respect to musculoskeletal disorder (MSD) risk, (b) to assess the relationship of force and repetition in fatigue failure studies of musculoskeletal tissues, and (c) to synthesize these findings. Background: Many epidemiological studies have examined the effects of force and repetition on MSD risk; however, relatively few have examined the interaction between these risk factors. Method: In a literature search, we identified 12 studies that allowed evaluation of a force-repetition interaction with respect to MSD risk. Identified studies were subjected to a methodological quality assessment and critical review. We evaluated laboratory studies of fatigue failure to examine tissue failure responses to force and repetition. Results: Of the 12 epidemiological studies that tested a Force × Repetition interaction, 10 reported evidence of interaction. Based on these results, the suggestion is made that force and repetition may be interdependent in terms of their influence on MSD risk. Fatigue failure studies of musculoskeletal tissues show a pattern of failure that mirrors the MSD risk observed in epidemiological studies. Conclusions: Evidence suggests that there may be interdependence between force and repetition with respect to MSD risk. Repetition seems to result in modest increases in risk for low-force tasks but rapid increases in risk for high-force tasks. This interaction may be representative of a fatigue failure process in affected tissues.

Spatial Variability in Concrete: Nature, Structure, and Consequences

1994 ◽  
Vol 47 (1S) ◽  
pp. S184-S196 ◽  
Author(s):  
D. Breysse ◽  
D. Fokwa ◽  
F. Drahy
Keyword(s):  
Probabilistic Models ◽  
Failure Process ◽  
Discrete Models ◽  
Material Modeling ◽  
Complex Phenomenon ◽  
Main Interest ◽  
Global Response ◽  
Micro Scale ◽  
Key Factor ◽  
Spurious Results

The failure process of concrete is a complex phenomenon in which the material inhomogeneities play an important role. Different ways of accounting for material disorder are commented on and examples are exhibited, showing the difficulties related to inhomogeneous material modeling. In a first part, results and limits via phenomenological probabilistic models (a probabilistic model of damage and a probabilistic numerical model of cracking) are pointed out. Then, results obtained on numerical simulations on lattices are studied. It is shown that the knowledge of the local disorder is a key factor for a better understanding of the global response (localization, size-effect, ...), even if these results can only be taken as qualitative ones. It appears that studies using numerical discrete models for concrete can lead to spurious results if the bias introduced by the discretization itself is not recognized and correctly accounted for. Finally it is shown with two examples (casted concrete and microcracked medium) how the structure of disorder can be identified and modelled. Some indications are given about the cases in which it seems useful to analyze the material at this micro-scale. The main interest seems to be their use for building phenomenological and material-related rules describing the response at a higher scale. The conclusion tries to separate the problems one has to treat in four main classes and to propose for each type of problem a better way to account for material disorder.

scholarly journals Entropy Balance in the Expanding Universe: A Novel Perspective

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 406
Author(s):  
Arturo Tozzi ◽  
James F. Peters
Keyword(s):  
Quantum Mechanics ◽  
Second Law Of Thermodynamics ◽  
Quantum Systems ◽  
Second Law ◽  
Quantum Vacuum ◽  
Expanding Universe ◽  
Cosmic Expansion ◽  
Thermodynamic Entropy ◽  
Local Observer ◽  
Relational Mechanism

We describe cosmic expansion as correlated with the standpoints of local observers’ co-moving horizons. In keeping with relational quantum mechanics, which claims that quantum systems are only meaningful in the context of measurements, we suggest that information gets ergodically “diluted” in our isotropic and homogeneous expanding Universe, so that an observer detects just a limited amount of the total cosmic bits. The reduced bit perception is due the decreased density of information inside the expanding cosmic volume in which the observer resides. Further, we show that the second law of thermodynamics can be correlated with cosmic expansion through a relational mechanism, because the decrease in information detected by a local observer in an expanding Universe is concomitant with an increase in perceived cosmic thermodynamic entropy, via the Bekenstein bound and the Laudauer principle. Reversing the classical scheme from thermodynamic entropy to information, we suggest that the cosmological constant of the quantum vacuum, which is believed to provoke the current cosmic expansion, could be one of the sources of the perceived increases in thermodynamic entropy. We conclude that entropies, including the entangled entropy of the recently developed framework of quantum computational spacetime, might not describe independent properties, but rather relations among systems and observers.

Experimental and Numerical Investigation of Torsion Fatigue of Bearing Steel

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
John A. R. Bomidi ◽  
Nick Weinzapfel ◽  
Trevor Slack ◽  
Sina Mobasher Moghaddam ◽  
Farshid Sadeghi ◽  
...  
Keyword(s):  
Fatigue Life ◽  
Crack Initiation ◽  
Normal Stress ◽  
Failure Mechanism ◽  
Fatigue Damage ◽  
Fatigue Failure ◽  
Damage Mechanics ◽  
Damage Model ◽  
Bearing Steel ◽  
Fatigue Damage Accumulation

This paper presents the results of torsion fatigue of widely used bearing steels (through hardening with bainite, martensite heat treatments, and case hardened). An MTS torsion fatigue test rig (TFTR) was modified with custom mechanical grips and used to evaluate torsional fatigue life and failure mechanism of bearing steel specimen. Tests were conducted on the TFTR to determine the ultimate strength in shear (Sus) and stress cycle (S-N) results. Evaluation of the fatigue specimens in the high cycle regime indicates shear driven crack initiation followed by normal stress driven propagation, resulting in a helical crack pattern. A 3D finite element model was then developed to investigate fatigue damage in torsion specimen and replicate the observed fatigue failure mechanism for crack initiation and propagation. In the numerical model, continuum damage mechanics (CDM) were employed in a randomly generated 3D Voronoi tessellated mesh of the specimen to provide unstructured, nonplanar, interelement, and inter/transgranular paths for fatigue damage accumulation and crack evolution as observed in micrographs of specimen. Additionally, a new damage evolution procedure was implemented to capture the change in fatigue failure mechanism from shear to normal stress assisted crack growth. The progression of fatigue failure and the stress-life results obtained from the fatigue damage model are in good agreement with the experimental results. The fatigue damage model was also used to assess the influence of topological microstructure randomness accompanied by material inhomogeneity and defects on fatigue life dispersion.

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