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by Alec Feinberg
Thermodynamic Degradation Science
Cover
Title Page
List of Figures
List of Tables
About the Author
Preface
1 Equilibrium Thermodynamic Degradation Science
1.1 Introduction to a New Science
1.2 Categorizing Physics of Failure Mechanisms
1.3 Entropy Damage Concept
1.4 Thermodynamic Work
1.5 Thermodynamic State Variables and their Characteristics
1.6 Thermodynamic Second Law in Terms of System Entropy Damage
1.7 Work, Resistance, Generated Entropy, and the Second Law
1.8 Thermodynamic Catastrophic and Parametric Failure
1.9 Repair Entropy
References
2 Applications of Equilibrium Thermodynamic Degradation to Complex and Simple Systems: Entropy Damage, Vibration, Temperature, Noise Analysis, and Thermodynamic Potentials
2.1 Cumulative Entropy Damage Approach in Physics of Failure
2.2 Measuring Entropy Damage Processes
2.3 Intermediate Thermodynamic Aging States and Sampling
2.4 Measures for System-Level Entropy Damage
2.5 Measuring Randomness due to System Entropy Damage with Mesoscopic Noise Analysis in an Operating System
2.6 How System Entropy Damage Leads to Random Processes
2.7 Example 2.8: Human Heart Rate Noise Degradation
2.8 Entropy Damage Noise Assessment Using Autocorrelation and the Power Spectral Density
2.9 Noise Detection Measurement System
2.10 Entropy Maximize Principle: Combined First and Second Law
2.11 Thermodynamic Potentials and Energy States
References
3 NE Thermodynamic Degradation Science Assessment Using the Work Concept
3.1 Equilibrium versus Non-Equilibrium Aging Approach
3.2 Application to Cyclic Work and Cumulative Damage
3.3 Cyclic Work Process, Heat Engines, and the Carnot Cycle
3.4 Example 3.1: Cyclic Engine Damage Quantified Using Efficiency
3.5 The Thermodynamic Damage Ratio Method for Tracking Degradation
3.6 Acceleration Factors from the Damage Ratio Principle
References
4 Applications of NE Thermodynamic Degradation Science to Mechanical Systems
4.1 Thermodynamic Work Approach to Physics of Failure Problems
4.2 Example 4.1: Miner’s Rule
4.3 Assessing Thermodynamic Damage in Mechanical Systems
4.4 Cumulative Damage Accelerated Stress Test Goal: Environmental Profiling and Cumulative Accelerated Stress Test (CAST) Equations
4.5 Fatigue Damage Spectrum Analysis for Vibration Accelerated Testing
References
5 Corrosion Applications in NE Thermodynamic Degradation
5.1 Corrosion Damage in Electrochemistry
5.2 Example 5.2: Chemical Corrosion Processes
5.3 Corrosion Current in Primary Batteries
5.4 Corrosion Rate in Microelectronics
References
6 Thermal Activation Free Energy Approach
6.1 Free Energy Roller Coaster
6.2 Thermally Activated Time-Dependent (TAT) Degradation Model
6.3 Free Energy Use in Parametric Degradation and the Partition Function
6.4 Parametric Aging at End of Life Due to the Arrhenius Mechanism: Large Parametric Change
References
7 TAT Model Applications: Wear, Creep, and Transistor Aging
7.1 Solving Physics of Failure Problems with the TAT Model
7.2 Example 7.1: Activation Wear
7.3 Example 7.2: Activation Creep Model
7.4 Transistor Aging
References
8 Diffusion
8.1 The Diffusion Process
8.2 Example 8.1: Describing Diffusion Using Equilibrium Thermodynamics
8.3 Describing Diffusion Using Probability
8.4 Diffusion Acceleration Factor with and without Temperature Dependence
8.5 Diffusion Entropy Damage
8.6 General Form of the Diffusion Equation
Reference
9 How Aging Laws Influence Parametric and Catastrophic Reliability Distributions
9.1 Physics of Failure Influence on Reliability Distributions
9.2 Log Time Aging (or Power Aging Laws) and the Lognormal Distribution
9.3 Aging Power Laws and the Weibull Distribution: Influence on Beta
9.4 Stress and Life Distributions
9.5 Time- (or Stress-) Dependent Standard Deviation
References
10 The Theory of Organization
Special Topics A
A.1 Introduction
A.2 The Key Reliability Functions
A.3 More Information on the Failure Rate
A.4 The Bathtub Curve and Reliability Distributions
A.5 Confidence Interval for Normal Parametric Analysis
A.6 Central Limit Theorem and Cpk Analysis
A.7 Catastrophic Analysis
A.8 Reliability Objectives and Confidence Testing
A.9 Comprehensive Accelerated Test Planning
References
Special Topics B
B.1 Introduction
B.2 Power Law Acceleration Factors
B.3 Temperature–Humidity Life Test Model
B.4 Temperature Cycle Testing
B.5 Vibration Acceleration
B.6 Multiple-Stress Accelerated Test Plans for Demonstrating Reliability
B.7 Cumulative Accelerated Stress Test (CAST) Goals and Equations Usage in Environmental Profiling
References
Special Topics C
C.1 Spontaneous Negative Entropy: Growth and Repair
C.2 The Perfect Human Engine: How to Live Longer
C.3 Growth and Self-Repair Part of the Human Engine
C.4 Act of Spontaneous Negative Entropy
References
Overview of New Terms, Equations, and Concepts
Key Words
New Terms, Equations, and Concepts
Please Do Cite the Author
Index
End User License Agreement
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Wiley Series in Quality & Reliability Engineering
Table of Contents
Cover
Title Page
List of Figures
List of Tables
About the Author
Preface
1 Equilibrium Thermodynamic Degradation Science
1.1 Introduction to a New Science
1.2 Categorizing Physics of Failure Mechanisms
1.3 Entropy Damage Concept
1.4 Thermodynamic Work
1.5 Thermodynamic State Variables and their Characteristics
1.6 Thermodynamic Second Law in Terms of System Entropy Damage
1.7 Work, Resistance, Generated Entropy, and the Second Law
1.8 Thermodynamic Catastrophic and Parametric Failure
1.9 Repair Entropy
References
2 Applications of Equilibrium Thermodynamic Degradation to Complex and Simple Systems: Entropy Damage, Vibration, Temperature, Noise Analysis, and Thermodynamic Potentials
2.1 Cumulative Entropy Damage Approach in Physics of Failure
2.2 Measuring Entropy Damage Processes
2.3 Intermediate Thermodynamic Aging States and Sampling
2.4 Measures for System-Level Entropy Damage
2.5 Measuring Randomness due to System Entropy Damage with Mesoscopic Noise Analysis in an Operating System
2.6 How System Entropy Damage Leads to Random Processes
2.7 Example 2.8: Human Heart Rate Noise Degradation
2.8 Entropy Damage Noise Assessment Using Autocorrelation and the Power Spectral Density
2.9 Noise Detection Measurement System
2.10 Entropy Maximize Principle: Combined First and Second Law
2.11 Thermodynamic Potentials and Energy States
References
3 NE Thermodynamic Degradation Science Assessment Using the Work Concept
3.1 Equilibrium versus Non-Equilibrium Aging Approach
3.2 Application to Cyclic Work and Cumulative Damage
3.3 Cyclic Work Process, Heat Engines, and the Carnot Cycle
3.4 Example 3.1: Cyclic Engine Damage Quantified Using Efficiency
3.5 The Thermodynamic Damage Ratio Method for Tracking Degradation
3.6 Acceleration Factors from the Damage Ratio Principle
References
4 Applications of NE Thermodynamic Degradation Science to Mechanical Systems
4.1 Thermodynamic Work Approach to Physics of Failure Problems
4.2 Example 4.1: Miner’s Rule
4.3 Assessing Thermodynamic Damage in Mechanical Systems
4.4 Cumulative Damage Accelerated Stress Test Goal: Environmental Profiling and Cumulative Accelerated Stress Test (CAST) Equations
4.5 Fatigue Damage Spectrum Analysis for Vibration Accelerated Testing
References
5 Corrosion Applications in NE Thermodynamic Degradation
5.1 Corrosion Damage in Electrochemistry
5.2 Example 5.2: Chemical Corrosion Processes
5.3 Corrosion Current in Primary Batteries
5.4 Corrosion Rate in Microelectronics
References
6 Thermal Activation Free Energy Approach
6.1 Free Energy Roller Coaster
6.2 Thermally Activated Time-Dependent (TAT) Degradation Model
6.3 Free Energy Use in Parametric Degradation and the Partition Function
6.4 Parametric Aging at End of Life Due to the Arrhenius Mechanism: Large Parametric Change
References
7 TAT Model Applications: Wear, Creep, and Transistor Aging
7.1 Solving Physics of Failure Problems with the TAT Model
7.2 Example 7.1: Activation Wear
7.3 Example 7.2: Activation Creep Model
7.4 Transistor Aging
References
8 Diffusion
8.1 The Diffusion Process
8.2 Example 8.1: Describing Diffusion Using Equilibrium Thermodynamics
8.3 Describing Diffusion Using Probability
8.4 Diffusion Acceleration Factor with and without Temperature Dependence
8.5 Diffusion Entropy Damage
8.6 General Form of the Diffusion Equation
Reference
9 How Aging Laws Influence Parametric and Catastrophic Reliability Distributions
9.1 Physics of Failure Influence on Reliability Distributions
9.2 Log Time Aging (or Power Aging Laws) and the Lognormal Distribution
9.3 Aging Power Laws and the Weibull Distribution: Influence on Beta
9.4 Stress and Life Distributions
9.5 Time- (or Stress-) Dependent Standard Deviation
References
10 The Theory of Organization
Special Topics A
A.1 Introduction
A.2 The Key Reliability Functions
A.3 More Information on the Failure Rate
A.4 The Bathtub Curve and Reliability Distributions
A.5 Confidence Interval for Normal Parametric Analysis
A.6 Central Limit Theorem and Cpk Analysis
A.7 Catastrophic Analysis
A.8 Reliability Objectives and Confidence Testing
A.9 Comprehensive Accelerated Test Planning
References
Special Topics B
B.1 Introduction
B.2 Power Law Acceleration Factors
B.3 Temperature–Humidity Life Test Model
B.4 Temperature Cycle Testing
B.5 Vibration Acceleration
B.6 Multiple-Stress Accelerated Test Plans for Demonstrating Reliability
B.7 Cumulative Accelerated Stress Test (CAST) Goals and Equations Usage in Environmental Profiling
References
Special Topics C
C.1 Spontaneous Negative Entropy: Growth and Repair
C.2 The Perfect Human Engine: How to Live Longer
C.3 Growth and Self-Repair Part of the Human Engine
C.4 Act of Spontaneous Negative Entropy
References
Overview of New Terms, Equations, and Concepts
Key Words
New Terms, Equations, and Concepts
Please Do Cite the Author
Index
End User License Agreement
List of Tables
Chapter 01
Table 1.1 Generalized conjugate mechanical work variables
Table 1.2 Some state variables
Table 1.3 Some common intensive and extensive thermodynamic variables [1, 4]
Table 1.4 Common thermodynamic processes
Table 1.5 Thermodynamic aging states [1, 2, 4]
Chapter 02
Table 2.1 Common time series transforms
Table 2.2 Four common thermodynamic potential and energy states
Chapter 04
Table 4.1 Typical constants for stress–time creep law
Table 4.2 Damping loss factor examples for certain materials
Table 4.3 Cumulative stress test goals: CAST equations
Chapter 05
Table 5.1 Estimated relative corrosion resistance
Table 5.2 Predicted corrosion rates and amounts for 1 year at 5 mA of current for anodic different metals [7]
Chapter 06
Table 6.1 Failure mechanisms and associated thermal activation energies
Special Topics A
Table A.1 Constant failure rate conversion table
Table A.2 Relationship between Cpk index and yield [1]
Table A.3 Life test data arranged for plotting
Table A.4 Field data and the renormalized groups
Table A.5 Multiple stress accelerated test to demonstrate 1 FMH [1]
Special Topics B
Table B.1 MTTF observed
Table B.2 Machine stress MTTF observed
Table B.3 Gaussian probabilities (%)
Table B.4 Multiple stress accelerated test to demonstrate 0.6 FMH
Table B.5 Optimized multiple stress accelerated test for 0.6 FMH
Table B.6 Profile of a product’s temperature exposure per year
Special Topics C
Table C.1 Human cyclic engine and possible stresses that shorten cycle life
List of Illustrations
Chapter 01
Figure 1.1 Conceptualized aging rates for physics-of-failure mechanisms
Figure 1.2 First law energy flow to system: (a) heat-in, work-out; and (b) heat-in and work-in
Figure 1.3 Fatigue
S–N
curve of cycles to failure versus stress, illustrating a fatigue limit in steel and no apparent limit in aluminum
Figure 1.4 Elastic stress limit and yielding point 1
Chapter 02
Figure 2.1 The entropy change of an isolated system is the sum of the entropy changes of its components, and is never less than zero
Figure 2.2 Cell fatigue dislocations and cumulating entropy
Figure 2.3 Gaussian white noise
Figure 2.4 Noise limit heart rate variability measurements of young, elderly, and CHF patients [10]
Figure 2.5 Noise limit heart rate variability chaos measurements of young and CHF patients [10]
Figure 2.6 Graphical representation of the autocorrelation function
Figure 2.7 (a) Sine waves at 10 and 15 Hz with some randomness in frequency; and (b) Fourier transform spectrum. In (b) we cannot transform back without knowledge of which sine tone occurred first
Figure 2.8 (a) White noise time series; (b) normalized autocorrelation function of white noise; and (c) PSD spectrum of white noise
Figure 2.9 (a) Flicker (pink) 1/
f
noise; (b) normalized autocorrelation function of 1/
f
noise; and (c) PSD spectrum of 1/
f
noise
Figure 2.10 (a) Brown 1/
f
2
noise; (b) normalized autocorrelation function of 1/
f
2
noise; and (c) PSD spectrum of 1/
f
2
noise
Figure 2.11 Some key types of white, pink, and brown noise that might be observed from a system
Figure 2.12 1/
f
noise simulations for resistor noise. Note the lower noise for larger resistors (power of 2) and higher noise for smaller resistors (power of 1.5)
Figure 2.13 Autocorrelation noise measurement detection system
Figure 2.14 Insulating cylinder divided into two sections by a frictionless piston
Figure 2.15 System (capacitor) and environment (battery) circuit
Figure 2.16 The system expands against the atmosphere
Figure 2.17 Mechanical work done on a system
Figure 2.18 Loss of available work due to increase in entropy damage
Figure 2.19 A simple system in contact with a heat reservoir
Figure 2.20 A system’s free energy decrease over time and the corresponding total entropy increase
Chapter 03
Figure 3.1 Conceptual view of cyclic cumulative damage.
Figure 3.2 Cyclic work plane
Figure 3.3 Carnot cycle in
P
,
V
plane
Figure 3.4 Cyclic engine damage Area 1 > Area 2
Chapter 04
Figure 4.1 Creep strain over time for different stresses where
σ
4
>
σ
3
>
σ
2
>
σ
1
Figure 4.2 Example of creep of a wire due to a stress weight
Figure 4.3 Wear occurring to a sliding block having weight
P
W
Figure 4.4 Graphical example of a sine test resonance
Chapter 05
Figure 5.1 Lead acid and alkaline MnO
2
batteries fitted data.
Figure 5.2 A simple corrosion cell with iron corrosion
Figure 5.3 Uniform electrochemical corrosion depicted on the surface of a metal
Chapter 06
Figure 6.1 Arrhenius activation free energy path having a relative minimum as a function of generalized parameter
a.
Figure 6.2 Examples of ln(1 +
B
time) aging law, with upper graph similar to primary and secondary creep stages and the lower graph similar to primary battery voltage loss
Figure 6.3 Log time compared to power law aging models
Figure 6.4 (a) Continuous function with numerous energy states. (b) Relative minimum energy states having different degradation mechanisms
Figure 6.5 Aging with critical values
t
c
prior to catastrophic failure.
Chapter 07
Figure 7.1 Types of wear dependence on sliding distance (time)
Figure 7.2 Capacitor leakage model
Figure 7.3 Beta degradation on life test data.
Figure 7.4 Life test data of gate-source MESFET leakage current over time fitted to the ln(1 +
Bt
) aging model. Junction rise was about 30°C.
Chapter 08
Figure 8.1 System with
n
particles and
n
env
environment particles
Figure 8.2 Diffusion concept
Chapter 09
Figure 9.1 Reliability bathtub curve model
Figure 9.2 Power law fit to the wear-out portion of the bathtub curve
Figure 9.3 Log time aging with parametric threshold
t
f
Figure 9.4 PDF failure portion that drifted past the parametric threshold
Figure 9.5 Creep curve with all three stages
Figure 9.6 Creep rate power law model for each creep stage, similar to the bathtub curve in Figure 9.1
Figure 9.7 Creep strain over time for different stresses where
σ
4
>
σ
3
>
σ
2
>
σ
1
Figure 9.8 Crystal frequency drift showing time-dependent standard deviation.
Special Topics A
Figure A.1 Reliability bathtub curve model
Figure A.2 Demonstrating the power law on the wear-out shape
Figure A.3 Modeling the bathtub curve with the Weibull power law
Figure A.4 Weibull hazard (failure) rate for different values of
β
[1]
Figure A.5 Weibull shapes of PDF and CDF with
β
= 2 [1]
Figure A.6 Weibull shapes of PDF and CDF with
β
= 0.5 [1]
Figure A.7 Normal distribution shapes of PDF and CDF;
μ
= 5,
σ
= 1 [1]
Figure A.8 Lognormal hazard (failure) rate for different
σ
values [1]
Figure A.9 Lognormal CDF and PDF for different σ values [1]
Figure A.10 Cpk analysis
Figure A.11 Life test: (a) Weibull analysis compared to (b) lognormal analysis test at 200°C [1]
Figure A.12 Field data (Table A.4) displaying inflection point as sub and main populations [1]
Figure A.13 Separating out the lower and upper distributions by the inflection point method [1]
Special Topics B
Figure B.1 Main accelerated stresses and associated common failure issues
Figure B.2 Common accelerated qualification test plan used in industry [1]
Figure B.3 Arrhenius plot of data given in Table B.1
Figure B.4 MTTF stress plot of data given in Table B.2.
Figure B.5 Sine vibration amplitude over time example
Figure B.6 Random vibration amplitude time series example
Figure B.7 PSD of the random vibration time series in Figure B.6
Special Topics C
Figure C.1
S–N
curve for human heart compared to metal
N
fatigue cycle life versus
S
stress amplitude
Figure C.2 Simplified body repair
Figure C.3 Charge and repair RC model for the human body
Guide
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