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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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Incorporate Damage




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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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Deformed View


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Incorporate Damage




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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%)


0 . 1

3 5 m 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%)


0 . 1

3 5 m 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%)


0 . 1

3 5 m 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%)


0 . 1

3 5 m 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%)


0 . 1

3 5 m 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%)


0 . 1

3 5 m 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%)


0 . 1

3 5 m 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%)


0 . 1

3 5 m m




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Incorporate Damage




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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!