A Fatigue Analysis for Lithium-ion Batteries Michael A. Stamps and Hsiao-Ying Shadow Huang

Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC Introduction and Background

Simulation Method and Results for LiFePO4

Conclusion

!! Batteries provide the vital storage link between energy generation and consumption around the world.

!! Energy demand is increasing, thus new

generation facilities are being built and require large scale batteries to store energy for future transmission or backup power.

!! Oil prices and CO2 emissions are also

increasing, driving the need for transportation alternatives (EV and PHEV).

Objective Energy Storage Need

EV, PHEV, and Gas vehicle comparison for Operation Cost & CO2 Emission per 15k miles driven.

Fracture and Fatigue Analysis

World oil consumption and price projected to rise at a relatively constant rate [1].

Applications

!! Choose LiFePO4 due to long cycle life (~2000 cycles), wide op. temps. (-20 to 60oC) and superior thermal stability (safe, incombustible cells).

!! Varying sized particles with varied initial crack sizes (nm scale) are analyzed via fracture mechanics.

!! Plane Stress, plate-like particles are used with loading according to misfit strains (observed during lithium insertion, FePO4 " LiFePO4).

!! Mode dependent stresses , Strain Energy Release Rates (G), and Stress Intensity Factors (K) are calculated using ANSYS software.

Crack between phases

-0.5

0.5

1.5

2.5

3.5

4.5

5.5

6.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

G (N

/m)

L/d

Strain Energy Release Rate 200nm x 90nm size

GI

GII

Gtotal

!"#$%&'&(&)*+,,-./,01.&

,/2*+,,&

./2*+,,&

3/2*+,,&

4/2*+,,&

1/2*+,,&

0/2*+,,&

5/2*+,,&

2/12& 2/02& 2/52& 2/)2& 2/62& ,/22& ,/,2&

!"#$"%

!&'(!

Fatigue Life Estimate LiFePO4

)*#+,!-./,00!

Bibliography

Simulation Set-Up for 2-Phase interface

Mode Dependent Stresses

Mode I dominance

increases as the crack grows.

!! G is the crack driving force. !! An Energy Approach is applied to

calculate da/dN and create a fatigue life estimate fit to the Paris law.

!! If G > 2!, propagation may occur. !=particle surface energy on the crack faces

!! Cycles to failure (Nf) can be calculated iteratively based on initial crack size.

As it is known batteries experience capacity loss (power loss) over time as the electrode materials degrade, this research investigates the effects of cycling induced stresses and fatigue on LiFePO4 cathode (positive electrode) particles to elucidate an understanding for crack propagation and fracture.

From Literature [2]

0

400

800

1200

1600

2000

0 0.2 0.4 0.6 0.8 1

Cyc

les

Initial Flaw Size (L/d)

Cycles to Failure

Nf

Good

Marginal

Insufficient

Colors represent HEV requirements [3].

[1] Data for this figure compile from: U.S. Energy Information Administration (EIA), 2011. [2] Gabrisch et al, Electrochemical and Solid State Letters, 11(3), A25-A29, 2008. [3] United States Council for Automative Research LLC (USCAR), "U.S. Advanced Battery Consortium: Energy Storage System Goals”, 2012.

!! Crack propagation and fracture is highly dependent on mode (I or II), misfit %, and particle size.

!! Smaller particles show reduced G (crack driving force). Max is always near L/d=0.5.

!! Fatigue cycle life estimate of 1800 cycles is fairly consistent with manuf. reported value (2000).

!! Understanding what happens at the nm-scale provides insight into what bulk-scale modifications could be made to improve the performance and life of batteries.

!! Histology were prepared with H&E stains. Photomicrographs were obtained via an optical microscope.

!! Circumferential aligned collagen fibers were notable in pulmonary valve leaflets.

!! The non-linear anisotropic, and heterogeneous nature of heart valve extracellular matrix is incorporated into our FEA.

A Synergistic Approach to Visualize and Understand Tissue-Cell Mechanical Interactions

Siyao Huang and Hsiao-Ying Shadow Huang Mechanical and Aerospace Engineering Department, North Carolina State University, Raleigh, NC

Introduction and Background

Methods and Results

Discussions and Conclusion

Microstructural Evolutions via Finite Element Simulations

Stress Distributions in Heart Valve Tissues P

ulm

onar

y va

lve

leaf

let,

en-fa

ce, 4

00x.

Current Knowledge: Heart valves constantly experience different stress states during cardiac cycles. Current Limitations: How tissue-level mechanical forces can translate into altered cellular stress states is unknown, which hinders a better understanding of the relationships between the mechanical stimuli, cellular mechanotransduction, cell migration, matrix synthesis, and tissue remodeling.

!! Biaxial testing was conducted via a BioTester 5000 (CellScale, Waterloo, CAN).

!! Porcine pulmonary valve (PV) Leaflet samples were tested circumferentially (x-axis) and radially (y-axis).

!! Cellular mechanotransduction might be directional-dependent due to higher stresses are observed in the circumferential direction via our finite element analyses. !! Current study provides new models for better understanding tissue-cell interactions in heart valves. !! Stress distribution is highly emphasized as a result of biomechanics related to collagen secretion, tissue structure integrity and remodeling influenced by mechanical forces. !! Virtual experiments of heart valve tissues provide translational models to clarify the force transmission roles of heterogeneously distributed collagen fibers and the force

receiving roles of randomly distributed cells in the matrix.

Objectives: Capturing the true micro-structure of collagen fibers is key to understand how forces are being transferred to the cellular-level. !! To investigate stress distributions in heart

valve tissues via an automated finite element analysis (FEA).

!! To establish the relations between stresses around cells and measured cell nuclei deformation for better understanding cell mechanobiology.

!!The tissue sample is divided into 9 overlapping regions. The cell is selected in the region 2 with the defined boundary. !!!c is higher than !R, suggesting higher cellular activity may occur along the preferred fiber direction.

Collagen fiber nonlinear anisotropy mechanical property is due to the ECM microstructure

4 m

m

4 mm (a) BioTester (b) Tungsten rakes

stretched PV leaflet

CCD camera

(c)

Strain (%)

Stre

ss (k

Pa)

Histological photo-micrographs

10 µm

50 µm

FEA mesh and skeleton

Biaxial stretching simulation

!! In the circumferential direction, point A has a higher stress value than B because the strain energy on the boundary of tissue is higher than the middle. !! In the radial direction, C is closer to the boundary, so that C receives higher energy, hence it has a higher peak stress, comparing to point A.

Stress Evolutions around a Cell in Heart Valve Tissues

!xx

!! The corresponding mechanical stress distributions under biaxial stretching around cells are computationally calculated via FEA.

!! The feature of inhomogeneous microstructure is apparently illustrated, and most local peak stresses are located around nuclei.

!! Higher mechanical stimulation occurs around the boundary, rather than in the belly area of the heart valve; therefore, cellular activities could be stronger around the boundary.

!! Phase boundary is experimentally observed aligned with bc plane.

!! Phase boundary moves along the a-direction, while lithium diffusion is along the b-direction.

!! An interfacial zone with a finite thickness exists between FePO4 and LiFePO4 phase.

!! Strain energy affected phase transformation

path (Simulation approach: Anisotropic thermal expansion)

A Diffusion Model in a Two-Phase Interfacial Zone for Nanoscale Lithium-ion Battery Materials

Cheng-Kai ChiuHuang and Hsiao-Ying Shadow Huang Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC

Introduction and Background

Methods and Results

Discussions and Conclusion

Phase Boundary Movement An Anisotropic Diffusion Model

!! Mechanical stress evolution is related to the lithium diffusion and phase transformation path in the particle. !! The interfacial zone is formed due the strain energy and lithium diffusion mainly happens in this area. !! During discharging, the diffusion channels are fully filled progressively while the interfacial zone sweeps through the particle along the a-direction. !! This anisotropic diffusion model helps explain the diffusion process in a single LiFePO4 particle and contributes to a better prediction of the stress development.

!! Accumulated strain energy indicates that the phase boundary movement along the a-axis is favored. !! Based on the simulation and avialable experimental data, we assume the diffusion mainly happens in the interfacial

zone. !! A single particle could be considered as a combination of many diffusion channels. !! The lithium-ion concentration profile in each channel within the interfacial zone could be calculated by 1D Fick’s law.

The Needs for Lithium-ion Batteries : e.g. Energy storage units for electronic products and transportation (EVs/PHEVs).

Motivations: !! Capacity loss during high charging/discharging rate. !! Experimentally observed particle fracture. !! A need for anisotropic diffusion model for LiFePO4. Characteristics of Lithium-Iron-Phosphate (LiFePO4): !! One dimensional lithium diffusion (along b-axis). !! Two phase system, Li-rich phase (LiFePO4) and Li-poor

phase (FePO4). !! Anisotropic volume change.

2

2

( , ) ( , )i ii

c x t c x tDt x

! !=! !

-200

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Stre

ss (k

Pa)

Strain

Stretched Sample-2 Stress vs. Strain

2s2 0-Degrees, X-Direction 2s2 0-Degrees, Y-Direction 2s2 30-Degrees, X-Direction 2s2 30 Degrees, Y-Direction 2s2 60-Degrees, X-Direction 2s2 60-Degrees, Y-Direction

n=4

Time

Biomechanical Properties of Skin

Taylor Gettys and Hsiao-Ying Shadow Huang Mechanical and Aerospace Engineering Department, North Carolina State University, Raleigh, NC

Introduction and Background

Methods and Results

Discussions and Conclusion

Directional Mechanical Properties via Biaxial Testing Directional Mechanical Properties in Skin Tissues

Current Knowledge: Collagen fibers arrangements within skin tissue determine its strength and its anisotropic behavior. Current Limitations: How subjecting skin to stretching changes its biomechanical properties is unknown. Subjecting skin to stretching could reduce the anisotropic properties of skin, creating uniform material properties benefiting many medical applications.

!! Reducing anisotropic properties, which eliminates weaknesses, occurs after skin tissue experiences an expansion processes. The expanded skin better serves patients in need of skin graft operations. The current study provides new methods for determining and comparing the directional mechanical properties of skin tissue.

!! The collagen fiber distribution in skin tissue becomes more homogeneous by subjecting samples to stretching, indicated by the similar material strengths in the X and Y-directions from the results of biaxial testing; however, preferred collagen alignment directions still exist.

!! Longer periods of stretching may have a more significant affect on the reduction in anisotropic properties.

Objectives: Determining the directional mechanical characteristics of skin tissue is key to understanding how the collagen arrangement affects the mechanical properties of skin tissue.

!! To investigate the relationship between collagen fiber orientation and tissue strength via biaxial testing.

!! To understand why subjecting skin to stretching has directional mechanical properties. Primarily, the difference in anisotropic properties are determined by comparing non-stretched and stretched samples.

Equipment: !! Biaxial testing was

conducted via a BioTester 5000.

!! Porcine epidermis 4 mm square skin samples were tested bi-axially.

Dis

plac

emen

t Procedure: !! Skin samples were stretched from 0% strain

to 35% to 0% over 30 second time period. !! 3 different skin samples were considered: !! Un-stretched !! Stretched 1, experienced the most stretch !! Stretched 2, experienced less stretch

!! Stretched samples were subjected to stretching for 24hrs in balloon tissue expander.

!! Each sample was tested five times at 0 degrees, 30 degrees and 60 degrees. Only tests 2-5 were considered.

!! Collagen fibers are distributed randomly within skin tissue. !! When stretched, fibers align in a preferred direction, which

causes the anisotropic properties.

-100

0

100

200

300

400

500

600

700

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Stre

ss (k

Pa)

Strain

Un-stretched Sample Stress vs. Strain

1s1 30-Degrees. X-Direction 1s1 30-Degrees, Y-Direction 1s1 60-Degres, X-Direction 1s1 60-degrees, Y-Direction 1s1 90-Degrees, X-Direction 1s1 90-Degrees, Y-Direction

n=4

-200

0

200

400

600

800

1000

1200

1400

1600

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Stre

ss (k

Pa)

Strain

Stretched Sample-1 Stress vs. Strain

2s1 0-Degrees, X-Direction 2s1 0-Degrees, Y-Direction 2s1 30-Degrees, X-Direction 2s1 30-Degrees, Y-Direction 2s1 60-Degrees, X-Direction 2s1 60-Degrees, Y-Direction

n=4

!! Corresponding stress and material stiffness was calculated for each samples’ rotation.

!! Samples’ mechanical properties become most anisotropic and non-linear in Zone 3.

!! Comparing material stiffness of the preferred and cross-fiber directions in Zone 3 indicate reduced anisotropic properties.

Forc

e Fo

rce

Time

Displacement

Stretch 15 sec

Release 15 sec

e1 e2

(c) 60-degree (a) 0-degree (b) 30-degree A relaxed tissue sample

Collagen fibers

(II) Mode I/II/III fractures caused by the accumulated dislocations

A Dislocation Based Stress Development in Lithium-ion Batteries Yixu Richard Wang and Hsiao-Ying Shadow Huang

Department of Mechanical and Aerospace Engineering, North Carolina State University

Introduction Method & Results

Bibliography

Conclusion The Needs for Li-ion Batteries

!! Energy storage is becoming a vital link between energy supply and demand. !! Portable electronic devices require batteries with high volumetric energy density. Electric drive transportations require batteries with high gravimetric energy density. !! Li-ion battery has both high volumetric & gravimetric energy densities[1].

!!We reported three different lithium intercalation-induced dislocation mechanisms explaining experimental observed cracks.

!!It is observed that mechanical stresses between two edge dislocations could be minimized when they are orthogonal to each other. !!The force field might be one key factor that push and attract lithium ion in the crystal and results in the capacity fade. !!The results provide links between stress fields and the observed structural failure in lithium-ion batteries.

!! Battery Components: Electrolyte, Separator, Anode, Cathode (LiCoO2, LiNiO2, LiMn2O4, LiFePO4

[2]).

Lithium-ion diffuse in the b-direction.

Stress Field for Multiple Edge and Screw Dislocation

Lithium Ion Diffusion and Dislocation Formation

[1] J. M. Tarascon, M. Armand, Nature, 414, A359-A367, 2001. [2] Sung-Yoon Chung, Jason Bloking and Yet-Ming Chiang, Nature Materials, pp. 123 - 128, 2001. [3] Ming Tang, Hsiao-Ying Shadow Huang, N. Meethong, Yu-Hua Kao, W. Craig Carter and Yet-Ming Chiang, Chemistry of Materials, 21, pp 1557-1571, 2009. [4] Chen, G., Song, X., and Richardson, T. J., 2006, "Electron Microscopy Study of the LiFePO4 to FePO4 Phase Transition," Electrochemical and Solid-State Letters, 9(6) pp. A295-A298. [5] Maxisch, T., & Ceder, G. (2006). Elastic properties of olivine LixFePO4 from first principles. Physical Review B, 73(17), 174112. doi:10.1103/PhysRevB.73.174112 [6] Indenbom, L.,. (1992). In Lothe J. (Ed.), Elastic strain fields and dislocation mobility Amsterdam ; New York : Elsevier Science Publishers ; New York, NY, USA [7] Hull, D., & Bacon, D. J. (2001). Introduction to dislocations (4th ed.). Oxford Oxfordshire ; Boston: Butterworth-Heinemann.

!!Stress variations for arbitrary dislocation directions are investigated. !!Dislocation 2 remains its Burger’s vector as (bx=1, by=0), while the dislocation1 rotates from 0˚ to 90˚ !!Superposition method issued to obtain the stress field of multiple dislocations in anisotropic LiFePO4 material. !!The stress fields manifesting between dislocations are numerically calculated via Mathematica.

Dislocation 1 rotation

Multiple dislocations present in particles

LiFePO4 as a modeling system. Cracks along c-axis is observed[4].

(I) Kinetics of the dislocation formation due to Li-diffusion

Stre

ss fi

eld[

5][6

] Fo

rce[

7] [F]12 =

[! ]1[b]2! [n]!! Formation of volume misfit due to the coherent interface[3]. Dislocations are induced during (dis)charging.

Multiscale Interactions of Mechanics, Microstructures, and Composition of Heart Valve Tissues

Brittany N. Balhouse1, Ashutosh Garg2 and Hsiao-Ying Shadow Huang2,3 1Biomedical Engineering, 2Aerospace Engineering, 3Mechanical Engineering, North Carolina State University, Raleigh, NC

Introduction and Background

Method and Results

Discussion

Aortic valve 400x Pulmonary valve 200x

Mechanical Testing Cellular Analysis Biochemical Analysis

________ 3 cm

The valvular interstitial cell cytoskeleton. Actin filaments are shown in green and the cell nuclei are in blue.

BioTester 5000

Tungsten BioRakes

Pulmonary valve sample, relaxed

5mm

Porcine heart Pulmonary valve leaflets Anatomy of the heart4 Method of dissection

[1] American Heart Association. [2] Courtesy of Chung, M.K., and Rich, M.W. Alcohol Health and Research World 14(4):269–276, 1990.

Pulmonary valve sample, stretched

5mm

5mm

5mm

5mm

___ 10 !"

Pulmonary valve, Masson’s stain, 1000x

Aortic valve, en-face, 400x

Pulmonary valve, en-face, 400x

15 !" 10 !"

10 !"

_ 60 !m

Pul

mon

ary

valv

e le

afle

t

Aor

tic v

alve

leaf

let

Fibrosa

Cross-sectional view 400x

Spongiosa

Ventricularis

_ 60 !m

!! Objective: Investigated the relationship of mechanical property, collagen fibers microstructure, and collagen concentrations in aortic and pulmonary semilunar valves.

!! Approximately 250,000 heart valve disease in USA in 2010[1]. Stenosis and insufficiency are the most common heart valve diseases, which are related to the mechanics of heart valves. !! Method of dissection:

1.! Each valve has three leaflets. Cartesian coordinate system was set before dissection.

2.! Leaflet samples were relaxed in HBSS for the physiological condition.

!! Function of heart valves: 1.! allow blood to flow through the heart smoothly. 2.! prevent retrograde flow of blood.

!! Biaxial testing was conducted via a BioTester 5000 (CellScale, Waterloo, CAN). !! ~7mm x 7mm sample were cut from leaflets. !! Samples were mounted and tested circumferentially (x-axis) and radially (y-axis). !! Evenly distributed boundary conditions were provided, which eliminates the variability between sample sizes. !! Aortic valves are stiffer in the circumferential direction. !! A greater variance in the directional strength of the aortic valve than in the pulmonary valve was found.

!! Tissue-Level: •! Histology were prepared with Masson or H&E stains. Photomicrographs were obtained via Leica DMLB Microscope. •! Circumferential aligned collagen fibers were notable in aortic valve leaflets. !! Cellular-Level: •! Immunohistochemical samples were prepared for a confocal microscope. •! Direction of actin filaments follows the nuclei long-axis.

!! A relationship exists between the mechanical strength, collagen fiber microstructure, and collagen concentration of a valve leaflet. !! Semilunar valve tissues have nonlinear anisotropy material properties due to the heterogeneous collagen fiber microstructure. !! A higher collagen concentration may be related to greater mechanical strength and may be location dependent. !! The mechanical property of semilunar valve tissues do not depend only on collagen concentration but how collagen fibers are arranged structurally at the microscopy level.

The valvular interstitial cell cytoskeleton

!! Collagen extracted from a leaflet sample into solution (0.5M acetic acid: distilled water = 0.029:1 & 50mg Pepsin A), dyed, centrifuged, and dissolved in Alkali reagent. !! A spectrophotometer and standard curve were used to calculate the concentrations. !!Use of distilled water and collagen extraction time may have substantial effects on results !!Higher collagen concentrations were observed on edge regions than on belly regions of PV leaflets (AV leaflets provided inconsistent location-dependent results)