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 |  موضوع: كتاب Development of GENOA Progressive Failure Parallel Processing Software Systems السبت 14 نوفمبر 2020, 6:24 pm | |
| 
أخوانى فى الله
أحضرت لكم كتاب
Development of GENOA Progressive Failure Parallel Processing Software Systems
Frank Abdi
Alpha STAR Corporation, Long Beach, California
Levon Minnetyan
Clarkson University, Potsdam, New York
و المحتوى كما يلي :
Contents
Executive Summary . E-1
1.1 Progressive Failure Simulation Software E-2
1.0 Summary of Phase II . 1-1
1.1 A New Approach To Progressive Failure Simulation 1-1
1.1.1 Three Dimensional Composites 1-1
1.1.2 Stiffness Properties of Three Dimensional Composites 1-2
1.2 GENOA-PFA Simulation Of 2D/3D Woven/Braided/ 1-3
Stitched PMC Structure
1.2.1 Executive Controller System (ECS) and Graphic 1-4
User Interface (GUI)
1.2.2 The Damage Tracking Process 1-5
1.2.3 Failure Evaluation Approach . 1-6
1.2.4 GENOA Finite Element Analysis . 1-8
1.2.5 Simulation of Damage Progression . 1-9
1.3 Summary of Phase II Progress 1-9
1.3.1 Improve Flexibility And Portability By 1-9
Modularization And Standardization
1.3.2 Methodology of Mesh Refinement in Progressive . 1-10
Failure Analysis
1.3.3 Re-evaluation with Restart 1-12
1.3.4 Modeling Of A Variety Of 2D/3D Woven/Braided/ . 1-14
Stitched Laminate Fiber Architecture
1.3.5 Generate Equivalent Woven/Braided/Stitched 1-15
Composite Material Properties
1.4 Simulation Of progressive fracture In Time Domain . 1-16
1.4.1 Low cycle Fatigue Loading 1-16
1.4.2 Simulate Progressive Fracture in PMC Structure . 1-17
Under Time Domain High Cyclic Fatigue Loading
1.4.3 Simulate Progressive Fracture Under Impact Loading . 1-18
1.4.4 Simulate Reshaping Of Braided Fiber . 1-18
Preforms To Assist Manufacturing
1.4.5 Perform Virtual Testing analyses . 1-21
1.4.6 Probabilistic Failure Analyses . 1-22
1.4.7 Improved Graphics User Interface (GUI) For . 1-22
Visualization (Including Animation) of Simulated Results
1.4.8 Porting GENOA-PFA Software to Unix (HP, SGI, IBM), 1-24
and NT Operating Systems
1.5 References 1-25Contents
ii
2.0 Modularization of CODSTRAN . 2-1
2.1 Implementation of Modular Finite Element Analysis 2-1
2.1.1 Modular Files Structure 2-3
2.1.2 Modularization of the CODSTRAN . 2-4
2.1.3 Review of Data Communication in Modular CODSTRAN . 2-5
2.1.4 Modularization Enhancement of CODSTRAN-FEM 2-7
2.1.5 Implementation of Algorithm 2-16
2.1.6 MCOD to FEM Source Code Structure . 2-16
2.1.7 Verification of the Modular Version of CODSTRAN (COD6) . 2-16
2.2 Testing and Validation 2-17
2.2.1 Model Definition (For Test Example) . 2-17
2.2.2 Comments MCOD to FEM 2-20
2.2.3 Validation of COD7MM With an Intermediate Example 2-20
(1000 DOF)
2.2.4 Validation of NESSUS Based COD7MM Modularization . 2-24
2.3 Conclusion, Problems, and Future Development and Validation 2-24
3.0 Methodology of Adaptive Mesh Refinement in Progressive 3-1
Failure Analysis
3.1 Modification of Conventional CODSTRAN Mesh Refinement Module 3-1
3.2 Verification of Adaptive Mesh Refinement 3-2
3.2.1 Test Specimen No 1 Flat Panel 3-2
3.2.2 Flat Panel Model Definition for Test Specimen No. 2 3-6
3.2.3 Flat Model Test Specimen No. 3 . 3-12
3.2.4 Verification of Boeing Crown Panel with 38 inches Saw Cut 3-17
4.0 Progressive Fracture of Composite Structures Under Cyclic Fatigue 4-1
4.1 Low Cycle Fatigue . 4-1
4.1.1 NASA Test Coupon Simulation . 4-2
4.1.2 Crown Panel Simulation . 4-4
4.1.3 Verification of Boeing 747 Crown Panel Simulation 4-7
4.2 High Cycle Fatigue 4-10
4.2.1 High Cycle Fatigue Simulation Methodology . 4-10
4.2.2 GENOA-PFA Modification for Cyclic Fatigue Simulation . 4-11
4.2.3 Simulation of PMC Panel Under Cyclic Load . 4-12
4.2.4 Simulation of Composite Plate Under Cyclic Loading . 4-14
4.2.5 Simulation of Composite Airfoil Under High Cyclic Loading . 4-17
4.3 Cyclic Loading of Built-up Composite Structure 4-10
4.3.1 Summary of Results 4-21Contents
iii
4.3.2 Generalization of Procedure 4-22
4.3.3 Conclusions 4-23
4.4 References 4-24
5.0 Simulating Manufacturing Process of Composite Textile . 5-1
Preform Reshaping
5.1 Introduction . 5-1
5.1.1 State of Software Simulation . 5-1
5.1.2 State of Software Development and Concept Verification 5-4
5.2 Technical Approach 5-5
5.3 Computational Simulation Cycle 5-11
5.4 Fiber Angle Change . 5-12
5.4.1 Validity of the Large Strain Approach . 5-13
5.4.2 Possible Areas of Improvement . 5-15
5.5 Fan Blade Mesh Fitting Simulation . 5-16
5.5.1 Evaluation of the Different Methods 5-17
5.5.2 Modifications to the Code . 5-18
6.0 Probabilistic Failure Analysis 6-1
6.1 Conceptual Model and Mesh Mapping . 6-4
6.2 Computational Simulation Procedure 6-4
6.3 Simulation of Composite Panels . 6-5
6.4 CDF and Sensitivity Analysis of ARA Model With Lap Joint . 6-8
6.5 CFF and Sensitivity Analysis of Crown Panel With 38-inch Saw Cut 6-11
6.6 References 6-15
7.0 Mechanics of 3-D Woven, Braided and Stitched Composites . 7-1
7.1 Methodology for Analytical Simulation of 3D Composites 7-2
7.1.1 Stiffness Properties of Three Dimensional Composites 7-6
7.1.2 Stress and Strength Analysis of Three Dimensional . 7-8
Composites
7.1.3 Woven Patterns . 7-10
7.1.4 Fiber Arrangement 7-11
7.1.5 Three Dimensional Hygrothermoelastic Properties 7-12
7.1.6 Two Dimensional Hygrothermoelastic Properties . 7-15
7.1.7 Stresses in the Primary Domain and in the Weaver Domain . 7-18
7.1.8 The Influence of Fiber Waviness . 7-20
7.2 Results and Discussion of 2D/3D Woven Composites 7-23
7.2.1 Formulation of the Effect of Ply Waviness on Composite 7-25
PropertiesContents
iv
7.3 Simulation of the Woven Composite . 7-27
7.3.1 Conclusion 7-34
7.4 Stitched Simulation Capability . 7-34
7.4.1 Modification of Delamination Criteria Based on Stitching 7-35
7.5 Test of Simulating Stitching Effect on a Composite Panel 7-35
8.0 Impact Loading of Woven/Braided/Stitched Composite Structure . 8-1
8.1 Modification of CODSTRAN for Impact Simulation Including Inertial
Effects of the Impacted Structure . 8-1
8.2 Modification of CODSTRAN for Impact Simulation not Including
Inertial Effects of the Impacted Structure . 8-4
8.3 Results and Discussion 8-4
9.0 Graphics User Interface (GUI) 9-1
9.1 Display of Stress, Strain, Eigen Value and Damage 9-2
9.2 PFA/FEM Attributes Visualization 9-4
9.3 Menu Visualization . 9-9
9.4 Mode of Failure Visualization . 9-10
9.5 Region Picking . 9-12
9.6 Movie of Failure Events 9-15Illustrations
v
E-1 Fiber Architecture Family Created By Different Preform E-2
Fabrication Techniques
E-2 GENOA, a Parallel Processing Software For Structural Analysis
of Polymer Matrix Composites, Utilizes a Hierarchical Multi-Level Approach on
Macro and Micro Scales . E-5
E-3 Contribution of Failure Modes at Damage Initiation, Crack . E-8
Turning and Final Fracture Events
E-4 (a) Tension Test Panel Mounted in the Load Frame, (b) Translaminar E-8
Shear Damage Zones in Tension Test Panel
E-5a Compression Test Panel After Failure . E-9
E-5b View Of Failure Zone Compression Test Panel E-9
E-6 Anti Symmetric Test Limit Loading Applied To SMV Fuselage and wing box . E-10
E-5 Identification of Damaged Nodes Location E-10
1-1 Idealized Fiber Yarn Segment in Unit Cell of 3D Braid Composites . 1-3
1-2 Pop-up Help Balloons Inform The User Reviewing Options Available . 1-4
In This Close-up View Of The Center Of A Model
1-3 A Schematic Diagram of the Principal Elements of the GENOA . 1-5
Progressive Failure Analysis (GENOA-PFA) S/W Package
1-4 Damage Tracking Expressed in Terms of Load vs. Displacement . 1-6
1-5a Fracture Path and Damage Progression with no adaptive Meshing 1-10
(1518 Nodes, 1208 Elements)
1-5b Fracture Path and Damage Progression with adaptive Meshing . 1-10
(2148 nodes, 1707 Elements)
1-6 Total DERR versus Load Comparison of Adaptive Meshing 1-11
and Non-Adaptive Meshing
1-7 Percent Damage Versus Load Comparison of Adaptive 1-11
Meshing and Non-Adaptive Meshing
1-8 DERR Versus Load Comparison of Adaptive Meshing and Non-Adaptive . 1-12
Meshing
1-9 Comparison of Original Damage with Restart damage Versus . 1-13
Load from Simulation of Three Stringer Tension Panel
1-10 Comparison of Original DERR with Restart DERR Versus . 1-13
Load from Three Stringer Tension Panel
1-11 Comparison Of Original and Restart Percent Change In 1-14
Damage Volume Vs. Load From Three Stringer Tension Panel
1-12 Schematics of (A) Layer-to-layer Angle Interlock, (B) Through-the- . 1-15
Thickness Angle Interlock, and (C) Orthogonal Interlock Weaves
1-13 Equivalent Laminate Moduli for Graphite Design . 1-15
1-14 Fiber And Matrix Stress Distributions In Composite System 1-15Illustrations
vi
1-15 Distribution Of Stress To Fiber And Matrix 1-16
1-16 Composite Strength Vs. Applied Stress (Right), & Failed 1-16
Layers In Composite Due To Environmental Loading
1-17 Boeing 747 Aluminum Crown Panel Finite Element Model . 1-17
1-18 Crack Length Growth With Loading Cycles 1-17
1-19 After GENOA Iterations (The Equivalent of 8 x 106 Cycles) 1-18
Complete Fracture Occurred at the Junction of the Vertical Support and
the Air Foil
1-20 Percent of Bond Failure (~50%) is Identified as Green-Yellow Contours 1-18
1-21 The Most Dominant Mode of Damage was Identified as Matrix 1-18
Failure in Transverse Tension
1-22 Stress Concentration Causing the Failure at the Junction 1-18
of the Vertical Support and the Air Foil
1-23 Initial and Reshaped Textile Preform . 1-19
1-24(a) As received Preform Sock of ±45 Orientation was Fitted on . 1-20
a Wind Mill Mandrel
1-24(b) As Received Preform Sock of ±45 Orientation was Fitted on 1-20
a Tip of Wind Mil Mandrel
1-24(c) As Received Preform Sock of ±45 Orientation was Fitted . 1-20
on a Root of Wind Mil Mandrel
1-25 Comparison of Analytical Vs Test Strains Ahead of Crack Tip for 1-21
Compression Panel
1-26 Photoelastic Prediction Provides a Visual Check of Color . 1-21
Contours for Comparison of Test and Simulation Results
1-27 GENOA Graphics User Interface: GENEX, Post Cycle, 3D Plot, 1-23
Xgenoa 2D
1-28 GENOA Post Cycle Tool Bar . 1-23
1-29 An Up-Close View of Default Display Properties Initiated from a 1-23
Pull-Down Menu
2-1 Integrated Computer Code for Simulating Damage Propagation . 2-2
of 3D Woven Composites
2-2 CODSTRAN Sequential Software Flow Diagram 2-3
2-3 CODSTRAN Modular Software Flow Diagram . 2-3
2-4a-e Tracing of the Nodal Normal Calculation in the FEM (MHOST) . 2-9
CODSTRAN Routine
2-5a-b Proposed Preliminary Functional Flow Chart Within Respect . 2-14
of External Pressure Loads
3-1 Schematic Of Mesh Refinement In The First Approach. (a) Original . 3-1
Element With Damaged Node, (b) Element Divided Into Five New ElementsIllustrations
vii
3-2 Schematic Of Mesh Refinement In The Second Approach. (a) Original . 3-2
Element With Damaged Node, (b) Element Divided Into Three New Elements.
3-3 Validation of Adaptive mesh refinement in PFA Simulation of . 3-2
Test specimen No. 1.
3-4 Meshes Generated Without Adaptive Mesh Refinement During . 3-3
FEM Analyses Of Test Specimen No. 1. At Iteration No. (a) 83, (b) 84, And
(c) 85 Or Final Fracture.
3-5 Meshes Generated With Adaptive Mesh Refinement During FEM 3-4
Analyses Of Test Specimen No. 1 At Iteration No. (a) 78, (b). 79, and
(c) 80 Or Final Fracture.
3-6 Normal Stress Distribution In The X-(Longitudinal) Direction . 3-5
Under Tensile Loading As Simulated Without Adaptive Mesh
Refinement For FEM Iteration No. (a) 83, And (b) 84
3-7 Distribution of Normal stress distribution in the x-(longitudinal) 3-6
direction under tensile loading as simulated with adaptive mesh
refinement at FEM Iteration No. (a) 78, and (b) 79
3-8 FEM mesh used for Test Specimen No. 2 in Validation of Adaptive . 3-6
Mesh Refinement in PFA.
3-9 Meshes Generated Without Adaptive Mesh Refinement During . 3-7
FEM Analyses Of Test Specimen No. 2 At Iteration No. (a) 50, (b). 51,
And (c) 52 At Final Fracture.
3-10 Meshes Generated With Adaptive Mesh Refinement During FEM 3-8
Analyses Of Test Specimen No. 2 At Iteration No. (a) 39, (b). 40, And (c) 41
Or Final Fracture.
3-11 Distribution Of Normal Stresses In The X (Longitudinal) . 3-9
Direction For Test Specimen No.2 Under Tensile Loading As
Simulated Without Adaptive Mesh Refinement At FEM Iteration No. (a) 50,
And (b) 51
3-12 Distribution Of Normal Stresses In The X (Longitudinal) . 3-10
Direction For Test Specimen No.2 Under Tensile Loading As
Simulated With Adaptive Mesh Refinement At FEM Iteration No. (a) 39,
And (b) 40
3-13a Damage Energy Rate Versus Applied Load for Specimen No. 1 3-11
With and Without Using Adaptive Mesh Refinement.
3-13b Total Damage Energy Rate Versus Applied Load for Specimen No. 1 . 3-11
With and Without Using Adaptive Mesh Refinement.
3-14a Damage Energy Rate Versus Applied Load for Specimen No. 2 With 3-12
and Without Using Adaptive Mesh Refinement.
3-14b Total Damage Energy Rate Versus Applied Load for Specimen No. 2 . 3-12
With and Without Using Adaptive Mesh Refinement.
3-15 Test Specimen No. 3 Without Adaptive Mesh Refinement, Original Model 3-13
3-16 Test Specimen No. 3 Without Adaptive Mesh Refinement, Damage Initiation . 3-13
3-17 Test Specimen No. 3 Without Adaptive Mesh Refinement 3-13
Damage Propagation, Finite Element No. 75Illustrations
viii
3-18 Test Specimen No. 3 Without Adaptive Mesh Refinement 3-14
Damage Propagation, Finite Element No. 76
3-19 Test Specimen No. 3 With Adaptive Mesh Refinement Damage 3-14
Initiation, Finite Element No. 75
3-20 Test Specimen No. 3 With Adaptive Mesh Refinement Damage 3-14
Propagation, Finite Element No. 76
3-21 Test Specimen No. 3 With Adaptive Mesh Refinement Damage 3-15
Propagation, Finite Element No. 77
3-22 Normal Stress In X-Direction (Longitudinal Direction) σX Distribution . 3-15
Under Tensile Loading Condition Without Adaptive Mesh Refinement
For Two Sequences Of Finite Element Runs. (a) Finite Element No. 75,
(b) Finite Element No. 76
3-23 Normal Stress In X-Direction (Longitudinal Direction) σX Distribution . 3-16
Under Tensile Loading Condition Without Adaptive Mesh Refinement
For Two Sequences Of Finite Element Runs. (a) Finite Element No. 75,
(b) Finite Element No. 76, And (c) Finite Element No. 77
3-24 IAS Boeing Panel Finite Element Model 3-17
3-25 Adaptive Mesh Refinement at Damage Initiation Under Internal . 3-18
Pressure of 8.5 Psi
3-26 Adaptive Meshing At Damage Propagation Under Internal Pressure Of 3-18
8.67 Psi
3-27 Adaptive Meshing At Damage Propagation Under Internal Pressure Of 3-19
8.97 Psi (Stage 1)
3-28 Adaptive Meshing At Damage Propagation Under Internal Pressure Of 3-19
8.97 Psi (Stage 2)
3-29 Adaptive Meshing At Damage Propagation Under Internal Pressure Of 3-20
8.97 Psi (Stage 3)
3-30 Adaptive Meshing At Damage Propagation Under Internal Pressure Of 3-20
8.97 Psi (Stage 4)
3-31 Adaptive Meshing At Damage Propagation Under Internal Pressure Of 3-21
8.96 Psi (Stage 5)
3-32 Adaptive Meshing At Damag E Propagation Under Internal Pressure Of 3-21
8.96 Psi (Stage 6)
4-1 S/N Curve for Aluminum . 4-1
4-2 Schematic of the NASA Lap Joint Test Coupon 4-2
4-3 FEM Mesh of the NASA Test Coupon 4-3
4-4 S/N Curve From Simulation of NASA Test Coupon 4-4
4-5 Material Property Degradation for 7050 Aluminum Plate 4-5
4-6 Damage Initiation Under Cyclic Loading at the Stress Amplitude of . 4-5
KSI AND 84,000 Cycles
4-7 Damage Propagation (Stage 1) Under Cyclic Loading With Maximum 4-6
Stress of 22 ksi at 84,000 +∆1 Cycles.Illustrations
ix
4-8 Damage Propagation (Stage2) Under Cyclic Loading With Maximum . 4-6
Stress of 22 ksi at 84,000 +∆2 Cycles.
4-9 Damage Propagation (Stage 3) Under Cyclic Loading With Maximum 4-6
Stress of 22 ksi at 84000 +∆3 Cycles.
4-10 Damage Propagation (Stage 4) Under Cyclic Loading With Maximum 4-6
Stress of 22 ksi at 84,000 +∆4 Cycles.
4-11 Damage Propagation (Stage 5) Under Cyclic Loading With Maximum 4-7
Stress of 22 ksi at 84,000 +∆5 Cycles.
4-12 Damage Propagation (Stage 6) Under Cyclic Loading With Maximum 4-7
Stress of 22 ksi at 84,000 +∆6 Cycles.
4-13 IAS Boeing Panel Finite Element Model 4-8
4-14 Damage Initiation Under Cyclic Loading With Maximum Internal . 4-8
Pressure of 8.6 ksi at 9,724 Cycles.
4-15 Final Fracture Pattern Under Low Cyclic Loading With Maximum . 4-9
Internal Pressure of 15 ksi at 10,720 Cycles.
4-16 Progressive Fracture Flow Diagram for High Cycle Fatigue . 4-10
4-17 Stiffened Composite Panel and Loading AS-4/HMHS: 48 Plies 4-13
[0/45/90]s6
4-18 Damage Progression under Cyclic Loading AS-4/HMHS: 48 4-13
Plies [0/45/90]{s6, Loaded at 50 Hz Solid line: cyclic load
amplitude of 3.56 kN (0.80 k) Short dashed line: cyclic load
amplitude of 7.83 kN (1.76 k) Long dashed line: cyclic load
amplitude of 16.37 kN (3.68 k)
4-19 First Natural Frequency Degradation under Cyclic Loading 4-14
AS-4/HMHS: 48 Plies [0/45/90]$_{s6$, Loaded at 50 Hz,
Solid line: cyclic load amplitude of 3.56 kN (0.80 k) Short
dashed line: cyclic load amplitude of 7.83 kN (1.76 k) Long
dashed line: cyclic load amplitude of 16.37 kN (3.68 k)
4-20 Second Natural Frequency Degradation under Cyclic Loading 4-14
AS-4/HMHS: 48 Plies [0/45/90]s6, Loaded at 50 Hz,
Solid line: cyclic load amplitude of 3.56 kN (0.80 k) Short
dashed line: cyclic load amplitude of 7.83 kN (1.76 k) Long
dashed line: cyclic load amplitude of 16.37 kN (3.68 k)
4-21 Third Natural Frequency Degradation under Cyclic Loading . 4-15
AS-4/HMHS: 48 Plies [0/45/90]s6, Loaded at 50 Hz
Solid line: cyclic load amplitude of 3.56 kN (0.80 k) Short
dashed line: cyclic load amplitude of 7.83 kN (1.76 k) Long
dashed line: cyclic load amplitude of 16.37 kN (3.68 k)
4-22 Composite Plate Finite Element Model . 4-15
4-23 Damage Progression under Cyclic Pressure Loading AS-4/HMHS: 4-16
4 Plies [±45]s, Pressurization frequency = 50 Hz Long dashed
line: cyclic pressure amplitude = 16 psi Solid line: cyclic
pressure amplitude = 20 psi Short dashed line: cyclic pressure
amplitude = 24 psi
4-24 Time of Fracture with Pressure Amplitude AS-4/HMHS: . 4-16
4 Plies [±45]s, Pressurization frequency = 50 HzIllustrations
x
4-25 First Natural Frequency Degradation with Fatigue Loading . 4-16
AS-4/HMHS: 4 Plies [±45]s, Pressurization frequency = 50 Hz
Long dashed line: cyclic pressure amplitude = 16 psi Solid
line: cyclic pressure amplitude = 20 psi Short
dashed line: cyclic pressure amplitude = 24 psi
4-26 Second Natural Frequency Degradation with Fatigue Loading . 4-16
AS-4/HMHS: 4 Plies [±45]s, Pressurization frequency = 50 Hz
Long dashed line: cyclic pressure amplitude = 16 psi
Solid line: cyclic pressure amplitude = 20 psi
Short dashed line: cyclic pressure amplitude = 24 psi
4-27 Third Natural Frequency Degradation with Fatigue Loading 4-17
AS-4/HMHS: 4 Plies [±45]s, Pressurization frequency = 50 Hz
Long dashed line: cyclic pressure amplitude = 16 psi
Solid line: cyclic pressure amplitude = 20 psi Short
dashed line: cyclic pressure amplitude = 24 psi
4-28 Composite Airfoil Finite Element Model 4-17
4-29 Damage Progression under Cyclic Loading AS-4/HMHS: . 4-18
16 Plies [+45/0/90/-45/90/0]s, Loading frequency = 50 Hz
Short dashed line: cyclic load amplitude = 11.83 N
Medium dashed line: cyclic load amplitude = 13.52 N
Long dashed line: cyclic load amplitude = 15.21 N
Solid line: cyclic load amplitude = 16.90 N
4-30 Number of Cycles to Fracture with Load Amplitude . 4-19
AS-4/HMHS: 16 Plies [+45/0/90/-45/90/0]s, Loading frequency = 50 Hz
4-31 First Natural Frequency Degradation with Fatigue Loading . 4-19
AS-4/HMHS: 16 Plies [+45/0/90/ -45/90/0]s, Loading frequency = 50 Hz
Short dashed line: cyclic load amplitude = 11.83 N
Medium dashed line: cyclic load amplitude = 13.52 N
Long dashed line: cyclic load amplitude = 15.21 N
Solid line: cyclic load amplitude = 16.90 N
4-32 Second Natural Frequency Degradation with Fatigue Loading . 4-19
AS-4/HMHS: 16 Plies [+45/0/90/-45/90/0]s, Loading frequency = 50 Hz
Short dashed line: cyclic load amplitude = 11.83 N
Medium dashed line: cyclic load amplitude = 13.52 N
Long dashed line: cyclic load amplitude = 15.21 N
Solid line: cyclic load amplitude = 16.90 N
4-33 Third Natural Frequency Degradation with Fatigue Loading 4-19
AS-4/HMHS: 16 Plies [+45/0/90/ mp-45/90/0]$_{s$,
Loading frequency = 50 Hz Short dashed line: cyclic
load amplitude = 11.83 N Medium dashed line: cyclic
load amplitude = 13.52 N Long dashed line: cyclic load
amplitude = 15.21 N Solid line: cyclic load amplitude = 16.90 N
4-34 Stiffened Composite Panel Cross-section and Plan 4-21
AS-4/HMHS: 16 Plies [0/45/90]s2 (all dimensions are in mm)
4-35 Stiffened Composite Panel Finite Element Model AS-4/HMHS: . 4-21
16 Plies [0/45/90]s2Illustrations
xi
4-36 Stiffened Composite Panel Damage Progression under Cyclic 4-21
Loading, AS-4/HMHS: 16 Plies [0/45/90]s2 Long dashed
line: cyclic pressure amplitude of 11.64 kPa at 50 Hz
Short dashed line: cyclic pressure amplitude of 23.29 kPa at 50 Hz
Solid line: cyclic pressure amplitude of 23.29 kPa at 70 Hz
4-37 Stiffened Composite Panel First Natural Frequency . 4-21
Degradation with Fatigue Loading AS-4/HMHS: 16 Plies [0/45/90]s2
Long dashed line: cyclic pressure amplitude of 11.64 kPa at 50 Hz
Short dashed line: cyclic pressure amplitude of 23.29 kPa at 50 Hz
Solid line: cyclic pressure amplitude of 23.29 kPa at 70 Hz
5-1 Initial and Reshaped Textile Preform 5-1
5-2(a) Step 1: As received Preform Sock of ±45 orientation to be fitted on . 5-2
a flat mandrel
5-2 (b) Step 2 : Preform Sock of ±45 Orientation Fitted On A Flat Mandrel 5-2
5-2 (c) Step 3: Preliminary fit of Step 2 Achieved Orientation To Be Fitted . 5-2
On A Curved Mandrel
5-2(d) Step 4:Best Fit Orientation Was Achieved And Fitted On A Boeing 5-2
GE90 Mandrel
5-3 Variety of Fabric Structure Such as Woven, Knitted, Braided, & . 5-3
Non-woven Will be Considered for Best Trade Selection
5-4 Current Weave Status of GENOA to Simulate 2D/3D Braided . 5-3
Fiber Architecture to Perform Ply Drop-offs
5-5 The Simulated State Conformance Of A Preform FEM To A . 5-5
Interior Of A Bent Mandrel
5-6 The Simulated State Of Conformance Of A Sock FEM to a 5-5
Exterior of a Mandrel
5-7 Simulated Fiber Orientation Angles in Ply No. 1 After Reshaping . 5-5
5-8 GENOA Current Status to Simulate 2D/3D Braided Fiber Architecture . 5-5
5-9 Computational Simulation Cycle 5-6
5-10 Pushing Loads . 5-6
5-11 Tensile Pulling Loads . 5-6
5-12 Elongation vs. Load With & Without Angle Computation 5-7
5-13 Poisson’s Ratio at Different Elongations For A Rectangular Plane Panel . 5-7
5-14 Contact Condition 5-8
5-15 Load Condition 5-8
5-16 Example of FEM Model of Sock FEM Model Conforming to 5-8
Mandrel (Grey) FEM Model
5-17 Example of FEM Model of Sock Entering FEM Model of . 5-8
Mandrel (Grey) Because of the Lack of a Sufficient Preventive Scheme.
5-18 Fitting of the cylindrical mesh over a cone. (a) Merged bases, . 5-10
(b) Intermediate step, (c) Final mesh.Illustrations
xii
5-19 Favorable comparisons of GENOA Simulation Results With 5-10
General Electric. Experimental Results On Fiber Preform Reshaping Tests
5-20 Damage Progression In Manufactured and [±45] Tubes 5-11
5-21 Computational Simulation Cycle 5-12
5-22 Deformation of an Elementary Box . 5-12
5-23 Fiber Angles for Different Elongation of a Rectangular Plane Panel 5-13
5-24 Poisson’s Ratio at Different Elongation for a Rectangular Plane Panel 5-14
5-25 Sock Over Fan Blade, Initial Geometrical Algorithm . 5-16
5-26 Sock Over Straight Mandrel . 5-18
5-27 Initial Sock and Fan Blade . 5-19
5-28 Step 1 – Fitting the Sock Over a Straight Mandrel 5-20
5-29 Step 2 – Fitting the Previous Sock Over the Fan Blade . 5-20
6-1a (a) GENPAM Probabilistic Software Flow Chart . 6-2
6-1b-c (a) GENPAM Probabilistic Software Flow Chart . 6-3
6-2 Damage Progression under Tension and Compression; . 6-6
Graphite/Epoxy: 48 Plies [0/45/90]s6, Solid lines = Unstitched
Composite, Dashed Lines = Stitched Composite
6-3 Damage Progression Under In-Plane Shear And 6-6
Out-Of-Plane Flexure; Graphite/Epoxy: 48 Plies [0/45/90]S6;
Solid Lines = Unstitched Composite; Dashed Lines =
Stitched Composite
6-4 Cumulative Distribution Function of MDE Failure Criterion . 6-7
for Out-of-plane Flexure of Panels; Graphite/Epoxy: 48 Plies [0/45/90]s6
6-5 Cumulative Distribution Function of End Displacement for 6-7
of-plane Flexure of Composite Panels; Graphite/Epoxy: 48 Plies [0/45/90]s6
6-6 Sensitivities of Uncertainties in Design Variables to 6-8
Composite MDE Failure Criterion; Graphite/Epoxy: 48 Plies [0/45/90]s6
6-7 Sensitivities of Uncertainties in Design Variables to 6-8
Composite Panel End Displacement; Graphite/Epoxy: 48 Plies [0/5/90]s6
6-8 Cumulative Distribution Function Of Circumferential Stress At 6-9
The Rivet On Which Damage Initiated
6-9 Cumulative Distribution Function Of Shear Stress At The 6-9
Rivet On Which Damage Initiated
6-10 Sensitivity Circumferential Stress Skin And Frame Thicknesses . 6-10
6-11 Sensitivity Shear Stress Skin and Frame Thicknesses 6-10
6-12 Cumulative Distribution Function of Circumferential Stress . 6-11
at the Crack Tip Where Damage Initiated
6-13 Cumulative Distribution Function Of Stress In The Direction . 6-12
of Stringers at Crack Tip Where Damage InitiatedIllustrations
xiii
6-14 Cumulative Distribution Function of Shear Stress at 6-12
Crack Tip Where Damage Initiated
6-15 Sensitivity of Circumferential Stress Skin, Stringer and 6-13
Frame Thicknesses
6-16 Sensitivity of Stress In The Stringer Direction Skin, Stringer . 6-13
and Frame Thicknesses
6-17 Sensitivity of Shear Stress to Skin, Stringer and Frame Thicknesses . 6-14
7-1 Idealized Fiber Yarn Segment in Unit Cell of 3D Braid Composites . 7-6
7-2 The Unit Cell Structure of a 3D Braided Structural Composites . 7-7
With Yarns Moving in Three Orthogonal Directions
7-3 The Unit Cell of the “Fiber Inclination Model” Composed of Four 7-7
Unidirectional Laminae
7-4 Schematics of (A) Layer-to-layer Angle Interlock, (B) Through-the- 7-11
Thickness Angle Interlock, and (C) Orthogonal Interlock Weaves.
7-5 Representative Layer Sequence of Fillers and Stuffers Through the 7-11
Thickness, with the Layer Thickness T1 and T2 Defined for the
Case shown
7-6 Schematic of Ply Division in 3D Woven Composites . 7-11
7-7 Wavy Tow Model for Analyzing the Influence of Fiber Waviness on . 7-21
Longitudinal Stiffness of Unidirectional Composites
7-8 Specimen with Three Different Weave Types Stuffers and Wrap 7-25
Weavers Appear as Light Ribbons while Sections of Fillers Appear
as Dark Patches
7-9 Stress-Strain Relations for Graphite/Epoxy Woven and Non-Woven . 7-28
Composite Laminates Subject to Tension and Shear Nx/Nxy = 20.
7-10 Damage Energy with Stress for Graphite/Epoxy Woven and . 7-28
Non-Woven Composite Laminates Subject to Tension and Shear Nx/Nxy = 20.
7-11 Structural Damage with Stress for Graphite/Epoxy Woven and 7-28
Non-Woven Composite Laminates Subject to Tension and Shear Nx/Nxy = 20.
7-12 Stress-Strain Relations for Graphite/Epoxy Woven and 7-28
Non-Woven Composite Laminates Subject to Tension and Shear Nx/Nxy = 10.
7-13 Damage Energy with Stress for Graphite/Epoxy Woven and . 7-28
Non-Woven Composite Laminates Subject to Tension and Shear Nx/Nxy = 10.
7-14 Structural Damage with Stress for Graphite/Epoxy Woven and .
Non-Woven Composite Laminates Subject to Tension and Shear Nx/Nxy = 10.
7-15 Stress-Strain Relations for Graphite/Epoxy Woven and 7-29
Non-Woven Composite Laminates Subject to Tension and Shear Nx/Nxy = 5.
7-16 Damage Energy with Stress for Graphite/Epoxy Woven and . 7-29
Non-Woven Composite Laminates Subject to Tension and Shear Nx/Nxy = 5.
7-17 Structural Damage with Stress for Graphite/Epoxy Woven and . 7-29
Non-Woven Composite Laminates Subject to Tension and Shear Nx/Nxy = 5.Illustrations
xiv
7-18 Effect of Shear on Ultimate Strength for Graphite/Epoxy Woven and 7-29
Non-Woven Composite Laminates Subject to Tension and Shear Nx/Nxy = 5.
7-19 Stress-Strain Relations for Graphite/Epoxy Woven and Non- . 7-30
Woven Composite Laminates Subject to Compression and Shear Nx/Nxy = 10.
7-20 Damage Energy with Stress for Graphite/Epoxy Woven and Non- 7-30
Woven Composite Laminates Subject to Compression and Shear Nx/Nxy = 10.
7-21 Structural Damage with Stress for Graphite/Epoxy Woven and Non- 7-31
Woven Composite Laminates Subject to Compression and Shear Nx/Nxy = 10.
7-22 Stress-Strain Relations for Graphite/Epoxy Woven and Non- 7-31
Woven Composite Laminates Subject to Compression and Shear Nx/Nxy = 5.
7-23 Damage Energy with Stress for Graphite/Epoxy Woven and Non- 7-31
Woven Composite Laminates Subject to Compression and Shear Nx/Nxy =5.
7-24 Structural Damage for Graphite/Epoxy Woven and Non- 7-31
Woven Composite Laminates Subject to Compression and Shear Nx/Nxy = 5
7-25 Effect of Shear on Ultimate Strength for Graphite/Epoxy Woven . 7-32
and Non-Woven Composite Laminates Subject to Compression with Shear
7-26 Short Beam Flexure Specimen for Graphite/Epoxy Woven 7-32
and Non-Woven Composite Laminates Subject to Transverse Loading
7-27 Load Displacement Relations for Graphite/Epoxy Woven and . 7-33
Non-Woven Composite Laminates Subject to Short Beam Transverse Loading
7-28 Damage Energy With Loading for Graphite/Epoxy Woven and Non- 7-33
Woven Composite Laminates Subject to Short Beam Transverse Loading
7-29 Damage Out of Plane Force Relations for Graphite/Epoxy 7-33
Woven and Non-Woven Composite Laminates Subject to
Short Beam Transverse Loading
7-30 Idealized Fiber Stitch Segment in Unit Cell of 3D Braid Composites . 7-35
7-31 Damage Progression Under Tension and Compression; . 7-37
Graphite/Epoxy: 48 Plies [0/+45/-45/90]s6; Solid Lines =
Unstitched Composite, Dashed lines = Stitched Composite
7-32 Damage Progression Under In-plane Shear and 7-37
Out-of-plane Flexure; Graphite/Epoxy: 48 Plies [0/+45/-45/90]s6;
Solid Lines =Unstitched Composite, Dashed Lines = Stitched Composite
8-1 Damaged Node Pattern during Failure 8-5
8-2 Photo-Elastic Isocromatic Pattern at Failure 8-5
8-3 8-3. Stress X at Critical Impact Event Before Failure . 8-5
8-4 Stress X at Critical Impact Event Before Failure . 8-5
8-5 Final Failure 8-5
8-6 Most Contributing Failure (Transverse Tensile) 8-5
8-7 Comparison of Force Vs. Time for Pseudo dynamic and static of PMC Cylinder
impacted by blade 8-6Illustrations
xv
8-8 Comparison of Displacement Vs. Time for Pseudo dynamic and static of PMC
cylinder impacted by blade . 8-6
8-9 Comparison of Velocity Vs. Time for Pseudo dynamic and static of PMC
cylinder impacted by blade . 8-5
8-10 Comparison of Damage Vs. Time for Pseudo dynamic and static of PMC
cylinder impacted by blade . 8-5
8-11 Comparison of DERR Vs. Time for dynamic and static of PMC cylinder
impacted by blade 8-7
8-12 Comparison of TDERR Vs. Time for dynamic and static of PMC cylinder 8-7
9-1 GENOA Graphics User Interface: GENEX, Post Cycle, 3D Plot, Xgenoa2D 9-1
9-2 GENOA Post Cycle Tool Bar . 9-1
9-3 An Up-Close View of Default Display Properties Initiated from a Pull-Down Menu 9-1
9-4(a) The Starting View of an Open Hole Tension FEM Mesh of a Model . 9-4
9-4(b) FEM Mesh Display After Activating All Display Attributes 9-4
9-4 Distribution of Modified Distortion Energy Damage 9-4
9-4(d) Distribution of Y-Moment Generated Stress Mode 9-4
9-4(e) Simultaneous Display of Multiple Properties and Modes on an FEM Mesh . 9-5
9-4(f) FEM Mesh Showing Ply Angle in Color Value Mode with Angle Values Labeled
on Mesh 9-5
9-4(g) FEM Mesh After Selecting Ply Stress Distribution Option 9-5
9-4(h) Boundary Conditions (Xdir) . 9-5
9-4(i) Center Of Gravity (Cg) For Each Element 9-6
9-4(j) Normal FEM Mesh And A Comparison With The Second Displacement FEM . 9-6
9-4(k) FEM Element Number 9-6
9-4(l) Forces Applied On Each Nodal Force Distribution 9-6
9-4(m) FEM Nodes Material Identification (Layer Type) . 9-6
9-4(n) FEM Mesh And Global Coordinate System . 9-6
9-4(o) FEM Node Number . 9-7
9-4(p) FEM Connectivity Normal At Cg . 9-7
9-4(r) Top Ply Schedule Orientation (Ply 1 Angle) . 9-7
9-4(s) Second Ply Schedule Orientation (Ply 2 Angle) . 9-7
9-4(t) Applied Nodal Pressure 9-7
9-4(u) FEM Mesh With Node Thicknesses Given . 9-7
9-4(v) Save Model Changes Into a File 9-8
9-4(w) Rotation View Controlled by X,Y, Z Coordinates . 9-8
9-5(a) Display Menu . 9-9
9-5(b) Edit Menu 9-9Illustrations
xvi
9-5(c) Field Menu . 9-9
9-5(d) Hide Menu . 9-9
9-5(e) Reset Menu 9-9
9-5(f) Window Menu 9-9
9-6(a) Modified Distortion Energy Damage Index 9-10
9-6(b) Distribution Of Upper Surface Isochromatic Photo-Elastic Fringe Pattern 9-10
9-6(c) Distribution Of Upper Surface Isoclinic Photo-Elastic Fringe 9-10
9-6(d) Distribution Of Upper Surface Isoclinic Photo-Elastic Fringe . 9-10
9-6(e) Total Damage Energy Release Rate Vs. Load 9-10
9-6(f) Local Damage Energy Release Rate Vs. Load 9-10
9-6(g) Collapsed Fem Model With Adaptive Meshing 9-11
9-6(h) Fracture Path And Damage Progression With Adaptive Meshing (2148 Nodes,
1707 Elements) 9-11
9-7(a-l) The pick command allows the user to select FEM attributes (nodes) for further
parameter editing . 9-12
9-8(a) Duplicate Nodes 1 9-13
9-8(b) Duplicate Nodes 2 9-13
9-8(c) Duplicate Nodes 4 9-13
9-8(d) Duplicate Nodes 6 Was Added To FEM . 9-13
9-8(e) Duplicate Nodes Have Been Added . 9-13
9-9(a) Normal Default Mode . 9-14
9-9(b) Figure 9-9(b). From (B) Pick A Complete Bound Of Line 9-14
9-9(c) Figure 9-9(c). Activated Region Mode . 9-14
9-9(d) Figure 9-9(d). Pick A Segment Through Nodes Using Polar Angles 9-14
9-9(e) Figure 9-9(e). Pick A Complete Region Of Nodes . 9-14
9-9(f) Figure 9-9(f). Regional Shaded Mode 9-14
9-10(a) Figure 9-10(a). Movie Player . 9-15
9-10(b) Figure 9-10(b). Damage Window 9-15
9-10(c) Figure 9-10 (c) Snapshot 1of Fracture Pattern . 9-15
9-10(d) Figure 9-10 (d) Snapshot 1of Fracture Pattern . 9-15
9-10(e) Figure 9-10 (e) Snapshot 3 of Fracture Pattern 9-16
9-10(f) Figure 9-10 (f) Percent Damage Vs. Force . 9-16
9-10(g) Figure 9-10 (g) Total Damage Energy Release Rate Vs. Load 9-16
9-10(i) Figure 9-10 (i) Local Damage Energy Release Rate Vs. Load . 9-16Tables
xvii
E-1 GENOA-PFA Vs. Other Durability and Damage Tolerance (D&DT) Solutions E-3
E-2 advantages and Disadvantages of D&DT Prediction Methods . E-3
E-3 MC Progressive Failure Simulation Key Multi-disciplinary Features . E-7
E-4 Demonstrated Progressive Failure Analysis (PFA) Capabilities E-10
1-1 Fourteen Damaged Modes Considered In GENOA 1-6
1-2 Summary of Results (NASA Coupon and Crown Panel) . 1-16
From Testing and Deterministic Simulation Analyses
2-1 MHOST FEM Scratch File Utilization . 2-1
2-2 Files Generated by MHOST FEM Module 2-4
2-3 MCOD to FEM Source Code Structure . 2-16
2-4 Coordinate and Nodal Averaged Normal Components from MHOST 2-17
2-5 Coordinate and Nodal Averaged Normal Components from MCOD to FEM . 2-18
2-6 Output of Nodal Running Loads From the COD6-MHOST (SCRA61) 2-18
2-7 Output of Nodal Running Loads From the MCOD to FEM 2-18
2-8 Output of General Forces From the COD6-MHOST (SCRA93) 2-19
2-9 Output of General Forces From the COD to FEM (SCRA93) 2-19
2-10 Intermediate Output From COD6-MHOST (Stored in SCRA78) . 2-19
2-11 Intermediate Output From MCOD to FEM (Stored in SCRA78) . 2-20
2-12 Generalized Nodal Forces From Files SCRA88 After 21 CODSTRAN . 2-21
Interactions
2-13 COD7 Volume of Structure is Computed as .2430864E+01 . 2-23
2-14 COD7MM+MHOST Volume of Structure is Computed as .2430864E+01 2-24
4-1 Test and Predicted Cycles to Failure vs Maximum Stress . 4-3
4-2 Summary of Results From Testing and Deterministic 4-7
Simulation Analyses
7-1 Designation of Woven Composite Types . 7-24
7-2 Fiber Volume Fraction of Specimen Considered . 7-24
7-3 Contribution of Stitched Fibers to Delamination Failure Criteria 7-36
9-1 Visualization of PFA STRESS, STRAIN, DAMAGE DATA . 9-2
9-2 Visualization of PFA STRESS, STRAIN, DAMAGE DATA
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