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Relationships Among Microstructural Featuresand Crack Propagation in Osteonal BoneIdentified Using Finite Element Analysis
Erin K. Oneida, Marjolein C.H. van der Meulen, Anthony R. Ingraffea
Cornell University
Ithaca, NY
12 th International Conference on FractureOttawa, CanadaJuly 12-17, 2009
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Outline
Motivation
Review
Objective Research Procedure
Results Discussion
Acknowledgements
(Mohsin et al., 2006)
Crack PropagatingAroundMicrostructuralFeature
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Motivation
Each year, 2 million Americans over age 50 suffer a skeletal fracture 1
Increased mortality 2 Related financial costs of more than $17 billion 1
Understanding relationships among geometry, material properties,and damage propagation could explain fracture risk and providedirection for preventative treatment development
1. Burge et al ., 2007 2. Center et al ., 1999
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Cancellous Bone
Cortical BoneOsteon Haversian
Canal
Lamella
3-7 m10-500 m
Bone: Complex, Hierarchical Material
Osteon HaversianCanal
Cross-section of cortical bonemicrostructure
150 mFemur(cm)
(Rho et al. , 1998 and Rho et al., 2002 )
InterstitialBone
Einterstitial > Eosteonal
CementLine
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Femoral Fracture 4
(cm)
Crack in Humerus 2
(m)
Atomic Separation 1
(angstrom)
1. Abraham et al ., 1998 2. Nalla et al. , 2003 3. Mohsin et al. , 2006 4. Perren, 2002
Fracture Events at Different Length Scales
Crack Around Osteon 3
(mm)
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Response upon encountering an osteondepends on crack length (Mohsin et al ., 2006):
100 m or less = stopped at cement lines 100-300 m = deflected at cement lines 400 m = able to penetrate cement lines
100 m
Osteon
Osteon
Crack Propagation Affected by Microsctructure
(Koester et al ., 2008)
A B C D
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Objective
To use computational modeling together with detailedexperimental data to identify the relationships amongmicrostructural features and damage evolution in cortical bone
100 m
+ Explain?
FE Model Experimental Data Crack Propagation Behavior
at the Microscale
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Research Plan Overview
Develop Representative Finite ElementModels
Incorporate Damage
Propagate Damage According toSpecific Criteria
Identify Relationships Among Geometry,Material Properties, and Damage Evolution
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From Data to Digital Bone
INPUT: Osteon Geometry : Radii: Outer, Haversian canal, lamellar layer Material Properties : Different elastic moduli for each region And More : Porosity, osteon percent area
Finite Element Model
(Rho et al., 2002)
Experimental Data
Developed code for automatic generation of cortical microstructure
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Examples of Generated Digital Bone
1 2
3 4
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Geometry :PorosityHaversian Canal DiameterOsteon DiameterOsteon % Area
Material Properties:EinterstitialEosteonal
Model and mesh generated in a few min. on
desktop computer
Osteon
Have rsian Canal
Microstructure Parameters of Interest
1 m m
Interstitial Bone
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Applied Boundary Conditions
1 m m
0.0625 mm thick
Plane
Displaced0.005 mm
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Research Plan Overview
Develop Representative Finite ElementModels
Incorporate Damage
Propagate Damage According toSpecific Criteria
Identify Relationships Among Geometry,Material Properties, and Damage Evolution
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Damage Incorporation Example
Penny-shaped crack template (radius = 0.06 mm) inserted using FRANC3D/NG (finiteelement-based fracture mechanics software developed in-house)
Crack explicitly represented as a geometric discontinuity and adaptive re-meshingemployed
CrackTemplate
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Penny-shaped crack template (radius = 0.06 mm) inserted using FRANC3D/NG (finiteelement-based fracture mechanics software developed in-house)
Crack explicitly represented as a geometric discontinuity and adaptive re-meshingemployed
Damage Incorporation Example
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Penny-shaped crack template (radius = 0.06 mm) inserted using FRANC3D/NG (finiteelement-based fracture mechanics software developed in-house)
Crack explicitly represented as a geometric discontinuity and adaptive re-meshingemployed
Damage Incorporation Example
Deformed View
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Research Plan Overview
Develop Representative Finite ElementModels
Incorporate Damage
Propagate Damage According toSpecific Criteria
Identify Relationships Among Geometry,Material Properties, and Damage Evolution
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Damage Propagation Framework
: Increment of Crack Growthat th Point
: Mode I Stress IntensityFactor at th Point
IN: Modelwith InitialCrack
Repeat CrackGrowth?
OUT: Model withGrown Crack
Finite ElementAnalysis
Compute Parameters of Interest
e.g., Stress Intensity Factors(KI, KII, KIII)
2
mean
i I
giveniK
K aa
i
Grow Crack Front According to ChosenGrowth Rule
e.g., Linear Elastic Fracture Mechanics:
i
I K
iai
AutomaticRe-meshing
YES
NO
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Initial Crack
Edge View(Deformation Scale Factor = 10)
Uniform Applied Displacement (1 m)
0 . 1
3 5 m m
+4.417e+02
+1.112e+03
+3.833e+02
+5.000e+02
+2.667e+02
+3.250e+02
+1.500e+02+2.083e+02
+3.333e+01+9.167e+01
-2.500e+01-8.333e+01-1.417e+02-2.000e+02
-2.695e+02
33 , MPa
(Avg: 75%)
Crack Growth Illustration
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Crack Grown 1 Step
+4.417e+02
+1.112e+03
+3.833e+02
+5.000e+02
+2.667e+02
+3.250e+02
+1.500e+02+2.083e+02
+3.333e+01+9.167e+01
-2.500e+01-8.333e+01-1.417e+02-2.000e+02
-2.695e+02
33 , MPa
(Avg: 75%)
Edge View(Deformation Scale Factor = 10)
0 . 1
3 5 m m
Crack Growth Illustration
Uniform Applied Displacement (1 m)
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Crack Grown 3 Steps
+4.417e+02
+1.112e+03
+3.833e+02
+5.000e+02
+2.667e+02
+3.250e+02
+1.500e+02+2.083e+02
+3.333e+01+9.167e+01
-2.500e+01-8.333e+01-1.417e+02-2.000e+02
-2.695e+02
33 , MPa
(Avg: 75%)
Edge View(Deformation Scale Factor = 10)
0 . 1
3 5 m m
Crack Growth Illustration
Uniform Applied Displacement (1 m)
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Crack Grown 2 Steps
+4.417e+02
+1.112e+03
+3.833e+02
+5.000e+02
+2.667e+02
+3.250e+02
+1.500e+02+2.083e+02
+3.333e+01+9.167e+01
-2.500e+01-8.333e+01-1.417e+02-2.000e+02
-2.695e+02
33 , MPa
(Avg: 75%)
Edge View(Deformation Scale Factor = 10)
0 . 1
3 5 m m
Crack Growth Illustration
Uniform Applied Displacement (1 m)
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Crack Grown 4 Steps
+4.417e+02
+1.112e+03
+3.833e+02
+5.000e+02
+2.667e+02
+3.250e+02
+1.500e+02+2.083e+02
+3.333e+01+9.167e+01
-2.500e+01-8.333e+01-1.417e+02-2.000e+02
-2.695e+02
33 , MPa
(Avg: 75%)
Edge View(Deformation Scale Factor = 10)
0 . 1
3 5 m m
Crack Growth Illustration
Uniform Applied Displacement (1 m)
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Crack Grown 5 Steps
+4.417e+02
+1.112e+03
+3.833e+02
+5.000e+02
+2.667e+02
+3.250e+02
+1.500e+02+2.083e+02
+3.333e+01+9.167e+01
-2.500e+01-8.333e+01-1.417e+02-2.000e+02
-2.695e+02
33 , MPa
(Avg: 75%)
Edge View(Deformation Scale Factor = 10)
0 . 1
3 5 m m
Crack Growth Illustration
Uniform Applied Displacement (1 m)
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Crack Grown 6 Steps
+4.417e+02
+1.112e+03
+3.833e+02
+5.000e+02
+2.667e+02
+3.250e+02
+1.500e+02+2.083e+02
+3.333e+01+9.167e+01
-2.500e+01-8.333e+01-1.417e+02-2.000e+02
-2.695e+02
33 , MPa
(Avg: 75%)
Edge View(Deformation Scale Factor = 10)
0 . 1
3 5 m m
Crack Growth Illustration
Uniform Applied Displacement (1 m)
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crk8
Crack Grown 7 Steps
+4.417e+02
+1.112e+03
+3.833e+02
+5.000e+02
+2.667e+02
+3.250e+02
+1.500e+02+2.083e+02
+3.333e+01+9.167e+01
-2.500e+01-8.333e+01-1.417e+02-2.000e+02
-2.695e+02
33 , MPa
(Avg: 75%)
Edge View(Deformation Scale Factor = 10)
0 . 1
3 5 m m
Crack Growth Illustration
Uniform Applied Displacement (1 m)
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Crack Grown 8 Steps
+4.417e+02
+1.112e+03
+3.833e+02
+5.000e+02
+2.667e+02
+3.250e+02
+1.500e+02+2.083e+02
+3.333e+01+9.167e+01
-2.500e+01-8.333e+01-1.417e+02-2.000e+02
-2.695e+02
33 , MPa
(Avg: 75%)
Edge View(Deformation Scale Factor = 10)
0 . 1
3 5 m m
Crack Growth Illustration
Uniform Applied Displacement (1 m)
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Research Plan Overview
Develop Representative Finite ElementModels
Incorporate Damage
Propagate Damage According toSpecific Criteria
Identify Relationships Among Geometry,Material Properties, and Damage Evolution
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Parameter Study: 3 Variations
GeometryPorosity 1: 5.5%Haversian Canal Diameter 2: 58.8 mOsteon Diameter 3: 246.8 mOsteon % Area 1: 41.0 %
Material Properties
Einterstitial1
: 25 GPaEosteonal : 25 GPa
Model #1 (Reference Model)
Geometry
Porosity: 5.5%Haversian Canal Diameter: 58.8 mOsteon Diameter: 246.8 mOsteon % Area: 41.0%
Material PropertiesEinterstitial : 25 GPaEosteonal : 12.5 GPa
Model #2 (Vary Materials)Geometry
Porosity: 12.7%Haversian Canal Diameter: 117.6 mOsteon Diameter: 246.8 mOsteon % Area: 41.0%
Material PropertiesEinterstitial : 25 GPaEosteonal : 25 GPa
Model #3 (Vary Geometry)
1. Rho et al., 2002 2. Wang and Ni, 2003 3. Wachter et al. , 2002
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Model #1 (Reference Model)
Model #2 (Vary Materials) Model #3 (Vary Geometry)
Parameter Study: 3 Variations
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Parameter Study: Methods Overview
Generate
ModelApply BCs Insert Crack FE Analysis
Grow Crack
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Results: Crack Front After 1 Growth Step
Canal (Models #1 and #2)
Canal (Model #3)
Osteon
Outer BoundaryCrack
X Coordinate (mm)
Y C o o r d i n a t e
( m m
)
Original Crack Front
Model #2 Crack Front
- - -Model #1 Crack Front
Model #3 Crack Front
Osteonal BoneInterstitial Bone
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Discussion of Results
Variation in crack front growth apparent between Models #1 and #2-When inside an osteon, crack grew less when modulus was lower
Future Studies will explore : Additional variations in material properties and geometry
apparent at the microscale
Different crack growth formulations (e.g., cohesive zone modeling) Variations in crack orientation, size, and number of cracks Different loading scenarios
Same crack front growth observed in Models #1 and #3
Cracks behaved as expected in all models for given loading scenario
Ultimately, developed modeling capabilities will be validated using
experimental data related to crack growth at the microscale
-Due to loading conditions and crack location, different radius had no effect
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Overall Discussion
Modeling framework created and used to study crack propagationin bone at the microscale: Model generation tool allowed for quick creation of variable
digital models of bone
Cracks were successfully inserted and grown according to chosencriteria Small parametric study allowed for investigation of effects of
material property and geometry variations on crack growth
With basic tools in place, a broader parametric investigation canbe performed in the future
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Acknowledgements
Thanks for financial support: Ross-Tetelman Fellowship Cornell Center for Materials Research (NSF DMR 0089992) NIH Grant AR 053571
Thanks for technical assistance: Dr. Bruce Carter Dr. Paul Wawryznek
Cornell Fracture Group Members
Thank-you for your time!