mcHf Iref Ire

Cobalt alloyStentMicrostructureModelling

s haicrfati

crack initiation (FCI). A multi-scale CoCr stent model is developed, including a 3D global J2 continuum

ateriaincludirings [

prediction is a necessary design requirement. L605 fatigue life data

studies have been reported for this alloy. Stress-life data has beenpublished for notched L605 specimens in a study on the use ofultrasonic methods for detecting cracks in fatigued specimens [3];however, no information on the cyclic behaviour of the material isprovided. Other studies provide high cycle fatigue (HCF) stress-life

decreasing yield strength, while aging below 800 C resulted inning the material.ons, looking at theon [7], changes int combinations ofenhancement via

development of assment. The L605

stent is an ideal application for this approach, as stent struts can be80 mm in thickness [1,10], compared to a grain size on the order of10 mm [11]. Consequently, with often less than ten grains through thestrut thickness, the performance of the stent is highly dependent onthe inhomogeneousmicrostructure. Thishasbeenveried inpreviousstudies formonotonicbehaviourof stent struts,usingcrystalplasticity(CP) constitutive modelling, which describes deformation due toplastic slip on individual slip systems in crystallographic grains [11e15]. However, this microstructure-sensitive method demands

* Corresponding author. Tel.: 353 (0)91 493020; fax: 353 (0)91 563991.

Contents lists availab

Biomat

ev

Biomaterials 35 (2014) 36e48E-mail address: c.sweeney4@nuigalway.ie (C.A. Sweeney).and cyclic stress-strain behaviour are essential inputs for devel-opment of successful fatigue assessment techniques. This allowsthe capture of energy dissipation and stresses and strains reachedcyclically in the material, which has direct impact on the life of acomponent. Microstructural characteristics, such as grain size andprecipitates, can have a signicant role in the fatigue performanceof L605 and, hence, must also be included in predictive modellingtechniques. A limited number of experimental characterisation

precipitation of coherent precipitates, strengtheOther studies focused on L605 in stent applicatieffect of annealing temperatures on precipitatigrain size and tensile properties under differencold working and annealing [8] and stent surfacean electrochemical process [9].

The primary objective of this study is themicromechanical approach to L605 fatigue assethe development of reliable and accurate methods for fatigue life reporting that aging above 800C produced incoherent precipitates,1. Introduction

The L605 CoCr alloy is a popular mof applications with fatigue loading,[1], gas turbine components and bea0142-9612/$ e see front matter 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.biomaterials.2013.09.087stent-artery model and a 2D micromechanical sub-model. Several microstructure realizations for thestent sub-model allow assessment of the effect of crystallographic orientations on stent fatigue crackinitiation predictions. Predictions of FCI are compared with traditional Basquin-Goodman total lifepredictions, revealing more realistic scatter of data for the microstructure-based FIP approach. Com-parison of stent predictions with performance of a 316L stent for the same generic design exposes thedesign as over-conservative for the CoCr alloy. In response, the micromechanical framework is used tomodify the stent design for the CoCr alloy, improving design efciency.

2013 Elsevier Ltd. All rights reserved.

l used in a broad rangeng biomedical implants2]. In such applications,

data and crack growth data for the L605 alloy [4,5], but again, donot report cyclic stress-strain data. Microstructural studies on L605primarily focus on microstructural evolution under applied heattreatments. Teague et al. [6] carried out a series of aging treatmentsto look at the effects of resulting precipitation on tensile behaviour,Keywords:FatigueCoCr alloy, including both microscopy and mechanical testing. Fatigue indicator parameters (FIPs) withinthe micromechanical framework are calibrated for the prediction of microstructure-sensitive fatigueExperimental characterisation for microstent fatigue

Caoimhe A. Sweeney a,*, Barry OBrien b, Peter E. MaMechanical Engineering, College of Engineering and Informatics, National University obBiomedical Engineering, College of Engineering and Informatics, National University o

a r t i c l e i n f o

Article history:Received 22 August 2013Accepted 24 September 2013Available online 10 October 2013

a b s t r a c t

Fatigue of CoCr alloy stentfracture, often driven by mmechanical framework for

journal homepage: www.elsAll rights reserved.echanical modelling of CoCr

ugh b, Sean B. Leen a

land Galway, Irelandland Galway, Ireland

s become a major concern in recent times, owing to cases of prematureostructural phenomena. This work presents the development of a micro-gue design, based on experimental characterisation of a biomedical grade

le at ScienceDirect

erials

ier .com/locate/biomateria ls

d (b

matextension to fatigue performance assessment of stents. Halwani et al.[16] reported two instances of stent fracture in CoCr alloy stentswithin 24 and 13 months. A clear need exists for improved fatigueanalysis in the stent design process. Current industry standardsemploy basic nite element (FE) models in conjunction with thestress-based Goodman technique, in accordance with FDA re-quirements [17], to ensure that stent operational life will exceed 10years. Microstructural effects are ignored, eliminating the possibilityof predicting crack formation in slip bands, as has been reported tooccur [16]. Attempts have been made in the literature to improvefatigue prediction methods for the stent application. Azaouzi et al.[18], Li et al. [19] and Schievano et al. [20] applied the traditionalGoodman approach to 3D FE 316L stainless steel (SS), L605 and plat-inumstentmodels, respectively. Basic tensile propertieswere used tocharacterize constitutive behaviour and microstructural effects wereneglected in all three cases, with the rst study concluding that amicromechanical approach is essential in stent fatigue assessment.Wiersma et al. [21] applied the theory of critical distances [22], acontinuum approach, which takes into account stress-gradients, toassess the fatigue performance of a biomedical grade 316L; howeveragain, microstructural effects are not considered using this approach.A continuum fracture mechanics approach has been used by Marreyet al. [4] toassess theeffectofa crack introducedonanL605stentstrutduring fatigue. A key conclusion of this work was the need for CPmodelling for stent fatigue assessment. Argente dos Santos et al. [23]employ a multi-scale damage-mechanics approach for prediction ofmicro-crack initiationduring fatiguefor two316Lstentdesigns.While

Fig. 1. Optical microscopy images of the L605 alloy, showing (a) longitudinal an

C.A. Sweeney et al. / Biomicro-scale damage is a key contribution of this study, microstruc-tural inhomogeneities introduced by grain boundaries and differentcrystallographic orientations are ignored, evident by the lack ofscatter in predictions. The Dang Van approach has been applied inanother study to assess the fatigue of a 316L stent [24], again claimingthe ability to capture grain-level phenomena; however, evaluation ofmesoscopic stresses as a function ofmacroscalemodels again ignoresthe inhomogeneous nature of the microstructure. Two studies haveemployed CP modelling to assess the fatigue performance of a 316Lstent [25,26]. McGarry et al. [25] calibrated the CP constitutivemodelformonotonic behaviour and carried out a simple Goodman analysis,while Sweeney et al. [26] developed the methodology further, car-rying out a rigorous cyclic calibration of the material behaviour andmaking microstructure-sensitive predictions of fatigue crack initia-tion (FCI) as well as Goodman-based total life predictions. The use ofmultiple microstructural realizations for the stent model producedscatter in predictions, successfully showing the effect of microstruc-tural inhomogeneity.

This work aims to develop a micromechanical framework,which can be used as a tool in the fatigue design and assessment ofCoCr alloy stents, for which a clear need has been explicitlyexpressed in past work [4]. The L605 CoCr alloy, commonly used incurrent generation cardiovascular stents [1], is experimentallycharacterised both microstructurally and mechanically, via micro-scopy, and tensile and low cycle fatigue (LCF) testing, respectively.The experimental data is used in the development of the L605micromechanical modelling framework, including realistic geom-etries, based on measured microstructures, and a CP model, cali-brated for both monotonic and cyclic behaviour. This framework isthen used to assess the fatigue performance of an L605 model for ageneric stent design, which is compared to previous work for a 316Lstent [26]. A multi-scale approach is adopted whereby boundaryconditions for the CP sub-model are extracted from a J2 continuumglobal stent-artery model. In order to assess the design of the stentand the potential for premature failure, microstructure-sensitivefatigue indicator parameters (FIPs) [27,28] are implemented forthe prediction of number of cycles to fatigue crack initiation. Use ofthe methodology as a design tool is demonstrated, where thechosen L605 stent design is modied to improve design efciency.

2. Experimental studies

This section outlines experimental work carried out on the L605 CoCr alloy,trade-named HAYNES 25 alloy [2], used in the as-received condition: a hot-rolledbar, solution-annealed at 1230 C, with chemical composition of 20 wt% chro-mium, 15 wt% tungsten, 10 wt% nickel, 3 wt% iron, 1.5 wt% manganese, 0.4 wt%silicon, 0.1 wt% carbon and the balance consisting of cobalt. The experimentalprogramme covers both the microstructural and mechanical characterization of theL605 alloy via microscopy, and fatigue and tensile testing, respectively.

) transverse views of the bar and (c) grain area distributions for the two views.

erials 35 (2014) 36e48 372.1. Microscopy

Optical microscopy was used to measure the crystallographic grain morphologyin the L605 microstructure. The L605 material was supplied in cylindrical bar form.Therefore, microscopy was carried out on both transverse cross-sections (parallel tothe cylindrical axis) and longitudinal cross-sections (perpendicular to the cylindricalaxis). The microscopy samples were mounted in an epoxy resin. Surface preparationwas achieved via manual grinding, across a range of grit sizes, automated polishing,with a range of diamond pastes, nishing with a 0.02 mm polishing suspension, andcleansing in an ultrasonic bath. An etching solution of 100ml HCl and 5 ml 30% H2O2was used [29].

Sample optical micrographs of the L605 microstructure from both longitudinaland transverse cross-sections can be seen in Fig. 1(a) and Fig. 1(b), respectively.Individual crystallographic grains are highlighted for illustrative purposes. A Matlabprogram was developed to extract information on grain area distributions fromseveral optical micrographs for both the longitudinal and transverse views, the re-sults shown in Fig. 1(c). An average distribution is also included in Fig. 1(c). There isclearly a high correlation between the two orientations, indicating an equiaxedmicrostructure. Assuming a hexagonal 2D grain shape, the average grain size wasfound from these distributions to be 32 mm. An ASTMgrain size of 5was observed forthe microstructure.

SEM imaging was also applied to the etched samples. A scanning electronmicrograph of the L605 microstructure can be seen in Fig. 2(a); precipitates appear

as light-coloured spots and some grain boundaries appear as light-coloured lines.This contrast between L605 matrix and precipitate material allowed image pro-cessing to be carried out using a Matlab code, developed for the extraction of in-formation on precipitate area distributions, including average precipitate area andfrequency of occurrence within the matrix, as shown in Fig. 2(b). A precipitate arearatio of 0.52% was observed. As highlighted in Fig. 2(a), precipitates appear both atgrain boundaries and within the matrix, with no evident preferential location.

EDX analysis was used in conjunction with SEM imaging to identify thecomposition of precipitates within the L605 matrix. Table 1 provides EDX data fortwo sample spectrums, one of which corresponds to the L605 matrix and the otherof which corresponds to a precipitate. The weight percentage of elements dominantin each spectrum are shown. Reasonably good agreement exists between thereadings shown for the L605 matrix and the manufacturer specications, providedat the start of Section 2; the carbon content in the EDX reading appears high, due tocarbon contamination on the surface of the SEM specimen, and peaks for some ofthe elements listed are too small to be detected. The nal column of Table 1 providesthe percentage change in weight percentage of each element when comparing theprecipitate to the matrix. The data shows that the precipitates have signicantlyincreased weight percentages of tungsten and carbon, while cobalt, chromium and

while a more jagged crack is evident on the specimen corresponding to the 1.2%

surface are observed in Fig. 5(b) and (c), corresponding to fatigue cracking and a naltensile overload, respectively. The plastic strain-life curve corresponding to theseL605 fatigue tests is shown in Fig. 6, including identication of the CofneMansonrelationship for total life, Nf, as a function of plastic strain range, Dp:

g1

a a

respectively, on a given slip system. The L605 matrix has a face-

Table 1EDX readings for chemical composition in a particle and within the L605 matrix.

Element Weight (%) % Change in weight %

Matrix Particle

Co 46.31 15.22 67Cr 20.74 10.9 47W 17.21 63.04 226Ni 11.13 3.46 222C 4.61 7.37 60

C.A. Sweeney et al. / Biomaterials 35 (2014) 36e4838strain range of Fig. 5(a), which has fractured into two pieces. Two types of fracturenickel contents have decreased.

2.2. Mechanical testing

Tensile and LCF tests are employed to characterise the monotonic and cyclicplastic behaviour of the alloy. The fatigue specimen design, based on ASTM stan-dards [30], is shown in supplementary Fig. S1. A light interferometer was used toensure that the nal surface roughness (Ra) in the gauge section of specimens wasbelow 0.2 mm. All tests were carried out at room temperature on an Instron 8500servo hydraulic systemwith hydraulic grips and V-shaped jaws. The tensile test wascarried out using displacement control at a rate of 1 103 mm/s per mm gaugelength and a video extensometer was used to measure the strain in the gauge lengthof the specimen. In order to characterise the LCF behaviour of the material, strain-controlled tests were carried out at four different strain ranges with a cyclic strainratio R min/max of1. An extensometer with knife-edged probes was attached tothe gauge length to measure, and hence control, strain and a strain rate of 0.01 s1

was used.The measured tensile behaviour of the L605 alloy is shown in Fig. 3(a). An

elongation to failure of over 60% is measured, the 0.2% offset yield strength is514 MPa, the ultimate tensile strength (UTS) for the material is 1075 MPa and theelastic modulus is measured to be 224 GPa. Tensile fracture occurred along a 450

crack path, as seen in Fig. 3(b). While localised necking at the crack site is notobserved, a large amount of surface roughening along the entire gauge length isevident. Comparing with a biomedical grade 316L SS [15], as shown in Fig. 3(a), theL605 CoCr alloy displays superior tensile behaviour both in terms of strength andductility, as reported by others [31e33].

Fig. 4(a) shows the measured evolution of the cyclic stress range for LCF tests at0.5%, 0.8%, 1.0% and 1.2% controlled cyclic strain. The material exhibits someinitial hardening, followed by slight softening within the rst 100 or so cycles.Thereafter, a stabilised stress range is exhibited, until a sudden drop in stress range,corresponding to termination of the test due to a 30% load drop in tension beingreached. This can be taken as failure. Fig. 4(b) shows a more detailed evolution ofstress-strain hysteresis loops for 1% applied strain range; cycle 4087 is the lastcycle before failure.

Cracked specimens are shown in supplementary Fig. S2 for the0.5%,0.8% and1.0% strain ranges; 1800 circumferential cracks are visible on these specimens,Fig. 2. (a) SEM image of the L605 alloy microstructure and (b) particle area distribution wiareas above 1 mm2.centred cubic (fcc) crystal structure [6] and, therefore, has 12{111}h110i slip systems. The resolved shear stress on a slip system iscalculated by:Nf DpC1

(1)

and the identied values of the C1 and g1 constants are given in Table 2.

3. Computational framework

3.1. Constitutive models

3.1.1. Crystal plasticity modelA key novelty of the present work is the development and

identication of a micromechanical, crystal plasticity constitutivemodel for themonotonic and cyclic plastic response of L605. Crystalplasticity (CP) [34e38] describes deformation in the crystal latticevia dislocation motion through the use of a deformation gradient Fwhich is decomposed into elastic and plastic components:

F Fe$Fp (2)

where Fe includes both elastic deformation and rigid body rotationand Fp represents the plastic deformation, attributed to crystallineslip. Schmids law is used to relate the slip rate on a slip system a,_ga, to the plastic velocity gradient:

Lp _Fp$F1p Xa

_gasamTa (3)

where s andm are the slip direction and normal to the slip plane,thin the L605 microstructure; the inset histogram continues the distribution for grain

sa ma5sa : s (4) xa x1a x2a (7)

Fig. 3. (a) Tensile curve for the L605 alloy compared with a biomedical grade 316 LVM [15] and (b) the fractured tensile specimen.

C.A. Sweeney et al. / Biomaterials 35 (2014) 36e48 39where s is the macroscopic stress tensor, dened by the elasticrelation:

sV

e strDe C : De (5)

where sVe is the Jaumann rate of Cauchy stress based on lattice spin,De is the elastic deformation gradient and C is the fourth ordertensor of elastic moduli, containing cubic elastic constants inaccordance with the fcc crystal structure of L605. The slip rate iscalculated as a function of slip system shear stress:

_ga _asgnsa xasa xaga

n

(6)

where xa is a kinematic back-stress, ga is an isotropic strain hard-ening parameter, _a is a reference strain rate and n is a rate sensi-tivity exponent. In the present model, in order to effect greaterexibility for simulation of the complex non-linear monotonic andcyclic micro-plasticity response, the kinematic hardening param-eter is a linear combination of two individual evolving back-stresses, both described by an Armstrong-Frederick evolution rule:Fig. 4. (a) Cyclic stress range evolution corresponding to LCF total strain ranges and (b) experange.which the evolution can be derived from Eq. (9):_xia Ci _ga Dixia j _gaj (8)

where i 1,2, Ci/Di is the saturation value for xi and Di controls therate of decay leading to saturation. Ci and Di are material constantscalibrated via comparisonwith the measured cyclic response of thematerial. The evolution of the hardening function of Asaro and co-workers is used:

gga g0 gN g0tanh hogagN g0

(9)where g0 is the critical resolved shear stress, gN is the saturationvalue of ga and h0 is the initial hardening modulus. The evolution ofthe hardening parameter is dened by:

_ga Xb

hab _gb (10)

where hab represents self (b a) and latent (bs a) hardening forrimental stress-strain hysteresis loops after various number of cycles for the 1% strain

where ci and gi are the J2-plasticity equivalents of Ci and Di,

C.A. Sweeney et al. / Biomat40haa hab hga h0sech2 h0gagN g0

(11)where ga is the accumulated slip over all slip systems dened bythe equation:

ga Xa

Zt0

j _gajdt (12)

The CP constitutive equations, including isotropic hardening,have been implemented in a user-material subroutine (UMAT)within the Abaqus framework by Huang [39], and have recentlybeen modied by the authors [26] to include non-linear kinematichardening, while this work introduces a second back-stress into the

Fig. 5. (a) Post-test LCF specimen for the 1.2% strain range, (b) fatigue striations inlocation of initial crack and (c) static fracture surface.implementation.

3.1.2. J2 Continuum modelThe J2 ow theory continuum constitutivemodel, formacroscale

modelling of L605, incorporates the key phenomena of cyclichardening and Bauschinger effect, via non-linear isotropic and

Fig. 6. Comparison of experimental data with tted CofneManson equation forplastic strain-life behaviour.respectively (of Eq. (8)). The evolution of isotropic hardening isdened by:

drp bQ rdp (16)

where Q is the saturation value of the isotropic hardening param-eter and b controls the rate of decay leading to saturation; both Qand b are constitutive constants calibrated as described below.

3.2. Finite element microstructure model

A micromechanical nite element model of the measuredmicrostructure is developed for the identication of the micro-scale behaviour of the L605 material under cyclic and tensileloading. A customized Matlab code is developed for generation ofthe 3D microstructure via superposition of a 3D Voronoi tessella-tion on a voxel mesh. In order to ensure that the grain volumedistribution of the resulting polycrystal accurately simulates theexperimental distribution, 2D grains were idealised as hexagonsand 3D grains as rhombic-dodecahedrons (as seen insupplementary Fig. S3). The resulting relationship between grainvolume (3D) and grain area (2D) is then given as follows:

V 12

p2A3

p3

2

(17)

where the common dimension d is the 2D to 3D link. This equationfacilitates calculation of experimental grain volume distributionkinematic hardening models, respectively. This model is based onthe following yield function:

f 32s0 x0 : s0 x0

1=2 k rp (13)

where s and x are the deviatoric stress and back-stress tensor,respectively, k is the initial cyclic yield stress and r(p) is the isotropichardening function. In order to capture the complex, non-linearkinematic hardening response of the material, a linear combina-tion of three back-stresses is employed, as follows:

x x1 x2 x3 (14)

where the non-linear evolution of each back-stress tensor, xi, isdened by the Armstrong-Frederick rule:

dxi 23cidp gixidp (15)

Table 2Fitted CofneManson constants forthe L605 alloy.

C1 1.49g1 1.77

erials 35 (2014) 36e48from the measured grain area distribution. A number of polycrystalmodel microstructures were generated to iteratively achieve cor-relation between polycrystal grain volume distribution and exper-imental distribution.

A key challenge for micro-scale modelling of the microscopyimages of Figs. 1(a), 1(b) and 2(a) is representation of precipitates inthe nal polycrystal model. As the average precipitate volume issmaller than the volume of a standard element in the mesh, aseven-element unit was used to replace a normal element in the

leading ultimately to failure [27,42,43]. It has been shown that amicrostructure-sensitive effective plastic strain FIP allowed pre-diction across both LCF and HCF regimes from calibration against

matmesh, as shown in Fig. 7, where a precipitate element lies at thecentre of the unit, surrounded by six matrix elements. The micro-scopy observations indicate no preferred location of precipitatesalong grain boundaries or within the matrix. Hence, theprecipitate-matrix unit is inserted randomly into the FE mesh togive the experimentally observed volume fraction of precipitates.The nal microstructure model is shown in Fig. 7; it has cubic di-mensions of (120 mm)3 and contains 28 crystallographic grains,with 3723 20-noded brick elements. Periodic boundary conditionsare applied to simulate macroscopic behaviour. Due to thecomputational expense associated with crystal plasticity modellingand the 3D nature of the micromechanical model, it is prohibitivelyexpensive to simulate a sufciently large number of grains toachieve a denitive representative volume element (RVE). How-ever, it has been shown previously by Jiang et al. [40], that it ispossible to predict a response for an inhomogeneous materialwhich lies between the lower and upper bounds of themacroscopicresponse, using periodic boundary conditions applied to a unit cellmicrostructure model which is smaller than a denitive RVE.

3.3. Constitutive model calibration

The CP and J2 continuum responses are calibrated against boththe experimental tensile response and the rst thirteen cycles ofloading for each applied LCF strain range. In the case of the J2continuum model, the approach of Lematre and Chaboche [41] isused for the initial estimation of constants. A least squares objectivefunction is implemented for identication of the optimised con-stants, as follows:

Xn Xm h i2

Fig. 7. Modelling methodology for incorporation of 0.52% area fraction of precipitatesin L605 polycrystal.

C.A. Sweeney et al. / BioFxk j1 i1

sexpi j ssimi j (18)

where n and m represent the number of strain ranges and a pre-determined number of stress-strain data points throughout thecyclic loading history, respectively, and siexp and sisim are theexperimentally measured and simulated stresses, respectively, atpre-determined sample strains. This minimisation function wasused for calibration of both the CP and J2 continuum constants.

For the CP model, the isotropic hardening function ga and theback-stress x1a are found to be sufcient for accurate calibration ofthe cyclic response, or small-strain regime. It was found, however,that an additional back-stress x2a was required to also achievesatisfactory calibration of the tensile response, or large-strainregime, while using one set of parameters for both tensile and cyclicresponses. Similarly for the J2 continuum model, the isotropichardening parameter r and the back-stresses x1 and x2 are used tocalibrate for cyclic behaviour, while the third back-stress x3 is usedfor capturing the large-strain L605 tensile response. Calibration ofthe constitutive models against both cyclic and tensile data isimportant in applications of high initial plastic deformation, whichinduces high residual or mean stresses, followed by fatigue, such asfor a stent where crimping, crimp recoil, deployment and recoilincur plastic deformation, followed by systolic-diastolic pulsatileloading.

The calibrated tensile (monotonic) responses of the J2 and CPconstitutive models are compared with the experimental data inFig. 8. Fig. 9 shows a comparison of predicted stabilised hyster-esis loops with the experiments, showing correlation of modeland measured data. Both models successfully capture the evo-lution from monotonic to stabilised cyclic hysteresis loops. Theoptimised constants for the J2 continuum and CP constitutivemodels are provided in Tables 3 and 4, respectively.

3.4. FCI predictions

A key objective of the present work is the assessment, includingcalibration and validation, of a micro-scale method for FCI predic-tion in L605. This is particularly important for stent applications,primarily due to the scale of stent struts relative to microstructuralfeatures such as grain size and carbides. A number ofmicrostructure-sensitive FIPs have been developed to predictlocation and number of cycles to FCI for a range of materials,

Fig. 8. Comparison of the J2 continuum and CP tensile curves with the L605 experi-mental data; the large-strain range is calibrated using the additional back-stress termsand the small-strain range (before dotted line) is calibrated using initial back-stressterms.

erials 35 (2014) 36e48 41one LCF test data point [28]; a similar approach will be adoptedhere. The same FIP has been successfully used to predict the loca-tions of experimentally observed FCI for given microstructures[44,45]. As for previous work on 316L stents [26], two candidatemicrostructure-sensitive FIPs are examined here, both imple-mented in the CP UMAT. The rst is the previously mentionedaccumulated effective plastic strain parameter [28], p, calculated asa function of the plastic velocity gradient, Lp:

_p 23Lp : Lp

1 =

2

; p Zt0

_pdt (19)

Use of p for prediction of number of cycles to FCI has beensuccessfully validated for a nickel-base alloy [28] and a 316L SS [46].The second microstructure-sensitive FIP is an accumulated strainenergy dissipation parameter [27], W, which sums energy dissi-pation over all crystallographic slip systems:

C.A. Sweeney et al. / Biomaterials 35 (2014) 36e4842W Xa

Zt0

sa _gadt (20)

Crack initiation is predicted to occur when critical values of theFIPs, pcrit and Wcrit, are reached. Unit cell LCF simulations for theexperimentally applied strain ranges are employed for the identi-cation of pcrit and Wcrit using the micromechanical unit cell ofFig. 7. In order to account for scatter in the microstructure-sensitivepredictions, ve realizations of random crystallographic orientationare applied to the cubic polycrystal for the four strain ranges. A highprobability of FCI at the free surface exists in the LCF and HCF re-gimes [47,48]. While periodic boundary conditions are commonlyused for comparing unit cell and RVE responses with macroscopicmaterial behaviour, the possibility of free surface FCI is therebyprecluded. Therefore the boundary conditions applied to the

Fig. 9. Comparison of J2 continuum and CP stabilised hysteresis loops w

Table 3Calibrated J2 continuum constants for theL605 alloy.

k 230 MPaQ 60 MPaB 9c1 240 GPag1 1846c2 50 GPag2 250c3 2.7 GPag3 0.55polycrystal model are designed to replicate a unit at the free surfaceof a fatigue specimen, whereby one surface is free, a planeboundary condition is applied to the opposite surface and the fourremaining surfaces are constrained by periodic boundary condi-tions. This facilitates the possibility of surface FCI in the identi-cation of pcrit and Wcrit.

The p and W FIPs predict number of cycles to FCI, however theexperimental L605 tests produce total life fatigue data. Therefore, adamage approach is employed for the back-calculation of an approx-imate Ni for each experimentally applied strain range. The damageevolution equation used is a function of the experimental Nf [49,50]:

D 1"1

NNf

! 11a# 1b1

(21)

where a and b are constants, identied to give the best t across allstrain ranges. Fig. 10(a) shows a comparison of damage curves from

ith the L605 experimental data for different applied strain ranges.

Table 4Calibrated CP constants for the L605 alloy.

g0 100 MPagN 130 MPah0 100 MPaC1 80 GPaD1 750C2 1.25 GPaD2 0.001

Eq. (21) with experimental damage, evaluated as D 1s/smax,where smax is the maximum peak tensile stress for a given LCF test.Ni is assumed to occur experimentally at a critical damage, Dc, asmarked in Fig. 10(a). A value of 0.0125 is chosen for Dc, based on acircumferential crack with depth equal to the standard element sizeinitiating at the free surface in a unit cell. The resulting Ni datapoints are shown along with experimental Nf data in Fig. 10(b). pcrit,and similarlyWcrit, are calibrated using data for a single strain rangevia the simple relation pcrit Ni/pcyc, where pcyc is the effectiveplastic strain accumulated over a stabilised cycle of loading, aver-aged over the ve simulations for that single strain range. pcrit andWcrit have been identied as 439.9 and 15.63 104 MJ m3,respectively, using Ni for the 0.5% strain range. Reasonableagreement is observed when these critical FIP values are used topredict number of cycles to FCI for the other three strain ranges, asshown in Fig. 10(b).

4. Stent fatigue application

The focus application of the present biomedical grade L605 alloyis the design of cardiovascular stents. The key objective of this workis the development of a multi-scale fatigue methodology for suchstents, in this case using the J2 continuum and CP constitutivematerial models. As a demonstration, this methodology is appliedto a generic stent geometry, based on the NIR stent, allowingcomparisonwith a previous study for 316L SS stent material [26]. Ituses a combination of a global 3D macroscopic stent-artery FE

model using J2 cyclic plasticity and a 2D micromechanical CP FEmodel for the smallest repeating unit in the generic geometry. Theload history includes simulation of crimp, deployment and systolic-diastolic fatigue of the stent; the fatigue boundary conditions forthe 2D sub-model are driven by the 3D global model.

4.1. J2 continuum global model

The global stent model consists of a single ring of the stent and athree-layered artery, as shown in Fig.11(a). The arterymodelled hasan inner diameter of 2.65 mm and realistic thicknesses and prop-erties are assigned to the arterial layers, the detail of which hasbeen provided in the previous study [26]. The loading includes (i)crimping of the stent to a diameter of 0.676 mm, (ii) deployment ofthe stent within the artery to a diameter of 3 mm and (iii) appli-cation of a cyclic pressure in the artery of 7.98 kPa (60 mmHg) withcyclic load ratio Rp pmin/pmax of 0, where elastic recoil is alsomodelled after the crimping and deployment stages. A schematic ofthe change in stent diameter throughout the loading history isprovided in Fig. 11(b). The cyclic change in stent diameter isextracted from the 3D global model and converted geometrically toa cyclic displacement applied to the micromechanical sub-model.

4.2. CP sub-model

The geometry used in the micromechanical sub-model repre-sents the smallest repeating unit in the stent, converted into a 2D

C.A. Sweeney et al. / Biomaterials 35 (2014) 36e48 43Fig. 10. (a) Comparison of curves for experimental data and the damage evolution relation afrom experimental Nf data via use of the damage evolution relation.nd (b) predictions of Ni using pcrit and Wcrit in comparison with Ni data back-calculated

matC.A. Sweeney et al. / Bio44geometry, shown in Fig. 11(c). 2D Voronoi Tessellation is employedvia a custom-written Matlab code to generate a random crystallo-graphic grain structure representative of that seen in annealedL605 tubes used in stent manufacture [11]. Once a representativemicrostructure morphology with high statistical correlation to theexperimental morphology is iteratively achieved, automaticmeshing is applied, followed by selective manual repair meshing toremove distorted elements. Automatic generation of precipitates inthe mesh was achieved via a Fortran program, to achieve a volumefraction of precipitates consistent with that of L605 stent tubing [8].The average element in the stent sub-model mesh has larger areathan the average precipitate in the L605 microstructure. Toaccommodate this, a 5-element unit, shown in Fig. 11(c), is used torandomly replace existing elements in the mesh, similar to the 7-element unit used for the 3D polycrystal. This allows the occur-rence of precipitates at the free surface and along grain boundaries.The measured area fraction of precipitate is achieved within thegenerated microstructure. The nal sub-model contains 1753crystallographic grains, 52798 4-noded, reduced integration,generalised plane strain elements and includes precipitates withareas in the range of 0.03e0.78 mm2, corresponding to an experi-mentally observed precipitate area range of 0.01e0.74 mm2.While a2D geometry is used for the stent sub-model, the micromechanicalanalyses carried out can be considered quasi-3D due to (i) the 3Dnature of the CP constitutive model, allowing slip in three di-mensions, and (ii) use of generalised plane strain elements,

Fig. 11. (a) 3D global stent-artery model, (b) schematic of change in stent diameter duringfacilitating the inclusion of precipitates.erials 35 (2014) 36e48allowing uniform strain in the third dimension. Different re-alizations of random crystallographic orientations are used togenerate seven stent sub-model microstructures in order to simu-late typical inhomogeneities observed in real stent microstructures.For comparative purposes a separate sub-model analysis is carriedout using the J2 constitutive model, but without the precipitates, asthe J2 constitutive model was calibrated against the macroscopicbehaviour of the alloy, i.e. including the effects of precipitates.

The loading steps of Fig. 11(b) are applied in the sub-model viadisplacement of a master node on the lower strut in Fig. 11(c).Boundary conditions are applied to maintain periodicity of the sub-model in the global stent structure; a more detailed description isprovided in previous work [26].

Two approaches are adopted for the fatigue assessment of thestent sub-model. The rst is a microstructure-sensitive approachfor the prediction of number of cycles to FCI,Ni, in the CP sub-modelanalyses via use of the p and W FIPs of Section 3.4:

Ni pcrit precoil

pcyc; Ni

wcrit wrecoilwcyc

(22)

where precoil and Wrecoil are values of the FIPs accumulated post-recoil, taking into account initial plastic deformation during thestent installation process.

The second method, used here for comparative purposes, is theindustry standard approach for predicting the number of cycles to

applied loading history and (c) 2D micromechanical sub-model with 5-element unit

fatigue failure, Nf. This total life approach uses a combination of theBasquin HCF equation and the Goodman equation for mean stresseffects, typically used in stent design practices under the recom-mendation of the US Food and Drug Administration (FDA) [17]. Thecombined equation is represented as follows:

Nf "

Ds

C2

1 smsTS

#g2

(23)

whereDs and sm are themaximumprincipal stress range andmean

matrix behaviour across all grain sizes and for different precipitatesizes and distributions. For an effective calibration of the matrixbehaviour, however, features such as grain size, precipitate size andfrequency of precipitates, as is provided in Section 2.1, must beincluded in the geometry of the calibration model. This approachneglects the initial and evolving dislocation distributions in theL605 matrix, which are inuenced by grain size and precipitates.While grain size and precipitate effects are not the focus of thecurrent study, future work will investigate the inuence of dislo-cation densities on fatigue behaviour of stents, in which strain-gradient CP formulations [44] will be used.

5.2. CoCr computational framework

Accurate calibration of the J2 and CP cyclic and monotonicplasticity models against the measured responses in Figs. 8 and 9 iscritical to the particular elasticeplastic loading history of stentdeployment and in-service life prediction. Tensile calibration al-lows the capture of stent deployment behaviour, during which thestent undergoes a large amount of plastic deformation, which inturn affects the residual stress distribution for mean stress effects

C.A. Sweeney et al. / Biomatmaximum principal stress, respectively, for a stabilised cycle ofloading, sTS is the ultimate tensile strength of the L605 CoCr alloyand C2 and g2 are Basquin constants calculated from HCF data forthe L605 alloy [4].

4.3. Results

Table 5 shows the microstructure-sensitive FCI predictions forthe L605 stent for all 7 microstructure realizations and for both pcritand Wcrit. The table also shows the Basquin-Goodman predictionsfor total life. As the latter is traditionally applied to macroscaleresults, which do not account for peaks due to microstructural in-homogeneities, a grain volume-averaging technique, described inmore detail in a previous study [26], is applied to Ds and sm, used inEq. (23), for the CP models. For comparative purposes these stressvalues are averaged over the average grain volume for the J2 con-tinuum sub-model. An average Basquin-Goodman total life of6.43 1014 cycles with standard deviation (SD) of 1.58 1015 ispredicted for the CP sub-models, compared with a total life of2.45 1016 cycles for the J2 sub-model.

The pcrit method predicts an Ni of 2.71 107 cycles(SD 1.36 107) and theWcrit method predicts an Ni of 3.48 107cycles (SD 2.48 107). The predicted locations of microstructure-sensitive FCI for both FIPs and all microstructure realizations areshown in Fig. 12(b). Clearly, FCI is predicted to have a high proba-bility of occurring along the inner radius of the top strut, the samelocation at which failure is predicted to occur for the J2 continuumsub-model, as shown in Fig. 12(a).

5. Discussion

5.1. Experiments

Quite a broad range of particle areas is observed embedded inthe L605 matrix, as seen from Fig. 2(b). Precipitate size can havesignicant inuence on the fatigue performance of a material; neprecipitates that are coherent with the matrix can strengthen thematerial behaviour and cause increased hardening, whereas coarseprecipitates, with incoherent precipitate-matrix interface, can actas stress concentrators and may offer free surfaces conducive tocrack initiation [51,52]. The effects of both types of precipitates on

Table 5Nf and Ni predictions for the CP stent unit cell simulations.

Realization Ni (pcrit) Ni (Wcrit) Nf

1 3.98 107 3.90 107 1.16 10122 3.95 106 2.35 106 4.07 10123 4.00 107 7.73 107 7.09 10114 2.20 107 3.12 107 6.37 1085 2.19 107 1.20 107 2.73 10146 2.20 107 3.11 107 1.18 108

7 4.00 107 5.10 107 4.22 1015tensile behaviour have been observed experimentally for L605 [6].Future work should investigate the inuence of precipitate size onfatigue behaviour to provide insight into desirable microstructuresfor stent materials. Previous studies on L605 have also found theprecipitates to have a tungsten-rich composition [6e8]. Teagueet al. (2004) identied precipitates in the as-received L605 materialas M6C and M23C6, where M represents metallic elements, such astungsten. Based on the analysis of the present study, it is possible toconrm that the precipitates are hard carbide particles and anelastic modulus is assigned accordingly in the simulations as714 GPa [53].

The fracture surface of the 1.2% strain specimen in Fig. 5(a)shows signs of a 450 crack at the left side of the specimen gaugelength, followed by a atter surface to the right. In Fig. 5(b) fatiguecrack fronts are seen at the edge of the shear crack, while a staticfracture surface is seen in Fig. 5(c). This indicates that initial crackgrowth occurred along a 45 crack path, followed by sudden staticfailure upon nal fracture.

It is assumed for this study that the behaviour of the L605matrixis unaffected by changes to microstructural features, such as grainsize and precipitates. Ensuing from this assumption, the L605tensile and cyclic data of Section 2.2. can be used to calibrate L605

Fig. 12. (a) Predicted site of fatigue failure for the J2 continuum sub-model and (b)predicted sites of fatigue crack initiation for the CP sub-models.

erials 35 (2014) 36e48 45on fatigue life. The additional back-stress terms of Eqs. (7) and (14)

sub-model analyses for one case has shown that omission of pre-cipitates results in increased number of cycles to FCI, but reducedtotal life. This in fact agrees with experimental observations thatprecipitates often promote crack initiation [54,55], but increaseresistance to crack growth by obstructing the crack path [56,57]. Itis also anticipated that the introduction of strain-gradient effects,i.e. increased hardening in regions with a high gradient of plasticdeformation, into the CP constitutive model would increase theinuence of precipitates on the lives predicted. Such a constitutivemodel can capture the grain size effect [58], i.e. the superior fatigueperformance of ner-grained materials, and also the increasedhardening experienced by matrix material surrounding pre-cipitates [59]. The inuence of strain-gradient effects on stent fa-tigue performance will be investigated in future work.

From Fig. 12(b), the locations of FCI predictions, while occurringin multiple regions, clearly highlight a critical region for crackinitiation in the notch area, along the inner radius of the top strut.While predictions using p and W do not take into accountcompressive stress effects (i.e. a crack-inhibiting environment), theprediction of this critical region is corroborated by the J2 continuumNf prediction (Fig. 12(a)), which does take into account compressivestress effects. Beam bending theory also supports the prediction ofFCI in this notch region. The upper strut can be viewed as a beamwith one end xed in the hinge region, which has experienced alarge upwards load at its free end. Therefore, the upper strut isexpected to experience cyclic compression on its outer radius and

matare critical to the accuracy of the tensile calibration in the large-strain region of Fig. 8 for the micro and macro-scales, respec-tively. Omission of these terms gives errors of up to 55% inmacroscopic tensile stresses. Such a response would result in grossunderestimation of the amount of strain hardening and, thus, stressmagnitudes achieved during stent deployment. Under-predictionof deployment stresses would result in reduced elastic recoverypredicted during recoil and, thus, an increase in predicted residualstresses during stent fatigue.

The damage evolution law of Eq. (21) provides a method forback-calculation of Ni from experimental Nf data. However, it can beseen from Fig. 10(b) that using the critical FIP values, pcrit andWcrit,identied for the 0.5% strain range, the majority of Ni predictionsfor the 1.2% strain range are longer than the experimentallyobserved number of cycles to failure. In Fig. 10(a), the least corre-lation exists between the experimental and calculated damageevolution curves for the1.2% strain range, particularly at D Dc. Infact, the experimental damage curve for the 1.2% strain rangeindicates that FCI occurs almost immediately before fatigue failure,as is predicted using the CP simulations of Fig. 10(b). It should alsobe noted that use of the damage evolution law of Eq. (21) tocalculate Ni at a constant critical damage Dc results in a constantratio of Ni/Nf across all strain ranges. A previous study, which de-scribes use of an ultrasonic method for detection of cracks betweenthe range of 30e110 mm in notched L605 fatigue specimens [3],reported that the Ni/Nf ratio increases with decreasing fatigue lifefor the L605 alloy. This supports the CP predictions of Fig. 10(b) forthe higher strain ranges, where Ni is predicted at larger numbers ofcycles than is predicted by the damage evolution law.

5.3. Stent fatigue simulations

The FDA recommends that stents are designed to have a mini-mum operational life of 10 years or approximately 4 108 cycles.Both the traditional J2 continuum approach and the average CP sub-model response predict total stent fatigue life several orders ofmagnitude greater than the FDA minimum requirement. In previ-ous work [26], for an identical geometry, CP analyses for a 316L SSstent predicted an average fatigue life of 7.27 108 cycles,compared to an average total life of 6.43 1014 cycles for the L605CP sub-models. The contrast in performance of the two materialsillustrates that, while the generic stent design is suitable for the316L SS material, it is a highly conservative design for the L605alloy. Therefore, the stent geometry could be modied, for the L605alloy, to improve design efciency. To investigate this, additionalL605 analyses were carried out for a modied stent geometry,where the stent strut cross-section was reduced by 20 mm in eachdimension. The results are compared in Fig. 13 with predictions forthe original stent geometry and with 316L predictions from previ-ous work [26]. The bar chart of Fig. 13 shows the average pre-dictions for CP sub-model analyses, with error bars marking therange of data and FDA minimum required Nf shown. At 1.28 1012cycles, the average total life predicted for the L605 thin strut ge-ometry is two orders of magnitude lower than for the original ge-ometry. However, this total life remains several orders ofmagnitude higher than the FDA recommended minimum total life,indicating that the thin strut design remains over-conservative.Therefore, according to the predictions of Fig. 13, a further reduc-tion in strut cross-sectional area could be adopted for the L605stent geometry, while still attaining acceptable fatigue perfor-mance. Thinner struts are highly desirable in stent geometries dueto increased exibility and reduced restenosis rates [1]. It isimportant to note, however, that the analyses carried out in thisstudy do not investigate strut necking during the installation pro-

C.A. Sweeney et al. / Bio46cess, which may also limit the stent design [13e15].FCI is predicted to occur early in operational life for both theoriginal and thinner strut designs, anywhere from a few weeks tomore than one year after installation of the stent. For all casesrepresented in Fig. 13, a signicantly narrower scatter band isseen for Ni predictions, compared with stress-based Basquin-Goodman total life predictions. This indicates that themicrostructure-sensitive FIP approach is a more reliable method forstent fatigue assessment. Returning to a comparison between L605and 316L, a broader range in Ni predictions is seen for the L605alloy. Precipitates in the L605 matrix are likely to be the source ofthis increased scatter, as they introduce additional microstructuralinhomogeneity, absent in the 316L microstructure. Additional L605

Fig. 13. Averages and scatter in total life and FCI predictions for the L605 thin strut andnormal strut sub-models and for a 316L normal strut sub-model.

erials 35 (2014) 36e48cyclic tension on its inner radius, which is conducive to cracking. If

the J2 continuummodel was calibrated for cyclic behaviour only, i.e.neglecting the large-strain monotonic hardening, the predictedlocation of Nf would be along the outer radius of the lower strut.Simple beam bending theory indicates that this region experiencescyclic compression, which is not conducive to cracking. This illus-trates the importance of accurate calibration of constitutive modelsagainst both monotonic and cyclic plasticity responses.

Fig. 14 has been constructed to assess the effect of crystallo-graphic orientation on FCI predictions. The maximum Schmid fac-tors with respect to the y-direction (the direction of loading appliedto the lower sub-model strut) are plotted for every grain in theoriginal L605 stent sub-model, across all seven crystallographicorientation realizations. Maximum Schmid factors for grains inwhich FCI is predicted to occur are clearly marked. The graphgenerally shows a trend for FCI to occur in grains with highmaximum Schmid factors. Interestingly, themost noticeable outlierin this trend (the pcrit prediction for realization 6) is the only casefor which FCI is predicted to occur in a grain along the outer radiusof the lower strut, a region in which x-direction loading is likely tobe signicant, compared with y-direction loading. Therefore, the

blood vessel is neglected; this may affect the fatigue lives predicted.

cardiac valve prosthesis: stress/life and damage-tolerant analyses. J BiomechEng 1986;108:153e60.

[8] Poncin P, Millet C, Chevy J, Proft JL. Comparing and optimizing Co-Cr tubing

61e76.

C.A. Sweeney et al. / BiomatClearly, an important next step, albeit computationally onerous, isthe development of a 3D micromechanical stent sub-model.Limited comparisons are provided in the literature betweencomputational methods for assessing stent performance andexperimental data. Those that do carry out comparisons aregenerally concerned with monotonic loading of the stent only[60,61] or patient-specic cases [20,62]. Therefore, experimentalvalidation of the micromechanical methodology for assessment ofstent fatigue design is a key future objective.

6. Conclusions

A micromechanical framework for the fatigue behaviour of abiomedical grade CoCr alloy has been presented, including realisticmicrostructure geometries, a crystal plasticity constitutive model

Fig. 14. Maximum Schmid factors relative to the y-direction for each grain in the L605NIR sub-model, for all seven realizations of crystallographic orientation. Maximummaximum Schmid factor relative to the principal loading directionfor this grain may be higher than shown and, consequently, may bein line with the general trend.

The present paper has employed, for illustrative purposes, a 2Dstent sub-model. Aside from the stiffer response of a 2D model, theout of plane loading experienced by the stent while installed in aSchmid factors of grains for which FCI has been predicted using the p and W FIPs aremarked.[12] Harewood F, Grogan J, McHUGH P. A multiscale approach to failure assess-ment in deployment for cardiovascular stents. J Multiscale Modelling2010;02(1).

[13] Harewood FJ, McHugh PE. Modeling of size dependent failure in cardiovas-cular stent struts under tension and bending. Ann Biomed Eng 2007;35:1539e53.

[14] McGarry JP, ODonnell BP, McHugh PE, OCearbhaill E, McMeeking RM.Computational examination of the effect of material inhomogeneity on thenecking of stent struts under tensile loading. J Appl Mech 2007;74:978e89.

[15] Murphy BP, Savage P, McHugh PE, Quinn DF. The stress-strain behavior ofcoronary stent struts is size dependent. Ann Biomed Eng 2003;31:686e91.

[16] Halwani DO, Anderson PG, Brott BC, Anayiotos AS, Lemons JE. The role ofvascular calcication in inducing fatigue and fracture of coronary stents.J Biomed Mater Res B Appl Biomater 2012;100B:292e304.

[17] FDA. Non-clinical engineering tests and recommended labeling for intravas-cular stents and associated delivery systems. http://www.fda.gov/for stent applications. In: Proceedings of the materials and Processes forMedical Devices Conference. ASM International; 2004.

[9] Prakash S, Engineer C, Rval A, Kothwala D, Jariwala A, Kotadia H, et al. Surfaceenhancement and characterization of L-605 cobalt alloy cardiovascular stentby novel electrochemical treatment. Artif Organs 2009;23:55e64.

[10] Garg S, Serruys PW. Coronary stents: looking forward. J Am Coll Cardiol2010;56:S43e78.

[11] Grogan JA, Leen SB, McHugh PE. Inuence of statistical size effects on theplastic deformation of coronary stents. J Mech Behav Biomed Mater 2013;20:[6] Teague J, Cerreta E, Stout M. Tensile properties and microstructure of Haynes25 alloy after aging at elevated temperatures for extended times. Metall MaterTrans A 2004;35:2767e81.

[7] Poncin P, Gruez B, Missillier P, Comte-Gaz P, Proft JL. L605 precipitates andtheir effects on stent applications. In: Proceedings of the materials and Pro-cesses for Medical Devices Conference. ASM International; 2005.with experimentally observed cyclic and monotonic hardeningbehaviour and in-built functionality to predict microstructure-sensitive fatigue crack initiation. The micromechanical frameworkhas been applied to the fatigue assessment of a generic stentplatform to demonstrate microstructure-driven design capability,resulting in efcient CoCr stent design. This work has successfullyillustrated the microstructure-sensitive nature of stent fatigue,including dependence of fatigue crack initiation site on crystallo-graphic orientation and scatter in number of cycles predicted tofatigue crack initiation due to different microstructure realizations,thus reafrming the need for microstructure-sensitive approachesin stent fatigue design.

Acknowledgements

The authors would like to acknowledge funding from the IrishResearch Council under the EMBARK and New FoundationsSchemes and the Irish Centre for High-End Computing (ICHEC) forthe provision of computational facilities and support.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.biomaterials.2013.09.087.

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Experimental characterisation for micromechanical modelling of CoCr stent fatigue1 Introduction2 Experimental studies2.1 Microscopy2.2 Mechanical testing

3 Computational framework3.1 Constitutive models3.1.1 Crystal plasticity model3.1.2 J2 Continuum model

3.2 Finite element microstructure model3.3 Constitutive model calibration3.4 FCI predictions

4 Stent fatigue application4.1 J2 continuum global model4.2 CP sub-model4.3 Results

5 Discussion5.1 Experiments5.2 CoCr computational framework5.3 Stent fatigue simulations

6 ConclusionsAcknowledgementsAppendix A Supplementary dataReferences