Christos Kassapoglou received his BS degree in Aeronautics and Astronautics and two MS degrees (Aeronautics and Astronautics and Mechanical Engineering) from Massachusetts Institute of Technology and his PhD degree from Delft University of Technology. Since 1984 he has worked in industry, first at Beech Aircraft on the all-composite Starship I and then at the Structures Research Group at Sikorsky Aircraft specializing on analysis of composite structures for the all-composite Comanche and other helicopters and leading internally funded research and NASA and the US Army funded program. Since 2001 he has been consulting with various companies in the US and Europe on applications of composites, damage tolerance and certification. He joined the Aerospace Engineering Department of the Delft University of Technology (Aerospace Structures) in 2008 as an Associate Professor. His interests include fatigue and damage tolerance of composites, design and optimization for cost and weight, and technology optimization. He has over 60 journal papers and 3 patents on related subjects. He is a member of AIAA, AHS, and SAMPE.

"This will help the readers – engineers who will be designing the next generation of airframe structures – to develop not only better understanding of underlying damage mechanisms, but also critical thinking andopen-mindedness needed for evaluation of any new simplified approaches that may emerge in the future" Professor Maria Kashtalyan, University of Aberdeen on behalf of the Aeronautical Journal, Oct 2017

• Series Preface ix Preface xi1 Damage in Composite Structures: Notch Sensitivity 11.1 Introduction 11.2 Notch Insensitivity 21.3 ‘Complete’ Notch Sensitivity 41.4 Notch Sensitivity of Composite Materials 5Exercises 6References 72 Holes 92.1 Stresses around Holes 132.2 Using the Anisotropic Elasticity Solution to Predict Failure 162.3 The Role of the Damage Zone Created Near a Hole 172.4 Simplified Approaches to Predict Failure in Laminates with Holes: the Whitney–Nuismer Criteria 192.5 Other Approaches to Predict Failure of a Laminate with a Hole 242.6 Improved Whitney–Nuismer Approach 252.7 Application: Finding the Stacking Sequence Which Results in Good OHT Performance 34Exercises 35References 393 Cracks 413.1 Introduction 413.2 Modelling a Crack in a Composite Laminate 423.3 Finite-Width Effects 453.4 Other Approaches for Analysis of Cracks in Composites 463.5 Matrix Cracks 49Exercises 52References 564 Delaminations 574.1 Introduction 574.2 Relation to Inspection Methods and Criteria 604.3 Modelling Different Structural Details in the Presence of Delaminations 634.3.1 Buckling of a Through-Width Delaminating Layer 634.3.2 Buckling of an Elliptical Delaminating Layer 694.3.3 Application – Buckling of an Elliptical Delamination under Combined Loads 734.3.4 Onset of Delamination at a Straight Free Edge of a Composite Laminate 754.3.5 Delamination at a Flange–Stiffener Interface of a Composite Stiffened Panel 844.3.6 Double Cantilever Beam and End Notch Flexure Specimen 884.3.7 The Crack Closure Method 924.4 Strength of Materials Versus Fracture Mechanics – Use of Cohesive Elements 964.4.1 Use of Cohesive Elements 99Exercises 100References 1035 Impact 1055.1 Sources of Impact and General Implications for Design 1055.2 Damage Resistance Versus Damage Tolerance 1095.3 Modelling Impact Damage as a Hole 1115.4 Modelling Impact Damage as a Delamination 1145.5 Impact Damage Modelled as a Region of Reduced Stiffness 1175.6 Application: Comparison of the Predictions of the Simpler Models with Test Results 1215.6.1 Modelling BVID as a Hole 1225.6.2 Modelling BVID as a Single Delamination 1235.6.3 Modelling BVID as an Elliptical Inclusion of Reduced Stiffness 1245.6.4 Comparisons of Analytical Predictions to Test Results – Sandwich Laminates 1245.7 Improved Model for Impact Damage Analysed as a Region of Reduced Stiffness 1255.7.1 Type and Extent of Damage for Given Impact Energy 1255.7.2 Model for Predicting CAI Strength 148Exercises 163References 1686 Fatigue Life of Composite Structures: Analytical Models 1716.1 Introduction 1716.2 Needed Characteristics for an Analytical Model 1756.3 Models for the Degradation of the Residual Strength 1776.3.1 Linear Model 1776.3.2 Nonlinear Model 1806.4 Model for the Cycles to Failure 1836.4.1 Extension to Spectrum Loading 1966.5 Residual Strength and Wear-Out Model Predictions Compared to Test Results 2006.5.1 Residual Strength Predictions Compared to Test Results 2006.5.2 Cycles to Failure Predictions Compared to Test Results (Constant Amplitude) 2026.5.3 Cycles to Failure Predictions Compared to Test Results (Spectrum Loading) 2046.6 A Proposal for the Complete Model: Accounting for Larger Scale Damage 2066.6.1 First Cycle, Tension Portion 2076.6.2 First Cycle, Compression Portion 2076.6.3 Subsequent Load Cycles 2086.6.4 Discussion 2086.6.5 Application: Tension–Compression Fatigue of Unidirectional Composites 2096.6.6 Application: Tension–Tension Fatigue of Cross-Ply Laminates 214Exercises 218References 2197 Effect of Damage in Composite Structures: Summary and Useful Design Guidelines 221Index 227

Christos Kassapoglou received his BS degree in Aeronautics and Astronautics and two MS degrees (Aeronautics and Astronautics and Mechanical Engineering) from Massachusetts Institute of Technology and his PhD degree from Delft University of Technology. Since 1984 he has worked in industry, first at Beech Aircraft on the all-composite Starship I and then at the Structures Research Group at Sikorsky Aircraft specializing on analysis of composite structures for the all-composite Comanche and other helicopters and leading internally funded research and NASA and the US Army funded program. Since 2001 he has been consulting with various companies in the US and Europe on applications of composites, damage tolerance and certification. He joined the Aerospace Engineering Department of the Delft University of Technology (Aerospace Structures) in 2008 as an Associate Professor. His interests include fatigue and damage tolerance of composites, design and optimization for cost and weight, and technology optimization. He has over 60 journal papers and 3 patents on related subjects. He is a member of AIAA, AHS, and SAMPE.

"This will help the readers – engineers who will be designing the next generation of airframe structures – to develop not only better understanding of underlying damage mechanisms, but also critical thinking andopen-mindedness needed for evaluation of any new simplified approaches that may emerge in the future" Professor Maria Kashtalyan, University of Aberdeen on behalf of the Aeronautical Journal, Oct 2017

• Series Preface ix Preface xi1 Damage in Composite Structures: Notch Sensitivity 11.1 Introduction 11.2 Notch Insensitivity 21.3 ‘Complete’ Notch Sensitivity 41.4 Notch Sensitivity of Composite Materials 5Exercises 6References 72 Holes 92.1 Stresses around Holes 132.2 Using the Anisotropic Elasticity Solution to Predict Failure 162.3 The Role of the Damage Zone Created Near a Hole 172.4 Simplified Approaches to Predict Failure in Laminates with Holes: the Whitney–Nuismer Criteria 192.5 Other Approaches to Predict Failure of a Laminate with a Hole 242.6 Improved Whitney–Nuismer Approach 252.7 Application: Finding the Stacking Sequence Which Results in Good OHT Performance 34Exercises 35References 393 Cracks 413.1 Introduction 413.2 Modelling a Crack in a Composite Laminate 423.3 Finite-Width Effects 453.4 Other Approaches for Analysis of Cracks in Composites 463.5 Matrix Cracks 49Exercises 52References 564 Delaminations 574.1 Introduction 574.2 Relation to Inspection Methods and Criteria 604.3 Modelling Different Structural Details in the Presence of Delaminations 634.3.1 Buckling of a Through-Width Delaminating Layer 634.3.2 Buckling of an Elliptical Delaminating Layer 694.3.3 Application – Buckling of an Elliptical Delamination under Combined Loads 734.3.4 Onset of Delamination at a Straight Free Edge of a Composite Laminate 754.3.5 Delamination at a Flange–Stiffener Interface of a Composite Stiffened Panel 844.3.6 Double Cantilever Beam and End Notch Flexure Specimen 884.3.7 The Crack Closure Method 924.4 Strength of Materials Versus Fracture Mechanics – Use of Cohesive Elements 964.4.1 Use of Cohesive Elements 99Exercises 100References 1035 Impact 1055.1 Sources of Impact and General Implications for Design 1055.2 Damage Resistance Versus Damage Tolerance 1095.3 Modelling Impact Damage as a Hole 1115.4 Modelling Impact Damage as a Delamination 1145.5 Impact Damage Modelled as a Region of Reduced Stiffness 1175.6 Application: Comparison of the Predictions of the Simpler Models with Test Results 1215.6.1 Modelling BVID as a Hole 1225.6.2 Modelling BVID as a Single Delamination 1235.6.3 Modelling BVID as an Elliptical Inclusion of Reduced Stiffness 1245.6.4 Comparisons of Analytical Predictions to Test Results – Sandwich Laminates 1245.7 Improved Model for Impact Damage Analysed as a Region of Reduced Stiffness 1255.7.1 Type and Extent of Damage for Given Impact Energy 1255.7.2 Model for Predicting CAI Strength 148Exercises 163References 1686 Fatigue Life of Composite Structures: Analytical Models 1716.1 Introduction 1716.2 Needed Characteristics for an Analytical Model 1756.3 Models for the Degradation of the Residual Strength 1776.3.1 Linear Model 1776.3.2 Nonlinear Model 1806.4 Model for the Cycles to Failure 1836.4.1 Extension to Spectrum Loading 1966.5 Residual Strength and Wear-Out Model Predictions Compared to Test Results 2006.5.1 Residual Strength Predictions Compared to Test Results 2006.5.2 Cycles to Failure Predictions Compared to Test Results (Constant Amplitude) 2026.5.3 Cycles to Failure Predictions Compared to Test Results (Spectrum Loading) 2046.6 A Proposal for the Complete Model: Accounting for Larger Scale Damage 2066.6.1 First Cycle, Tension Portion 2076.6.2 First Cycle, Compression Portion 2076.6.3 Subsequent Load Cycles 2086.6.4 Discussion 2086.6.5 Application: Tension–Compression Fatigue of Unidirectional Composites 2096.6.6 Application: Tension–Tension Fatigue of Cross-Ply Laminates 214Exercises 218References 2197 Effect of Damage in Composite Structures: Summary and Useful Design Guidelines 221Index 227

Christos Kassapoglou received his BS degree in Aeronautics and Astronautics and two MS degrees (Aeronautics and Astronautics and Mechanical Engineering) from Massachusetts Institute of Technology and his PhD degree from Delft University of Technology. Since 1984 he has worked in industry, first at Beech Aircraft on the all-composite Starship I and then at the Structures Research Group at Sikorsky Aircraft specializing on analysis of composite structures for the all-composite Comanche and other helicopters and leading internally funded research and NASA and the US Army funded program. Since 2001 he has been consulting with various companies in the US and Europe on applications of composites, damage tolerance and certification. He joined the Aerospace Engineering Department of the Delft University of Technology (Aerospace Structures) in 2008 as an Associate Professor. His interests include fatigue and damage tolerance of composites, design and optimization for cost and weight, and technology optimization. He has over 60 journal papers and 3 patents on related subjects. He is a member of AIAA, AHS, and SAMPE.

"This will help the readers – engineers who will be designing the next generation of airframe structures – to develop not only better understanding of underlying damage mechanisms, but also critical thinking andopen-mindedness needed for evaluation of any new simplified approaches that may emerge in the future" Professor Maria Kashtalyan, University of Aberdeen on behalf of the Aeronautical Journal, Oct 2017

• Series Preface ix Preface xi1 Damage in Composite Structures: Notch Sensitivity 11.1 Introduction 11.2 Notch Insensitivity 21.3 ‘Complete’ Notch Sensitivity 41.4 Notch Sensitivity of Composite Materials 5Exercises 6References 72 Holes 92.1 Stresses around Holes 132.2 Using the Anisotropic Elasticity Solution to Predict Failure 162.3 The Role of the Damage Zone Created Near a Hole 172.4 Simplified Approaches to Predict Failure in Laminates with Holes: the Whitney–Nuismer Criteria 192.5 Other Approaches to Predict Failure of a Laminate with a Hole 242.6 Improved Whitney–Nuismer Approach 252.7 Application: Finding the Stacking Sequence Which Results in Good OHT Performance 34Exercises 35References 393 Cracks 413.1 Introduction 413.2 Modelling a Crack in a Composite Laminate 423.3 Finite-Width Effects 453.4 Other Approaches for Analysis of Cracks in Composites 463.5 Matrix Cracks 49Exercises 52References 564 Delaminations 574.1 Introduction 574.2 Relation to Inspection Methods and Criteria 604.3 Modelling Different Structural Details in the Presence of Delaminations 634.3.1 Buckling of a Through-Width Delaminating Layer 634.3.2 Buckling of an Elliptical Delaminating Layer 694.3.3 Application – Buckling of an Elliptical Delamination under Combined Loads 734.3.4 Onset of Delamination at a Straight Free Edge of a Composite Laminate 754.3.5 Delamination at a Flange–Stiffener Interface of a Composite Stiffened Panel 844.3.6 Double Cantilever Beam and End Notch Flexure Specimen 884.3.7 The Crack Closure Method 924.4 Strength of Materials Versus Fracture Mechanics – Use of Cohesive Elements 964.4.1 Use of Cohesive Elements 99Exercises 100References 1035 Impact 1055.1 Sources of Impact and General Implications for Design 1055.2 Damage Resistance Versus Damage Tolerance 1095.3 Modelling Impact Damage as a Hole 1115.4 Modelling Impact Damage as a Delamination 1145.5 Impact Damage Modelled as a Region of Reduced Stiffness 1175.6 Application: Comparison of the Predictions of the Simpler Models with Test Results 1215.6.1 Modelling BVID as a Hole 1225.6.2 Modelling BVID as a Single Delamination 1235.6.3 Modelling BVID as an Elliptical Inclusion of Reduced Stiffness 1245.6.4 Comparisons of Analytical Predictions to Test Results – Sandwich Laminates 1245.7 Improved Model for Impact Damage Analysed as a Region of Reduced Stiffness 1255.7.1 Type and Extent of Damage for Given Impact Energy 1255.7.2 Model for Predicting CAI Strength 148Exercises 163References 1686 Fatigue Life of Composite Structures: Analytical Models 1716.1 Introduction 1716.2 Needed Characteristics for an Analytical Model 1756.3 Models for the Degradation of the Residual Strength 1776.3.1 Linear Model 1776.3.2 Nonlinear Model 1806.4 Model for the Cycles to Failure 1836.4.1 Extension to Spectrum Loading 1966.5 Residual Strength and Wear-Out Model Predictions Compared to Test Results 2006.5.1 Residual Strength Predictions Compared to Test Results 2006.5.2 Cycles to Failure Predictions Compared to Test Results (Constant Amplitude) 2026.5.3 Cycles to Failure Predictions Compared to Test Results (Spectrum Loading) 2046.6 A Proposal for the Complete Model: Accounting for Larger Scale Damage 2066.6.1 First Cycle, Tension Portion 2076.6.2 First Cycle, Compression Portion 2076.6.3 Subsequent Load Cycles 2086.6.4 Discussion 2086.6.5 Application: Tension–Compression Fatigue of Unidirectional Composites 2096.6.6 Application: Tension–Tension Fatigue of Cross-Ply Laminates 214Exercises 218References 2197 Effect of Damage in Composite Structures: Summary and Useful Design Guidelines 221Index 227