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AFGROW | DTD Handbook

Handbook for Damage Tolerant Design

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- Sections
  - 1. Introduction
    - 0. Introduction
    - 1. Historical Perspective on Structural Integrity in the USAF
    - 2. Overview of MIL-HDBK-1530 ASIP Guidance
    - 3. Summary of Damage Tolerance Design Guidelines
      - 0. Summary of Damage Tolerance Design Guidelines
      - 1. Summary of Guidelines
      - 2. Design Category
      - 3. Inspection Categories and Inspection Intervals
      - 4. Initial Damage Assumptions
        
        0. Initial Damage Assumptions
        1. Intact Structure Primary Damage Assumption
        2. Continuing Damage
        3. Fastener Policy
        4. In-Service Inspection Damage Assumptions
        5. Demonstration of Initial Flaw Sizes Smaller Than Those Specified
      - 5. Residual Strength Guidelines
        
        0. Residual Strength Guidelines
        1. Fail-Safe Structure at Time of Load Path Failure
        2. Determining the Residual Strength Load for Remaining Structure
      - 6. Required Periods Of Safe Damage Growth
        
        0. Required Periods Of Safe Damage Growth
        1. Slow Crack Growth Structure
        2. Fail Safe Multiple Load Path Structure
        3. Fail Safe Crack Arrest Structures
      - 7. Illustrative Example Of Guidelines
        
        0. Illustrative Example Of Guidelines
        1. Slow Crack Growth Structure
        
        0. Slow Crack Growth Structure
        1. Initial Flaw Sizes Assumed to Result from Manufacturing
        2. Choice of Inspection Category
        3. In-Service Non-Inspectable Category
        4. Depot Level Inspectable Category
        
        2. Fail Safe Structure
        
        0. Fail Safe Structure
        1. In-Service Inspection Consideration
        2. Initial Flaw Considerations
        3. In-Service Flaw Assumptions Following Inspection
        4. Adjacent Structure Damage Following the Failure of the Major Load Path
        5. Analysis of Intact Structure–Residual Strength Guidelines and Damage Growth Limits
        6. Analysis of Intact Structure (Alternate Requirement)
        7. Discussion of Intact Structure Analysis
        8. Analysis of Remaining Structure Subsequent to Load Path Failure
        9. Derivation of Residual Strength Load
        10. Incremental Damage Growth Da
        11. Alternative-Analysis of Remaining Structure Subsequent to Load Path Failure
        12. Summary and Comments
    - 4. Sustainment/Aging Aircraft
      - 0. Sustainment/Aging Aircraft
      - 1. Widespread Fatigue Damage
      - 2. The Effect of Environment and Corrosion
    - 5. References
  - 2. Fundamentals of Damage Tolerance
    - 0. Fundamentals of Damage Tolerance
    - 1. Introduction to Damage Concepts and Behavior
      - 0. Introduction to Damage Concepts and Behavior
      - 1. Damage Growth Concepts
      - 2. Damage Growth Behavior/Concepts
    - 2. Fracture Mechanics Fundamentals
      - 0. Fracture Mechanics Fundamentals
      - 1. Stress Intensity Factor – What It Is
      - 2. Application to Fracture
      - 3. Fracture Toughness - A Material Property
      - 4. Crack Tip Plastic Zone Size
      - 5. Application to Sub-critical Crack Growth
      - 6. Alternate Fracture Mechanics Analysis Methods
        
        0. Alternate Fracture Mechanics Analysis Methods
        1. Strain Energy Release Rate
        
        0. Strain Energy Release Rate
        1. The Griffith-Irwin Energy Balance
        2. The Relationship between G, Compliance, and Elastic Strain Energy
        
        2. The J-Integral
        
        0. The J-Integral
        1. J-Integral Calculations
        2. Engineering Estimates of J
        
        3. Crack Opening Displacement
    - 3. Residual Strength Methodology
    - 4. Life Prediction Methodology
      - 0. Life Prediction Methodology
      - 1. Initial Flaw Distribution
      - 2. Usage
      - 3. Material Properties
      - 4. Crack Tip Stress Intensity Factor Analysis
      - 5. Damage Integration Models
      - 6. Failure Criteria
    - 5. Deterministic Versus Proabilistic Approaches
    - 6. Computer Codes
      - 0. Computer Codes
      - 1. Structural Analysis
      - 2. Life Prediction
        
        0. Life Prediction
        1. NASGRO Fracture Analysis Software
        2. AFGROW Fracture Analysis Software
        3. Cracks2000 Structural Integrity Software
      - 3. PRobability Of Fracture (PROF)
    - 7. Achieving Confidence in Life Prediction Methodology
    - 8. References
  - 3. Damage Size Characterizations
    - 0. Damage Size Characterizations
    - 1. NDI Demonstration of Crack Detection Capability
      - 0. NDI Demonstration of Crack Detection Capability
      - 2. NDI Capability Evaluation for Cracks
        
        0. NDI Capability Evaluation for Cracks
        1. Basic Considerations in Quantifying NDI Capability
        2. Design of NDI Capability Demonstrations
        3. Sample Size Requirements
        4. POD Analysis
      - 3. NDI Capability Evaluation for Corrosion
        
        0. NDI Capability Evaluation for Corrosion
        1. Corrosion Metrics
        2. Corrosion Specimen Selection and Design
        3. Example of Evaluating the Capability of an Eddy Current Inspection to Detect Hidden Corrosion in Lap Joints
    - 2. Equivalent Initial Quality
      - 0. Equivalent Initial Quality
      - 1. Description of Equivalent Initial Quality Method
      - 2. Example Application of Equivalent Initial Quality Method
      - 3. Other Applications of Equivalent Flaw Size Distributions
        
        0. Other Applications of Equivalent Flaw Size Distributions
        1. Durability Analysis
        2. Risk Analysis
    - 3. Proof Test Determinations
      - 0. Proof Test Determinations
      - 1. Description of the Proof Test Method
      - 2. Examples
    - 4. References
  - 4. Residual Strength
    - 0. Residual Strength
    - 1. Introduction
      - 0. Introduction
      - 1. Slow Crack Growth Structure
      - 2. Fail-Safe Structure
    - 2. Failure Criteria
      - 0. Failure Criteria
      - 1. Ultimate Strength
      - 2. Fracture Toughness - Abrupt Fracture
      - 3. Crack Growth Resistance – Tearing Fracture
        
        0. Crack Growth Resistance – Tearing Fracture
        1. The Apparent Fracture Toughness Approach
        2. The Resistance Curve Approach
        3. The J-Integral Resistance Curve Approach
    - 3. Residual Strength Capability
      - 0. Residual Strength Capability
      - 1. Single Load Path Residual Strength Diagrams
      - 2. Built-Up Structure Residual Strength Diagrams
    - 4. Single Load Path Structure
      - 0. Single Load Path Structure
      - 1. Abrupt Fracture
      - 2. Tearing Fracture
    - 5. Built-Up Structures
      - 0. Built-Up Structures
      - 1. Edge Stiffened Panel with a Central Crack
      - 2. Centrally and Edge Stiffened Panel with a Central Crack
      - 3. Analytical Methods
      - 4. Stiffener Failure
      - 5. Fastener Failure
      - 6. Methodology Basis for Stiffened Panel Example Problem
      - 7. Tearing Failure Analysis
      - 8. Summary
    - 6. References
  - 5. Analysis Of Damage Growth
    - 0. Analysis Of Damage Growth
    - 2. Variable-Amplitude Loading
      - 0. Variable-Amplitude Loading
      - 1. Retardation
        
        0. Retardation
        1. Retardation Under Spectrum Loading
        2. Retardation Models
      - 2. Integration Routines
      - 3. Cycle-by-Cycle Analysis
    - 3. Small Crack Behavior
    - 4. Stress Sequence Development
      - 0. Stress Sequence Development
      - 1. Service Life Description and Mission Profiles
      - 2. Sequence Development Techniques
      - 3. Application of Simplified Stress Sequences for Design Studies
    - 5. Crack Growth Prediction
      - 0. Crack Growth Prediction
      - 1. Cycle Definition and Sequencing
      - 2. Clipping
      - 3. Truncation
      - 4. Crack Shape
      - 5. Interaction of Cracks
    - 6. References
  - 6. Examples of Damage Tolerant Analyses
    - 0. Examples of Damage Tolerant Analyses
    - 1. Damage Tolerance Analysis Procedure
    - 2. Damage Development And Progression
      - 0. Damage Development And Progression
      - 1. Slow Crack Growth Structure
      - 2. Multiple Load Path, Fail Safe Structure
      - 3. Crack Arrest, Fail Safe Structure
    - 3. Slow Crack Growth Structure
    - 4. Multiple Load Path Structure
    - 5. Fail Safe Multiple Load Path Structure
  - 7. Damage Tolerance Testing
    - 0. Damage Tolerance Testing
    - 1. Introduction
    - 2. Material Tests
      - 0. Material Tests
      - 1. Fracture Toughness Testing Methods
        
        0. Fracture Toughness Testing Methods
        1. Plane-Strain Fracture Toughness
        2. R-Curve
        3. Crack Initiation J-Integral
      - 2. Sub-Critical Crack Growth Testing Methods
        
        0. Sub-Critical Crack Growth Testing Methods
        1. Crack Growth Rate Testing
        2. Stress Corrosion Cracking
    - 3. Quality Control Testing
    - 4. Analysis Verification Testing
      - 0. Analysis Verification Testing
      - 1. Structural Parameter Verification Techniques
        
        0. Structural Parameter Verification Techniques
        1. Compliance
        2. Moiré Fringe
        3. Photoelasticity
        4. Crack Growth Rate
      - 2. Residual Strength Methods-Verification
      - 3. Crack Growth Modeling-Verification
    - 5. Structural Hardware Tests
      - 0. Structural Hardware Tests
      - 1. Test Conditions
      - 2. Initial and Continuing Damage
      - 3. Residual Strength Testing
      - 4. Damage Tolerance Test Articles
      - 5. Evaluation and Interpretation of Test Results
    - 6. References
  - 8. Force Management and Sustainment Engineering
    - 0. Force Management and Sustainment Engineering
    - 1. Force Structural Management
      - 0. Force Structural Management
      - 1. Force Structural Management Plan (FSMP)
      - 2. Loads/Environment Spectra Survey (L/ESS)
      - 3. Individual Aircraft Tracking (IAT)
    - 2. Sustainment Engineering
      - 0. Sustainment Engineering
      - 1. Widespread Fatigue Damage
      - 2. Corrosion
      - 3. Structural Risk Analysis
    - 3. References
  - 9. Structural Repairs
    - 0. Structural Repairs
    - 1. Required Analysis
    - 3. Spectrum Analysis for Repair
      - 0. Spectrum Analysis for Repair
      - 1. Definition of Stress Histories
      - 2. Spectra Descriptions
        
        0. Spectra Descriptions
        1. Exceedance Curve Descriptions
        2. RMS Descriptions
      - 3. Crack Growth Analysis
        
        0. Crack Growth Analysis
        1. Generation of Crack Growth Curves
        2. Analysis of Observed Behavior
        3. Interpertation and Use of Crack Growth Rate Curves
        4. Analysis for Multiple Stress Histories
    - 4. Life Sensitivity for Stress Effects
    - 5. Life Sensitivity Analysis for Hole Repair
    - 6. Blend-Out Repairs
    - 7. Residual Strength Parametric Analysis
    - 8. References
  - 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
    - 0. Guidelines for Damage Tolerance Design and Fracture Control Planning
    - 1. Design Loads Spectrum
    - 2. Material Selection
      - 0. Material Selection
      - 1. Crack Growth Resistance and Fracture Toughness
      - 2. Material Property Control
    - 3. Structural Configuration Analysis
      - 0. Structural Configuration Analysis
      - 1. Critical Parts List
      - 2. Inspection Method Development
      - 3. Demonstration Test Development
    - 4. Manufacturing Process
      - 0. Manufacturing Process
      - 1. Review of manufacturing process and inspections
      - 2. Development of Critical Parts Accountability
    - 5. References
  - 11. Summary of Stress Intensity Factor Information
    - 0. Summary of Stress Intensity Factor Information
    - 1. Background of Stress Intensity Factors
    - 2. Methodology For Determining Stress Intensity Factors
      - 0. Methodology For Determining Stress Intensity Factors
      - 1. Principle of Superposition
      - 3. Finite Element Methods
        
        0. Finite Element Methods
        1. Direct Methods
        2. Indirect Methods
        3. Cracked Element Methods
    - 3. Selected Stress Intensity Factor Cases
    - 5. Computer Codes
      - 0. Computer Codes
      - 1. NASGRO Fracture Analysis Software
      - 2. AFGROW Fracture Analysis Software
      - 3. Cracks2000 Structural Integrity Software
    - 6. References
- Examples
  - 1. FAC Problems
    - 0. Computing Stress Intensity Factor Histories
    - 1. Predicting Residual Strength - Fuselage Section
    - 2. Crack Interaction and Multi-Site Damage
    - 3. Predicting Ductile Tearing and Residual Strength - Flat Sheet
  - 2. Merc Problems
    - 0. Crack Growth Prediction - Center Wing Component
    - 1. Damage Tolerance Analysis - Windshield Doubler
    - 2. Sensitivity of Crack Growth Rates to Operating Conditions
    - 3. Influences of Retardation Models on Crack Growth Predictions
  - 3. NRC Problems
    - 0. Quantifying Corrosion in Lap Joints
    - 1. Residual Life Assessment - Corroded Lap Joints
    - 2. Effect of Discontinuity States on the Risk Assessment - Corroded Lap Joints
  - 4. SIE Problems
    - 0. Crack Growth Analysis - Main Cargo Door (MSD Cracks)
    - 1. Damage Tolerance Analysis - Wing Main Spars
    - 2. Crack Growth Analysis - Main Cargo Door (Primary and Continuing Damage)
    - 3. Damage Tolerance Analysis - Rear Wing Spar
    - 4. Crack Growth and Residual Strength Analyses - Lap Joint
  - 5. UDRI Problems
    - 0. Crack Growth Analysis - Front Wing Spar
    - 1. Risk Assessment - Fail Safety of a Stringer
    - 2. Risk Assessment - Multiple Element Damage
    - 3. Risk Assessment - Corrosion in a Lap Joint

Section 9.3.3.0. Crack Growth Analysis

The simplest manner for differentiating a curve is by using the secant method, i.e.

(9.3.5)

where (a₁, F₁) and (a₂, F₂) represent two different points on the crack growth life, crack length (a) versus flights (F) curve. The derivative is considered to be the slope of the curve at the mean crack length of the two points, ie.

(9.3.6)

The mean crack length provides the ability to calculate the stress-intensity factor coefficient (K/s) for the geometry associated with the crack growth life curve. To describe the crack growth rate as a function of stress-intensity factor, it is necessary to have either a formula or graph that relates stress-intensity factor to crack length for a known external loading condition. For example, if the stress-intensity factor is related to gross stress conditions (s_gross) by the formula

(9.3.7)

Then the stress-intensity factor coefficient is

(9.3.8)

and Equation 9.3.8 is evaluated for a = a_mean (Equation 9.3.6). Note that b is typically a function of crack length.